new measurement 2 part 1commondrive.pbworks.com/f/tg+for+book+2-1+me.pdf · 2010. 10. 3. · 2...

2 Teacher’s Guide for Workbook 2

Measurement covers two topics: length and mass. The concepts for both topics are analogous and are taught in a similar manner. Begin with direct comparisons (this pencil is longer than that pencil, this book is heavier than that piece of paper, and so on) and then move to indirect comparisons.

Materials for Length Students need a large number of connecting cubes (also called snap cubes or linking cubes) and paper clips of two sizes, 3 cm long and 5 cm long. String, straws, and base ten blocks are also required for some lessons. If you are purchasing connecting cubes, be sure to get 2 cm cubes that can link in different directions.

You can also use BLM Connecting Cubes (page xxx) to make your own manipulatives: photocopy the BLM onto thick paper as many times as necessary and cut out the chains of 10 “cubes.” (Do not cut out each individual 2 cm square.) To measure something, students can place the chain along the object and mark on the chain where the object ends. If the object is longer than 10 connecting cubes, students will need to use more than one chain.

Materials for Mass Many activities and exercises in lessons ME2-19 through ME2-22 require the use of pan balances. To ensure that every student has direct hands-on experience using a balance, activities and exercises are best done individually. If you do not have enough balances for each student, create stations for students to work at individually or do the class activities as demonstrations. Make sure all the pans are balanced before giving them to students, especially at first. Once your students can comfortably use pan balances, you might teach them to balance the pans themselves.

The same tools and units used to study length can be used to study mass. Pennies also work well. To keep the quantities manageable, choose different objects to compare by mass than you chose to compare by length. For example, a JUMP Math workbook is a reasonable number of paper clips long, but a very unreasonable number of paper clips in weight. We have included a list of average masses of common objects at the end of this introduction.

Mass vs. Weight At this level, we use the terms weight and mass interchangeably. Weight technically refers to the force of gravity pulling an object down (that’s why people have less weight in lower gravity), and is what pan balances and playground seesaws compare. Mass technically refers to the amount of matter in an object and does not change in outer space where the force of gravity is lower. It is appropriate with children in grade 2 to use the word mass to mean “how strongly an object pulls down when you try to lift it.”

EstimatingStudents are often asked to estimate and then measure length or mass. If you are using a worksheet for assessment, make sure students estimate before they measure. When introducing concepts and solving problems

Measurement 2 Part 1

A list of online sources for purchasing connecting cubes.

onLinE GuidE

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as a class, encourage students to estimate, check, and then estimate for different objects: knowing how your estimate compares to the actual measurement gives you a better idea of what a quantity like 1 m looks like, and helps you to make a better estimate the next time.

Recurring Game Spinner Make a spinner with four equal areas (e.g. labelled “widest,” “wider,” “narrowest,” and “narrower”). Give each pair of students a spinner and one each of the following objects: a playing card, two index cards of different sizes, a JUMP Math workbook, a stamp, and a soup box. Explain the following rules: Player 1 chooses an object from the collection. Player 2 spins the spinner and then chooses an object that is (wider or narrower) than the object that Player 1 chose or that is (widest or narrowest) of all remaining objects, depending on the spin. Player 1 then spins the spinner and takes a turn. Play continues in this way. Players may not find an object more than once. The pair wins when they have “found” all their objects. They lose if they cannot find any object satisfying their requirements. Strategy: Try to choose objects that have middle width whenever possible. Students could make a concrete organized list by ordering the objects from narrowest to widest. Advanced variation: Use a greater number of objects.

Curriculum differencesStudents following the Ontario Curriculum should cover all sections in this unit. Students following the WNCP curriculum should not be assessed on sections ME2-14 to ME2-18, which cover centimetres and metres (a Grade 3 topic under the WNCP curriculum).

Making an organized list

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Measurement 2 — introduction


Average Masses of Common objects (in grams)

glue stick 19

eraser 9.2

baby carrot 15

toonie 7.3

loonie 7

grape 6

paint brush 5

party blowout 4.75

quarter 4.4

sheet of paper (8 1/2 × 11) 4.3

badminton birdie 4

nickel 3.95

tens block 3.7

2-cm connecting cube 3.6 plastic knife 2.5

penny 2.35

balloon 2.1

dime 1.75

popsicle stick 1.3

pistachio 1.3

big (5-cm) paper clip 1.3

Kleenex 1

1-cm connecting cube 0.8

raisin 0.6

small (3-cm) paper clip 0.4

straw 0.34

chocolate chip 0.34

toothpick 0.135

pillow (large) 1500

JUMP workbook 563

1 container of bubbles 251

apple 251

tomato 251

medium stapler 188

pear 164

scarf 150

banana 141

stuffed animal (15 cm tall) 112

small potato 98

hairbrush 78

toque 75

1 container of finger paint 66

new containers of playdough (50g) 64

adult scissors 55

tennis ball 53

pencil case 38

liquid paper 33

mitten 32

granola bar 30

skipping rope 22

kid scissors 21

200 g and up 1-200 g

under 1 g

100-200 g

50-100 g

20-50 g

5Measurement 2-Measurement 1-Average Masses of Common objects (in grams)

Average Masses of Common objects (in grams)

glue stick 19

eraser 9.2

baby carrot 15

toonie 7.3

loonie 7

grape 6

paint brush 5

party blowout 4.75

quarter 4.4

sheet of paper (8 1/2 × 11) 4.3

badminton birdie 4

nickel 3.95

tens block 3.7

2-cm connecting cube 3.6 plastic knife 2.5

penny 2.35

balloon 2.1

dime 1.75

popsicle stick 1.3

pistachio 1.3

big (5-cm) paper clip 1.3

Kleenex 1

1-cm connecting cube 0.8

raisin 0.6

small (3-cm) paper clip 0.4

straw 0.34

chocolate chip 0.34

toothpick 0.135

pillow (large) 1500

JUMP workbook 563

1 container of bubbles 251

apple 251

tomato 251

medium stapler 188

pear 164

scarf 150

banana 141

stuffed animal (15 cm tall) 112

small potato 98

hairbrush 78

toque 75

1 container of finger paint 66

new containers of playdough (50g) 64

adult scissors 55

tennis ball 53

pencil case 38

liquid paper 33

mitten 32

granola bar 30

skipping rope 22

kid scissors 21

200 g and up 1-200 g

under 1 g

100-200 g

50-100 g

20-50 g


introduce length. Hold two coloured pencils in one hand so that the bottoms are concealed in your fist. Stagger the pencils so that the longer pencil appears shorter. ASK: Which colour of pencil looks longer? Reveal the bottoms of the two pencils and then line them up. ASK: Now which colour looks longer? Why did we get different answers? Which pencil really is longer?

Have several coloured pencils available. Line them up two at a time and have students tell you which pencil is longer. Line up different ends, i.e., line the writing end of one with the non-writing end of the other.

An optical illusion. SAY: I am going to show you something magical, something we call an optical illusion! Take a red and blue pencil, close in length (the red pencil is longer by less than 1 cm). Hold the shorter blue one vertically and the longer red one horizontally. Ask students to predict which pencil is longer, then check their predictions. Explain that objects that sit vertically (from top to bottom) often look longer than objects that sit horizontally (from side to side).

Review comparative words: shorter and longer. With the red and blue pencils lined up properly, SAY: The red pencil is longer than the blue pencil so we say the blue pencil is shorter than (meaning not as long as) the red pencil. Longer and shorter are opposites. Write “longer” and “shorter” on the board. Repeat the exercise several times, using different pairs of coloured pencils. ASK: Which pencil is shorter?

Review superlative words: longest and shortest. Using groups of three or more coloured pencils, demonstrate the meanings of the words “shortest” and “longest.” Write “shortest” and “longest” on the board. Repeat the exercise a few times.

Compare when the ends are not lined up. Show or draw the following arrangement:

ME2-1 LengthPage 142

CuRRiCuLuM ExPECTATionSOntario: 1m46, 2m47WNCP: 1SS2; 2SS8

voCABuLARYhow long shorter shortest longer longest length

GoalsStudents will compare the lengths of straight objects directly, by lining up the ends.

PRioR KnoWLEdGE REQuiREd

none

MATERiALS

BLM Rectangles (page xxx)BLM Triangles (page xxx)coloured pencils of different lengths (5 for each student, 10 for the teacher)

red

blue

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ASK: Which pencil is longer? How can you tell even though no ends are lined up? (Possible answer: The red pencil is longer because there is extra red at both ends.) Repeat with more arrangements.

Now show the following and ask students to predict which pencil will be longer when they are lined up correctly and to explain why:

PRoMPT: Is there more extra red at one end or extra blue at the other end? (There is more extra blue at one end than extra red at the other end.) Then line the pencils up correctly to check the prediction. Repeat with pencils that gradually become more similar in length.

use folding to compare lengths (adapted from Mathematics 1 for Elementary School published by Tokyo Shoseki). Show students a rectangular piece of paper. SAY: Let’s find out which side is longer, the top or the side. Have students discuss in pairs how they can compare the lengths of the two sides. SAY: So far, we only know how to compare lengths by lining up the objects. ASK: How can we line up the top of this paper with the side? (fold the sheet on the diagonal) Demonstrate this and mark on the longer side where the shorter side ends.

Using BLM Rectangles, give students several different precut rectangles or ask students to cut the rectangles out themselves. Challenge them to discover which side is longer. Ask students to draw a line along the longer side with a coloured marker or crayon.

Bonus Using BLM Triangles, give students precut triangles and ask them to use the folding method described above to determine which side is the longest. Ask students to draw a line along the longest side with a coloured marker. If there are two longest sides, draw a line along both of them.

Making and investigating conjectures, Mental math and estimation

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redblue

ACTiviTY 1

Spinner (length). (See ME 2 Part 1 – Introduction) Use several objects of different lengths (ExAMPLES: pencil, eraser, water bottle, JUMP Math workbook, ruler, tens block, large paper clip) and a spinner with four equal areas labelled “longest,” “longer,” “shortest,” and “shorter.”

Changing into a known problem

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mark here

Measurement 2-1


Super Super Superwords by Bruce McMillan Numerous illustrated examples of comparatives and superlatives.

ConnECTion

ME2-2 Width and HeightPage 143

CuRRiCuLuM ExPECTATionSOntario: 1m39, review, 2m5, 2m6, 2m7WNCP: 2SS8, [R, v] WNCP: 1SS1, review, [C, Cn, v]

voCABuLARY width length height opposite longer / shorter shortest wider / narrower narrowest taller tallest

GoalsStudents will identify and compare widths and heights of objects that have an obvious front.

introduce width. Explain that the distance across an object, from side to side, is called the width. Illustrate with a JUMP Math workbook: hold up the workbook and run your fingers along the front, first up and down, then side to side. ASK: Which way is the width? Is it this way (show from side to side) or this way (show from top to bottom)? Write “width” on the board. Explain that when you look at a book so that you can read it, the width is the distance across, from side to side. Ask volunteers to show the width of various objects: the blackboard, a window, the door, a bookshelf, and so on.

Compare widths. Place a JUMP Math workbook on the blackboard ledge. Explain that the workbook is not as wide as the blackboard. We say the blackboard is wider than the workbook. Write “wider” on the board, explaining that the word wider is used when comparing two widths. Ask students to find other objects in the classroom that are wider than their workbook, using their workbooks to check directly.

narrower and narrowest. Remind students that shorter is the opposite of longer (ME2-1). Explain that narrower is the opposite of wider. Write “narrower” on the board. Give each student three objects to compare, for example, an index card, a playing card, and a storybook. ASK: Is the book wider or narrower than the index card? (wider) Is the playing card wider or narrower than the index card? (narrower) Next, explain that just as something can be the longest or the shortest in a group of objects (ME2-1), something can be the widest or narrowest. Write the words “widest” and “narrowest” on the board. Continue making comparisons using the same three objects that you passed out. ASK: Which object is the widest? (the storybook) Which object is the narrowest? (the playing card) Now add a stamp to each student’s collection of objects. ASK: Is the playing card still the narrowest? (no) Is the book still the widest? (yes) Continue adding objects with an obvious front where the width (from side to side) is easy to identify and compare.


Can compare the lengths of straight objects Understands shorter and longer

MATERiALS

objects for each student to compare, such as an index card, a playing card, a storybook, a stamp a toy car BLM Height (page xxx)BLM Height and Width (page xxx)

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Taller and tallest, shorter and shortest. Explain that the distance up and down is called height. Write “height” on the board. Ask a volunteer to stand up, choosing a student who is of average height. ASK: Who thinks they are taller than (use the volunteer’s name)? How can we check? Accept and try answers. Ask a second volunteer to stand back to back with the first volunteer. Repeat the exercise with volunteers who think they are shorter. Now line up several volunteers according to height. ASK: Who is the tallest? Who is the shortest? Next, invite several students of below-average height to come to the front. ASK: Who is the tallest? Ask that tallest person to stay at the front and invite two very tall volunteers to come to the front, thus making the first person the shortest. Explain that a person can be the tallest in one group but the shortest in another group; it depends on the group.

Finding the width of three-dimensional objects. Show students a toy car and ask them to identify the front of the car. Have volunteers trace a finger along the car from front to back, side to side, and top to bottom. ASK: Which way is the width of the car—from front to back, side to side, or top to bottom? (from side to side) Draw a car on the board viewed from the side (the front should still be visible—see picture in margin). ASK: Is the side facing us the front of the car or one of the sides? Where is the front of the car? Trace your finger along the car on the board from top to bottom, front to back, and side to side. Ask students to tell you (thumbs up or down) if the distance you’re tracing is the width or not. Add lines to the drawing, like those on the worksheet, to identify each dimension and trace or colour the line that represents the width. Repeat with other drawings of concrete objects, such as a toy train, book, chair, bench, and so on. Have students also identify the height of these drawn objects.

ExtensionIf your students are familiar with rectangles, explain that shapes such as rectangles do not have a front, so it is not clear which distance across is the width. Mathematicians have defined the width of rectangles to be the shortest side and the length to be the longest side. Give students rectangles from BLM Rectangles (page xxx) and ask students to trace the rectangles so that the width, the shorter side, goes from side to side (not up and down).

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ACTiviTY 1

Spinner. (See ME 2 Part 1 – Introduction) Use several objects of different widths or heights (ExAMPLES: for width- a playing card, two index cards of different sizes, a JUMP Math workbook, a stamp, and a soup box) and a spinner with four equal areas labelled “widest,” “wider,” “narrowest,” and “narrower” (or “tallest”, “taller”, “shortest”, “shorter”).

BLM Height and Width

ExTRA PRACTiCE

Visualizing

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Hints for playing “I Spy.”

onLinE GuidE ACTiviTY 2

Play “I Spy”. ExAMPLE: I spy something that is narrower than this sheet of paper.

Measurement 2-2

BLM HeightStudents cut out the animals and order them from shortest to tallest (in real life).

ExTRA PRACTiCE


ME2-3 Long and ShortPages 144-145

CuRRiCuLuM ExPECTATionSOntario: 1m39, review, 2m1, 2m2, 2m6, 2m7 WNCP: 1SS1, review, [ME, R, v, C]

voCABuLARY longer / shorter wider / narrower

Long and short are relative. Hold up a short pencil. ASK: Is this a long pencil or a short pencil? Is it longer or shorter than most pencils? Next, hold up a long paper clip. ASK: Is this a long paper clip or a short paper clip? Is it longer or shorter than most paper clips? Which is longer: the long paper clip or the short pencil? (hold them side by side to check) Why do we call the pencil short even though it’s longer than the paper clip? (it’s shorter than most pencils) Why do we call the paper clip long even though it’s shorter than a pencil? (it’s longer than most paper clips) Explain to students that when we say a pencil is long or short, we mean that it is longer or shorter than most pencils. ASK: Does anyone have a pencil that is shorter than the long paper clip? Does anyone have a pencil that is shorter than a short paper clip?

Give each student two chains of connecting cubes (one long and one short) and two paper clips (one long and one short). Ask students to hold up the long paper clip. Then ask students to hold up the short chain of cubes. Ask students to predict which will be longer, the short chain or the long paper clip, and then to compare the two objects directly. Write the following statements on the board, read them aloud, and ask volunteers to fill in the blanks with either “longer” or “shorter”. Write the words on the board as a reminder. Accept answers that students can justify (for example, a desk may be wider than a very narrow room such as a closet). A short tail on an elephant is than a long tail on a mouse. (longer)A long tree branch is than a long pencil. (longer)A long paper clip is than a short snake. (shorter)A narrow room is than a wide desk. (wider)A narrow desk is than a wide floor. (narrower)A tall adult is than a short giraffe. (shorter)A short adult is than a tall 2-year-old. (taller)A wide thumb is than a narrow arm. (narrower)

GoalsStudents will learn that measurement terms, such as long and short, are relative.


Can compare lengths and widths directly

MATERiALS

3 cm and 5 cm paper clips (at least one per student) a short pencil (at least 6 cm long) and a long pencil short chains (3 cubes) of 2 cm connecting cubes (one per student) long chains (10 cubes) of 2 cm connecting cubes (one per student) BLM narrow or Wide (page xxx)

Making and investigating conjectures

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variations: Use a pocket chart to create sentences similar to those given above, change only one word at a time, and ask students to identify the correct missing measurement word. ExAMPLE:

A long finger is than a long thumb.

A short finger is than a long thumb.

A short arm is than a long thumb.

Give students cards with the words “longer” and “shorter” and ask them to hold up the words they would use to complete more sentences. ExAMPLES:

A long pencil is than a short pen. (longer)A short stapler is than a long paper clip. (longer)A short pencil is than a short stapler. (shorter)A short stapler is than a short pencil. (longer)

Measurement depends on perspective. Draw the picture in the margin on the board and name the people, from left to right, Mary, Naima, and Rita (or use your students’ names). SAY: Mary says Naima is tall. Rita says Naima is short. ASK: Why does Mary say that Naima is tall? (Naima looks tall to Mary because Naima is taller than Mary.) Why does Rita say that Naima is short? (Niama looks short to Rita because Rita is taller than Naima.) Who is right? (They both are!)

Show students a crayon. SAY: Mary thinks this is a crayon and Rita thinks this is a marker. ASK: Who is right? (Mary) How is being tall or short different from being a crayon or a marker? (A crayon is always a crayon, but something can be tall to one person and short to another person.)

Give students the following problems and ask them to draw and name stick figures with the specified characteristics. Check students’ work to assess understanding

1. Rita says Mary has short hair. Naima says Mary has long hair. 2. Sarah says that Anna is tall. Anna says that Sarah has long hair. (Anna is taller than Sarah. Sarah’s hair is longer than Anna’s hair.) 3. Melanie says Tim is tall. Nathan says Mike is short and Mike says Tim is short. 4. Suma says Meena is short and has short hair. Meena says Nancy is tall and has long hair. Nancy says Suma is tall and has short hair. 5. Anna and Nancy both say Sarah is tall. Leah says Sarah is short. Anna says Nancy is short.

Bonus Ask students to make up their own problem and exchange with a partner to solve.

BLM narrow or Wide

ExTRA PRACTiCE

Complete the sentence: A tall baby is shorter than a short ______.

JouRnAL

Drawing a picture

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Using logical reasoning

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Measurement 2-3


ME2-4 More LengthPage 146

CuRRiCuLuM ExPECTATionSOntario: 1m39, 1m40; review, 2m1, 2m2, 2m3, 2m4, 2m7WNCP: 1SS1, review, [R, PS, ME, C, v]

voCABuLARY longer / shorter taller / shorter wider / narrower length width height

GoalsStudents will compare lengths and distances around objects indirectly, but without units.

Three indirect comparisons. ASK: Are you taller now than you were last year? Can you stand back-to-back with yourself from last year to show me? Discuss how they can know without standing back-to-back with themselves from last year. Many students already use indirect comparison when they use a mark on the wall to compare their height one year to their height in a previous year.

Show students how they can use symmetry to compare body parts—since the same fingers on both hands are (approximately) the same length, you can compare two fingers on one hand (e.g., right thumb and right baby finger) by comparing one finger to the same finger on the other hand (e.g., right thumb and left baby finger).

Finally, have students use paper to compare measurements for which it is impossible to make a direct comparison, e.g., the length and width of a book—you can’t fold the book, so cut a piece of paper to have the same length and width as the book and then fold that to see which side is longer.

Compare using a third object. ASK: How can I check which is longer without using a piece of paper? What if we had something that was the same length as one side of the book? How would that help us compare the two sides? Can we make something the same length as one side of the book? Give each student a book that is shorter and narrower than a sheet


Can compare two lengths directly

MATERiALS

multiple copies of a book that is shorter and narrower than a sheet of paper (one for each student) paper scissors masking tape base ten materials connecting cubes 3 cm and 5 cm paper clips straws string pencils popsicle sticks BLM Matching Lengths (page xxx)

Changing into a known problem.

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Changing into a known problem. Using logical reasoning.

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of paper. Make these materials available to students: scissors, masking tape, base ten materials, connecting cubes, 3 cm and 5 cm paper clips, straws, string, pencils, popsicle sticks. Ask students to work in pairs to find a solution using materials of their choice. Discuss the solutions that students discover. Sample solutions: draw a line the same length; build a chain the same length from connecting cubes or paper clips or base ten blocks. noTE: It is acceptable at this point for students to string together paper clips of different sizes, as long as the chain is the same length as one side of the book. ASK: Did some groups use different methods to find out which side is longer? (yes) Did every group get the same answer? (yes, with different methods they still had the same answer) Why did every group get the same answer? (the length doesn’t change, i.e., the length stays the same, even when different tools or methods are used to measure)

Compare two methods of measurement. Demonstrate making the length of the top of a book on a strip of paper and then compare that length to the length of the side of the book (see margin).

Use that marking to compare the side of the book to its top. Make sure students can identify the top and the side of an object. Demonstrate using a JUMP Math workbook and on a classroom blackboard. SAY: We have used two methods to compare lengths: cutting or folding paper, and marking on paper. ASK: Which way is it easier to compare? Why? (students’ answers may vary)

Measure something bigger than a piece of paper. ASK: How can we find out which side of your desk is longer? Can we use a regular sheet of paper to measure, like we did when measuring the length of the book? (no) Why not? (it’s not long enough) What can we do? Open up the discussion. Possible answers: tape sheets of paper together to make one long sheet; use many paper clips. Add a rule: students can only use string and scissors. Give individual students or pairs time to solve the problem.

Compare lines to compare objects. Draw on the board:

Ask students to predict which rectangle is the longest. Demonstrate to students how to mark the length of the first rectangle on a piece of paper, as you marked the length of the book on a piece of paper. Then transfer the mark on the piece of paper, identifying the first rectangle’s length, to a line:

Ask volunteers to use the same method to measure the lengths of the other two rectangles you drew on the board. ASK: Was your prediction correct?

BLM Matching Lengths. Students find the length of each bar indirectly, by marking the length on a separate sheet of paper, and then colour matching bars the same colour. The colour of the bars, from top to bottom, should be red, black, yellow, green, blue.

Selecting tools and strategies. Reflecting on other ways to solve a problem.

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Reflecting on the reasonableness of an answer.

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Reflecting on other ways to solve a problem

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ExTRA PRACTiCE


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Measurement 2-4


ME2-5 distance Around7

CuRRiCuLuM ExPECTATionSOntario: 1m39, 1m40; review, 2m2, 2m3, 2m4, 2m7 WNCP: 1SS1, review, [PS, R, ME, C]

voCABuLARY distance around longer / shorter taller / shorter wider / narrower length width height

GoalsStudents will compare the distance around objects indirectly.

Problem-solve ways to compare lengths around small objects. Tell students that you would like to know whether the length around their wrists is longer or shorter than the length around a water bottle. Trace the distance around both your wrist and the bottle so that students know what “distance around” means. Write “distance around” on the board. Students should work in pairs. Give each pair three measuring tools and explain that they may decide which tools to use; they may not need all three. ExAMPLES: string, a marker, and scissors; strips of paper, a pencil, and scissors; connecting cubes, masking tape, and a pencil; base ten materials, ribbon, and a pencil.

Bonus Find a way to compare lengths without using any of the measuring tools.

Students’ solutions may include:

• Wrap a tool (such as string, paper, or ribbon) around your wrist and another tool around the bottle, cut each tool (or mark the length with a marker or pencil), then compare them to see which is longer;

• Wrap a tool around the water bottle, mark or cut one full length around the bottle, then wrap the same tool around your wrist and see if it goes all the way around (or if it wraps around more than once);

• Make a mark on the bottle, roll the bottle along a table (start and end at the mark), mark the spot on the table where the bottle stopped, then do the same with your wrist to compare.

discuss the advantages and disadvantages of various tools. ASK: Who used base ten materials? Were they easy or hard to use? Why? Who


Can compare two lengths directly

MATERiALS

water bottles string markers scissors pencils strips of paper masking tape connecting cubes base ten materials ribbon a stretchy bracelet JUMP Math workbook

Selecting tools and strategies

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used ribbon? Did anyone use base ten materials and ribbon? Were there problems using the string? The tape? The paper? Which tool(s) would you use if you had to do it over again?

using a bracelet to measure distance around is not a good choice. Wrap a stretchy bracelet first around your wrist and then around a pencil case. SAY: Look! This bracelet fits perfectly around my wrist and around the pencil case. They must both be the same distance around. See if anyone challenges your claim. Now have a volunteer measure your wrist with a strip of paper and another volunteer measure the pencil case with another strip of paper. Ask students to predict whether the strips will be the same length. Check students’ predictions and then ASK: Can you explain why the bracelet fit perfectly around my wrist and the pencil case, even though they are not the same distance around? (The bracelet stretches, so it changes length.)

use string to make the distance around. Demonstrate making a piece of string the same length as the distance around your desk. Ask volunteers to hold the string tight and straight as you reach the corners. After cutting the string the correct length, label it with a piece of masking tape ( “ ’s desk”) and hang it on the wall.

Now have students work in pairs to measure an object of their choice from various objects found in the classroom. ExAMPLES: a desk, a connecting cube, a chair seat, or a JUMP Math workbook. Explain that by “distance around” you mean the distance an ant would walk around the outside of the object if it was lying on a table. Trace the ant’s path around the workbook with your finger. If the book was standing on its end on the table, the distance around for the ant would be very different. Trace the path again. Have volunteers trace the distance around other objects. Ensure that all students can identify the distance around. Write the names of all the objects on the board and ask students to predict their order from longest to shortest distance around.

Students should label their strings as you labeled the string that measured your desk. Add all the strings to the wall. Check measurements. ASK: Did all groups have the same measurement for the same objects? Discuss reasons for any differences. (Possible answers: not holding the string straight, having extra string on the end, measuring the distance around in a different direction, measuring with more than one piece of string but taping them together so that they overlap.) As a class, order the strings from longest to shortest. Then order the objects measured from longest distance around to shortest distance around.

On the worksheet, students will compare and order the distance around additional objects, including one object of their choice. Ask students to predict the order of the objects before they begin.

Selecting tools and strategies.

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Justifying the solution

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ME2-6 Measuring LengthPages 148-149

CuRRiCuLuM ExPECTATionSOntario: 1m30, 1m31, 1m40; 2m1, 2m2, 2m3, 2m5, 2m6, 2m7, 2m31WNCP: 2SS3, 2SS4, [R, ME, v, C, Cn]

voCABuLARY measure closer to about exactly estimate

GoalsStudents will measure the lengths of straight objects (to the nearest unit) using connecting cubes as a unit.


Can count and order numbers Can compare lengths directly Can describe distance as “closer to” or “farther from” Knows the concept of “how many more than”

MATERiALS

2-cm connecting cubes JUMP Math workbook ruler pencil case BLM Practise Measuring (page xxx)

Workbook page 148. Complete this worksheet together. Give students 2 cm connecting cubes to line up alongside the pictures. Discuss the advantages to assigning numbers to lengths. ASK: How can we tell without lining the objects up which is the shortest and which is the longest? (compare the numbers of cubes lined up alongside the objects) As a class, order the objects from shortest to longest using numbers.

Guess and check. Show students a 2-cm connecting cube and a ruler. Have students guess how many connecting cubes long the ruler is. Place two connecting cubes alongside the ruler and ask students to guess again. Repeat, placing more connecting cubes alongside the ruler after each guess to continually provide students with more information. Emphasize the correct measurement by writing “The ruler is 16 long.” ASK: Did your guesses get closer to the correct measurement as we continued? (yes) Why do you think this happened? (as you get closer to the end of the ruler, you form a better idea of how many cubes are needed to measure the ruler; the more you know, the better your guess)

introduce the word estimate. Explain that when we make guesses based on something we know, the guess is called an estimate; the more we know, the closer our estimate will be to the right answer. Write “estimate” on the board. Emphasize that an estimate is not a wild guess, but a guess based on information. To estimate means to think and then guess.

More practice. Have students estimate and then measure the length, width, or height of several objects using 2 cm connecting cubes. Use objects with straight sides that are less than 2 m long. ExAMPLES: a JUMP Math workbook, a pencil case, a pencil, an eraser, a desk, the distance between

BLM Practise MeasuringStudents measure by placing actual connecting cubes next to the pictures.

ExTRA PRACTiCE

Guessing, checking, and revising

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two volunteers. Record the measurements in connecting cubes. ExAMPLE: 10 long.

Compare quantities to compare length. ASK: Is the JUMP Math workbook longer or shorter than the pencil case? How can you know just from looking at the numbers? What was the longest object measured? The shortest object? Which was longer: the pencil or the eraser? A lot longer or a little longer? Is there an object that is almost the same length as the pencil case? How do you know? (because the numbers are close) As a class, order the numbers from largest to smallest, then order the objects from longest to shortest. ASK: How can we check directly to see if this is the right order? Demonstrate lining the objects up beside each other in the order listed. Are they in order from longest to shortest?

Length and “closer to.” Drawing a picture Draw a bar on the board that is between 5 and 6 blackboard erasers long. Trace 5 erasers above it and 6 erasers below. ASK: How long is the bar? Is it longer or shorter than 5 erasers? (longer) Is it longer or shorter than 6 erasers? (shorter) SAY: We can see that the bar is not exactly 5 erasers long and not exactly 6 erasers long—the bar is between 5 and 6 erasers long. ASK: Is the bar closer to 5 erasers long or closer to 6 erasers long? Write the words “closer to” on the board. Highlight the distances between the end of the bar and the last eraser above and below it:

Explain that the bar is closer to 5 erasers, so we say the bar is “about 5 erasers long.” Write “about” on the board. Repeat with bars of different lengths.

Ask students to make a chain 5 connecting cubes long, then finish this sentence: Some objects that are about 5 cubes long are....

ExtensionBLM using a Grid to Measure Length (pages xxx–xxx). On the first page, students use equally spaced vertical lines to measure and compare the lengths of horizontal bars. On the second page, students use a grid to measure and order the lengths of vertical and horizontal bars.

Reflecting on the reasonableness of an answer

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Measurement 2-6


ME2-7 unitsPage 150

CuRRiCuLuM ExPECTATionSOntario: 1m30, 1m31; 2m2, 2m3, 2m4, 2m7, 2m31, 2m33WNCP: 2SS3, 2SS4, 2SS5, [R, C]

voCABuLARY unit of measurement about

GoalsStudents will understand why certain objects make better units of measurement than others and how to use them.


Can measure objects using different units

MATERiALS

big (5 cm) paper clips small (3 cm) paper clips 2 cm and 1 cm connecting cubes tape, paper, a metre stick several elastics of the same size straws (and string) BLM Measuring in Any direction (p xxx)

introduce “unit of measurement.” Write the expression on the board. Explain that a unit of measurement is something that you can measure with over and over again. Using the same unit to measure different objects allows you to make comparisons, even when you can’t place the objects side by side. ASK: What units of measurement have you seen already? (connecting cube, blackboard eraser)

units of measurement must be the same length. Give everyone in the class a mix of small paper clips and big paper clips. Tell them to make a chain using any 5 paper clips and to cut a strip of paper that is as long as their chains, but ask one student to use only small paper clips and another to use only big paper clips. Have many volunteers tape their strips of paper to the board. Compare the length of the strips directly. SAY: All these strips are 5 paper clips long, but they are not all the same length! Why not?

Show or draw a pencil that is 4 big paper clips long and a pencil that is 5 small paper clips long (see margin). Tape or lay the paper clips alongside each pencil.

ASK: Which pencil is longer? How can we tell? Shouldn’t 5 paper clips be longer than 4 paper clips? (Yes, but only if the paper clips are the same size.)

Now show pencils that are both 8 paper clips long, but use paper clips of different sizes, as shown below. SAY: Both pencils are 8 paper clips long, but they are not the same length!

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Explain that when we measure, we need to use units that are the same length.

Good units are objects for which it is easy to find many of the same size. Explain to students that paper clips are good units because it is easy to find many that are the same size. You can use many small paper clips or you can use many big paper clips. ASK: Are elastics good units? (no) Take many elastics of the same size and demonstrate how their length changes because they are stretchy.

using connecting cubes to measure. Show two sticks being measured with connecting cubes (see diagram). ASK: Which stick is exactly 4 connecting cubes long? Should we count the linking part of the cube as part of the length? Will all the units be the same size if we do that? Explain that the linking part is part of the length of the cube, but if we want to use the connecting cube as a unit by linking many of them together, we cannot count that part.

Choosing between various units. You will need a metre stick, several big and small paper clips, several big and small (2 cm and 1 cm) connecting cubes, several straws, and string (to string straws together). Ask students if they would use a metre stick as a unit to measure their JUMP Math workbooks. Demonstrate trying this. Explain that because the workbook is shorter than the metre stick, we can only say that the workbook is less than one metre stick long. ASK: Is the workbook closer to 0 or 1 metre sticks long? (0) Show a pencil and ask the same thing. SAY: Both the pencil and the workbook are about 0 metre sticks long. Which one is longer? (show them side by side to see that the workbook is longer) Can you tell that from the measurement? (no) A metre stick is not very useful for measuring the workbook and pencil. What could we use instead? (paper clips, connecting cubes) Explain that for lengths shorter than a metre stick, it is better to use units shorter than a metre stick. Then demonstrate trying to measure the length of the classroom with paper clips. Explain that you would need too many paper clips, so it is better to use a metre stick.

Now, try measuring your desk with each of the following: a metre stick, straws (string several straws together to hold them straight, paper clips

Emphasize that a metre stick is less useful because a measurement of, say, about 2 metre sticks, isn’t as useful as a measurement of, say, 9 drinking straws; it simply doesn’t tell you as much. Show many lines on the board that would measure about 2 metre sticks but would measure about 8, 10, 11, or 12 drinking straws. Have students decide what unit to use to measure various objects around the room.

ACTiviTY

Invite students to identify classroom objects that would make good units of measurement. Discuss the units students find as well as any good units that they miss. Have each student draw and name a unit to add to a class poster titled “Good Measuring Units.” Students can refer to the poster when they are looking for units in later activities.


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Teaching notes and BLM for identifying good units.

onLinE GuidE

ExTRA PRACTiCE

BLM Measuring in Any directionBefore assigning this BLM, model turning objects to measure them, as shown on the BLM. Discuss why the answers are the same.


ME2-8 How to MeasurePage 151

CuRRiCuLuM ExPECTATionSOntario: 1m30, 1m31; 2m1, 2m3, 2m4, 2m7, 2m31 WNCP: 2SS3, 2SS4, [R, PS, C]

voCABuLARY stretchy firm distance how far farther length

GoalsStudents will learn that length is measured as the longest an object can be.

How to measure straight objects. Emphasize the importance of properly lining up the units you are going to measure with; you must keep them in a straight line, with no overlap or gaps. It is also important not to change the orientation of units (such as paper clips) that have different lengths and widths. Demonstrate that the width of a paper clip is a much different measurement than the length. Just as you cannot use long and short paper clips as units, you cannot use their length and width as units at the same time. To decide if a measurement has been taken correctly, students should ask themselves these questions: 1. Are the units all the same length? (need yes) 2. Are the units lined up in a straight line, end to end? (need yes) 3. Are the units overlapping? (need no) 4. Are there gaps between the units? (need no)

Some curved objects can be stretched out to measure. Hold up two pieces of curled ribbon. ASK: Which one is longer? How can we compare them? Discuss.

Length is the longest an object can be. Attempt to measure a curled piece of string or ribbon as is using paper clips. Explain that when the string is stretched out till it’s straight, it’s actually longer than it looks when it’s curled. Stretch the string to demonstrate and measure its true length.

SAY: The string looks 4 paper clips long but it is actually 6 paper clips long. Explain that length refers to the longest an object can be. Give students different lengths of string or ribbon to order from shortest to longest.

Stretchy objects can be measured along their bodies. Draw a snake on the board:


Can measure the length of straight objects

MATERiALS

string curled ribbon small paper clips connecting cubes BLM Measure Straight or Curved (p xxx–xxx)

21

ASK: Can the snake be longer than it looks? Can we stretch it out more? Explain that the snake is sleeping and you can’t move it. ASK: How can we measure the snake using string? Illustrate the process (straighten the string, not the snake!):

The snake looks 5 paper clips long, but it is actually 8 paper clips long.

Firm objects must be measured straight. Bring in a firm, curved object such as a bottle or vase. Tell students that you want to make a string as long as the object is tall. Then demonstrate an incorrect method: place the string along the side of the object and cut the string when you have covered the full length of the curves.

ASK: Do you think this string will be as long as the object is tall? Demonstrate how the string is actually taller than the object. Explain that when we measure a firm object that cannot be stretched like a snake or a piece of ribbon, we have to measure straight instead of along the object. Then ask students how they would make a string as long as their own bodies—are they firm like the vase or stretchy like the snake?

Choosing the correct way to measure. Have students choose the correct way to measure various concrete objects, some stretchy (so the correct way to measure is along the object it self using string) and some firm (so the correct way is measuring straight). ExAMPLES: A toy car, a stuffed toy snake.

BLM Measure Straight or Curved. Students decide which way of measuring is correct—along the object’s body or straight.


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ACTiviTY

Have students work in groups of three to make pieces of string the same length as their heights. Groups can then mix their strings up and students can try to find their own strings. (Ensure that all pieces of string are the same colour.) Discuss the strategies students used after they finish. Did they match strings to individuals directly or indirectly? Emphasize that there are often many ways to solve the same problem.


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ME2-9 Measuring distancePage 152

CuRRiCuLuM ExPECTATionSOntario: 1m31; 2m1, 2m2, 2m6, 2m7, 2m31, 2m32 WNCP: 2SS3, [R, v, C]

voCABuLARY far apart closest farthest distance travelling route

GoalsStudents will learn that distance is measured along a route taken.


Can measure objects using different measurement units

MATERiALS

base ten blocks big (5 cm) paper clips small (3 cm) paper clips 2 cm connecting cubes rulers masking tape paper for each student BLM Measuring distances (p xxx)

How far apart? Draw two points on the board that are about 90 cm apart. ASK: How can I measure how far apart the two points are? Discuss students’ suggestions. Then draw a line between the two points using a metre stick and explain that the distance between the two points is the length of the line between them. SAY: Since we know how to find the length of a line, we have just changed this problem into a problem we already know how to solve. Have several possible units available to choose from (base ten blocks, paper clips, connecting cubes, rulers, and so on) and ask the class to choose one of them to measure the line with. Have a volunteer measure the line using the chosen unit of measurement. Explain that because the line is, say, about 9 tens blocks long or 3 rulers long, we can say that the two points are about 9 tens blocks apart or 3 rulers apart.

Have three volunteers stand apart from one another. Using your students’ names, ASK: How far apart are Tom and Pam? How far apart are Tom and Lina? Who is closer to Tom—Pam or Lina? How do you know? (Students could measure using a volunteer’s foot length as the unit of measurement by having the volunteer walk from Tom to Pam or Lina using heel-to-toe steps.)

Have three volunteers measure the distance from their desks to the door, in rulers, and record the number and unit on a card (ExAMPLE: 11 rulers). Volunteers can use masking tape to create a straight line (on the floor) from their desks to the door. Have the volunteers line up according to number, from smallest to largest. ASK: Whose desk is closest to the door? Whose desk is farthest from the door? Do two people have desks that are about the same distance from the door? How do you know? (the numbers are close)

Distance is measured along the travelling route. SAY: Sam and Mary made a play baseball field for their dolls. Create a baseball diamond on the floor and label the bases. Make the distance between home plate and second base, and between first base and third base, 1 m. Use tape to show the lines of the

Teacher’s Guide for Workbook 2


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baseball diamond. Explain the basic rules of baseball for students who are unfamiliar with the game.

ASK: How can we measure the distance the dolls have to run from home plate to second base? Have ready a chain of 20 big paper clips and demonstrate placing them in a straight line from home plate to second base. SAY: Second base is 20 paper clips away from home plate. Is that how far the dolls have to run? Why not? (The dolls are not allowed to run directly from home plate to second base. The rules of baseball say that the dolls have to pass through first base before going to second base.) Have students guess how far a doll has to run (in paper clips), and record various answers. Have a volunteer check (the volunteer will need more that 20 paper clips). Together as a class, count the paper clips the volunteer used. Then tell students that there is a runner on first base and ASK: How far does the doll have to run in order to get to home plate? Take various guesses and have another volunteer measure. Again, count together the total number of paper clips.

Measure the distances from desks to the door along the travelling route. SAY: An ant travelling from a student’s desk to the door would use the routes we’ve already measured, but we’re bigger and need to use different routes. Trace the routes that students use with masking tape. Have the same volunteers as above measure, using rulers, the distance along the travelling route from their desks to the door. The volunteers may need additional helpers. ASK: Whose desk is farthest from the door? How do you know? Discuss how to deal with approximate lengths (e.g., when one part of the path is almost 2 rulers long, record it as 2 rulers).

Practise finding distances along paper. Give each student a piece of paper and demonstrate folding it twice, as follows:

Point to the two points shown below and ask students to find out how far one point is from the other when you travel along the paper. Students might use small paper clips or 2 cm connecting cubes as measurement units.

Bonus Find the distance around the whole shape.

BLM Measuring distances. Students place actual blocks on top of the pictures.

home plate

1st 3rd

2nd

1 m

Measurement 2-9

ExTRA PRACTiCE


ME2-10 Measure distance AroundPage 153-154

CuRRiCuLuM ExPECTATionSOntario: 2m1, 2m2, 2m3, 2m34WNCP: 2SS3, [PS, R, ME, C], 3SS5

voCABuLARY distance how far farther length

GoalsStudents will learn how to measure the distance around.

Find the distance around rectangles. Draw the following rectangle on the board; include the square grid markings. SAY: I want to find out how far a person has to go to walk around this rectangle. Explain that the side of each square in the picture has the same length. Then SAY: Let’s find the distance around by counting the sides of each square that the person has to walk through:

Give students rectangles cut from 2 cm grid paper and have them count the distance around the rectangles. Which of their rectangles has the biggest distance around? The smallest?

Measure distance around using connecting cubes. Give students connecting cubes and rectangles cut from plain paper. Demonstrate how to use the cubes to measure the distance around the rectangles. Ensure students understand not to count cubes in the corners, but just those along the edges of the paper, since it is the total length of the sides that you are measuring. Students can write the number of cubes on the paper as they count.

1 2 3 4

5

6

10 9 8 7

12

11


Can measure lengths using non-standard units Can find the closest whole number of units to measure a given length Can count to 20 Can add more than two numbers together

MATERiALS

rectangles cut from 2 cm grid paper and plain paper connecting cubes pre-made paper tens blocks (to tape to the board) string paper clips tens blocks BLM distance Around with My unit (p xxx)BLM distance Around Curved Shapes (p xxx)

123

4 5 6 7 ...

1234 5 6 7 8 ...

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Again, have students decide which of their rectangles have the largest distance around and which have the smallest distance around.

Add side lengths to get the total. Refer to the first picture you drew on the board. SAY: I have another way to find the distance around the rectangle. The total distance is the distance to go along all the sides put together. We can add the sides: 4 + 2 + 4 + 2 = 12. Have students verify that this results in the same answer found previously. Repeat with these rectangles: 3 squares by 5 squares, 1 square by 6 squares, 4 squares by 4 squares.

The distance around non-rectangular shapes. Draw several non-rectangular shapes with straight sides on the board and have volunteers find the distance around each one using paper tens blocks as a unit. ExAMPLES: triangle, pentagon, trapezoid, parallelogram. Students should find the length of each side and then add all the side lengths together. Have students predict which shape has the largest and smallest distance around before measuring.

Practice. Have students work in pairs to measure the distance around various objects in the classroom (restrict them to objects that have straight sides) using connecting cubes or paper clips, and check each other’s measurements for discrepancies. Students try to draw one shape each so that next have one student draw a shape on 2 cm grid paper and measure its distance around. The other student then tries to draw a shape with a longer distance around. They check by measuring and comparing. Variation: The second student tries to draw a shape with a shorter distance around.

Bonus Have students work in pairs to create two shapes, one inside the other, so that the inside shape has a longer distance around. Students could draw the shapes on 2 cm grid paper.

The distance around curved shapes. Show students how to measure the distance around with string and then measure the length of the string using paper clips. Then compare measuring with string to measuring with paper clips directly. Discuss reasons for any discrepancies (e.g., the chain of paper clips will not fit as tightly against an object as the string).

Extension Students create their own shapes. Give students 8 toothpicks or 8 popsicle sticks each. Have them create as many different shapes as possible, all with a distance around of 8 units. Have them record their work in their journals. Students might use modelling clay to help the sticks stay together. Then give students 12 sticks and challenge them to make any or all of the following, using all the sticks: • a square • different rectangles (ExAMPLES: 1 by 5 or 2 by 4) • different triangles (ExAMPLES: 4, 4, 4, or 2, 5, 5)

Reflecting on other ways to solve a problem, using logical reasoning

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Measurement 2-10

ExTRA PRACTiCE

BLM distance Around Curved Shapes.

ExTRA PRACTiCE

BLM distance Around with My unit. Students choose their own unit and measure the distance around various objects.


ME2-11 Comparing unitsPage 155

CuRRiCuLuM ExPECTATionSOntario: 1m41, 1m42; review, 2m1, 2m2, 2m4, 2m7 WNCP: 2SS2, [R, C]

GoalsStudents will discover, by looking for a pattern, the relationship between the size of a unit and the number of units needed to measure length.

Compare tens blocks to a chain of connecting cubes. Prepare chains of 2 cm connecting cubes that are 5 cubes (10 cm) long. Ideally, each chain should be a single colour to make them easy to distinguish from one another. Give half the class some of these chains and half the class tens blocks.

Ask students to measure the length of their desks is using whatever you’ve given them. Record students’ answers on the board. (Answers will be the same.) Then have students measure other objects, such as a floor tile, a ruler, the length of an arm, and the width of a desk. Have a volunteer measure a JUMP Math workbook using chains of cubes and ASK: How many tens blocks long will the workbook be? Why do you think that? Justifying the solution (e.g. because we always get the same answers for both)

Pair students up so that each pair has both tens blocks and chains. ASK: Why are we always getting the same answer? Lead students to discover that the chains and tens blocks are the same length. Demonstrate measuring


Can compare lengths directly and indirectly Can measure lengths using non-standard units (e.g., connecting cubes)

MATERiALS

tens blocks chains of five 2 cm connecting cubes OR cut the chains on BLM Connecting Cubes in halfstraws a metre stick big (5 cm) paper clips small (3 cm) paper clips 2 cm connecting cubes BLM Compare Cubes to Paper Clips (p xxx–xxx)

Looking for a pattern

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an object such as a metre stick using both units. Place one of each unit alongside the metre stick, then another, and so on, so that students see that for any length, the number of each unit needed is the same.

Compare straws to tens blocks. Repeat the above with straws in place of chains of connecting cubes, this time emphasizing that we always need fewer straws than tens blocks because straws are longer than tens blocks.

Compare straws to metre sticks. Now draw a line about 3 m long on the board. Show students a metre stick and ASK: Will we need more straws or metre sticks to measure the length of the line? About how many straws do you think we will need? About how many metre sticks? Why do you think we will need more straws than metre sticks? Measure and compare. Emphasize that you didn’t need as many metre sticks as straws because metre sticks are longer than straws—the longer your unit of measurement, the fewer units you need.

Compare big paper clips to connecting cubes. Ask students to measure a pencil crayon with paper clips and then with connecting cubes. Record several of their measurements on the board. Discuss possible variations in the measurements (e.g., two students have pencils that are 3 paper clips long but different numbers of connecting cubes long). ASK: Did you need to use more paper clips or connecting cubes to measure the pencil crayon? (more connecting cubes) Why? (Connecting cubes are shorter, so you need more of them to fill up the whole length.)

Have students do BLM Compare Cubes to Paper Clips

Write the names of the objects from BLM Compare Cubes to Paper Clips on the board for students. Have students measure the objects they estimated using both units and record their measurements in their journals. ExAMPLE: The ruler is about 15 long. The ruler is about 6 long.

Making and investigating conjecture

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ACTiviTY

Have students measure the length of their desks using various units: small paper clips, big paper clips, 2 cm connecting cubes, straws cut to a length of 4 cm. Students can record the number of each unit they needed to measure their desks in a chart. They should order the units from shortest to longest. As a class, discuss whether the number of units needed became larger or smaller as the units became longer.

Making a table/chart

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ME2-12 When You do not Have Many unitsPage 156

CuRRiCuLuM ExPECTATionSOntario: 2m2, 2m3, 2m4, 2m7, 2m31 WNCP: 2SS2, 2SS3, 2SS4, [R, C]

voCABuLARY measure

GoalsStudents will problem-solve a way to measure when they have only two units instead of many.

Measure using hand lengths. SAY: I want to measure how many hand lengths long my desk is, but I have only two hands, so I can’t place many hands on my desk at once. Demonstrate what you mean by hand lengths. ASK: How can I measure my desk? Have students discuss the problem in pairs. If students suggest making copies of your hand, ask if there is another way. Demonstrate removing the first hand placed, keeping the second hand down as a marker, and putting your first hand down again. Continue in this way, counting as you go.

Have students measure their desks using their own hand lengths. Ask several volunteers for their measurements and discuss differences: Who needed more hand lengths: Teah or Julia? Whose hand do you think is longer? Check predictions.

Measure using hand widths. Demonstrate counting the number of hand widths you need to cover the full length of your desk, being sure to keep your thumb and fingers pressed together.

Have students measure their desks using their hand widths. ASK: Did you need more hand widths or hand lengths to cover the length of your desk?


Knows the relationship between the size of a unit and the number of units needed to measure a given object Can measure lengths using non-standard units

MATERiALS

2 playing cards, 2 index cards, and 2 letter-sized sheets of paper for each student masking tape pencil crayons

Reflecting on other ways to solve a problem.

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Using logical reasoning.

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(hand widths) Why do you think that happened? (Hand widths are shorter than hand lengths, so we need more of them to make the same length.)

Measure using only two units. To complete Workbook page 156, students will measure their desks using both the length and width of their hands, 2 playing cards, 2 index cards, and 2 letter-sized sheets of paper.

Measure using only one unit. Show students how to measure the length of the blackboard using only one metre stick by marking with chalk where the metre stick ends each time. Do it twice: once taking care to line up the stick horizontally along the edge and once having the stick go diagonally up and down. ASK: Which way is the correct way to measure? Why? What did I use to make sure the metre stick was always straight? (the blackboard edge) SAY: I want to know how many metre sticks long the classroom is. ASK: What could I use to make sure I keep the metre stick straight? (If the floor has tiles, you could use their borders; otherwise, you could use a classroom wall if possible.) SAY: I don’t want to write on the floor with the chalk. ASK: How can I keep track without using chalk? What can I use instead? (Suggest writing on masking tape. Use a piece of tape the full length of the floor and write markings on it where the metre stick begins and ends)

Have students measure their desks using only one playing card, masking tape, and pencil crayons. Students could place a strip of masking tape to cover the full length of their desk and place markings at the end of each unit.

Compare measuring with one to measuring with many. Have students measure their desks using many playing cards, index cards, and/or sheets of paper. ASK: Do you get the same answer as when you used only one or two of each unit? What might have caused any discrepancies? (Students may not have kept the unit on the desk in the right place when there is no other unit beside it, students may not have lined up the units properly when using several units, and so on.)


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ACTiviTY

Measure the Classroom. Have students determine the length of the room using heel-to-toe footsteps. Encourage them to compare and discuss their measurements with a partner. Ensure that students understand that the length of the room must be measured straight, so they must walk in a straight line.

Measurement 2-12

1metre


ME2-13 EstimatingPage 157-158

CuRRiCuLuM ExPECTATionSOntario: 1m30, 1m31, 1m32, 1m39, 1m42; 2m1, 2m2, 2m3, 2m7, 2m31 WNCP: 2SS2, 2SS4, [ME, R, C]

voCABuLARY unit estimate measure closer check

GoalsStudents will problem-solve a way to measure when they have only two units instead of many.

Estimate length in paper clips. ASK: How many big paper clips do you think we will need to make a chain as long as your JUMP Math workbook? Record students’ estimates on the board and choose one of the middle numbers. Link that many paper clips together and then ASK: Is the guess too high or too low? Should my next guess be higher or lower? A lot or a little? Continue to ask questions and modify estimates until you have a chain as close to the length of the book as possible. (The answer is 6.) Repeat with small paper clips and 2 cm connecting cubes. Repeat to measure a pencil.

use known measurements to estimate lengths of new objects. ASK: About how many big paper clips do you think we will need to make a chain as long as a ruler? Will we need more paper clips than for the book, less than for the pencil, or a number in between? Place the ruler and pencil next to the book to help students decide. Record students’ guesses and check. Repeat with other objects such as a pair of scissors, a water bottle, a tens block, or an eraser.

Reinforce the importance of keeping the paper clips straight. Measure the JUMP Math workbook using 8 big paper clips that aren’t properly lined up. ASK: Is the book 8 paper clips long? What do I mean when I say that something is 8 big paper clips long? How long would that be? Have a volunteer demonstrate how long 8 big paper clips are.


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Can count Can order numbers Can determine what is “closer to” Can measure using connecting cubes

MATERiALS

big (5 cm) paper clips small (3 cm) paper clips 2 cm connecting cubes JUMP Math workbook, pencil, and other objects to measure BLM Estimate with Paper Clips (page xxx) BLM Measure with Paper Clips (page xxx)BLM Estimate with My own unit (pages xxx) BLM Estimate with Cubes (page xxx)

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BLM Estimate with Paper Clips and BLM Measure with Paper ClipsStudents record their estimates and measurements of classroom items. BLM Estimate with My own units. Students choose their own units.BLM Estimate with Cubes. Students estimate lengths of lines on a page.

Estimate the measurement with one unit given the measurement with another unit. Hold up a ruler and demonstrate that it is about 6 big paper clips long. SAY: I want to estimate how many connecting cubes long it is. ASK: Should I guess a number that is more than 6 or less than 6? (more than 6) Why? (Connecting cubes are shorter than paper clips, so I will need more of them.) Have students guess how many connecting cubes you will need and record their answers. Place 3 connecting cubes along the length of the ruler to start. Ask students if they want to guess again or if they think their original estimates are still good. Then place a few more connecting cubes and ask students again if they want to revise their guesses. Repeat this process. ASK: Were you right to guess a number more than 6? Did you need a lot more than 6 connecting cubes or just a little more? (a lot more) Did it surprise you that we needed so many more connecting cubes than paper clips?

Demonstrate measuring another object, such as a pencil case, with connecting cubes. Say the pencil case is 12 cubes long. Show a small paper clip next to a cube and ASK: Which is longer: a connecting cube or a small paper clip? (a small paper clip) Will we need more connecting cubes or more small paper clips to measure the pencil case? (connecting cubes) If the pencil case is 12 connecting cubes long, about how many small paper clips do you think we will need? Record students’ answers and then allow them to revise their guesses as you place more small paper clips along the length of the pencil case, as above. Confirm that you do indeed need fewer paper clips.

Extensions1. Have students estimate how many small paper clips it would take to

measure the length of the classroom. If each student made a chain of 10 paper clips and students put all their chains together, would they have enough? Have them check their prediction as a class. (You might choose to string the chains together for students while they are out of the room.) Each student might attach their name to one of the paper clips in the chain so that they know which chain they created. If possible, use coloured paper clips and give each student 10 paper clips of the same colour to link together.

2. What is longer: 100 small paper clips or the height of one school floor? Hang a chain of paper clips from the stairs to check. Use the chains made in Extension 1.

Measurement 2-13

ExTRA PRACTiCE


ME2-14 CentimetresPages 159-161

CuRRiCuLuM ExPECTATionSOntario: 2m1, 2m2, 2m3, 2m5, 2m7, 2m31 WNCP: [Cn, C, R], optional, 3SS3

voCABuLARY ruler centimetre (cm) standard units

GoalsStudents will learn how to use a centimetre ruler.

Create a ruler with small paper clips as the unit. Prepare a chain of several small paper clips linked together. Tape the paper clips horizontally to a transparency and draw a pencil 2 paper clips long directly above it, lined up correctly. Use an overhead projector to project the paper clips and pencil on the board. ASK: How many paper clips long is the pencil? Mark the number 2 where the pencil ends. Then draw another pencil 3 paper clips long and ASK: How many paper clips long is this pencil? Draw a mark at the 3 and write 3 underneath it. SAY: Any object that is exactly as long as this pencil is 3 paper clips long. Repeat with pencils that are 1 and 4 paper clips long.

Then remove the paper clips (without marking the 0) and explain that anything that ends at the 3 will be 3 paper clips long and anything that ends at the 4 will be 4 paper clips long. Take a strip of paper that is 4 paper clips long. Place it on the transparency once so that it ends at the 3 and again so that it ends at the 4. SAY: I forgot to put where to start! Put the paper clips back on the transparency and make a mark before the first paper clip. ASK: What number should we mark here? What number is before 1 on the number line? (0) SAY: Anything that starts here and ends here (point to the 0 mark) doesn’t have any length at all, so it is 0 paper clips long.

Rulers do the counting for you. Now remove the paper clips and explain that you have a tool that will count how many paper clips long an object is; this tool is called a ruler. Write “ruler” on the board. SAY: We don’t need the paper clips anymore. Have several pieces of paper of various lengths, some


Can measure lengths using non-standard units

MATERiALS

a transparency and overhead projector small paper clips and strips of construction paper (various lengths, including 4 paperclips long) various classroom objects to measure 30 small (1 cm) connecting cubes for each student one 30 cm ruler and metre stick for each student BLM Concrete Rulers Without Pictures (p xxx)BLM Ruler or Counting (p xxx)BLM Concrete Rulers (p xxx)BLM Measure with a Ruler (p xxx)BLM Measuring with Centimetres (p xxx)finished copies of BLMs Practice Measuring (p xxx) and BLM Measure with Paper Clips(p xxx)

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exactly a whole number of paper clips long and others not. Demonstrate measuring the first one using this number line that counts the paper clips for them (the ruler), then have volunteers measure the others; emphasize the importance of starting at the 0. Include very short strips of paper that are less than half a paper clip long. Put the paper clips back on the transparency, but lengthen the chain first (add paper clips) and mark higher numbers on the ruler. Have students measure much longer strips of paper.

Measure using small connecting cubes and rulers. Give students small connecting cubes and a copy of BLM Ruler or Counting. Students measure the real objects pictured to complete the first column on the BLM. Then give students a small-connecting-cube ruler (from BLM Concrete Rulers) to measure the same objects again and complete the second column. Discuss whether students got the same answer both ways, and if not, why not. PRoMPTS: Did you forget to line up one end of the object with the 0? Did you count the cubes properly or were there so many that you got lost in the counting? Which way of measuring was easier? Which way was less work? (using the ruler) Why? (because the ruler does the counting for us)

Relate the length of small connecting cubes to the spaces on a normal ruler. Give each student a regular ruler (30 cm long) and 30 small connecting cubes. Have students line up the cubes on the ruler so that they fit in the markings. ASK: What do you notice? (The spaces between the markings are the same length as the cubes; the cubes fit exactly between the markings.) Explain that the length of each small cube is called a centimetre and people use centimetres to make rulers. Write “centimetre” on the board. Students can practise measuring with a ruler by completing BLMS Measure with a Ruler and Measuring with Centimetres. Students can measure the pictures directly on the page (they are all a whole number of centimetres) or else measure the real objects if available.

Measure longer objects. Have students use rulers to measure objects that are between 20 and 30 cm long, such as a sheet of paper. Students work in pairs; each student measures the same objects, one at a time, and then they compare their results, looking for discrepancies. Then ask students to measure objects that are more than a ruler long but less than a metre long using a meter stick. Remind them to line up the 0 mark on the metre stick with the end of the object. Objects they might measure include the width of a doorway, the length of a bookshelf, a width of a window, the length of an arm, and the distance around a garbage can (using string and the metre stick). Emphasize how much easier it is to have the ruler count for them when there are many centimetres to count.

Centimetre and cm. Write “centimetre” on the board again and have a volunteer find and circle the letters c and m in the word. Tell students that people often write just cm for centimetre. Write “cm” on the board.

Reflecting on what made the problem easy or hard

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Measurement 2-14

Name or draw objects in the classroom that are about 1 cm long or 1 cm wide.

JouRnAL

ACTiviTY

Have students find objects that are about 1 cm long, wide, or high in the classroom.

ExTRA PRACTiCE

Use BLM Concrete Rulers or BLM Concrete Rulers Without Pictures to make the same comparison using concrete materials. Students can re-measure objects on: BLM Practise Measuring, BLM Measure with Paper Clips, or Workbook p. 157. Compare answers.


ME2-15 Measuring using Centimetres GridsPage 162

CuRRiCuLuM ExPECTATionSOntario: 2m1, 2m2, 2m5, 2m7, 2m31, 2m32 WNCP: [R, Cn, C], optional, 3SS3

voCABuLARY long wide tall grid centimetre (cm)

GoalsStudents will measure objects on a grid horizontally and vertically.

Review rulers. List, in a chart, all the similarities between a number line and a ruler. (the markings are equally spaced; the numbers go in order and start at 0; both are tools that do the counting for you).

using rulers when the object doesn’t start at 0. Draw a “straws” ruler on the board and explain that the units are straws. Place a strip of paper so that it starts at the 2 mark and ends at the 5 mark. SAY: I want to find out how long this paper strip is. ASK: Is it 5 straws long because it ends at the 5? (no) Why not? (because we didn’t start at the 0) How many straws long do you think it will be if I start at the 0? (3 straws) Using logical reasoning Demonstrate moving the paper to start at 0 to check students’ predictions. SAY: I moved the paper back a few spaces. Let’s count the number of spaces I moved back. Draw arrows to indicate counting back. (2) Then place a strip of paper on the “straws” ruler that starts at 5 and ends at 12. ASK: How many places do we have to move the paper to make it start at 0? Count out moving 5 spaces back. Explain that the end of the paper started at 12 and we moved it 5 spaces back. Where did it end up? (at the 7) Write on the board: 12 − 5 = 7. Repeat with different lengths and positions. ExAMPLES: start at 3 and end at 8, count back from 3 to 0 (8 − 3 = 5); start at 6 and end at 13, count back from 6 to 0 (13 − 6 = 7); start at 4 and end at 8, count back from 4 to 0 (8 − 4 = 4).

Another way to use subtraction to measure objects that don’t start at 0. Demonstrate that a piece of paper that is 11 straws long starts at 0 and ends at 11. Explain that you want to take away part of the paper. Cut off the first 4 straw lengths. ASK: How long is the piece I took away? How can you tell? (the section between 0 and 4 was cut off) SAY: Starting at 4 and ending at 11 is another way of saying that I started with 11 straw lengths and took away 4 of them. ASK: How many straw lengths do you think I have left? (11 − 4 = 7) To check, move the object back to start at 0 and verify that it now ends at the 7. Repeat with different lengths and positions. ExAMPLES: a strip of paper 10 straws long, cut off 2 (10 − 2 = 8; move the


PRoBLEM SoLvinG

Connecting

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Can measure using centimetres Can subtract by counting forward

MATERiALS

several strips and pieces of paper to measure (see lengths below) grid paper BLM Chains of units (p xxx)

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paper remaining back to 0 to check); a strip of paper 9 straws long, cut off 5 (9 − 5 = 4); a strip of paper 15 straws long, cut off 7 (15 − 7 = 8).

Check answers by counting the spaces. Remind students of the first measurement, starting at 2 and ending at 5. Demonstrate again how you found the length of the paper by moving it back to 0 (the length was 3 straws long), and then write the subtraction sentence 5 − 2 = 3 on the board. ASK: Can you think of another way to find the length of the paper without moving the paper back to 0? Discuss various answers. Demonstrate how to count the spaces from 2 to 5 using arrows from one number to the next as you count. Re-measure several other paper lengths found above by counting the spaces (without moving the paper strip to 0). ExAMPLES: start at 3 and end of 8; start at 6 and end at 13; start at 4 and end at 8. Point out that this method is like subtracting by counting forward.

introduce vertical rulers. Now draw a vertical “straws” ruler on the board beside the horizontal ruler. Cut out a piece of paper that is 3 straws tall and 6 straws long. Have a volunteer measure the length using any method (either start at 0 and count the spaces or place the paper between any two numbers and count the spaces). SAY: We now know that the paper is 6 straws long. Notice that it is also quite tall. Write “tall” on the board. ASK: Is there a way to measure how tall the paper is? Discuss answers. Some students may decide to turn the paper sideways to measure along the horizontal ruler; they may also measure along the vertical ruler. Continue to demonstrate how to count the leaps between numbers. Explain that the horizontal ruler can be used to measure how long an object is while the vertical ruler can be used to measure how tall an object is. Repeat with more pieces of paper. ExAMPLES: 2 straws tall and 8 straws long; 1 straw tall and 5 straws long; 3 straws tall and 2 straws long. Explain to students that sometimes objects are taller than they are long.

introduce grids. Show students a piece of grid paper, either large grid paper for demonstration purposes or 1 cm × 1 cm grid paper. Write “grid paper” on the board. Explain that using grid paper is another way to measure how long and how tall objects are. Draw a rectangle that is 10 units tall and 5 units long on your grid paper. SAY: There are no numbers on the grid paper, but there is a starting point and an ending point on each side of our rectangle. Count the number of squares between the starting point and ending point. This is like counting the number of straw lengths. Demonstrate how to count by drawing arrows from the beginning to the end on both sides of the rectangle.

Give students 1 cm × 1 cm grid paper and have them draw their own shapes or objects on it. Then have partners measure each other’s shapes.

Connecting

PRoCESS ExPECTATion

Measurement 2-15

ExTRA PRACTiCE

BLM Chains of units


ME2-16 Estimating CentimetresPage 163

CuRRiCuLuM ExPECTATionSOntario: 2m1, 2m2, 2m7, 2m30, 2m31 WNCP: [R, C], optional, 3SS3

voCABuLARY estimate finger predict

GoalsStudents will use a finger to approximate measurements in centimetres. Students will compare their estimates to measurements made using a ruler.

use finger width as an approximate centimetre. Give each student a ruler. Have them place each finger in turn, including the thumb, between the grid marks on the ruler. ASK: Which finger is closest to being 1 cm wide? Which finger is furthest from being 1 cm wide? Students will need this information for Activity 1. SAY: Even though one of your fingers is not exactly 1 cm wide, it is pretty close, so it can be used to measure a centimetre when you only need an answer that is close to the right answer.


Can measure in centimetres

MATERiALS

a ruler for each student various small articles to finger measure (see below) paint and cardboard rectangles string or yarn in many different colours glue BLM Lights (p xxx)

ACTiviTY 1

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Distribute paint and cardboard rectangles of various lengths. Have students use fingerprints (using the same finger) to measure the length of the rectangles. Make the rectangles wide enough so that students can write or fingerpaint the number of fingerprints as well. Students will measure each length a different way: once with the finger they chose as being closest to 1 cm wide and once with the finger furthest from being 1 cm wide.

You will have to wait until the fingerprints have dried to continue. If possible, have students do this part of the Activity before recess, lunch, or another break in your day, and come back to it afterwards.

Have students circle the measurement that they think will be closest to the actual measurement in centimetres. ASK: Was your prediction correct? How close was your finger measurement to the actual centimetre measurement?

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Review using only one unit to measure. SAY: Just as you didn’t need many copies of your hand to measure your desks, you don’t need many copies of your finger to measure objects with your finger width. Draw a line 10 cm long on the board. Measure it using your index finger (put chalk on your finger to make fingerprints) and then have a volunteer measure it using his or her index finger. Have the class predict which measurement will be closer to the centimetre measurement. Measure the line using a ruler to check. Then place your finger and the volunteer’s finger between the markings to see whose finger is closer to 1 cm wide.

Explain that students can use the finger measurement as an estimate for the number of centimetres. Give students various objects to measure using the finger that is closest to a centimetre wide. ExAMPLES: pencil case, pencil, lunch bag, JUMP Math workbook, name tag, playing cards, file cards. To ensure that students measure correctly (with no gaps or overlapping between the units), they can

• make and use a fingerprint ruler • cut paper the same length as the object and measure the paper with fingerprints, or • use the corresponding fingers from both hands (see Measure using hand lengths in ME2-12).

Then have students re-measure each object using a centimetre ruler and record the ruler measurement. Students can record their finger and centimetre measurements using the following format: Estimate: about cm Measurement: about cm

Estimate centimetres without using fingers. Have students estimate how many centimetres long, tall, or wide objects are, and then check using a ruler. Stick to objects that are less than 30 cm long. To estimate, students should make educated guesses based on their experiences with centimetres thus far.


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ACTiviTY 2

Give each student a copy of BLM Lights. They will start by working individually but will complete the BLM in groups of three.

Students need to cut three pieces of string or yarn to put all around the house frame, door, and window on the BLM. Have students use their fingers to estimate how long to make each piece and then use a ruler to measure how long to make each piece. Students may record their estimates and actual measurements. Have ready many colours of string in one-metre lengths. Collect the BLMs and give each student one string to cut or let students choose the colour they want. Suggest that students add 4 cm to each measurement just in case (because it is easier to cut string that is too long than add to string that is too short).

After they have cut their strings, divide students into groups of three so that all members of a group have strings of a different colour. Have

Measurement 2-16


The need for standard units. SAY: A long time ago, people didn’t use paper clips or connecting cubes or even centimetres to measure lengths. They used other things. For example, in ancient Egypt, they used cubits. A cubit is the length from the tip of your middle finger to the outside of your elbow. Show this length on your arm. Use Activities 2 and 3 to illustrate the disadvantages of such a unit of measurement and the need for standard units.

students arrange their strings in order from shortest to longest. Make sure that all group members have the same corresponding string lengths. Students can braid their strings together and glue them to one BLM or they can trade strings and decorate their own BLMs with different colours. If your number of students is not divisible by 3, have ready strings of different colours that are the correct lengths (plus 4 cm) for leftover pairs or individuals: 39 + 4 = 43 cm (the frame), 18 + 4 = 22 cm (the door), 20 + 4 = 24 cm (the window).

Real world

ConnECTion ACTiviTiES 3-4

3. Tell students that you want to make a table that is 4 cubits high. Have students each make one leg using their own cubit and then get into groups of 4 to make a table. Students can roll old newspapers to make the legs and use bristol board to make the tabletop. (Rolling newspapers diagonally works well; the ends are thinner and easier to cut off.) Then have students lay a pencil on their tables. ASK: Does the pencil roll off? Why? Why aren’t the legs the same height? Explain to students that the ancient Egyptians recognized the need for everyone to use the same, or a standard, cubit. ASK: Whose arm do you think they used to determine the length of a standard cubit? The king’s! Discuss how people recorded and shared the king’s cubit so that everyone would know what it was. (They used a wooden stick with lines scratched in it to show the length of the king’s cubit, just as we use rulers.)

4. Have students make rulers using their hand lengths (from wrist to fingertip) as units. Then have them use their rulers to measure the length and width of their desks. The next day, bring in a sheet of newspaper with the same length and width as the students’ desks, as measured using your own hand length. Tell students that you used their measurements, so the newspaper should fit on their desks. Try it out, and ASK: But I used the same number of hand lengths that you used. Why didn’t my newspaper fit on your desk? (because my hand lengths are longer than yours, so our units weren’t the same) Explain that one of the reasons it is important for everyone to agree on how long the units are is so that we can both measure different objects and know if one will fit on top of the other. Discuss other situations where one might want to know if things will fit (ExAMPLE: will the plant fit between the bookshelf and the door).

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Extensions1. Have students measure objects that are longer than a ruler with a ruler.

ASK: What do you do when the object is longer than a ruler? PRoMPTS: Can you use the ruler the way you used your hands to measure your desks or your fingers to measure smaller objects? Would masking tape help?

2. Inches. SAY: Some people don’t use centimetres as their standard unit; they use inches. Explain that 2 inches are about 5 cm long.

a) ASK: Is a big connecting cube longer or shorter than 1 inch? How do you know? (Each connecting cube is 2 cm long, so 2 connecting cubes must be 4 cm long. Notice that 4 cm is less than 5 cm or 2 inches. Since you need more than 2 connecting cubes (or more than 4 cm) to make 2 inches, the connecting cube must be shorter than 1 inch.)

b) ASK: A line is 4 inches long. How long is it in centimetres? (2 inches is 5 cm, so 4 inches is 10 cm)

Bonus What is the length of the line in connecting cubes (or how many connecting cubes fit into 10 cm)? (This can be checked directly by drawing a line that is 10 cm long and counting the connecting cubes that fit onto it.)

c) Show students a ruler with inches marked on it and explain that Lucas measured a box using this ruler. The box is 10 inches long. What is its length in centimetres? (2 inches is 5 cm, so 4 inches is 10 cm, 6 inches is 15 cm, 8 inches is 20 cm, and 10 inches is 25 cm) Students might verify this by using an inch ruler and a centimetre ruler and lining up the zero marks.

Measurement 2-16

Teacher’s Guide for Workbook 2

ME2-17 MetresPage 164

CuRRiCuLuM ExPECTATionSOntario: 2m1, 2m2, 2m4, 2m5, 2m7, 2m31 WNCP: [R, Cn, C], optional, 3SS3

voCABuLARY metre (m) centimetre (cm)

GoalsStudents will measure lengths in metres.

introduce the metre stick. ASK: What unit would you use to measure longer distances, such as the length of the classroom? Record suggestions on the board. Choose one of the smaller units suggested, such as a cube. ASK: Do you think that using a cube would be an easy way to measure such a long distance? Can you think of anything else that we could use to measure the length in a faster and easier way?

Show students a metre stick without telling students how long it is. Use it to draw a line 100 cm long and ask students to predict how long the stick and line are using a single tens block. Make a mark at the end of the tens block as you move it along the line. Count the marks to check students’ predictions. Then have students predict how long the line is in centimetres. Record their answers. Have a volunteer measure the line using the metre stick. Then show students that the metre stick is divided into 100 cm.

Give students a metre-long piece of string and have them verify that the string is one metre long (by lining it up with a metre stick and seeing that it starts at 0 and ends at 100 cm). Then have students use the string to find objects in the classroom which are about 1 m in length, width, or height, and objects which are more than and less than 1 m in length, width, or height.

Measure using metres. Ask students to predict how many metres long the blackboard is. Demonstrate how to measure using a metre stick. Emphasize that you do not make a mark at the end of the stick as you did for tens blocks; you make a mark at exactly 100 cm because that’s how long a metre is. Demonstrate making the measurement incorrectly another way, by holding the stick diagonally. Have a volunteer make the mark correctly by holding the stick straight along the board. (One way to ensure the stick is straight is to align it with the blackboard ledge.)

Make your own metre stick. Students can make their own metre stick by rolling newspaper up tightly and taping it with masking tape. Cut the newspaper roll so that it is exactly one metre long by lining it up with the 0 and 100 cm marks on the metre stick. It is convenient to roll the newspaper diagonally so that the ends are only one layer thick and easier to cut. As a


Can use a number line Can skip count on number line Can line up units and objects being measured Can use a ruler Understands centimetres

MATERiALS

tens blocks newspaper and masking tape a metre stick for each student


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class, determine how many metre sticks long the classroom is from side to side and from front to back. ASK: If we use all our metre sticks, do you think we can measure the distance to the principal’s office? The library? The exit door? Predict the distances in metre sticks and then check it.

Compare the newspaper metre stick to string and to a regular metre stick. The newspaper metre stick is less likely to bend than a string the same length. It is more convenient than a regular metre stick because we don’t have to worry about making marks at 0 or 100; we only need to mark where the beginning and end are. However, the newspaper metre stick is less convenient than a regular metre stick if we want to measure lengths that are less than a metre long because it doesn’t have any markings.

Practise measuring with only one metre stick. SAY: Since your newspaper metre sticks are exactly one metre long, you don’t have to worry about where to make a mark; it is always at the end of the stick. Have students measure several objects in the class with their metre sticks, using masking tape to mark the end of each stick measurement. Instead of using a piece of tape the full length of the object being measured, you could teach students to cut off small pieces of tape and use the edge of the tape itself as a marking. Students can verify their measurements by combining their metre sticks to ensure they get the same answer using multiple units as when using a single unit. Similarly, students who complete the worksheet at or near the same time can so the same thing to verify their answers. Students can also practise measuring distances around large objects using a metre stick (or a length that measures a metre) and string. ExAMPLES: the classroom, the school field, the gymnasium.

Extensions1. When students are not in the room, draw two lines on the board, both one

metre stick long, with arrows at the ends as shown. Ask students to predict which line is longer without the arrows. Then have a volunteer check by comparing both to a metre stick.

2. ASK: How could you use a metre-long piece of string to identify objects that are about half a metre? (fold the string in half)

3. Introduce the term millimetre. Point out the small lines on a metre stick (or a ruler) and explain that a millimetre is the distance between them. Challenge students to figure out how many millimetres are in a centimetre, then in a metre.

4. SAY: Keisha lives five blocks from the school and eats lunch there. Each block is about 15 m long. ASK: How far does she travel each day, to get there and back? AnSWER: She goes ten blocks altogether, so count by 15s (15, 30, 45, …) and stop when you have 10 fingers up, to get 150. So Keisha travels 150 m each day.

Number sense to 1000 is linked to longer and larger measurements in a variety of ways.


PRoBLEM SoLvinG

Draw an object that is about 1 m wide and 1 m tall.

JouRnAL

Literature— How Much, How Many, How Far, How Heavy, How Long, How Tall is 1000? by Helen nolan

ConnECTion

Measurement 2-17


ME2-18 Estimate MetresPages 165-166

CuRRiCuLuM ExPECTATionSOntario: 2m1, 2m2, 2m4, 2m5, 2m6, 2m7, 2m30, 2m31, 2m33 WNCP: [R, v, Cn, C], optional, 3SS3

voCABuLARY centimetre metre measure about

GoalsStudents will estimate measurements in metres and then measure using a metre stick.

Predict and then check. Have students predict whether their height is more than, about the same as, or less than two metres. Then have pairs check by making a string that is either the same length as their height or making a string that is 2 metres long.

use units that are about the same size to find approximate measurements. SAY: Remind me what makes a good unit of measurement. (It is easy to find many units the same size.) SAY: I want to tell a friend how big our classroom is. She doesn’t need to know exactly how big it is; she just wants an idea. I’m going to take big steps all the way across the room to see how many steps it takes. ASK: Do you think my steps are good units? Can I take many steps that are all the same size? Will my steps be at least close to the same size? SAY: Even though steps are not all exactly the same size, they will all be close to the same size if I try to take big steps all the time. This won’t tell me exactly how long the classroom is, but it will give me a good idea. Sometimes, that’s all you need.

use outstretched arms as an approximate unit. Modelling SAY: Let’s estimate how many students with outstretched arms we will need to go all the way across the room. ASK: Will this give an exact measurement of how long the classroom is? (no, because the outstretched arms of students are not all the same length, but they are close) Will we need more or less students than metre sticks? PRoMPT: Are outstretched arms longer or shorter than a metre stick? (longer, so we’ll need fewer of them) Have students perform this measurement. ASK: Were your predictions correct?

Large steps are about a metre long. Hold a metre stick up vertically and ask a volunteer to try to take a step that is about as long as a metre stick. Measure from the heel of the back foot to the toe of the front foot and mark the length of the student’s step with masking tape. Compare the length of the step to the metre stick. ASK: Do we need a longer step or a shorter step


Can use a metre stick to measure

MATERiALS

string metre sticks for students working in pairs masking tape BLM About one (p xxx–xxx)BLM Metre or Centimetre? (p xxx) compasses


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drawing

Extensions 1. Measure using both cm and m. (E.g. The classroom is 4 m and 23 cm wide.) 2. Measure small distances using a compass.

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to match the metre stick? Have the same volunteer take another step that they think will be the same length as a metre stick. Continue until the student has taken a step that is very close to a metre long. In pairs, have students take a step they think will be a metre long while their partner measures and tells them to take a longer or shorter step. Then have them take 5 steps they think will be about a metre each and have a partner check using a metre stick. Emphasize that it is much harder to take five big steps all in a row than five steps walking normally. Suggest that students lead off with the same foot each time: take one giant step; bring your back foot forward and place it next to your other foot, with the heel directly in front of the front toe; then take another giant step.

Then SAY: I want to know about how many metre sticks long the classroom is. Have the students take giant steps across the room to help you find out. Remind them to take identical steps and to lead off with the same foot each time. Then have a volunteer use a metre stick to measure the length of the classroom. ASK: Did we get the same answer both ways? Were our answers close? Which way was faster? Explain that when we are in a hurry and we just need to know about how long a room is in metres, we can use giant steps instead of metre sticks to find out. Discuss situations where it is important to know exact measurements. ExAMPLES: a race, making a ruler to sell, making paper to put in a book, making legs for a table.

About a metre or a centimetre? Have students decide whether given objects are about 1 cm or about 1 m wide, tall, or high. ExAMPLE: Hold up a pair of scissors and show the height of the scissors when they are lying flat. ASK: Are the scissors about a centimetre wide, tall, or long? Have students find other objects with a dimension that is about 1 m or 1 cm.

Bonus Students who finish BLM About one (1) might pretend the 3 × 3 grid is a completed tic-tac-toe board. ASK: Who went first, cm or m? (the one that had more turns—cm) Who won?

Measure with centimetres or metres? Draw on the board a line that is about 85 cm long. Have a volunteer measure with a newspaper metre stick how long it is in metres. (about 1 m) Then have a volunteer measure how long it is in centimetres, by using a metre stick (about 85 cm). ASK: Which measurement gives you more information? Is it better to use centimetres or metres to say how long it is? (centimetres gives more information) Does it make sense to measure the distance from here to the principal’s office using centimetres? SAY: Although it would be more exact, it would be very inconvenient because there would be so many centimetres. For long distances, it is better to use metres, and for short distances, it is better to use centimetres. Have students decide whether to use centimetres or metres to measure various lengths and the distance around various objects. ExAMPLES: an envelope, the board, the teacher’s desk, a rug or carpet, a book, a door frame, the height of the room, the ceiling, one floor tile.

Metre and m. Write “metre” on the board and circle the letter m. Explain that just like people often write just cm for centimetre, people often write just m for metre.

Guessing, checking, and revising

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Selecting tools and strategies Connecting

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Measure in either metres or centimetres: cutlery, plates, size of bedroom, stairway railings, kitchen sink, TV, favourite chair, and so on.

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Measurement 2-18

I would use a metre stick to measure .

I would use a centimetre ruler to measure .

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ExTRA PRACTiCE

About oneStudents identify and draw objects with height, width, and/or length about 1 cm or 1 m.

ExTRA PRACTiCE

BLM Metre or Centimetre?


ME2-19 Comparing MassesPages 167-168

CuRRiCuLuM ExPECTATionSOntario: 1m39; review, 2m1, 2m2, 2m4, 2m5, 2m7 WNCP: 1SS1, 2SS3, [R, Cn, C, v]

voCABuLARY heavy / heavier / heaviest light / lighter / lightest mass

GoalsStudents will understand mass in terms of heaviness (the heavier an object, the greater its mass). Students will develop an understanding that measurement terms such as heavy and light are relative and depend on perspective.

introduce “heavy” and “light.” Show students two small closed boxes with “secret” contents, one of books and the other of cotton balls. Demonstrate lifting the box of books with difficulty. Invite volunteers to try to lift it. SAY: This box is hard to lift. ASK: What word do we use to describe objects that are hard to lift? (heavy) What might be in the box that makes it so heavy? Record answers on the board. Repeat with the box of cotton balls, using “light” instead of “heavy.” Write “light” and “heavy” on the board. After you have recorded many guesses, SAY: One box contains books and the other box contains cotton balls. Can they tell which one is which? Have a volunteer open the boxes to check.

introduce mass. Have volunteers place books in your open hands: two books in one hand and five in the other. Move the hand with 5 books down to show how heavy the books are. ASK: What happened to my hand when the books got too heavy? (it moved down) Have students work in groups of 4 and have each student hold 1 JUMP Math workbook in one hand and 3 in the other hand. ASK: Does the hand with 3 move down more? (yes) SAY: Just as length tells how long something is, mass tells how heavy something is. Write the word “mass” on the board. The more heavy something is—the more it pulls down when you try to lift it up—the larger its mass is.


Understands comparatives such as longer and shorter Can compare masses directly

MATERiALS

a small box of books a small box of cotton balls large resealable plastic bags objects of various masses (see below) pan balances 5 connecting cubes and a piece of paper for each student 2 springs spinners with various labels (see below) a heavy book and a light book (see below) a long pencil and a short pencil BLM Compare Masses (p xxx)BLM Heavy or Light? (p xxx)


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Looking for a pattern

PRoBLEM SoLvinG Heavier and lighter. Remind students that an object that is “more long” than another object is called longer. ASK: What should we call an object that is more heavy than another object? (heavier) Write the word “heavier” on the board. SAY: Shorter means “not as long as.” What should we call “not as heavy as”? (lighter) Write the word “lighter” on the board.

Give students several objects of different masses. Have students hold two objects at a time, one in each hand. Have students show you which object is heavier by moving down the hand that is being pulled down more. (Students can exaggerate the movement.)

Heaviest and lightest. Explain the meaning of “heaviest” and “lightest” and write both words on the board. SAY: Heaviest means heavier than all the other objects. Lightest means lighter than all others. Give students three objects (say, a straw, a workbook, and a pencil case). ASK: Which object is heaviest? (the workbook) Which object is lightest? (the straw)

Balances. ASK: Have you seen seesaws in the park? Show students a pan balance. SAY: This much smaller version of a seesaw is called a pan balance and it works like a seesaw. The heavier side goes down and the lighter side goes up. Write “pan balance” on the board.

does shape affect mass? Give each student 5 connecting cubes. Have students make a shape with their cubes and then pair up with another

Visualizing

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ACTiviTY 1

Have students work in pairs. Give each pair four objects of different masses (ExAMPLES: a glue bottle, a stapler, a tennis ball, a small stuffed animal), each placed in a large plastic resealable bag. Have both students compare the objects by weight and order them from lightest to heaviest. Then, one student in each pair blindfolds the other. Blindfolded students should name all four objects to ensure they remember them (if some of your students have trouble remembering four objects, they can use only three). Then, partners hand the blindfolded students one of the plastic bags and blindfolded students try to guess the contents. If a guess in incorrect, the partner replies by saying whether the object is heavier or lighter than the guess. Students take three turns and then switch roles.

ACTiviTiES 2-3

2. Which object? Choose five objects of different masses (ExAMPLES: a JUMP Math workbook, a connecting cube, scissors, a full water bottle, a chair) and start by thinking of one of the objects. Students ask yes/no questions using the words “heavier” and “lighter” to determine which object you are thinking of.

3. Spinner (mass). (See ME 2 Part 1 – Introduction) Use several objects of different masses (ExAMPLES: stapler, connecting cube, paper clip, deck of playing cards, eraser) and a spinner with four equal areas labelled “lighter,” “heavier,” “lightest,” “heaviest.”


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ExAMPLES: eraser paper clip stapler pencil workbook glue bottle


student who made a different shape. ASK: Do your shapes have the same mass? Why? (yes, changing shape doesn’t change mass) Then give each student a piece of paper. Have half the class make a paper airplane and half the class make a fan. Have partners compare their shapes’ masses. ASK: Did folding the paper in different ways change its mass? (no, changing shape doesn’t change mass)

does stretching change an object’s mass? Take two springs and show that they have the same mass. ASK: Do you think the mass will change if I stretch one of them? Stretch one of the springs into a circle and interlock it with itself so that it holds its stretched position. Then put it back on the pan balance. ASK: Do the pans still balance? (yes) Why? (stretching an object doesn’t change its mass)

A seesaw or a pan balance? ASK: Do you think this pan balance can compare your weight to mine like a seesaw would? Would the seesaw do as good a job at comparing 5 paper clips to a connecting cube? What would happen to the seesaw if you put 5 paper clips on one side and a connecting cube on the other? (nothing) Ask students what they would use to decide which is heavier between the following: • a stapler or scissors (a pan balance) • your sister or your brother (a seesaw) • a monkey or a cow (a seesaw) • a pencil or an eraser (a pan balance)

Heavy and light are relative. Hold up two books, one heavy and one light. Ask: Which book is lighter? Which book is heavier? Then hold up a short

ACTiviTiES 4-6

4. Give each pair of students a big ball of modelling clay. SAY: You can play with the modelling individually, but first you need to make sure each person has the same amount. The challenge is to separate the ball into two equal shares by using the pan balance. Demonstrate by taking a large ball and splitting it into two obviously uneven pieces. ASK: Which side of the balance will go down? Which person would get more modelling clay? How can we make it fair? (take some from the heavier piece and add it to the lighter piece) Take a small amount from one pan and put it on the other; continue until the pans balance.

5. i Spy. Hold up a pair of scissors. SAY: I spy, with my little eye, something that is ____ than the scissors (e.g., lighter, heavier, about as heavy as). Provide other clues if necessary (ExAMPLE: Susan has a red one on her desk.) but ensure that students constantly check their guesses against the first clue by using a balance.

6. Spinner (mass and length). Provide several objects of varying masses and lengths. ExAMPLES: scarf, mitten, stapler, connecting cube, paper clip, deck of playing cards, pillow, stone. Students also need a spinner with four equal areas labelled “longer,” “shorter,” “lighter,” and “heavier.” This game emphasizes the difference between length and mass, and in particular that longer objects can be lighter.


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Making an organized list

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pencil and a long pencil. Ask students to predict which pencil is heavier. Test their prediction on a balance. ASK: Which is heavier: the light book or the heavy pencil? Why did I call the book light even though it is heavier than both pencils? (Because the book is lighter than most books; for a book, it is light.) Why did I call the pencil heavy even though it is lighter than the book?

Then ask students to imagine a heavy mouse and a light cat. ASK: Which do you think will be heavier? (the light cat) What do we mean when we call the mouse heavy? (it is heavier than most other mice) What do we mean when we call the cat light? (it is lighter than most other cats)

Have students name some heavy toys. ASK: Would any of those toys be heavier or lighter than a light adult elephant? A light baby elephant?

Give students cards with the words “heavier” and “lighter” written on them and have students hold up the correct card to complete sentences like the ones listed below (or have students show a thumbs up for lighter—up is the direction the pan goes when the object is lighter—and a thumbs down for heavier). Write one sentence on the board, then change one or two words at a time and ask if the answer changes. You could also prepare word cards in advance and use a pocket chart. ExAMPLES: A heavy car is than a light chair (heavier)A light car is than a light chair (heavier)A light car is than a heavy chair.A light table is than a heavy chair.A heavy table is than a heavy chair. Other objects you might compare: book, blanket, towel, plant, dog, person.

Measurement depends on perspective. SAY: Sarah said that the wheelbarrow filled with leaves was heavy. Her elder brother Lucas said it was light. ASK: Who do you think was right? (They’re both right.) Why did they disagree on whether it was heavy or light? (Lucas is stronger and so finds things easier to lift.) What are some things they would both agree are light? What are some things they would both agree are heavy?

Draw a picture of an ant on the board. Ask students if they have ever seen an ant carrying a crumb. ASK: Do you think the ant found the crumb heavy or light? Would you find the crumb heavy or light? If an ant tried to carry a whole banana, would the banana be heavy or light for it? Is a banana heavy or light for you? Have students complete BLM Heavy or Light?

Extensions1. Have students work in groups of three to share modelling clay evenly, as

they did in pairs in Activity 1.

2. BLM Guess and Check (p xxx). Students compare various objects against a benchmark (a pencil). They predict first and then check with a balance.

3. Complete the following sentences: A heavy snowball is lighter than a light . A light human is heavier than a heavy .


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Compare the weight of popped and unpopped popcorn kernels, and bread and toasted bread.

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Measurement 2-19

ExTRA PRACTiCE

BLM Compare MassesStudents decide which object is heavier based on the balance.


ME2-20 Measuring MassPages 169-171

CuRRiCuLuM ExPECTATionSOntario: 1m34, 1m39; 2m3, 2m5, 2m7, 2m36, 2m42 WNCP: 1SS1; 2SS3, [R, C, Cn]

voCABuLARY measure closer to about exactly estimate

GoalsStudents will measure the masses of objects using connecting cubes as a unit.

Practise measuring using connecting cubes. Give each student several connecting cubes and an object to weigh (ExAMPLES: pencil, eraser, crayon, pencil case, crackers, straw). Have students use pan balances to determine how many connecting cubes linked together have the same mass as the object. Students then check their answers with another student who measured the same object. ASK: Did you both use the same number of connecting cubes?

Compare quantities to compare masses. Have several volunteers tell what they measured and how many connecting cubes they needed. Record their measurements on the board. Have students compare the masses of pairs of objects based on the numbers and then check by directly comparing the objects on the balance.

Together as a class, order the numbers from largest to smallest, then order the objects from heaviest to lightest. ASK: How can we check directly to see if this is the right order? Demonstrate comparing the objects on the pan balance, two at a time.

Predict which object will need more connecting cubes to balance. ASK: Will a pencil case need more or fewer connecting cubes than an eraser? Why? (The pencil case should need more because it is heavier.) Repeat with various objects available in the class. Then discuss using other units. ASK: Will the pencil case also need more paper clips than the eraser? Will the pencil case need more straws to balance it than the eraser will? Check the predictions as a class.

The word “measure.” SAY: When we assign a number to the mass of an object, we are measuring the mass of that object rather than just comparing its mass to other objects. Write the word “measure” on the board. We could say that a pair of scissors is lighter than a book, but saying that the pair of


Can order numbers Knows how many more than

MATERiALS

connecting cubes paper clips various objects to weigh (see below) pan balances


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scissors weighs 6 connecting cubes gives more information. Brainstorm other objects that are lighter than a book but do not weigh the same as a pair of scissors.

Mass and “closer to.” Show an eraser that is, say, lighter than 6 connecting cubes but heavier than 5 connecting cubes. ASK: Is the mass of the eraser closer to 5 connecting cubes or 6 connecting cubes?

Explain that the eraser’s mass is closer to 5 connecting cubes than 6 connecting cubes because the balance didn’t move down as much. Write the words “closer to” on the board. We say “about” 5 cubes to mean that the eraser’s mass is not exactly 5 cubes, but it is closer to 5 cubes than to any other number. Write the word “about” on the board. Draw more pairs of pan balances like the ones above and have students choose the closest mass.

How much heavier and how many more? Have students compare objects by asking not only which object is heavier (because its mass is more connecting cubes than the other object), but also how much heavier it is—how many more connecting cubes does it need than the other object?

Good units for measuring mass are easy to find and that all have exactly the same mass. Discuss whether different objects are good units for measuring mass. ExAMPLES:• big paper clips (yes) • elastics (yes – they stretch, but stretching doesn’t change mass) • connecting cubes (yes) • animal shapes made from origami (yes – different lengths but same mass) • paper snowflakes (no, made from the same paper, but with different amounts cut out) • tens and ones blocks together (no)

ACTiviTY

Have students work in pairs to find objects that have a mass of about 5 connecting cubes. In your journal, make a list of the objects you found.

JouRnAL

Number Sense

ConnECTion

drawing

Measurement 2-20


ME2-21 Estimating and Measuring MassPages 172-173

CuRRiCuLuM ExPECTATionSOntario: 1m34, 1m39; 2m1, 2m2, 2m7, 2m36 WNCP: 2SS3, [R, ME, C]

voCABuLARY unit estimate

GoalsStudents will estimate masses by guessing, checking and revising and by comparing to objects already measured.

Review the term “unit of measurement.” Ask students what units they have used to measure length and what units they have used to measure mass.

Balance the pans by adding one paper clip at a time. SAY: I want to measure how many paper clips will balance the paint brush. Put the paint brush on one side of the balance and place a paper clip on the other side. Continue placing paper clips on the other side, one at a time, until the pans balance. ASK: How many paper clips balanced the brush? (probably 4)

Balance the pans by guessing a number and then adding paper clips. Tell students that you want to measure how many paper clips will balance the scissors and begin adding one at a time. Then SAY: It might take too long to continue adding them one at a time. Can you think of a faster way? Take several suggestions. Have students guess how many paper clips you will need and choose a middle number from their guesses. Have prepared chains of 10 ahead of time and ASK: How many chains of 10 do I need to check your prediction? How many extra single paper clips do I need? Place that many paper clips on the balance to check their prediction. ASK: Was the guess too high or too low? Should my next guess be higher or lower? Students could show a thumbs up to mean “higher” and a thumbs down to mean “lower.” A lot or a little? Continue in this way until the pans balance.

Balance the pans by guessing a number and then adding or removing one at a time. ASK: Do you think the stapler will need more paper clips than the paint brush (above) or fewer? More than the scissors (above) or fewer? Have volunteers compare the objects by holding one in each hand at the same time. Ask them to estimate how many paper clips will balance the stapler. Record their answers on the board and choose a good middle number from their guesses. Use the same guessing, checking and revising strategy to find the correct number of paper clips. Invite volunteers to help.

Discuss how estimating makes measuring easier. SAY: Most of the work is done for you when you guess a number close to the correct answer. If


Understands “closer to” Can measure masses using connecting cubes Can order numbers Can count objects grouped in tens and ones

MATERiALS

connecting cubes paper clips various objects to weigh (see below) pan balances


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your original guess is really close to the answer, you hardly have to do any guessing or revising. The closer your guess, the less work you have to do.

Practise estimating. Ask students how many big paper clips they think you will need to balance a glue stick. Have them guess and then show thumbs up or thumbs down, as before, to mean add paper clips or remove paper clips. Repeat with small paper clips, then big (2 cm) connecting cubes, and finally small (1 cm) connecting cubes. Additional ExAMPLES: coins, plastic cup, small stone, file cards.

Measurement 2-21


ME2-22 Comparing unitsPages 174-175

CuRRiCuLuM ExPECTATionSOntario: 2m1, 2m2, 2m7, 2m36WNCP: 2SS2, [R, C]

voCABuLARY unit estimate more / less

GoalsStudents will relate the size of units of mass to the number of units.

Compare pairs of scissors to tens blocks. Give pairs of students several pairs of scissors and tens blocks, a pan balance, and an object to weigh (ExAMPLES: stapler, raw potato, small stuffed toy). Different groups could be given different objects. Have students measure the object first with scissors and then with tens blocks. Record several of their measurements on the board (e.g., 6 scissors and 63 tens blocks). ASK: Did you need more scissors or tens blocks? (tens blocks) Everyone needed more tens blocks than scissors—why do you think that happened? Is it because the length is different? The colour? What is it about these objects that’s causing the numbers to be so different? (the weight or mass)

Compare big paper clips to connecting cubes. Give pairs of students several big paper clips and several connecting cubes. Ask students to measure a pencil crayon with paper clips and then with connecting cubes. Record several of their measurements on the board (e.g., 3 paper clips and 1 connecting cube). Discuss why some pairs of students might have used the same number of connecting cubes (say 2) while needing different numbers of paper clips (say 5 and 6). Explain that one pencil might weigh just a little more than 2 connecting cubes and another might weigh just a little less than 2 connecting cubes. ASK: Did you need to use more paper clips or connecting cubes to measure the pencil crayon? (more paper clips) Why do you think that happened? (paper clips weigh less than connecting cubes, so you need more paper clips to have the same mass as the pencil crayon)


Can count Can order numbers Understands closer toCan measure mass

MATERiALS

big paper clips (include prepared chains of 5) connecting cubes tens blocks pairs of scissors various objects to weigh and to use as units (see below) pan balances deflated balloon metre stick straw


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ACTiviTY

Have students measure an object such as a pencil case or pair of scissors using various units. Give each student several units: plastic knives (2.5 g), badminton birdies (4 g), grapes (6 g), big paper clips

53

Compare other units: which do you need more of? Have students predict whether they would need more straws or connecting cubes to measure various objects (ExAMPLES: a pencil case, a pencil, a workbook, an eraser). Then check the predictions together as a class.

use different units to decide which is heavier. SAY: This pencil case weighs 10 connecting cubes. Verify this using a pan balance. Then explain that an unknown object weighs 6 straws. ASK: Does the unknown object weigh more or less than the pencil case? (less) PRoMPTS: Do 6 straws weigh more or less than 6 connecting cubes? (less) Do 6 straws weigh more or less than 10 connecting cubes? (less) Then bring out a balloon (not blown up) and explain that this is the unknown object. Put the balloon on the balance and verify that it does indeed weighs 6 straws. Then verify that it weighs less than the pencil case. noTE: When choosing objects and units for this demonstration, make sure you need fewer of the lighter units.

Relate comparing different units of mass to comparing different units of length. Show students a metre stick and a straw. SAY: I have two bookshelves at home. One of them is 3 metre sticks long and the other is 2 straws long. ASK: Can you tell without measuring which one is longer? (yes) How? (A straw is shorter than a metre stick, so 2 straws are shorter than 2 metre sticks and also shorter than 3 metre sticks.)

You can’t always use different units to decide which is heavier. SAY: I have two objects, a skipping rope and a pencil. Which is heavier? (skipping rope; check using a pan balance) SAY: One of them weighs 10 straws and the other weighs 6 connecting cubes. Guess which is which. ASK: Do you think that 10 straws are heavier or lighter than 6 connecting cubes? Can we use the fact that 10 is more than 6 to answer this question? (no, because straws are lighter than connecting cubes, so more straws could still weigh less) Compare 10 straws to 6 connecting cubes on a pan balance. Explain that since 6 connecting cubes are heavier, the skipping rope (which is heavier) must weigh 6 connecting cubes and the pencil must weigh 10 straws. Demonstrate further using other objects available in the classroom.

(1.3 g). Ask students to write how many of each unit they needed to measure their object. Show students how to make a chart by naming or drawing the units in order from lightest to heaviest. Students should record their measurements in the chart.

ASK: Did the number of units needed to measure the object become larger or smaller as the units become heavier? State the findings in mathematical language. ExAMPLE: The heavier the measurement unit is, the fewer units are needed to measure.

Making a table/chart

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ME2-23 Problems and PuzzlesPage 176

CuRRiCuLuM ExPECTATionSOntario: 2m1, 2m2, 2m5, 2m7, 2m36WNCP: 2SS2, [R, C, Cn]

voCABuLARY unit estimate more / less

GoalsStudent will solve problems involving length and mass.

discuss actions that change mass, length, or both. ExAMPLES: Adding butter to a piece of bread will add mass without changing length; biting a piece of licorice will reduce both; stretching a spring will add length without changing mass.

Extensions1. BLM What is different? asks students to decide what is different between

the objects in the picture. Students are given two or three choices between length, height, distance around, and mass.

2. Have students draw a line on one sheet of paper that is 25 big connecting cubes long (the line will need to be jagged).

3. BLM Mass and Length Puzzles provides more puzzles like those in the Workbook. The first question asks students to determine if the race between ants is fair. Since both ants have to run the same distance and both ants are carrying the same mass, the race is fair.

4. Discuss how raisins are made from grapes (the water is taken out of the grape to make a raisin). ASK: Which will weigh more: a raisin or a grape? Have students investigate how many raisins will balance a grape. How many raisins will balance two grapes? Three grapes? Predict how many will balance 5 grapes, and then check the prediction.


Can measure length and mass

MATERiALS

BLM What Changes? (p xxx)

Connecting

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ACTiviTY

open a store selling fudge. Have ready many pieces of “fudge” (modelling clay cut into pieces of different sizes). Have students help you price the fudge by weight, and discuss why weight is a better choice than length. Suggest making each connecting cube of weight cost 1 cent, so a piece of fudge that weighs 11 connecting cubes will cost 11 cents. Students could make price tags for the pieces.

Extension— Compare jelly beans in bowls of different masses.

onLinE GuidE

Connecting

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ExTRA PRACTiCE

BLM What Changes?

Connecting

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Real Life

ConnECTion

new measurement 2 part 1commondrive.pbworks.com/f/tg+for+book+2-1+me.pdf · 2010. 10. 3. · 2...

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