measurement in the middle school world

MeasurementIn the

Middle School World

Jennifer Meggett

Christine Giovannelli

Zachry Middle School

NISD

0 11/2

1/4

2/4

3/41/8 3/8

2/8

4/8

5/8

6/8

7/8

Magnified Inch

Personalize the Math Personalize the Math ChartChart

(modified from original by (modified from original by Karen Duncan NISD)Karen Duncan NISD)

Personal Note:I use this activity frequently during the unit. I tell the students that the most important parts are the key words. I NEVER grade this activity except as a participation grade.

Each student needs a copy of the Each student needs a copy of the math chart to annotate.math chart to annotate.

Keywords: covering, painting, tiling, and carpeting.

Look for problems that talk about filling.

P

A²

V³

parallelogram

borders, fencing, fringe, framing

Save for last

P = Perimeter of the base

B = Area of the base

ab

c

rotation, revolution, around

Ladder, diagonal

I talk them through the first time. Each time after that I give them time to try and put everything they remember on the sheet. Then we talk through the entire presentation again. Eventually many students can even talk through the activity.

I encourage the students to annotate the math chart in the TAKS Test Booklet before starting the test.

TAKS Obj. 4 TEK 6.8, 7.9, 7.13

Materials: Rulers, Yard sticks, Meter sticks Recording Sheet Objects to measure I nstructions:

1. Estimate the each object with the measurement given. 2. Measure the each object with the measurement given. 3. Find the diff erence between your estimate and the actual

measurement. 4. Complete each object bef ore moving on to the next.

Follow up questions: Answer the questions on the back of your recording sheet.

1. Which unit of measurement was easiest to estimate? Why? 2. Did your diff erence between the estimate and actual get

smaller when moving through each unit of measurement? Explain why this would happen.

3. Compare the measurements f or the width of the hall way. What can you tell me about the diff erent measurements?

4. Give examples of visible body parts that could help you to remember the size of each unit of measurement.

Objects to Measure: Estimate Actual Difference

Measure in INCHES:

Width of the hall

Floor tile

Desk top

Width of the door

Locker

Measure in FEET:

Width of the hall

Floor tile

Desk top

Width of the door

Locker

Measure in YARDS:

Width of the hall

Floor tile

Desk top

Width of the door

Locker

Measure in CENTIMETERS:

Width of the hall

Floor tile

Desk top

Width of the door

Locker

Measure in METERS:

Width of the hall

Floor tile

Desk top

Width of the door

Locker

Estimation

Actual

DifferenceEstimation of MeasurementREAL WORLD Lab

TAKS Obj. 4 TEK 6.8, 7.9, 7.13

Materials: Rulers, Yard sticks, Meter sticks Recording Sheet Set of A and P RW Cards Objects to measure Mathematics Chart I nstructions:

1. Work with a partner. 2. Shuffl e cards and place them upside down. 3. Draw a card, record the object to measure on

your lab sheet. 4. Determine best unit of measurement to use.

Record the length (ℓ) and width (w) 5. Determine the correct f ormula, record it. 6. Substitute measurements f or ℓ and w. 7. Solve.

Follow up questions: Answer the questions on the back of your recording sheet.

1. Explain what perimeter is and how to fi nd it.

2. Give 5 real world reasons of when you would need to fi nd the perimeter of an object.

Object/ Shape Dimensions Perimeter Area

  Unit: Formula: Formula:

  ℓ= Substitution: Substitution:

  W= Answer: Answer:

Table Desk top

Floor tile Whiteboard

Computer screen Math textbook

Locker door Door window

Water fountain frontStep on the

Stairs

Materials: Mathematics Chart Recording Sheet Cardboard Coins Yarn, tape Large piece of paper I nstructions for lab:

1. Choose a coin, write its name on your recording sheet.

2. Use the ruler on the Mathematics Chart to

determine the dimensions needed; radius (r) and diameter (d).

3. Find what Pi, π, is worth on the Mathematics

chart.

4. Determine the correct f ormula, record it.

5. Substitute measurements in f ormula.

Object: ___________________________Draw the shape and label the dimensions:

Diameter:_______ Radius:_______ Pi:______

CIRCUMFERENCE:Formula: _________________________Substitution: ______________________Work:

Answer: ________________

AREA:Formula: _________________________Substitution: ______________________Work:

Answer: ________________

Circumference and AreaCoin Lab

Activity:1. Choose a coin.2. Cut a piece of yarn the length around

the edge of the coin.3. Tape it on your large paper. What does

this represent? Label it.4. Cut a piece of yarn the length of the

diameter of the coin.5. Tape it under the longer piece of yarn.

Label it.6. How many pieces do you need to cut to

get close to the longer piece of yarn? Cut them and tape them down.

7. Repeat above with a piece of yarn the length of the radius.

Follow Up Activity and Questions

Questions:1. How many diameters are

needed to go around the circumference?

2. How many radii are needed to go around the circumference?

3. What do you multiply the diameter by to get the circumference?

4. What is a definition of Pi, π ?5. How is Pi, π, represented

numerically?

Circumference

Radius

Diameter

Materials: Mathematics Chart Recording Sheet Cardboard Triangles I nstructions for lab:

1. Choose a triangle; write its name on your recording sheet. Acute, Obtuse, Right and Equilateral, I sosceles, Scalene

2. Draw the triangle and label its dimensions. 3. Use the ruler on the Mathematics Chart to

determine the dimensions needed; sides, height, base. Round to the nearest tenth.

4. Determine the correct f ormula, record it.

5. Substitute measurements in f ormula.

6. Solve.

Triangle Name __________________________Draw the shape and label the dimensions:

Perimeter:Formula: _________________________Substitution: ______________________Work:

Answer: ________________

AREA:Formula: _________________________Substitution: ______________________Work:

Answer: ________________

Perimeter and AreaTriangles

Materials: Mathematics Chart Recording Sheet DiCut Shapes I nstructions:

1. Choose a polygon. 2. Use the ruler on the Mathematics Chart to

determine the dimensions needed; length (l), width (w), base (b), height (h), radius (r), or diameter (d).

3. Determine the correct f ormula, record it. 4. Substitute measurements in f ormula. 5. Solve.

Follow up questions: Answer the questions on the back of your recording sheet.

1. Explain what perimeter is and how to find it.

2. Give 5 real world reasons of when you would need to find the perimeter of an object.

3. Explain what area is and how to find it.

4. Give 5 real world reasons of when you would need to

find the perimeter of an object.

ShapeDimensions ℓ,w,h,b,r,d

Perimeter / Circumference Area

    Formula: Formula:

    Substitution: Substitution:

    Answer: Answer:

Area and PerimeterWith DiCut Lab

2 (l) + 2 (w)Perimeter of a

Rectangle

dCircumference of a

Circle

½ bhArea of a Triangle

Add all sidesPerimeter

½ PlLateral Surface

Area of a Pyramid

bhArea of a Rectangle

2rhLateral Surface Area of a Cylinder

r²Area of a Circle

2rCircumference of a

Circle

2(l + w)Perimeter of a

Rectangle

I = prtSimple Interest

Formula

Ph + 2BTotal Surface Area

of a Prism

2r(h + r)Total Surface Area

of a Cylinder

a² + b² = c²Pythagorean

Theorem

3.14Pi

PhLateral Surface Area of a Prism

22/7Pi

s²Area of a Square

lwArea of a Rectangle

1/3 BhVolume of a

Pyramid or Cone

2rh + 2r²Total Surface Area

of a Cylinder

4sPerimeter of a

Square

6s²Surface Area of a

Cube

BhVolume of a Prism

or CylinderArea of a Triangle

bh2

Cards for 8th Grade Formula Math Chart SWAT

I cut these out and put on 3x5 cards. Then I can draw one out and call out the words. Students will find the correct formula on the screen and SWAT it.

12 Pl

TAKS: All Objectives TEK: 7.4, 7.9, 7.13, 7.14

Materials: Set of matching cards I nstructions: There are so many ways to use these:

Turn them upside down and play memory Shuffl e and play Go Fish Kagan – Quiz, Quiz, Trade Create partners, give one to each students

have them match up and that is they are partners f or other activities.

Cut out and glue on paper Review flash cards Writing prompts f or journaling

V = Bh

P = s+s+s+s

C = πd

A = ½ bh

Formula Matching

8th Grade Formula One Math

(Courtesy of Karen Duncan NISD)

This is an activity that can be used to get students familiar with the TAKS Formula Chart. There are 16 ppt slides in all. You can use all or part of them. This activity can be as simple as having the students “recognize” what formula to use in order to solve a particular problem or recognizing the formula and then actually solving it.

What is the total surface area in square inches of the cylinder shown below?

A. 96π in2

B. 128π in2

C. 104π in2

D. 384π in2

1

The teacher shows a problem from the ppt presentation to the class.

A B C D

1 26S s 4P s

1 2

1 2

1

2

( )or

2b b h

A

A b b h

1

2

or2

bhA

A bh

2

22 2 or

2 ( )

S rh r

S r h r I prt

2 2 or

2( )

P l w

P l w 2 2 2b ca

3 227

3.14 or

orA lw

A bh 2A s V Bh *

4 2S rh 2orV Bh V r h 2A r

2 or

C=

C r

d

*B represents the area of the Base of a solid figure

Prob # Answer Prob # Answer

1. 9.

2. 10.

3. 11.

4. 12.

5. 13.

6. 14.

7. 15.

8. 16.

A2 This is the answer for the problem.

Go on to the next ppt slide unless you want the students to solve them.

Choose a word or group of words for students to locate real world pictures of. Have students bring in pictures and glue to bulletin board paper. Label the top of the paper with the word of the week and hang in the classroom or around the school in the hallways. Ideas of places to locate examples: newspapers, magazines, junk mail, take a picture and print or email in. Students will get creative looking for examples. Take five minutes and have students show their picture/example and explain how it is representing the word of the week. If a student’s example is incorrect have them listen to the other examples and re-examine their picture to see if they can find an example. Lots of times you will hear them say “Oh look there is” and start discussing other math word examples. Some word ideas for the Measurement Unit:

Examples that you would use measuring with: Inches, feet, yards, centimeters, meters, ounces, cups, gallons, ect...

Perimeter

Word of the Week

Volume Activity Directions This lab is designed to help students understand the formulas for volume. They will compare the volume of a cylinder and cone, a large cube and a square pyramid, and a sphere and a large cylinder.

Materials:

large tub to work in

water

pitcher (I use a 2 cup pitcher)

funnel

a set of relational solids (same base and

height)

a copy of the lab for each student

Procedures:

I do not explain the purpose of this lab as I want my students to figure it out for themselves.

I do however, explain and demonstrate how to use the funnel and pour into the solids.

I work with groups of 3-4 students and have them come to the station table to do all the pouring under my supervision.

Then they go back to the group seats to discuss and record.

We discuss how to look at the solid to determine when it is full (at eye level).

I emphasize that ALL water is to stay over the tub.

Volume Activity 

A.Select the large cylinder and cone.

1. How many times do you think you can fill up the cone and pour into the cylinder before the cylinder will be full? _________

2. Fill the cone with water and pour the water into the cylinder.3. Repeat until the cylinder is full.

Done at seat.

Done with me.

4. How many filled cones did it take to fill the cylinder? __________

At seat

3

5. Pour from the filled cylinder back into the EMPTY cone.

6. Look at the cylinder. What fraction of water is missing?__________

With me

1/3

7. Discuss # 1-6 with your teacher and explain your answers.

8. Empty the cylinder and cone.

9. Look at the formula for Volume of a cylinder on your math chart and write it here.

10.Look at the formula for Volume of a cone on your math chart and write it here.

11.Explain how the two formulas are different and why.

With me

At seat

V = Bh

V = 1/3 Bh

Choose one of the following to complete using the words from the back. A minimum of _____ words must be used.

PowerPoint

Children’s book

Poster for Classroom

Picture Dictionary

Your Creative Idea

Video

Song

Picture or poster showing example of

terms

Make a game

How the points add up

20 pts Real world pictures

10 pts

Use minimum words assigned

10 pts

Correct Spelling

20 pts

Correct Definitions or Explanations

10 pts

Drawn examples (how it would look on paper)

10 pts

Neatness

10 pts

Present to class

10 pts

Creative

Directions for Perimeter, Area, and Volume with Scale Factors

Purpose:

These labs are designed to help students understand the relationship of scale factor in perimeter, area, and volume. I do not tell the students the relationship at the beginning.

My desire is for them to find the relationships.

Notes:

I highly suggest that you do not do both of these in the same week.

Do one and then practice application problems with it for several days.

This gives the students a chance to become comfortable with those operations before adding more.

Then move on to the other activity.

Volume with Scale Factors

Part 1A.Construct this prism out of cubes. L = 1 cube, W = 1 cube, H = 1 cube

1) Draw prism A.

2) Label prism A.

3) Volume = __________

1

11

1 cubic unit

Volume with Scale Factors

Part 1B. Construct this prism out of cubes. L = 2 cubes, W = 2 cubes, H = 2 cubes

1) Draw prism B.

2) Label prism B.

3) Volume = __________

2

22

8 cubic units

Volume with Scale Factors

Part 1C. Construct this prism out of cubes. L = 3 cubes, W = 3 cubes, H = 3 cubes

1) Draw prism C.

2) Label prism C.

3) Volume = __________

3

33

27 cubic units

Volume with Scale Factors

Part 1D. Construct this prism out of cubes. L = 4 cubes, W = 4 cubes, H = 4 cubes

1) Draw prism D.

2) Label prism D.

3) Volume = __________

4

44

64 cubic units

Prism A Prism B

LengthWidthHeight

Volume

Volume Scale Factor Data Sheet

1 2

1 8

X 2

X 8

Scale Factor

Prism A Prism C

LengthWidthHeight

Volume

Volume Scale Factor Data Sheet

1 3

1 27

X 3

X 27

Scale Factor

Prism A Prism D

LengthWidthHeight

Volume

Volume Scale Factor Data Sheet

1 4

1 64

X 4

X 64

Scale Factor

Part 2

E.Compare prism A to prism B.

1) What is the scale factor for length, width, & height? __________

2) What is the scale factor for volume?

__________

X 2

X 8 = 2³

Part 2

F. Compare prism A to prism C.

1) What is the scale factor for length, width, & height? __________

2) What is the scale factor for volume?

__________

X 3

X 27 = 3³

Part 2

G. Compare prism A to prism D.

1) What is the scale factor for length, width, & height? __________

2) What is the scale factor for volume?

__________

X 4

X 64 = 4³

Part 3

Perimeter scale factor is ____________ to scale factor for length and width.

Area scale factor is the length and width scale factor _________________.

Volume scale factor is the length and width scale factor _________________.

Equal/congurent

squared

cubed

Example: Prism 1 has a length, width, & height of 5 cm. Prism 2 has a length, width, & height of 10 cm. What is the scale factor for length, width, & height? __________

What is the volume of Prism 1? __________ Prism 2? ____________

What is the scale factor for the 2 volumes? ___________ OR ________

5

55

10

1010

X 2

125 cm³

1000 cm³

X 8 X 2³

Jennifer MeggettJennifer.Meggett@nisd.net

Christine GiovannelliChristine.Giovannelli@nisd.net

Measurement

In The

Middle School World