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Unit 4 Extending Decimals, Grade 5

5E Lesson Plan Math Grade Level: 5 Subject Area: MathLesson Title: Extending Decimals Unit Number: 4 Lesson Length: 6

daysLesson Overview

This unit bundles student expectations that address foundational understandings of decimals as well as adding and subtracting of decimals through the thousandths place. According to the Texas Education Agency, mathematical process standards including application, a problem-solving model, tools and techniques, communication, representations, relationships, and justifications should be integrated (when applicable) with content knowledge and skills so that students are prepared to use mathematics in everyday life, society, and the workplace.

During this unit, students are formally introduced to the thousandths place. Students build upon the idea that our base-ten place value system extends infinitely to very small values as well as very large values, and that each place-value position is one-tenth the value of the place to its left and 10 times the position to the right. Students relate previous representations of decimals to the hundredths with concrete and pictorial models to develop their conceptual knowledge of decimals through the thousandths. Students are expected to use expanded notation and numerals to represent the value of a decimal through the thousandths. Students use comparison symbols to compare and order decimals to the thousandths and round decimals to the tenths or hundredths place. Students continue to estimate solutions and extend addition and subtraction with decimals to include the thousandths place. Numerical expressions are revisited as a means for students to communicate their solution process and to solve problem situations involving decimals.

Unit Objectives:Students will…

Build upon their knowledge of the base-ten place value system, including that each place-value position is one-tenth the value of the place to its left and 10 times the position to the right

Relate previous representations of decimals to the hundredths with concrete and pictorial models to develop their conceptual knowledge of decimals through the thousandths

Use expanded notation and numerals to represent the value of a decimal through the thousandths

Use comparison symbols to compare and order decimals to the thousandths Round decimals to the tenths or hundredths place Estimate solutions Extend addition and subtraction with decimals to include the thousandths place Communicate their solution process using numerical expressions Solve problem situations involving decimals

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Standards addressed:

TEKS:5.1A – Apply mathematics to problems arising in everyday life, society, and the workplace.5.1B – Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.5.1C – Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.5.1D – Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.5.1E – Create and use representations to organize, record, and communicate mathematical ideas.5.1F – Analyze mathematical relationships to connect and communicate mathematical ideas.5.1G – Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.5.2A – Represent the value of the digit in decimals through the thousandths using expanded notation and numerals. (Supporting Standard)5.2B – Compare and order two decimals to thousandths and represent comparisons using the symbols >, <, or =. (Readiness Standard)5.2C – Round decimals to tenths or hundredths. (Supporting Standard)5.3A – Estimate to determine solutions to mathematical and real-world problems involving addition, subtraction, multiplication, or division. (Supporting Standard)5.3K – Add and subtract positive rational numbers fluently. (Readiness Standard)5.4F – Simplify numerical expressions that do not involve exponents, including up to two levels of grouping. (Readiness Standard)

ELPS:

ELPS.c.1A use prior knowledge and experiences to understand meanings in EnglishELPS.c.1E internalize new basic and academic language by using and reusing it in meaningful ways in speaking and writing activities that build concept and language attainmentELPS.c.1F use accessible language and learn new and essential language in the processELPS.c.2D monitor understanding of spoken language during classroom instruction and interactions and seek clarification as neededELPS.c.2G understand the general meaning, main points, and important details of spoken language ranging from situations in which topics, language, and contexts are familiar to unfamiliarELPS.c.2H understand implicit ideas and information in increasingly complex spoken language commensurate with grade-level learning expectations

Misconceptions:

Some students may think placing zeros at the end of a decimal number always affects the value of the number rather than being used as a place-holder (e.g., In 0.400 the zeros do not affect the value, but in 0.04 the zero in the tenths place does affect the

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value.) Some students may think you can only round certain numbers to a specific place value,

rather than being able to round to any given place value (e.g., The decimal number 34.25 can be rounded to the nearest tenths place, ones place, tens place, hundreds place, etc.)

Some students may use the digit in the tenths place to determine how many boxes to shade in on a hundredths grid (e.g., shading in 8 of the 100 boxes for 0.8) rather than determining the value of the number written as hundredths (e.g., shading in 80 of the 100 boxes of 0.80).

Some students may order decimals incorrectly by trying to relate whole number understandings to decimal understandings (e.g., 0.29 is greater than 0.6 because 29 is greater than 6) rather than using decimal place value understandings (e.g. 0.29 is less than 0.60).

Some students may order decimals based on the number of digits in the number, rather than determining its value. (e.g. 0.123 is greater than 0.45 because 0.123 has three digits and 0.45 only has two digits.)

Underdeveloped Concepts:

Some students may record a literal translation of the symbols (e.g., record 0.53 as “zero point fifty-three or “point five tenths and three hundredths”)

Some students may not know how to correctly read the symbols (ex: < is read “less than”, > is read “greater than”)

Some students may not relate multiple representations to the same decimal amount (base-10 blocks, decimal grids, money, place value chart, etc.)

Note: Please reference the 2014-2015 Implementation TAG Tool for any instructional gaps that might be associated with the transition to the 2012 Adopted TEKS.

Vocabulary:

•Compare numbers – to consider the value of two numbers to determine which number is greater or less or if the numbers are equal in value•Compatible numbers – numbers that are slightly adjusted to create groups of numbers that are easy to compute mentally•Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n}•Decimal number – a number in the base-10 place value system used to represent a quantity that may include part of a whole and is recorded with a decimal point separating the whole from the part•Digit – any numeral from 0 – 9•Estimation – reasoning to determine an approximate value•Expanded notation – the representation of a number using place value (e.g., 985,156,789.782 as 900,000,000 + 80,000,000 + 5,000,000 + 100,000 + 50,000 + 6,000 + 700 + 80 + 9 + 0.7 + 0.08 + 0.002 or 9(100,000,000) + 8(10,000,000) + 5(1,000,000) + 1(100,000) + 5(10,000) +6(1,000) + 7(100) + 8(10) + 9 + 7(0.1) + 8(0.01) + 2 (0.001) or 9(100,000,000) + 3


8(10,000,000) + 5(1,000,000) + 1(100,000) + 5(10,000) +6(1,000) + 7(100) + 8(10) + 9 + 7 (1/10) + 8(1/100) + 2 (1/1000))•Expression – a mathematical phrase, with no equal sign, that may contain a number(s), a unknown(s), and/or an operator(s)•Fluency – efficient application of procedures with accuracy•Front-end method – a type of estimation focusing first on the largest place value in each of the numbers to be computed and then determining if the next smallest place value(s) when grouped should be•Numeral – a symbol used to name a number•Order numbers – to arrange a set of numbers based on their numerical value•Order of operations – the rules of which calculations are performed first when simplifying an expression•Parentheses and brackets – symbols to show a group of terms and/or expressions within a mathematical expression•Place value – the value of a digit as determined by its location in a number, such as ones, tens, hundreds, one thousands, ten thousands, etc.•Positive rational numbers – the set of numbers that can be expressed as a fraction , where a and b are whole numbers, and b ≠ 0 which includes the subsets of whole numbers and counting (natural) numbers (e.g., 0, 2, etc.)•Rounding – a type of estimation with specific rules for determining the closest value•Standard notation – the representation of a number using digits (e.g., 985,156,789.782)•Trailing zeros – a sequence of zeros in the decimal part of a number that follow the last non-zero digit, and whether recorded or deleted, does not change the value of the number•Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}•Written notation – the representation of a number using written words (e.g., 985,156,789.782 as nine hundred eighty-five million, one hundred fifty-six thousand, seven hundred eighty-nine and seven hundred eighty-two thousandths)

Related Vocabulary:

About Equivalent Number line Approximately Estimate Open number line Ascending Hundredths Position Base-10 place value system Greater than (>) Sum Descending Less than (<) Tenths Difference Magnitude Thousandths

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Equal to (=)

List of Materials:

Day 1

Materials: Scissors (1 per student) Glue stick (1 per student) Math journals Handouts Needed:

“Exploring Place Value Chart”

Day 1 Continued:

Materials: Calculators (1 per set of partners) Math journals Handouts Needed:

“Place Value Relationships with Calculator”

Day 2

Materials: Math journals

Day 3

Materials: Math journals Mini whiteboard Dry-erase markers and eraser

Day 4

Materials: Dry-erase marker and eraser Handouts Needed:

“Using a Number Line to Compare & Order Decimal Numbers” “Place Value Chart” (laminated) “Comparing and Ordering Numbers” “Rounding Decimal Numbers- Number Lines” “Rounding Decimal Numbers” “Estimating Addition & Subtraction Problems- Decimals”

Day 5

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Materials: Slightly deflated ball or pillow (for tossing game) Construction paper Glue Math journals Dry-erase markers and eraser Dice Handouts Needed:

“Comparing Decimals” “Expanded Notation” “Expanded Notation- Decimals” “Rounding Decimals- Nearest Tenth” “Rounding Money” “Adding Decimals” “Subtracting Decimals”

Day 6Materials:Unit 4 Performance Assessment

INSTRUCTIONAL SEQUENCEPhase 1: ENGAGE

Day 1

Materials: Scissors (1 per student) Glue stick (1 per student) Math journals Handouts Needed:

“Exploring Place Value Chart”

Activity:

Put students in small groups. Each student will need 1 pair of scissors and a glue stick (they do not use the glue until after the discussion). Give each student in the group a copy of page 1 of the handout titled, “Exploring Place Value Chart”. Have students cut out the place value words individually and then work with their group to sort the place values into the correct order on the blank place value chart. Although students are discussing with their group, each student is individually accountable for sorting their place value cards on their own place value chart.

After giving groups a chance to sort the place values, lead a group discussion so that each group can determine whether they sorted the place values correctly. After any corrections 6


have been made, then students may use their glue sticks to glue the place value words onto the chart. Students may glue their completed place value chart into their math journals.

Discuss the correct order of the place values.

o One billions placeo Hundred millions placeo Ten millions placeo One millions placeo Hundred thousands placeo Ten thousands placeo One thousands placeo Hundreds placeo Tens placeo Ones placeo Tenths placeo Hundredths placeo Thousandths place

Next, have each group create a definition for what “place value” means. After each group has created what they think place value means in their own words, have them share with the class.

Student definitions should include: place value is the value of a digit as determined by its location in a number, such as ones, tens, hundreds, one thousands, ten thousands, etc.

Ask:

What do you notice on the place value chart?A decimal point; commas; etc.

What do you think the purpose of the decimal is?The decimal point is recorded to separate the whole part of a decimal number from the fractional part of a decimal number when written.

How is the decimal point read? The decimal point is stated as “and” when read aloud.

What is a whole number?Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}

On which side of the decimal are the whole numbers on?The whole part of a decimal number is recorded to the left of the decimal point when written and stated as a whole number.

What is a decimal number?Decimal number – a number in the base-10 place value system used to represent a quantity that may include part of a whole and is recorded with a decimal point separating the whole from the part. The decimal place values on

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the chart are the tenths, hundredths, and thousandths. What else represents part of a whole like decimals?

Fractions On which side of the decimal are the decimal numbers on?

Decimals and fractions both represent part of a whole; therefore, we can say that the fractional part of a decimal number is recorded to the right of the decimal point.

What do you notice that is different about the way the decimal place values are written?

“ths” at the end What is a digit?

Digit – any numeral from 0 – 9

What’s the teacher doing?

Raising questions and encouraging responses

Monitoring students as they work together

What are the students doing?

Accessing prior knowledge about the base-ten place value system so that they can comprehend new information

Engaged and participating in the place value sorting activity

Phase: EXPLORE

Day 1 Continued:

Materials: Calculators (1 per set of partners) Math journals Handouts Needed:

“Place Value Relationships with Calculator”

Activity:

Have students partner up and each set of partners needs a calculator. Give students the handout titled “Place Value Activity with Calculator”. (Students really enjoy this activity; however, some calculators do not go very high in place value. Students should be able to figure out the pattern even if the calculators do not show the full answer up to the billions place.)

Partner 1 works with the calculator first, while Partner 2 records the answers on the handout. Partner 1 should begin by entering 0.001 into the calculator. Partner 2 should write 0.001 onto the first place value chart at the top of the handout.

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Then, Partner 1 should push x 10 on the calculator to multiply by 10. Partner 2 records the answer that is displayed on the calculator (the number will be 0.01) on the second place value chart directly below the first.

Partner 1 should leave this answer displaying on the calculator. Emphasize that the students do NOT need to push the clear button at any time during this activity unless they make a mistake. Partner 1 should then push x 10 on the calculator to multiply the previous answer by 10. Once again, Partner 2 records this number (the answer will be 0.1) on the third place value chart directly below the second.

Partner 1 should leave this answer displaying on the calculator, and without pushing clear, should push x 10 to multiply the previous answer by 10. Partner 2 then records this number (the answer will be 1.0) on the fourth place value chart.

Both partners should continue with the previous steps listed above until all 13 of the place value charts have been filled in sequentially.

During this activity, ask:

What do you notice happening each time that you multiply by 10?Multiplying a number by 10 increases the place value of each digit.

What is a base-ten place value system?A number system using ten digits 0 – 9.

What happens when moving left across the places?

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Relationships between the places are based on multiples of 10. When moving left across the places, the values are 10 times the position to the right.

Have students use their math journals to draw a place value chart with arrows pointing to the left, as shown in the figure below. These arrows are a great visual for students to remind them that as you move left across the place value chart, each place value is 10 times the previous value.

Students should also add the following notes to their math journals.

As they are taking notes, ask:

What patterns do you notice when multiplying by 10?

Partner 1 may push the “clear” button on the calculator now if the teacher wishes, or they may leave the last number (1,000,000,000) displaying on the screen. Next, have students switch

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roles. Partner 1 will do the recording and Partner 2 will use the calculator. Students should now use the bottom portion of the handout. If the calculator was cleared, Partner 2 should enter the number 1,000,000,000 into the calculator. Partner 1 should record this number onto the first place value chart on the bottom portion of the page.

Then, Partner 2 should push ÷ 10 on the calculator to divide by 10. Partner 1 records this number (the answer will be 100,000,000) on the second place value chart directly below the first.

Partner 2 should leave this answer displaying on the calculator. Emphasize again that students do NOT need to push the clear button at any time during this activity unless they make a mistake. Partner 2 should then push ÷ 10 on the calculator to divide the previous answer by 10. Once again, Partner 1 records this number (the answer will be 10,000,000) on the third place value chart directly below the second.

Both partners should continue with the previous steps listed above until all 13 of the place value charts have been filled in sequentially on the bottom portion of the page. Partner 2 may push the “clear” button on the calculator when this is completed.

Have students return to their math journals again to the place value chart they drew. Now, have them add arrows pointing to the right, as shown in the figure below. These arrows are a great visual for students to remind them that as you move right across the place value chart, each place value is one-tenth of the previous value. While students are writing in their journals, ask:

What do you notice happening each time that you divide by 10?Dividing a number by 10 decreases the place value of each digit.

What happens when moving right across the places?Relationships between the places are based on multiples of 10. When moving right across the places, the values are one-tenth of the position to the left.

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Students should also add the following notes to their math journals. As they are taking notes, ask:

What patterns do you notice when dividing by 10?


Observing students as they work cooperatively

Ask inquiry-oriented questions to assist in examining student thinking:

Why is the base-10 place value

What are the student’s doing?

Working together collaboratively as they complete the calculator activity

Making generalizations

Sharing ideas

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system an efficient way to represent numbers?

Why is it important to understand the value of numbers?

What relationships exist within our number system and how are they used?

How are numbers, large or small, represented and communicated using the base-10 place value system?

Phase: EXPLAIN

Day 2

Materials: Math journals

Activity:

Each student needs their math journal. Ask students to write the following notes in their journal as you have a class discussion on the decimal values.

Zeroes can be added to the right of a decimal number- this does not change the value.

0.1 = 0.10 = 0.100 1 tenth = 10 hundredths = 100 thousandths

0.01= 0.0101 hundredth = 10 thousandths

Zeroes in between the decimal point and the digit do change the value of the number.

0.001 ≠ 0.01 ≠ 0.1

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1 thousandth ≠ 1 hundredth ≠ 1 tenth

Write the following number on the board for students to see:

985,156,789.782

Ask:

What is expanded form?Expanded form is the representation of a number as a sum of place values

Ask students to write the number 985,156,789.782 in expanded form vertically in their math journal. Have them turn their math journals so that the lines are vertical on the page. This will help the students to keep the places in order. Monitor students and check to see that they have written the expanded form correctly.

900,000,000 80,000,000 5,000,000 100,000 50,000 6,000 700 80 9

0.7 0.08

+ 0.002985,156,789.782

(This is a picture example of what this would look like with the notebook paper turned.)

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Ask students to look at the last 3 terms and write them beside the decimal numbers as fractions. Ensure that students can recognize expanded form written vertically or horizontally, and the fractional parts of the number whether they are written as decimals or fractions.

900,000,000 80,000,000 5,000,000 100,000 50,000 6,000 700 80 9

0.7

0.08

+ 0.002 985,156,789.782

900,000,000 + 80,000,000 + 5,000,000 + 100,000 + 50,000 + 6,000 + 700 +

80 + 9 + 0.7 + 0.08 + 0.002

Ask:

Does zero need to be included when writing a number in expanded form?

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Zero may or may not be written as an addend to represent the digit 0 in a number.

Have students write this definition in their math journal.

Expanded notation – the representation of a number as a sum of place values where each term is shown as a digit(s) times its place value

Write this number on the board for students to see:

985,156,789.782

Lead students in the process of writing the number in expanded notation horizontally in their math journal.

(9 x 100,000,000) + (8 x 10,000,000) + (5 x 1,000,000) + (1 x 100,000) + (5 x 10,000) + (6 x 1,000) + (7 x 100) + (8 x 10) + (9 x 1) + (7 x 0.1) + (8 x 0.01) + (2 x 0.001)

Next, remind students that parentheses can be used to represent multiplication, instead of writing the multiplication symbol. Lead students in the process of writing the same number in expanded notation using parentheses without the multiplication symbol.

9(100,000,000) + 8(10,000,000) + 5(1,000,000) + 1(100,000) + 5(10,000) + 6(1,000) + 7(100) + 8(10) + 9(1) + 7(0.1) + 8(0.01) + 2 (0.001)

Next, remind students that decimals can also be represented as fractions. Lead students in the process of writing the same number in expanded notation using fractions to represent the fractional part of the number.

9(100,000,000) + 8(10,000,000) + 5(1,000,000) + 1(100,000) + 5(10,000) +6(1,000) + 7(100)

+ 8(10) + 9(1) + 7( ) + 8( ) + 2 ( ))

Remind students that these are all different ways to write the same number in expanded notation. Students should be comfortable with all of these different forms of expanded notation.

Day 3

Materials: Math journals Mini whiteboard Dry-erase markers and eraser

Activity:

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Have students write this equation in their math journal:

489.32 x 10 =

Explain to students that when multiplying a decimal number by 10, the place value of each digit is increased just like it is with whole numbers. In this case, the decimal is moved to the right.

489.32 x 10 = 4893.2

Have students write down this equation next:

489.32 ÷ 10 =

Explain to students that when dividing a decimal number by 10, the place value of each digit decreases. When dividing by 10, the decimal is moved to the left.

489.32 ÷ 10 = 48.932

Have students put journals aside and get out their dry-erase markers and whiteboards. Have students write down this equation on their whiteboard:

[4(100) + 8(10) + 9 + 3 (110) + 2 (

1100 )] x 10 =

Ask:

What form is this number written in?Expanded notation

Remind students that the parentheses in this equation are representing multiplication. Now, explain to students that multiplying a number by 10 increases the place value of each digit. Ensure that students understand that this entire equation is being multiplied by 10, and we know that because the equation is inside of brackets. Explain to students that the terms inside of the brackets are all being multiplied by 10; therefore, each term in the expression is multiplied by 10.

Explain to students that when going from left to right, multiplying 4(100) times 10 can be 17


shown as 4(1000). This can clearly be shown in expanded notation because a zero is added.

[4(100) + 8(10) + 9 + 3 ( ) + 2 ( )] x 10 = 4(1000)

Ask students to show on their whiteboard what would happen to 8(10) when it is multiplied by 10. Students should have this written:

[4(100) + 8(10) + 9 + 3 ( ) + 2 ( )] x 10 = 4(1000) + 8(100)

Ask students to show what would happen to 9 when it is multiplied by 10. Students should have this written:

[4(100) + 8(10) + 9 + 3 ( ) + 2 ( )] x 10 = 4(1000) + 8(100) + 9(10)

Ask students to show what would happen to 3 ( ) when it is multiplied by 10. Students should have this written:

[4(100) + 8(10) + 9 + 3 ( ) + 2 ( )] x 10 = 4(1000) + 8(100) + 9(10) + 3

Ask students to show what would happen to 2 ( ) when it is multiplied by 10. Students should have this written:

[4(100) + 8(10) + 9 + 3 ( ) + 2 ( )] x 10 = 4(1000) + 8(100) + 9(10) + 3 + 2( )

Students should now understand that when multiplying an expression by 10, each term in the expression is multiplied by 10 and the place value of each digit is increased ten times.

Have students write this equation:

[4(100) + 8(10) + 9 + 3 ( ) + 2 ( )] ÷ 10 =

Explain to students that when dividing a number by 10, the place value of each digit decreases. Allow time for students to practice writing what would happen to each term within the brackets as it is divided by 10.

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[4(100) + 8(10) + 9 + 3 ( ) + 2 ( )] ÷ 10 = 4(10) +8 + 9( ) + 3( ) + 2( )

Day 4

Materials: Dry-erase marker and eraser Handouts Needed:

“Using a Number Line to Compare & Order Decimal Numbers” “Place Value Chart” (laminated) “Comparing and Ordering Numbers” “Rounding Decimal Numbers- Number Lines” “Rounding Decimal Numbers” “Estimating Addition & Subtraction Problems- Decimals”

Activity:

Ask:

What 3 symbols can be used to compare numbers?<, >, = (less than, greater than, equal to)

Write the following numbers on the board for students to see:

5.08 5.008

Call on a student to come up to the board and write <, >, or = in between the numbers to compare them. The student should have the greater than symbol (>) written. Ask the student to explain their reasoning.

5.080 > 5.008

Next, write the following numbers on the board:

5.08 5.080

Call on another student to come up to the board and write <, >, or = in between the numbers to compare them. The student should have the equal to (=) symbol written. Ask the student to explain their reasoning.

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5.080 = 5.080

Pass out the handout titled, “Using a Number Line to Compare Decimal Numbers” to each student. Explain to students that a number line is a great tool that can be used to help them compare numbers. Guide students through the process of labeling the numbers on the number line and using <, >, or = to compare. Explain to students that the number that is closer to 0 is the smaller number, and the number that is further away from 0 is the greater number.

Laminate the handout “Place Value Chart”. Have students use dry erase markers to write numbers in chart and compare.

Have students compare 28.674 and 28.634 by writing the numbers in the correct place values on the chart. Students should begin comparing the digits with the highest place value. If these digits are the same, then they should continue by comparing the next smallest place until the digits are different.

Have students wipe off their charts and compare the numbers 5.080 and 5.008 by writing them in the correct place values on the chart.

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Have students wipe off their charts and compare the numbers 7.108 and 7.220 by writing them in the correct place values on the chart.

Display the handout titled “Comparing and Ordering Numbers” using a projector (or pass copies of the handout out to each student). Have students use their laminated place value chart to help answer the questions as independent practice.

Ask: Can anyone explain what rounding is?

Rounding is a type of estimation with specific rules for determining the closest value.

Explain to students that a number line can be used to help them round a decimal number. If a number lies below the halfway point, it will round “down”. If a number lies on or above the halfway point, it will round “up”. Display the handout titled “Rounding Decimal Numbers- Number Lines” on a SMART board. Call on students to come up and use the SMART board to draw on the number lines and help them answer the questions. (This handout can be printed on paper as well.) Guide students through the process of using the number lines to help them round decimal numbers.

Next, pass out the handout titled “Rounding Decimal Numbers”. Have students practice rounding by looking at the digit to the right of the place to which they are rounding. If the digit in the place to the right is greater than or equal to 5, then the digit in the place being rounded increases by 1. However, if the digit in the place to the right is 4 or less, then the digit in the place being rounded remains the same. The digits to the right of the place being rounded are then replaced with zeroes.

Pass out the handout titled “Estimating Addition & Subtraction Problems- Decimals”. Guide students as they solve the word problems and have them justify their estimations. Remind students that when adding and subtracting decimal numbers, the decimals must be lined up in the correct place value.

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Ask: How do you know if your answer is reasonable?

The answer is reasonable if it is close to the estimate.

Write the problem below on the whiteboard for students to see:

18.7 – 7.3 + 4.18

Ask: What should be solved first, according to the order of operations? Addition and subtraction are solved from left to right; therefore subtract 18.7 – 7.3 to get

11.4 first, then add 11.4 + 4.18 to get 15.58.


Facilitating students’ understanding of numbers used in everyday life.

Ask: What are numbers and how are

numbers used in everyday life?

How and why do different situations or labels affect the relative size (magnitude) of the number?

When might estimation be used in real-word situations?

Encourage students’ understanding of mathematical operations and strategies that may be used to represent and solve a variety of problem situations in everyday life.

Ask: How does the context of the

situation determine the operation(s) needed to represent and solve the


Using previous observations and findings to apply new knowledge in problem solving situations

Providing responses to questions and explaining their findings

Taking notes and completing handouts using knowledge that has been gained

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problem? What determines which

strategy might be used to accurately represent and solve a given problem?

Communicating the idea that estimation is used in everyday life.

Ask: Why is estimation a critical

strategy in the real-world? What are different ways to

estimate?

Explaining that a problem-solving model can be applied to critically reason through various problem situations in order to solve problems and analyze solutions.

Ask: How can the information in a

problem be analyzed to determine the question being asked and the relevant information provided and/or needed?

What types of plans and/or strategies can be used to solve problems?

How can solutions to problems be determined?

How can solutions to problems be justified?

How can the reasonableness of solutions and the problem solving process be evaluated?

Phase: ELABORATE

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Day 5

Materials: Slightly deflated ball or pillow (for tossing game) Construction paper Glue Math journals Dry-erase markers and eraser Dice Handouts Needed:

“Comparing Decimals” “Expanded Notation” “Expanded Notation- Decimals” “Rounding Decimals- Nearest Tenth” “Rounding Money” “Adding Decimals” “Subtracting Decimals”

Activity:

Place Value TossFor this activity, you will need a ball, or pillow, for students to toss to one another (a slightly flattened volleyball works really well for this game). The teacher begins the game by tossing the ball to a student. The student must say “ones” before they catch the ball. That student then tosses the ball to another student, who must say “tens” before they catch it. As the game continues, students must say the next place value name (“hundreds”, “thousands”, “ten thousands”, etc.) before they catch the ball, all the way up to “(one) billions”. After the one billions place is called, the place value names start over again with “ones”. This activity can also include decimal places (thousandths, hundredths, tenths, ones, tens, etc.).

Interactive Place Value Flip- Chart

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Cut strips of construction paper and glue into math journal to create an interactive place value flip-chart. Write the place value names on the front of each flap using markers. Underneath the flaps, write a decimal number in standard, expanded, and word form. Using the example number 13.756 as shown in the picture above, expanded notation could be added to show: (1 x10) + (3 x 1) + (7 x 0.1) + (5 x 0.01) + (6 x 0.001). (http://www.rundesroom.com/2012/09/math-journal-sundays-decimal-numbers.html)

“Comparing Decimals” Handout (with dry-erase place value chart)The laminated “Place Value Chart” (from Day 4) is a wonderful tool for students to use along with the dry-erase markers to compare numbers. Students can compare the numbers on the handout “Comparing Decimals” by writing the digits in the correct place value columns on the chart. After using a dry-erase marker to compare the numbers on the place value chart, students need to write <, >, or = to compare the numbers on the handout.

The laminated place value chart can also be used for a partner activity. Each partner takes turns rolling a die to create digits for a 10 digit number. Once the numbers are created, partners compare numbers. The person with the bigger numbers gets a point.

HandoutsThe following handouts may be completed with a partner during class if time allows, or as practice for homework.

Expanded Notation Expanded Notation- Decimals Rounding Decimals- Nearest Tenth Rounding Money Adding Decimals *Have students choose 8 problems to estimate to the side of the

exact answer Subtracting Decimals *Have students choose 8 problems to estimate to the side of the

exact answer

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http://www.rundesroom.com/2012/09/math-journal-sundays-decimal-numbers.html



Encouraging students to apply and extend the concepts they have learned


Applying and utilizing all learned material in new ways

Phase: EVALUATE

Day 6Materials:

Unit 4 Performance Assessment

Activity:

Unit 4 Performance Assessment

Mathematics Grade 5 Unit 04 PA 01

Analyze the problem situation(s) described below. Organize and record your work for each of the following tasks. Using precise mathematical language, justify and explain each solution process.

Humboldt Paper Company sells different thicknesses of paper for different types of projects.

1) The paper company wants to create a brochure that describes the products they sell. They would like to order the types of papers from thinnest to thickest paper so that it is easy for their customers to find the paper they want.

a) Represent the value of each of the thicknesses using numerals and expanded notation.

b) Create a table that orders the paper names and their thicknesses from thickest to thinnest.

c) Write a comparison statement using the symbols >, <, or = to compare the thickness of two of the paper types.

mpany looks at the table and wonders if rounding all of the thicknesses to a common place-value might be easier for their customers to read. Before they round them all, they want to 26


make sure it doesn’t change the order of the papers from thinnest to thickest.

a) Explain how to round each of the thicknesses. Then, predict if it would change the order of the different types of paper.

b) Round each of the paper thicknesses to the tenths place-value.

c) Write a comparison statements using symbols >, <, or = to explain any changes that may occur in the original order of thinnest to thickest.

d) Round each of the paper thicknesses to the hundredths place-value.

e) Write a comparison statements using symbols >, <, or = to explain any changes that may occur in the original order of thinnest to thickest.

f) Compare and contrast the effects of rounding the paper thicknesses to the tenths place versus rounding the paper thicknesses to the hundredths place. Explain why there would be changes to the order.

3) Another company who makes party invitations decides to purchase some of the paper to create wedding invitations. Each invitation will have one layer of Vellum paper with a different layer of paper on top. The envelope for the invitation can hold thicknesses up to 0.505 mm.

a) Write an expression that can be used to determine the maximum paper thickness that can be paired with the sheet of vellum to create the invitation.

b) Estimate the thickness of paper that can be paired with the sheet of vellum to create the initiation.

c) Simplify the expression and identify which paper type(s) can be paired with the vellum to create the invitation.


Assessing student learning


Demonstrating understanding

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copy of 5e model example blank document_for … · web view5.3k – add and subtract positive...

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