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Step Up to the TEKS by GF Educators, Inc.

Fifth Grade Math Book

Teacher Edition

Copyright © 2014

www.StepUpTEKS.com

Teacher:

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Step Up to the TEKS

Fifth Grade Math Book

by GF Educators, Inc.

Table of ContentsNumerical Representations and Relationships Represent Value of Decimals (5.2A) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 Compare and Order Decimals (5.2B) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6 Round Decimals (5.2C). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11 Identify Prime/Composite Numbers (5.4A) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16 Describe Parentheses/Brackets (5.4E) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21 Simplify Numerical Expressions (5.4F) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26

Computations and Algebraic Relationships Estimate for Solutions (5.3A) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31 Multiply Using Standard Algorithm (5.3B) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .36 Divide Using Standard Algorithm (5.3C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .41 Represent Multiplication of Decimals (5.3D) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .46 Solve Using Multiplication of Decimals (5.3E) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .51 Represent Division of Decimals (5.3F) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .56 Solve Using Division of Decimals (5.3G) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .62 Fractions with Unequal Denominators (5.3H). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .67 Multiply Whole Numbers and Fractions (5.3I) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .72 Represent Division with Unit Fractions (5.3J) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .77 Add and Subtract Rational Numbers (5.3K) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .82 Division with Unit Fractions (5.3L) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .87 Solving for Unknowns (5.4B) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .92 Numerical Patterns from Equations (5.4C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .97 Additive and Multiplicative Patterns (5.4D) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .102

Geometry and Measurement Perimeter, Area (5.4H) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .107 Classify Two-Dimensional Figures (5.5A) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .112 Recognize Unit Cubes (5.6A) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .117 Volume with Unit Cubes (5.6B) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .122 Conversion of Measurement Systems (5.7A). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .127 Coordinate Planes (5.8A) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .132 Understanding How to Graph Ordered Pairs (5.8B). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .137 Graphing Ordered Pairs (5.8C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .142

Data Analysis and Personal Financial Literacy Representations of Data (5.9A) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .148 Scatterplots (5.9B) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .154 Tables, Plots, and Graphs (5.9C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .160 Taxes (5.10A) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .166 Gross and Net Income (5.10B) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .171 Expenses and Income (5.10E) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .176 Balancing a Budget (5.10F) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .181

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15th Grade Mathematics © 2014

BackgroundInformation

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Student Expectations -

Category

TEKS

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Vocabulary

Understanding the TEKS

Essential Question(s)Why is it important to place the zeros between the decimal and the number when putting a number in expanded notation?How do you represent a digit in expanded form?Why do you need to represent a number in expanded form?

Since whole numbers have been emphasized in previous grades, with the introduction of decimals in fourth grade, the place value of numbers containing decimals will be emphasized in fifth grade.

Exponential Notation, Expanded Form, Standard Form

Student Expectations - Supporting Standard

Represent Value of DecimalsNumerical Representations and Relationships

The student will demonstrate an understanding of how to represent and manipulate numbers and expressions.

Number and operations. The student applies mathematical process standards to represent, compare, and order positive rational numbers and understand relationships as related to place value. The student is expected to represent the value of the digit in decimals through the thousandths using expanded notation and numerals.

Grade Student is expected to...

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3.2A compose and decompose numbers up to 100,000 as a sum of so many ten thousands, so many thousands, so many hundreds, so many tens, and so many ones using objects, pictorial models, and numbers, including expanded notation as appropriate3.2B describe the mathematical relationships found in the base-10 place value system through the hundred thousands place

4th

4.2A interpret the value of each place-value position as 10 times the position to the right and as one-tenth of the value of the place to its left4.2B represent the value of the digit in whole numbers through 1,000,000,000 and decimals to the hundredths using expanded notation and numerals4.2E represent decimals, including tenths and hundredths, using concrete and visual models and money

6th None

7th None

8th 8.2C convert between standard decimal notation and scientific notation

TEKS 5.2A

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© 2014 2 5th Grade Mathematics

Name: Engaging

Activity

A

Determine the place value of the underlined digit in each number. Example: In the number 5,278.96, the 9 is in the tenths place.

1 In the number 16.51, the 5 is in the _______________ place.




Write each number in Expanded Form.

5 3.27 =

6 12.43 =

7 8.65 =

8 214.82 =

Write each number in Standard Form.

9 ________ = (8 x 10) + (4 x 1) + (5 x 0.1) + (9 x 0.01)

10 ________ = (6 x 10) + (7 x 1) + (3 x 0.1) + (3 x 0.01)

11 ________ = (3 x 10) + (3 x 1) + (2 x 0.1) + (8 x 0.01)

12 ________ = (9 x 10) + (8 x 1) + (9 x 0.1) +(8 x 0.01)

13 ________ = (1 x 100) + (0 x 10) + (6 x 1) + (2 x 0.1) + (4 x 0.01)

14 ________ = (9 x 100) + (6 x 10) + (1 x 1) + (3 x 0.1) + (5 x 0.01)

15 ________ = (1 x 100) + (1 x 10) + (0 x 1) + (9 x 0.1) + (5 x 0.01)

Numerical Representations and Relationships

Name:TEKS 5.2A Supporting

Represent Value of Decimals

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Thinking Mathematically

Putting the Pieces Together

Why is it important to place the zeros between the decimal and the number when putting a number in expanded notation?The zeros act as place holders.How do you represent a digit in expanded form?Expanded form uses the sum of the digit of each place value multiplied by the place value.Why do you need to represent a number in expanded form?Expanded form helps to explain the meaning of place value.

The number 54.672 has a decimal point. It could quickly be looked at as a number with a comma. Pay close attention to the decimal point and where it is located. The zeros between the decimal point and the number are important for place value.

I can represent a value of a digit.


How do you represent the digit 7 in expanded notation in the number 54.672?

A 1 x 7B 0.1 x 7C 0.01 x 7D 0.001 x 7

Represent Value of Decimals

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Name: Guided

Practice

GP Represent Value of DecimalsNumerical Representations and Relationships


1 How is six billion, four hundred one thousand, six and three thousandths written as a number?

A 641,600,000.003B 6,401,006.003C 6,000,401,006.003D 6,000,401,006.03

2 How is 300 + 40 + 9 + 0.04 + 0.008 written as a number?

A 349,048B 34,948C 349.48D 349.048

3 On Tuesday, Martin gave each plant 43.5 milliliters of water. On Wednesday he gave them 4.35 milliliters of water. On Friday, Martin poured 44.254 milliliters of water on each plant, and on Monday each plant received 44.9 milliliters of water. Write the amount of water Martin gave each plant in expanded notation in the table below.

Day Expanded Notation

TuesdayWednesday

Friday

Monday

4 How do you represent the digit two in expanded notation in the number 125.765?

A 10 x 2B 100 x 2C 0.01 x 2D 0.001 x 2

You must show your work.When numbers are expanded or written in standard form, the placement of the decimal point and the zeros are very important concerning place value. They take up a place.

Hint: The digit 2 in the number represents a value in reference to its place value.

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Answer Key

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Name: Answer Key

AK Represent Value of DecimalsNumerical Representations and Relationships TEKS 5.2A Supporting

Activity1 tenths2 hundredths3 tens4 hundredths5 (3 x 1) + (2 x 0.1) + (7 x 0.01)6 (1 x 10) + (2 x 1) + (4 x 0.1) + (3 x 0.01)7 (8 x 1) + (6 x 0.1) + (5 x 0.01)8 (2 x 100) + (1 x 10) + (4 x 1) + (8 x 0.1)

+ (2 x 0.01)9 84.5910 67.3311 33.2812 98.9813 106.2414 961.3515 111.95

Teaching Model1 BGuided Practice1 B2 D

3

Day Expanded Notation

Tuesday 10 x 4 + 1 x 3 + 0.1 x 5

1 x 4 + 0.1 x 3 +0.01 x 110 x 4 + 1 x 4 + 0.1 x 2 + 0.01 x 5 + 0.001 x 4

Wednesday

Friday

10 x 4 + 1 x 4 + 0.1 x 9Monday

4 AIndependent Practice Page 3 SE1 A2 D3 D4 D5 B6 B7 403.0628 BPage 4 SE1 B2 B3 B4 A

5

Runner Expanded Notation

Paul 10 + 9 + 0.8

10 + 9 + 0.7 + 0.0510 + 9 + 0.6

Bob

Ron

10 + 9 + 0.5 + 0.07Ed

6

Category Expanded Notation

Points per Game 30 + 0.1

6 + 0.20.3 + 0.02 + 0.007

Rebounds per Game

3 Point %

0.4 + 0.04 + 0.009 + 0.0007Field Goal %

Statistics

30.16.2

0.327

0.4497

0.8 + 0.03 + 0.005Free Throw % 0.835

Activity: This is a great activity to present the value of decimals in three different ways. This should help establish a better understanding of decimals place value.

Teaching Model: The value of the digit is 7 is dependant on its position in the number.

Guided Practice: Three different ways of representation are presented. Make sure students understand all three.

Independent Practice:When grading, note if the students have more difficulty in any certain method of converting. Address that method.

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Vocabulary


Essential Question(s)

Compare, Order, Thousandths

Why is the placement of the zeros important when comparing the numbers above?Why do you need to order decimals?Explain the method of comparing two decimals.

This TEKS specifically states the comparing and ordering of two decimals using <, >, =. Place value with decimals needs to be completely understood when comparing and ordering.

Compare and Order DecimalsNumerical Representations and Relationships

Student Expectations - Readiness Standard


Number and operations. The student applies mathematical process standards to represent, compare, and order positive rational numbers and understand relationships as related to place value. The student is expected to compare and order two decimals to thousandths and represent comparisons using the symbols >, <, or =.


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3rd3.2D compare and order whole numbers up to 100,000 and represent comparisons using the symbols >, <, or =

4th4.2C compare and order whole numbers to 1,000,000,000 and represent comparisons using the symbols >, <, or =4.2F compare and order decimals using concrete and visual models to the hundredths

6th6.2D order a set of rational numbers arising from mathematical and real-world contexts

7th None

8th8.2D order a set of real numbers arising from mathematical and real world contexts

TEKS 5.2B

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EngagingActivity

A

Compare each pair of numbers using <, >, or =. If needed, use a number line to show your work.

Ex

Fill in the empty box below with the inequality symbol that correctly compares the numbers in each row.

1.021

0.007

8.002

12.91

3.074

0.67

5.301

8.021

0.02

1.21

5.310

3.704

0.607

1

2

3

4

5

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42.09

90.039

113.28

7.23

2.18

54.032

90.21

42.8

54.49

113.128

7.22

0.218

7

8

9

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11

12

12.191

6.79

3.34

3.57

3.78

8.95

1.26

0.334

0.679

1.28

3.8

0.895

13

14

15

16

17

18

8.75

2.66

9.2

2.19

2.63

8.73

0.219

9.19

19

20

21

22

3.6

<


Name:TEKS 5.2B Readiness

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TeachingModel

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Why is placement of the zeros important when comparing the numbers above?

Zeros act as place holders when comparing numbers.Why do you need to order decimals?Ordering of decimals gives students reference points on which to make comparisons.Explain the method of comparing two decimals.Compare decimals by comparing each place value starting with the greatest place value.

The placement of the zeros in a number can change a number as much to the right of the decimal point as it does to the left of the decimal point.

I can compare and order two decimals because I understand place value.


Which is a correct comparison?

A 10.23 > 10.203 B 10.23 < 10.230C 10.23 = 10.203D 10.203 < 10.2

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GuidedPractice

GP Compare and Order DecimalsNumerical Representations and Relationships

Name:TEKS 5.2B Readiness

1 Which is a correct comparison?

A 80.08 > 80.2 B 80.8 < 80.08C 80.08 = 80.080D 80.080 > 80.8

Fisherman Fish Length (Inches)

Scott 24.375

24.357

24.307

Ronnie

Eddie

24.37Ruiz

2 Scott and his friends were out fishing. The fish they caught all appeared to be the same size. The lengths of their fish are listed in the table. Help Scott compare the size of each fish by placing >, <, or = in between each set of numbers.

24.375 24.357

24.357 24.307

24.307 24.37

24.37 24.375

3 According to the table in question #2, which comparison is true?

A Ruiz’ fish length < Eddie’s fish length B Ronnie’s fish length > Scott’s fish lengthC Eddie’s fish length > Scott’s fish lengthD Ronnie’s fish length < Ruiz’ fish length

You must show your work.The numbers are the same; it’s the placement of the zeros that change the value. Do not let that confuse your students. If you know the value of each place in a number, you will not be confused.

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Answer Key

AK Compare and Order DecimalsNumerical Representations and Relationships TEKS 5.2B Readiness

Teaching Model1 A

Guided Practice1 C2 >, >, <, <3 D

Independent Practice Page 7 SE1 D2 D3 D4 D5 C6 B7 B8 B

Page 8 SE1 =, >, <, >, =2 D3 >, =, <, <

Page 9 SE1 A2 D3 B4 C

Page 10 SE1 B2 A

Activity: Pay close attention to the zeros. The placement of a zero is sooooo important.

Teaching Model: The digits used are all the same. The placement of the zero is what makes the difference.

Guided Practice: Three different ways of representation are presented. Make sure students understand all three.

Independent Practice:Reading the place value of the number is one skill area. The direction of the sign is another skill area. Pinpoint the area of confusion when a problem is missed.

Page 7When the answers are using words to describe or explain the relationship, place the number above the description to visually see the numbers that are being compared.

Page 8The second question has justification answer choices. Select the correct answer and read the justification carefully to judge for reasonableness.

Page 10These questions reach the process level of problem solving. Read correctly and compare each from the numbers on the charts.Sam

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Essential Question(s)Why is it important to look at the hundredth place when rounding to the nearest tenth?Why is important to be able to round decimals?Why is it necessary to round a decimal?

Rounding is limited to the tenths and hundredths.

Tenths, Hundredths, Round

Round DecimalsNumerical Representations and Relationships

Student Expectations - Supporting StandardNumber and operations. The student applies mathematical process standards to represent, compare, and order positive rational numbers and understand relationships as related to place value. The student is expected to round decimals to tenths or hundredths.


Category1

TEKS 5.2C


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3rd3.4B round to the nearest 10 or 100 or use compatible numbers to estimate solutions to addition and subtraction problems.

4th

4.2D round whole numbers to a given place value through the hundred thousands place4.4G round to the nearest 10, 100, or 1,000 or use compatible numbers to estimate solutions involving whole numbers

6th None

7th None

8th None

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Name: Engaging

Activity

A

Round each number to the nearest tenth.

1 14.256

2 21.209

3 54.681

4 135.227

5 767.029

6 43.589

7 1.87

8 4.52

9 1.51

10 7.25

Round each number to the nearest hundredth.

11 538.481

12 2,039.509

13 78.331

14 45.883

15 98.909

16 62.376

17 1.925

18 9.556

19 5.692

20 6.282

21 2.857


Name:TEKS 5.2C Supporting

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Why is it important to look at the hundredth place when rounding to the nearest tenth?When rounding to the tenths, you have the next place value as your reference point.Why is it important to be able to round decimals?Rounding decimals is necessary to make estimates of values.Why is it necessary to round a decimal?When working problems, more precise decimal values may not be needed.

Do not let money confuse you. The hundredth place is still the hundredth place in money. It takes 100 pennies to make one dollar. It takes 10 dimes to make one dollar.

I can round decimals to the nearest tenth and hundredth.


Carol used 7.3 yards of fabric to make a tablecloth. The material cost $2.64 a yard, but was on sale for $1.77 a yard. Which is the sale price rounded to the nearest tenth?

A $2.00B $1.80C $1.70D $1.78

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Name: Guided

Practice

GP Round DecimalsNumerical Representations and Relationships


1 What is 484.2675 rounded to the nearest hundredth?

A 500B 484.268C 484.27D 484.3

2 What is 29.7091 rounded to the nearest tenth?

A 29.71B 30C 29.709D 29.70

3 Alexis is a gold miner. She found 12.823 ounces of gold. When reporting the weight, she rounded it to the nearest tenth of an ounce. What weight did Alexis report?

A 12.8 ouncesB 13 ouncesC 12.82 ouncesD 12.9 ounces

You must show your work.Circle the place value that the numbers should be rounded to. Then underline the next number to the right.

Hint: Use the rule of rounding; 1-4 the previous digit remains the same, 5-9 the digit rounds up.

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Answer Key

AK Round DecimalsNumerical Representations and Relationships TEKS 5.2C Supporting

Activity1 14.3 2 12.2 3 54.74 135.2 5 767 6 43.67 1.9 8 4.5 9 1.510 7.3 11 538.48 12 2,039.5113 78.33 14 45.88 15 98.91 16 62.3817 1.93 18 9.5619 5.69 20 6.28 21 2.86

Teaching Model1 B

Guided Practice1 C2 D3 A

Independent Practice Page 13 SE1 C2 A3 A4 $1.705 $2.306 A

Page 14 SE1 A2 36.5

3

Runner Time (sec)

Donovan Bailey 9.835

9.768

9.766

Asafa Powell

Justin Gatlin

9.763Asafa Powell

9.683Usain Bolt

9.572Usain Bolt

Rounded NumberRount to

Tenth

Hundredth

Tenth

Hundredth

Tenth

Hundredth

9.89.779.89.769.79.57

4 C

Activity: Just look at he number to the right of the number being rounded.

Teaching Model: Critical reading: Asking for sale price rounded to the nearest tenth.

Guided Practice: Check for understanding.

Independent Practice:This TEKS is requiring mastery of the ability to round to the nearest tenth or hundredth. This is insuring mastery of rounding before solving problems is addressed.

Each question is addressing rounding to either the tenth or hundredths place in various situations, but still just basically rounding a number.

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Essential Question(s)Why is it important to know that a number is prime?What is the difference between a prime and composite number?What do prime and composite numbers have in common?

The student must understand what constitutes a prime number and a composite number. Each time a number is evaluated, these components must be identified.

Prime, Composite

Identify Prime and Composite NumbersNumerical Representations and Relationships

Student Expectations - Supporting StandardTEKS 5.4A

Category1


Algebraic reasoning. The student applies mathematical process standards to develop concepts of expressions and equations. The student is expected to identify prime and composite numbers.


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3rdNone

4thNone

6thNone

7thNone

8thNone

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EngagingActivity

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If a number is prime, put a P in the box. If a number is composite, put a C in the box.

8 9 13 21 11 34 22 17 12 27

Help the pilgrim find the turkey by following the path of prime numbers.

133 105 108 8 78 60 107 39 108 116 135 60 86

102 132 42 81 81 126 5 71 43 114 102 58 60

70 12 18 40 51 12 84 49 61 41 60 135 102

133 102 138 46 58 129 22 56 66 103 31 13 127

96 9 72 38 45 40 25 80 18 108 85 99 139

98 86 24 35 92 12 18 31

26 105 113 103 80 102 54 79

19 2 31 126 22 38 19 11

101 18 10 65 69 97 79 12

103 19 90 138 106 9 104 135 64 106 3 60 9

35 67 111 128 133 96 10 98 68 60 139 17 108

108 113 23 79 56 15 102 48 34 112 110 127 130

39 72 38 79 72 108 42 71 29 131 95 2 55

105 102 85 79 61 89 127 23 12 31 61 3 58



Identify Prime and Composite Numbers

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Why is it important to know that a number is prime?You need to know prime numbers when evaluating factors of a number.

What is the difference between a prime and composite number?Prime numbers have only 2 factors; 1 and itself. Composite numbers have more than 2 factors.What do prime and composite numbers have in common?The number 1 is a factor of both prime and composite numbers.

Evaluate each number by the rules for a prime and composite number.

I can identify a prime and a composite number.


Which number is a prime number?

A 7B 8 C 6D 4

Identify Prime and Composite

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GPNumerical Representations and Relationships


1 Which number is a composite number and not a prime number?

A 3 C 5 B 7 D 9

2 Which is a prime factor of the composite number 16?

A 3 C 4 B 2 D 8

3 Madison used the oval mirrors to make 4 designs, as shown below. Which design is composed of a composite number of tiles?

Design 1

Design 2

Design 3

Design 4

A Design 1B Design 2C Design 3D Design 4

You must show your work.Apply the rules for prime versus composite before selecting an answer.

Identify Prime and Composite Numbers

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Answer Key

AK Identify Prime and Composite NumbersNumerical Representations and Relationships TEKS 5.4A Supporting

Teaching Model1 A

Guided Practice1 D2 B3 D

Independent Practice Page 17 SE1 A2 B3 C4 C5 B6 D7 B8 C9 A10 B11 D

Page 18 SE1 D2 A

The Teaching Model, Guided Practice and Independent Practice are all dependent on the student’s ability to analyze a number by determining if it can be broken down, or not. Each number must be evaluated or instantly recognized, such as, 3, 5, 7, 1, 13, 17, etc.

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Essential Question(s)Why is it important to follow the order of operations?What is the difference between parentheses and brackets?

This is the first time order of operations is presented. It is important to make sure students understand the rules of order. Students need to understand when parentheses and brackets are used.

Order of Operations, Parentheses, Brackets

Describe Parentheses and BracketsNumerical Representations and Relationships



Algebraic reasoning. The student applies mathematical process standards to develop concepts of expressions and equations. The student is expected to describe the meaning of parentheses and brackets in a numeric expression.

Category1

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3rd3.5C describe a multiplication expression as a comparison such as 3 x 24 represents 3 times as much as 24

4thNone

6th6.7A generate equivalent numerical expressions using order of operations, including whole number exponents, and prime factorization

7thNone

8thNone

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Name: Engaging

Activity

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Insert brackets to obtain the answer shown.

a 12 – 5 x 7 = 49 b 24 – 3 x 5 = 9 c 18 + 3 x 5 = 105 d 32 – 5 x 2 + 4 = 2 e 16 – 2 x 7 = 2 f 1 + 5 x 3 – 2 = 6 g 5 + 2 x 3 - 1 = 9 h 3 + 4 x 2 + 6 = 56 i 3 x 25 – 13 + 4 = 40 j 4 + 3 x 4 – 4 =12 k 16 – 4 + 3 = 15 l 12 – 3 x 2 = 6

Insert parentheses to make the statement true.

1 82 – 4 • 2 = 156

2 22 – 4 • 3 ÷ 2 = 5

3 8 + 16 ÷ 4 + 18 = 24

4 72 – 8 • 6 – 5 = 64

5 3 • 4 + 1 + 5 = 30

6 32 ÷ 4 + 16 – 4 • 3 = 4

7 32 + 8 • 3 ÷ 4 = 30

8 15 – 3 ÷ 1 ÷ 6 = 2

9 88 ÷ 22+ 8 ÷ 3 = 4

10 18 ÷ 3 + 3 – 2 = 1

11 16 – 8 ÷ 4 + 10 = 12

12 5 • 5 + 5 – 5 = 45

13 6 + 6 ÷ 6 • 6 = 42

14 200 – 90 + 80 + 20 = 10

15 What do parentheses tell you to do in a math problem?

16 What do brackets tell you to do in a math problem?


Name:TEKS 5.4E Supporting

Describe Parentheses and Brackets

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Why is it important to follow the order of operations?The correct answer will not be achieved if the correct order of operations is not followed.

What is the difference between parentheses and brackets?Parentheses are used for the most inner grouping and brackets are used for the outer grouping.

Work inside the parentheses or brackets first. Do any multiplication or division next from left to right. Last, do all addition and subtraction from left to right.

I can describe the meaning of parentheses and brackets.


How do the brackets and parentheses affect the order of operations for the expression [50 + (20 – 3) x 6] ÷ 2?

A The division operation is the last step. B The addition operation is the first step. C The multiplication operation is the third step.D The parentheses do not change the order of operations.


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1 Which choice gives the correct order of operations needed to find the value of 4 – 8 (2 + 6) ÷ 2?

A –, ×, +, ÷ B –, +, ×, ÷ C ×, ÷, –, + D +, ×, ÷, –

2 Which is a reason to use parentheses in a numerical expression?

A To define which operation should be performed first

B To move multiplication in front of addition in the order of operations

C To change addition to multiplicationD Parentheses do not change the order of operations

3 George started with the following expression: 6 – 2 ÷ 4 + 4 × 2

He then added the parentheses shown below. (6 – 2) ÷ 4 + 4 × 2

How do the parentheses change the order of operations for the expression?

A The parentheses change the order of operations from –, ×, +, ÷ to ×, ÷, –, +

B The parentheses change the order of operations from ÷, ×, –, + to –, ÷, ×, +

C The parentheses change the order of operations from –, ÷ , ×, + to ÷, ×, –, +

D The parentheses do not change the order of operations.

You must show your work.The correct order of operations is necessary in order to get the correct value for an expression.


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Answer Key

AK Describe Parentheses and BracketsNumerical Representations and Relationships TEKS 5.4E Supporting

Teaching Model1 A

Guided Practice1 D2 A3 B

Independent Practice Page 21 SE1 C2 D3 B4 D5 A6 C

Page 22 SE1 B2 A3 D4 C

Activity: The students must apply the rules of order of operations on each and every problem. The repetition of this activity will reinforce the concept for future implementation.

Teaching Model: The sequence of operations according to brackets and parentheses is assessed. Make sure the students thoroughly understand what is being asked and clarify if needed.

Guided Practice: Three different formats are presented. Make sure the students understand the process and procedure of each one. If there is confusion, clarify before going any further.

Independent Practice:Two pages are provided to reinforce each format to implement the process. Please do not leave this concept if there is any confusion. The understanding of brackets and parentheses is so important in upper level math.

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This SE represents a subset of simplifying expressions using order of operations as the number of levels of grouping is limited to two levels. An example of two levels of grouping is (3+7)/(5-3). Students are expected to use the order of operations to simplify numerical expressions. Because fluency with addition and subtraction of positive rational numbers is expected, expressions may include fractional values when adding or subtracting.

Expressions, Grouping

Why is order important?What is the correct order in which to simplify an expression?How can grouping symbols be used to simplify mathematical expressions?

Numerical Representations and Relationships TEKS 5.4F Readiness

Student Expectations - Readiness Standard


Algebraic reasoning. The student applies mathematical process standards to develop concepts of expressions and equations. The student is expected to simplify numerical expressions that do not involve exponents, including up to two levels of grouping.

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4thNone

6th6.7A generate equivalent numerical expressions using order of operations, including whole number exponents, and prime factorization

7thNone

8thNone

Simplify Numerical Expressions

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Simplify each of the following.

9 - [(8 + 7 - 5) ÷ 2]

[7 - (2 + 4 - 3)] x 6

6 x [(3 + 4) - 5] - 8

[5 + (18 ÷ 6 - 2)] x 7

8 ÷ [(4 + 3) - 5] + 9 x 7

[4 + (27 ÷ 3)] - 2 x 6

[(30 ÷ 5) - 4] + 8

17 - [(8 + 5 + 3) ÷ 4] - 9

9 + 5 x 8 - [(56 ÷ 8 - 4) x2]

5 x [18 ÷ (4 + 5)] - 9

12 x [16 - (6 + 7 )] ÷ 4 x 7

[63 ÷ (7 + 2)] - 4

5 + [(4 + 7 - 3) ÷ 4] + 6

[72 ÷ (2 + 3 + 4)] - 6 + 9 x 5

9 - [64 ÷ (6 + 2)] + 5 x 8

2 x [7 + (8 - 3 - 2)]

[8 x (4 + 2)] - 7 x 6 + 5

12 + 6 - [81 ÷ (2 + 7)]

1 2

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Simplify Numerical ExpressionsNumerical Representations and Relationships

Name:TEKS 5.4F Readiness

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Order of operations is necessary to be able to simplify the expression correctly. Grouping of parentheses and brackets must be simplified first. Multiplication and division is then performed in order from left to right followed by addition and subtraction in order from left to right.

Why is order important?A decided order is needed for consistency of values.

What is the correct order in which to simplify an expression?Grouping of parentheses and brackets must be simplified first. Multiplication and division is then performed in order from left to right followed by addition and subtraction in order from left to right.How can grouping symbols be used to simplify mathematical expressions?Grouping symbols help better organize an expression and make it easier to read and use.

I can simplify numerical expressions.Numerical Representations and Relationships

What is the value of the expression below?

[(8 x 6) – 9 ÷ 3] + 2

A 69

B 47

C 9

D 23


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1 What is the value of the expression below?

30 − 7 × (2 + 1)

A 69

B 47

C 9

D 23

2 A set of parentheses is missing from the expression below.

18 – 6 + 2 • 3 + 4

Which of the following expressions has the parentheses in the correct place for the expression to equal 10?

A 18 – (6 + 2 • 3) + 4 B (18 – 6 + 2) • 3 + 4C 18 – 6 + (2 • 3 + 4)D 18 – (6 + 2) • 3 + 4

3 Which does not have the same solution as the expression below?

18 − (3 + 2) × 2

A 3 x 6 – 5 x 2

B (12 + 5 x 4) ÷ 4

C [4 x (6 + 2) – 8] ÷ 3

D 18 – 3 + 2 x 2

You must show your work.CAUTION: Verify that students are using the correct order to simplify.

Hint: Have student underline which operation to do first.


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Answer Key

AK Simplify Numerical ExpressionsNumerical Representations and Relationships TEKS 5.4F Readiness

Activity1 4 2 1 3 24 4 67 5 4 6 43 7 42 8 10 9 4 10 63 11 43 12 3 13 1 14 13 15 41 16 11 17 20 18 9

Teaching Model1 B

Guided Practice1 C2 A3 D

Independent Practice Page 25 SE1 B2 D3 484 D5 D6 1

Page 26 SE1 C2 A3 C4 B5 B6 C

Page 27 SE1 B2 C3 C

Page 28 SE1 B2 A3 D

Activity: The students must apply the rules of order of operations on each and every problem. The repetition of this activity will reinforce the concept for future implementation. Grouping of parentheses and brackets must be simplified first. Multiplication and division is then performed in order from left to right followed by addition and subtraction in order from left to right.

Teaching Model: The parentheses and brackets are provided to assist in the order of operations.

Guided Practice: In question number 2, the order must be determined using the rule “multiplication and division left to right then addition and subtraction left to right.”

Independent Practice:Further practice which reinforces the order of operations is provided.

Page 27 and 28 both introduce new formats.

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This TEKS focuses on the student using estimation with all four mathematical operations with both math problems and real-world problems

Estimation, Solutions, Mathematical Problems, Real-World Problems, Addition, Subtraction, Multiplication, Division

How can you use estimation to solve math problems?Why would you want to use estimation to solve math problems?How do you estimate to solve math problems?

Estimate for SolutionsComputations and Algebraic Relationships TEKS 5.3A Supporting

Student Expectations - Supporting StandardNumber and operations. The student applies mathematical process standards to develop and use strategies and methods for positive rational number computations in order to solve problems with efficiency and accuracy. The student is expected to estimate to determine solutions to mathematical and real-world problems involving addition, subtraction, multiplication, or division.

The student will demonstrate an understanding of how to perform operations and represent algebraic relationships.

TEKS 5.3A

Category2


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3.4A solve with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction

4th4.4A add and subtract whole numbers and decimals to the

6th None

7th7.3A add, subtract, multiply, and divide rational numbers fluently7.3B apply and extend previous understandings of operations to solve problems using addition, subtraction, multiplication, and division of rational numbers

8th None

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Back to School Sale:

Shirts - $17.50 Shorts - $11.75

Jeans - $13.75 Snickers - ?????

Shoes - $35

1 Using the information in the sale ad, approximately how much would it cost to buy 2 shirts, 3 shorts, 4 jeans and 1 pair of shoes? How did you determine your answer?

2 If you had $50.00 to spend and wanted to buy a pair of shoes and jeans, about how much money would you have left?

3 If you bought 5 pairs of snickers for $130.00, about how much did each pair cost?

4 If you bought 11 pairs of shorts, approximately what was the total cost?

Explain how you used estimation to find your answers. How else could you estimate to solve the problem?

Computations and Algebraic Relationships


Estimate for Solutions

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Estimation uses rounding to help simplify numbers to solve the problems. However, strict rounding rules do not always apply to estimation problems. Ask the students how and why they are making the decisions on the numbers they are using to solve the problem. It is important that the student determines the appropriate operation for each problem.

How can you use estimation to solve math problems?Estimation is used when it is not necessary to get an exact answer to a problem.Why would you want to use estimation to solve math problems?You might want to estimate when purchasing items to determine if you have enough money.How do you estimate to solve math problems?When you estimate, you round your numbers to a certain place value to get a good approximation of the solution.

I can use estimation to solve real world problems.


A commercial airplane is loaded with 98 suitcases in the cargo department. Each suitcase weighs about 47 pounds. Which of the following is a reasonable estimate of the total weight of the suitcases?

A 3,600 poundsB 4,500 poundsC 5,000 poundsD 150 pounds


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GPComputations and Algebraic Relationships


1 The 4-H Club had an exhibit at the county fair. They had a total of 198 visitors on Thursday and Friday night, 267 visitors on Saturday, and 153 visitors on Sunday. Which is the best estimate of the total number of visitors to the 4-H booth during these 4 days?

A 600B 700C 900D 1,000

2 Kenny’s dad filled the car with 15.25 gallons of gas on Monday. On Thursday his dad filled the car with 13.63 gallons of gas. What is the best estimate of the amount of gas his dad bought in those two days to the nearest tenth of a gallon?

A 30 gallonsB 29 gallonsC 28.9 gallonsD 28.8 gallons

3 Reese owns vending machines. He used the following information to estimate the total number of bags of chips Reese needs to order to fill his vending machines.

● There are vending machines in 5 schools. ● There are 10 − 15 vending machines in each

school. ● There are 40 − 45 bags of chips in each

machine.What is the best estimate of the total number of bags of chips Reese needs to purchase?

A 50 B 400C 1,500D 3,000

You must show your work.Hint:Make sure students are writing down the problem they are using for their estimation. Ask students why they decided to estimate to that value. Ask students what operation they are using to solve the problem


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Answer Key

AK Estimate for SolutionsComputations and Algebraic Relationships TEKS 5.3A Supporting

Activity1 $1632 $49, but tax must be paid3 $264 $132

Teaching Model1 C

Guided Practice1 B2 C3 D

Independent Practice Page 31 SE1 D2 C3 B4 D5 A6 A

Page 32 SE1 C2 B3 B4 B5 C

Activity: Simple rounding is required to the nearest whole number.

Teaching Model: Multiplication with zeros make estimation so easy.

Guided Practice: Question 3 is a process problem with the greatest number and the least number determined with the answer within that range.

Independent Practice:Various formats are addressed on page 32. Process problems are included.

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This TEKS is a fluency TEKS which implies the student knows how to start the problem and continues working on the problem until finished. This TEKS explicitly states that a 3-digit number is multiplied by a two-digit number using the standard algorithm which implies the understanding of place value.

Note: Algorithm is define as a step-by-step process. Standard Algorithm would be the usual process that teachers have been teaching children for years.

Multiplication, Fluency, Three-Digit Number, Two-Digit Number, Algorithm, Place Value

What is the process for multiplying a three-digit number by a two-digit number?How does place value relate to multiplying a three-digit number by a two-digit number?What does fluency mean?

Multiply using Standard AlgorithmComputations and Algebraic Relationships



Number and operations. The student applies mathematical process standards to develop and use strategies and methods for positive rational number computations in order to solve problems with efficiency and accuracy. The student is expected to multiply with fluency a three-digit number by a two-digit number using the standard algorithm.


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3rd3.4E recall facts to multiply up to 10 by 10 with automaticity and recall the corresponding division facts, 3.4F recall facts to multiply up to 10 by 10 with automaticity and recall the corresponding division facts, 3.4G use strategies and algorithms, including the standard algorithm, to multiply a two-digit number by a one digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties

4th

4.4B determine products of a number and 10 or 100 using properties of operations and place value understandings, 4.4C represent the product of 2 two-digit numbers using arrays, area models, or equations, including perfect squares through 15 by 15, 4.4D use strategies and algorithms, including the standard algorithm, to multiply up to a four-digit number by a one-digit number and to multiply a two-digit number by a two-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties, 4.4H solve with fluency one- and two-step problems involving multiplication and division, including interpreting remainders

6th 6.3E multiply and divide positive rational numbers fluently

7th7.3A add, subtract, multiply, and divide rational numbers fluently7.3B apply and extend previous understandings of operations to solve problems using addition, subtraction, multiplication, and division of rational numbers

8th None

TEKS 5.3B

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Wendy and Lyn both solved the following problem.

Lyn

359x 67

2513

4,677

+ 2154

Wendy

359x 67

2513

24,053

+ 21540

Either Lyn or Wendy made a mistake. Who made the mistake and what was the mistake?

What advice would you give the girl who got the wrong answer to help her understand her mistake?


Name:TEKS 5.3B Supporting

Multiply using Standard Algorithm

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© 2014 5th Grade Mathematics

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For students to do this TEKS fluently, they should start the problems without much hesitation. Students may want to estimate their answer first to help verify their solution.

What is the process for multiplying a three-digit number by a two-digit number?

The process for multiplying a three-digit number by a two-digit number first requires three-digit number to be multiplied by the ones digit, then the three-digit number being multiplied by the tens digit with the alignment being in the tens place. These two numbers are then added together.How does place value relate to multiplying a three-digit number by a two-digit number?

Place value is important because the three-digit number is multiplied by the ones and the tens making sure the alignment of the numbers holds to the correct place value.What does fluency mean?

Fluency does not necessarily mean speed, but starting the problem and understanding how the problem works, so I can finish the problem.

I can multiply a three-digit number by a two-digit number with ease.


Fill in the boxes below to solve the multiplication problem.

380 x 62

+

Multiply Using Standard Algorithm

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GuidedPractice


Name:TEKS 5.3B Supporting

1 Dante collects baseball cards. He has 168 packages of cards. Each package contains 14 cards. How many baseball cards does Dante have altogether?

A 182B 672C 1680D 2352

2 The Renaissance Hotel has a ballroom that can fit 239 tables. 14 people can sit at each table. Tito solves the problem below to find the total number of people that can sit at the table in the ball room.

239 x 14

956 2391195

Tito says that 1,195 can sit in the ball room. Is Tito correct? Explain your answer.

3 Admission to an amusement park is $24 per student. Blackland Prairie Elementary plans on taking 260 students to the amusement park. How much will the admission to the amusement park cost altogether?

A $1,560 because (2 x 260) = 520 and (4 x 260) = 1,040 and 520 + 1040 = 1,560.

B $284 because 260 + 24 = 284C $10,920 because (2 x 260) = 520 and

(40 x 260) = 10,400 and 520 + 10,400 = 10,920.

D $6,240 because (4 x 260) = 1,040 and (20 x 260) = 5,200 and 1,040 + 5,200 = 6,240.

You must show your work.Hint:Make sure the students are using the correct standard algorithm. Make sure the students understand the necessity of place value when multiplying three-digit and two-digit numbers.

Multiply using Standard Algorithm

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Answer Key

AK Multiply using Standard AlgorithmComputations and Algebraic Relationships TEKS 5.3B Supporting

Teaching Model1 23,560

Guided Practice1 D2 No, Tito forgot the place

value of the 13 D

Independent Practice Page 35 SE1 71 x 15 + 45 + 202 3,456 paper clips3 C4 A5 2,680 plants

Page 36 SE1 A2 B3 C4 20,6645 A

Page 37 SE1 B2 D3 B

Activity When the tens place was multiplied, the answer was not placed under the tens place. Wendy placed a zero to avoid placing the answer under the ones place rather than the tens place.

Teaching ModelMake sure the students understand that when multiplying by tens, the answer is started under the tens place.

Guided PracticeAgain reinforce why the answer must be place over one space when multiplying by the tens place.

Independent Practice The understanding of implementing the standard algorithm must be mastered before practicing its use in solving problems.

Page 37 has justification answers required.

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This TEKS requires students to divide to a four-digit number by a two-digit number with accuracy. Students should use strategies such as estimation, as well as the standard algorithms.

Proficiency, Quotient, Four-Digit, Dividend, Three-Digit Divisor, Strategies, Algorithm, Place Value

What is proficiency?What does division mean?What is the process for division?




Number and operations. The student applies mathematical process standards to develop and use strategies and methods for positive rational number computations in order to solve problems with efficiency and accuracy. The student is expected to solve with proficiency for quotients of up to a four-digit dividend by a two-digit divisor using strategies and the standard algorithm.

Category2

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3rd3.4K solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts

4th

4.4E represent the quotient of up to a four-digit whole number divided by a one-digit whole number using arrays, area models, or equations4.4F use strategies and algorithms, including the standard algorithm, to divide up to a four-digit dividend by a one-digit divisor4.4H solve with fluency one- and two-step problems involving multiplication and division, including interpreting remainders

6th6.3E multiply and divide positive rational numbers fluently

7th 7.3A add, subtract, multiply, and divide rational numbers fluently

8th None

Divide using Standard Algorithm

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Mr. Jackson is ordering supplies for his restaurant. Today, he will purchase canned tomatoes by the case, boxes of minced garlic, and flour. Canned tomatoes are sold in cases of 32 cans. A box of minced garlic contains 12 jars. Mr. Jackson buys 25 pound bags of flour.

1 Mr. Jackson already has 100 pounds of flour at the restaurant. About how many more bags should he buy if he needs 1,500 pounds of flour?

2 Mr. Jackson ordered 6,400 cans of tomatoes. How many cases did he order?

3 Mr. Jackson decided to buy 112 boxes of garlic. How many total jars will he have?

4 The next month Mr. Jackson placed an order for 2,600 pounds of flour. How many bags did he order?




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Students should understand the concept of division is to determine the number of equal groups contained within the numbers. Students may use a variety of strategies to solve division problems, but it is essential that students can also use the standard algorithm, which includes understanding the importance of place value.

What is proficiency?Proficiency also means accurately.

What does division mean?Division means to determine how many equal groups are in a number.What is the process for division?Estimate to find the number to divide by, then multiply, subtract, bring down the next number and repeat until all numbers are used.

I can solve division problem with a four-digit dividend and a two-digit divisor.


A total of 840 students attend Fulkes Middle School and are split evenly into 40 classrooms. How many students are in each classroom?

A 800, because 840 – 40 = 600.B 3, because 80 ÷ 40 = 2 and 40 ÷ 40 = 1 and 2 + 1 = 3.C 33,600, because 40 x 800 = 3200 and 40 x 40 = 1600 and

3200 + 1600 = 33,600.D 21, because 800 ÷ 40 = 20 and 40 ÷ 40 = 1 and 20 + 1 = 21.


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Practice



1 Forest Creek Elementary School has 2,160 pencils. The principal wants to give an equal number of pencils to her 24 teachers. She set the division problem up below to determine how many pencils each teacher should receive. Fill out the boxes to help the principal finish her problem.

2,16024

2 Heather is preparing for a triathlon. Every week she jogs 20 miles, swims 15 miles and bikes 25 miles. If Heather jogged for 460 miles, how many miles will she have swam and biked?

Swam ______________

Biked ______________

3 Coach Pool’s softball team is selling pies for a fund-raiser. They need to sell 2,400 pies to reach their goal. If there are 32 members on the softball team, how many pies does each player need to sell to reach their goal?

A 75, because 240 divided by 32 is 70 with a remainder of 16 and 160 divided by 32 is 5.

B 80, because 240 divided by 3 is 80 and 0 divided by 2 is 0, then 80 + 0 = 80.

C 800, because 24 divided by 8 is 8 and 0 divided by 2 is 0 and 0 divided by 2 is 0.

D 40, because 30 x 2 is 60 and 2400 divided by 60 is 40.

You must show your work.Hint:Ask student to use estimation to help determine the solution. Ask students to explain the process or strategies they are using to determine the solution. Make sure students are using place value appropriately in their process.


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Answer Key

AK Divide using Standard AlgorithmComputations and Algebraic Relationships TEKS 5.3C Supporting

Activity1 562 2003 1,344 4 104

Teaching Model1 D

Guided Practice1 902 345 miles, 575 miles3 A

Independent Practice Page 40 SE1 15 packages2 A3 C4 D

Page 41 SE1 A2 343 B

ActivityJust because the concept is division does not mean that all the problems will be division. Watch out!!!

Teaching ModelThe answer choices are justifying the answer given. Watch out, common errors are presented. Make sure the answer is reasonable and addressing the question being asked.

Guided PracticeThree different formats are presented to verify understanding.

Independent Practice Page 41, Question 3 is checking the students understanding of the procedure and a common error that occurs.

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Vocabulary



This TEKS is focused on the conceptual understanding of multiplying decimals. The models need to help students understand the importance of place value when multiplying decimals.

Decimals, Representation, Hundredths, Objects, Pictorial Models, Area Models

How do you represent multiplication using models?How do you use the area model to represent multiplication?Why would you use models to represent multiplication of decimals?

Represent Multiplication of DecimalsComputations and Algebraic Relationships



Category2

TEKS 5.3D

Number and operations. The student applies mathematical process standards to develop and use strategies and methods for positive rational number computations in order to solve problems with efficiency and accuracy. The student is expected to represent multiplication of decimals with products to the hundredths using objects and pictorial models, including area models.


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6th6.3E multiply and divide positive rational numbers fluently

7th7.3B apply and extend previous understandings of operations to solve problems using addition, subtraction, multiplication, and division of rational numbers

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EngagingActivity

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Match the problem to the model.


Name:TEKS 5.3D Supporting

Represent Multiplication of Decimals

2.4 x 5.1

2.2 x 5.1

2.4 x 0.5

0.2 x 0.5

1.3 x 2.7

0.3 x 0.7

1.3 x 0.2

0.3 x 0.2

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TeachingModel

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Students need a variety of experiences with models to help them understand the concept of multiplying decimals. This TEKS is all about modeling to help develop the algorithm, not about applying the algorithm.

How do you represent multiplication using models?Models can be used to show how multiplication is repetitive addition.

How do you use the area model to represent multiplication?Models such as the area model can be used to show partial sums to help understand the importance of place value.Why would you use models to represent multiplication of decimals?Representing multiplication of decimals through models helps to understand the concept of multiplication of rational numbers.

I can represent multiplication of decimals to the hundredths place.


Heather wants to make cookies for her party. The recipe calls for 2.5 cups of flour for each recipe. She wants to make 3.5 recipes. She created the area model below to help her find out how much flour she needs.

How much flour does Heather need to make 3.5 recipes of cookies?

A 8.75 cupsB 6.25 cupsC 6.50 cupsD 5.25 cups


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GuidedPractice


Name:TEKS 5.3D Supporting

1 The area model below represents 0.2 x 0.8.

What is 0.2 x 0.8?

_________________

2 Wynell is making quilts. She uses 2.3 meters of fabric for each quilt. If she makes a quilt for each of her four children, how much fabric does she need?

A 6.3 metersB 1.7 metersC 8.12 metersD 9.2 meters

3 Armando bought 2.6 pounds of grapes. The grapes cost $1.50 per pound.

How much did the 2.6 pounds of grapes cost?

_________________

You must show your work.Hint:Ask students to explain their models they are using to represent multiplication of decimals. Ask students how place value is represented in their model.


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Answer Key

AK Represent Multiplication of Decimals

Computations and Algebraic Relationships TEKS 5.3D Supporting

Activity1 d2 c3 a4 g5 e6 b7 h8 f

Teaching Model1 A

Guided Practice1 0.162 D3 $3.90

Independent Practice Page 44 SE1 0.282 $3.253 5.984 A5 $2.24

Page 45 SE1 0.322 B

ActivityIt is the same concept as using area models for whole number multiplication. Remember: The number going across times the number going down.

Note: The hundred square models, b-0.3x0.7, f-0.3x0.2, and g-0.2x0.5, represent the whole number 1 divided into 100 single squares with each row representing ten 10s. The open squares, c-2.2x5.1, d-2.4x5.1, and e-1.3x2.7, represent whole numbers. The criss-crosses are hundredths. The long slices are tenths.

Teaching Model2.5 going across the top and 3.5 going down. Blank squares are whole numbers. Slices represent tenths. Criss-cross squares represent hundredths.

Guided PracticeQuestion 1: The whole big square is a whole number. All the little squares are hundredths. Each row is tenths. Across the top x Down the sideQuestion 2: The blank squares are whole numbers. 4 x 2.3Question 3: 2.6 x 1.5

Independent Practice Page 44, Question 5 is 2.8 across the top and 0.8 down the side.

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