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Step Up to the TEKS by GF Educators, Inc.

Fourth Grade Math Book

Teacher Edition

Copyright © 2014

www.StepUpTEKS.com

Student:

Teacher:

Classroom:

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Step Up to the TEKS

Fourth Grade Math Book

by GF Educators, Inc.

Table of ContentsNumerical Representations and Relationships Interpret Base-Ten (4.2A) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 Represent Value of Digits (4.2B) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5 Compare and Order-Represent (4.2C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11 Round Whole Numbers (4.2D) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16 Represent Decimals (4.2E) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19 Compare and Order Decimals (4.2F). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24 Relate Decimals to Fractions (4.2G) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29 Determine Decimal on Number Line(4.2H) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34 Represent Sum of Fractions (4.3A) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38 Decompose a Fraction (4.3B). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .42 Determine Equivalent Fractions (4.3C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .46 Represent Comparison of Fractions (4.3D). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .50 Represent Distance from Zero (4.3G). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .56

Computations and Algebraic Relationships Represent/Solve Add/Sub Fractions (4.3E) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60 Evaluate Reasonableness Fractions (4.3F) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .66 Add/Subtract whole and Decimals (4.4A) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .69 Determine Products (4.4B). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .75 Represent Products (4.4C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .79 Multiply Using Strategies/Algorithms (4.4D) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .83 Represent Quotients (4.4E) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .87 Divide Using Strategies/Algorithms (4.4F) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .91 Round 10, 100, or 1,000 (4.4G) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .95 Solve with Fluency (4.4H) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .99 Represent Multi-Step Problems (4.5A). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .105 Represent Input-Output (4.5B) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .112

Geometry and Measurement Solve Problems Perimeter/Area (4.5D) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .118 Identify Attributes (4.6A) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .124 Identify Symmetry (4.6B) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .128 Identify Triangles (4.6C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .132 Classify by Lines and Angles (4.6D) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .136 Determine Measurement of Angles (4.7C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .142 Draw Angles Given Measure (4.7D) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .148 Determine Angle Adjacent Angles (4.7E) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .152 Identify Measurement Units (4.8A) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .156 Convert Measurements (4.8B) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .160 Solve Measurement Problems (4.8C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .164

Data Analysis and Personal Financial Literacy Represent Data (4.9A) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .170 Solve Problems Using Data (4.9B) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .175 Distinguish Between Fixed/Variable Expenses (4.10A) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .179 CalculateProfit(4.10B). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .182 Describe Financial Instructions (4.10E) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .185

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14th Grade Mathematics © 2014

BackgroundInformation

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Student Expectations -

Category

TEKS

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Understanding the TEKS

Essential Question(s)Each place value to the right is multiplied by . Each place value to the left is multiplied by .

Since the number system we use is based on 10, then each place value to the left is multiplied by 10, and each place value to the right is multiplied

by 110 or divided by 10.

Base-Ten, 10 Times, Place Value, Tenth, Hundredths

Student Expectations - Supporting StandardNumber and operations. The student applies mathematical process standards to represent, compare, and order whole numbers and decimals and understand relationships related to place value. The student is expected to 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 left.

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

Grade Student is expected to...

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1stNone

2ndNone

3rd3.2B describe the mathematical relationships found in the base-ten place value system through the hundred thousands place

5th5.2A represent the value of the digit in decimals through the thousandths using expanded notation and numerals

6thNone

TEKS 4.2A

Category1

Describe Base-TenPlace Value

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© 2014 2 4th Grade Mathematics


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1 million = 10 x hundred thousands 1 hundred thousand = 110 x 1 million

1 hundred thousand=10 x ten thousands 1 ten thousand = 110 x 1 hundred thousand

1 ten thousands = 10 x 1 thousands 1 thousand = 110 x 1 ten thousand

1 thousand = 10 x hundreds 1 hundred = 110 x 1 thousand

1 hundred = 10 x tens 1 tens = 110 x 1 hundred

1 tens = 10 x ones 1 ones = 110 x 1 tens

1 ones = 10 x tenths 1 tenths = 110 x 1 ones

1 tenths = 10 x hundredths 1 hundredths = 110 x 1 tenths

Make a desk chart for each student to have on their desk as a reference to learn the relationship between the place values. Write the value of the number in the box that

represents the words. (Multiplying by 110 is the same as dividing by 10.

Base-Ten


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EngagingActivity

A Name:Name:Describe Base-TenPlace Value

Every time you cross over to another place value to the left, it is times 10.

Every time you cross over to another place value to the right, it is times 101

or divided by 10.

1 How many zeros are in 100? So 10 is multiplied 2 times. 10 x 10

2 How many zeros are in 1,000? So 10 is multiplied 3 times. 10 x 10 x 10

3 Each place value to the right is multiplied by110 .

What does 110 of 10 look like in decimals?

4 What does 110 of

110 look like in decimals?

Base-Ten and ZerosThousands Hundreds Tens Tenths Hundredths

10 10 10 10 10

110

110

110

110

110

1,000 100 10 0.1 0.01

X XXX

TEKS 4.2A Supporting

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EngagingActivity

A Name:TEKS 4.2A Supporting


Base-TenNumber 10 Times the

Number

110 of the Number

50

0.3

7,000

26

430

0.3

15,000

360,000

270,000,000

58

496

729,000

0.7

0.3

384,000

472,000

3.7

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TeachingModel

TM I can ...

Thinking Mathematically

Putting the Pieces Together

Make sure the students understand how multiplying by 10 moves the place value to the left. 10 x 10 = 100 100 X 10 = 1,000 1,000 x 10 = 10,000

Make sure the students understand how multiplying by 110 moves the place value to

the right.

100 x 110 = 10 10 x

110 = 1 1 X

110 = 0.1 0.1 x

110 = 0.01

I can interpret the value of a number as 10 times or as 1/10 of a number.

Complete the table.

Number 10 Times the Number

110 of the Number

20 200 2.0

0.8

6,000

700,000,000

0.09

Interpret Base-TenPlace Value

Each place value to the right of the decimal point is multiplied by .

Each place value to the left of the decimal point is multiplied by 10.

110

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GuidedPractice

GP Name:Name:TEKS 4.2A Supporting

Interpret Base-Ten

Place Value

1 If 37,000 is 37 x 1,000, then 68,000 is x 1,000.

2 Complete this statement:

100 is 10 times as much as ___ _.

3 Complete these statements with “10 times as much” or “ 1

10 as much”:

300 is as 30.

0.06 is as 0.6.

5,000 is as 500.

800 is as 8,000.

4 Lanahasbeensavingonlydimesintwodifferentpiggy banks during the month of September. She visited the bank and exchanged her dimes for dollar bills. Complete the following chart.

Number of Dimes

Number of Dollars & Cents

55

76

Explain what you did to change the dimes to dollars?

How many total dollars will she be able to exchange for her dimes?

You must show your work.

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Answer Key

AK Interpret Base-Ten

TEKS 4.2A Supporting

Teaching Model: They must understand the concept of multiplying by 10 when moving one place value to the left.

and multiplying by 110 when moving one place

value to the right. Add-on a zero to the left and take a zero away to the right.

Guided Practice: There are three different formats on this page pertaining to this concept. Make sure the students understand each.

Page 3 SE: “Interpret” is presented in the first problem and must be read carefully. The others pertain to the student’s interpretation

of 10, 110, and

1100 .

Page 4 SE: Reinforce when to multiply by 10 and when to

multiply by 110.

Activity1. 22. 33. 0.14. 0.01

Activity1. 500-52. 70,000-703. 260-2.64. 4,300-43.05. 9-0.096. 150,000-1,5007. 3,600,000-36,0008. 2,700,000,000-27,000,0009. 580-5.810. 4,96011. 49.612. 7,290,000-72,90013. 7-0.0714. 91.30-0.91315. 3,840,000-38,40016. 4,720,000-47,20017. 37-0.37

Teaching Model1. 8 -- 0.082. 60,000 -- 6003. 7,000,000,000 -- 70,000,0004. 0.9 -- 0.09

Guided Practice1. 682. 10

3. 10, 110, 10,

110

4. $5.50, $7.60 Divided by 10 $13 and 1 dime

Independent Practice Page 3 SE1. B2. D3. C4. B

Page 4 SE1. A2. D3. C4. A5. A6. B7. B

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Essential Question(s)What is a digit?What is a number?Whatisthedifferenceinadigitandanumber?

The students need to understand the concept of composing a number by placing ones, tens, and hundreds into one number. Standard Form (526) The concept of decomposing by breaking it down into its value. Expanded Form(500+20+6)Thefluencyandanalysisinvolvedintheprocessskillsmanipulates decomposing through the 5-break down. (772 = 500 + 200 + 50 + 20 + 2) Great for understanding rounding later.

Standard Form, Expanded Form, Word Form, Digit, Decimals, Numerals

Student Expectations - Readiness Standard


Number and operations. The student applies mathematical process standards to represent, compare, and order whole numbers and decimals and understand relationships related to place value. The student is expected to represent the value of the digit in whole numbers through 1,000,000,000 and decimals to the hundredths using expanded notation and numerals.


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1st1.2C use objects, pictures, and expanded and standard forms to represent numbers up to 120.

2nd2.2B use standard, word, and expanded forms to represent numbers up to 1,200.

3rd

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 appropriate


6th None

TEKS 4.2B

Category1

Represent Value of DigitsPlace Value

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EngagingActivity

A Name:TEKS 4.2B Readiness


Standard Form Expanded Form Word Form

1,000,000 + 500,000 + 3,000 +

80 + 3

357,001

four million,six hundred thousand,

two

3,340,110

200,000 + 30,000 + 500 + 40 + 7

seven hundred thousand,fifty-three

482,067

30,000 + 5,000 + 1,000 + 50 + 20 +

7

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TeachingModel

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Numbers can be composed and decomposed. Numbers can be manipulated to

solve problems. Use place value and the ability to manipulate numbers to solve

problems.

What is a digit? A symbol used to make numbers. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

What is a number? An amount or measure: 245, 4, 1.05

What is the difference between a digit and a number? Digits are used to make up numbers.345 is a number. The 3, 4, and 5 are all digits.

I can represent a value of a digit as a number or expanded notation.


1 Which of the following is 413.26 represented in expanded notation?

A 400 + 10 + 3 + 0.02 + 0.06

B 400 + 10 + 3 + 0.2 + 0.6

C 40 + 10 + 3 + 0.2 + 0.06

D 400 + 10 + 3 + 0.2 + 0.06

2 Which of the following is true about the number 6.48?

A The digit 4 has the value of 0.04.

B The digit 6 has the value of 600.

C The digit 8 has the value of 0.08.

D The digit 4 has the value of 40.

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GuidedPractice

GP

1 Create a number with:• a5intheten-thousandsplace• a2inthetensplace• a9inthehundredthsplace

Write digits in the boxes to represent the number.

2 Ella entered this number into her calculator.

17:00

mc m+ m- mr

12,345

What number should she add to this

number to increase the digit in the

thousands place by 6?____________

3 By how much would the value of 4,536 be decreased if the 4 were replaced by a 1?

A 3

B 300

C 3,000

D 30,000

Name:Name:Represent Value of DigitsPlace Value TEKS 4.2B Readiness

4 I am a number. When you switch my ten-thousands digit with my hundreds digit, I become 915,874. What number am I?

A 958,174

B 985,174

C 918,574

D 951,874

5 Which statement about the number 426.18 is not true?

A The digit 2 has the value of 20.

B The digit 8 has the value of 0.08.

C The digit 1 has the value of 10.


6 Which statement about the number 58.47 is true?

A The digit 4 has the value of 40.

B The digit 8 has the value of 80.

C The digit 7 has the value of 0.07.


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Answer Key

AK Represent Value of DigitsTEKS 4.2B Readiness

Activity: Numbers seen in different ways for flexibility.

Teaching Model: Digits make up a number. Digits are symbols, and numbers have value. Use them that way when you talk to the students.

Guided Practice: Several different formats are presented for understanding.

Independent Practice:Several different formats are presented developing fluency and flexibility with numbers.

Activity:1,503,083357,0014,600,0023,340,110230,547700,053482,06726,070

Teaching Model1. D2. C

Guided Practice1. Answers May Vary2. 6,0003. C4. B5. C6. C

Independent Practice Page 7 SE1. B2. D3. B4. A

Page 8 SE1. B2. 259,6953. D4. D5. C

Page 9 SE1. B2. D3. C

Page 10 SE1. B2. A3. B

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Category

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Essential Question(s)The symbol > always points to the number.The symbol < always points away from the number.

The students will be comparing whole numbers only to 1,000,000,000.Ifthefirstdigitsarethesame,thengotothenextplacevalueandcompare.

Example: 34,536-----34,524-----34,523

Compare and Order goes through 100,000 in third grade.

Symbols: <, >, = Greater than , Less than, Digit, Order

Student Expectations - Supporting Standard


Number and operations. The student applies mathematical process standards to represent, compare, and order whole numbers and decimals and understand relationships related to place value. The student is expected to compare and order whole numbers to 1,000,000,000 and represent comparisons using the symbols >, <, or =.


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1.2E use place value to compare whole numbers up to 120 using comparative language.1.2F order whole numbers up to 120 using place value and open number lines.1.2G represent the comparison of two numbers to 100 using the symbols >, <, or =.

2nd2.2D use place value to compare and order whole numbers up to 1,200 using comparative language, numbers, and symbols (>, <, or =).

3rd 3.2D compare and order whole numbers up to 100,000 and represent comparisons using the symbols >, <, or =

5th 5.2B compare and order two decimals to thousandths and represent comparisons using the symbols >, <, or =

6th 6.2D order a set of rational numbers arising from mathematical and real-world contexts

TEKS 4.2C

Category1

Compare and Order and RepresentPlace Value

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EngagingActivity

A

Usethedigitstomake5differentnumbers.

1

Now use these numbers to make these statements true.

2

3

4

5

Name:Name:Compare and Order and RepresentPlace Value TEKS 4.2C Supporting

4 6 5

Greater Than, Less Than

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I can compare and order whole number through 1,000,000,000.

Compare and Order-RepresentPlace Value

A group of numbers is shown below.

254,374,728 254,375,228 254,385,228 254,375,238

Which statement about two of these numbers is true?

A 254,385,228 = 254,375,228, because 228 = 228

B 254,374,728 > 254,375,228, because 728 > 228

C 254,375,228 < 254,375,238, because 28 < 38

D 254,374,728 > 254,375,238 because 728 > 238

The students need to understand place value and to look carefully at the two largest place values of the numbers being compared. If the first numbers are the same, then look at the second and keep going until the numbers are different and can be compared.

The symbol > always points to the smallest number.

The symbol < always points away from the largest number.Sa

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GuidedPractice

GP Name:Name:Compare and Order-RepresentPlace Value TEKS 4.2C Supporting

1 Which pair of numbers is true?

A 5,109 > 5,190B 7,805 < 7,850C 7,805 > 7,981D 5,109 = 5,190

2 Four people collect baseball cards as shown on the table.

Name Baseball Cards

Charles

Jose

Juan

James

352

225

265

275

Since Jose had more cards than anyone else, he decided to give 55 of his cards to James. Which statement is true after Jose gave away 55 of his cards?

A James' cards < Juan's cardsB Charles' cards > James' cardsC James' cards > Juan's cardsD James' cards > Jose's cards

3 Charlie manages an amusement park. On July 2nd there were 794,329 tickets sold. On July 3rd there were 6,978,310 tickets sold. On July 4th there were 35,439,301 people that enjoyed the park. On July 5th, a Sunday, 6,898,739 people came. Compare the number of tickets sold each day using <, >, and =.


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Answer Key

AK Compare and Order-RepresentTEKS 4.2C Supporting

ActivityAnswer may vary

Teaching Model1. C

Guided Practice1. B2. C3. 794,329 < 6,978,310 6,978,310 < 35,439,301 35,439,301 > 6,898,739

Independent Practice Page 13 SE1. <, >, >, <, <2. D3. D4. C5. D6. D7. D

Page 14 SE1. C2. B3. D4. D

Page 15 SE1. A2. D3. >, <, >, <4. B5. C6. >, <, >, <

Teaching Model: The digits in the place values are the same until the ten thousands place. The students must keep comparing until they reach numbers that are different.

Guided Practice: Watch out for problem two. The changes must be made before they can be compared.

Independent Practice:Look carefully at the digits and the place values each represents.

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Essential Question(s)What strategy do you use when rounding?

The students are expected to be able to round place value to the hundred thousands place.

Round, Nearest

Student Expectations - Supporting StandardTEKS 4.2D

Category1


Number and operations. The student applies mathematical process standards to represent, compare, and order whole numbers and decimals and understand relationships related to place value. The student is expected to round whole numbers to a given place value through the hundred thousands place.


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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

5th5.2C round decimals to tenths or hundredths

6thNone

Round Whole NumbersPlace Value

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EngagingActivity

A Name:Round Whole NumbersPlace Value TEKS 4.2D Supporting

Round each number to the place value specified.

1 Round 271,688 to the nearest ten thousand.

2 Round 2,797,559 to the nearest hundred thousand.

3 Round 7,589,307 to the nearest thousand.

4 Round 254,580 to the nearest hundred.


6 Round 473,582 to the nearest ten.

7 Round 973,197 to the nearest ten thousand.

8 Round 77,591 to the nearest thousand.


10 Round 3,745,890 to the nearest ten thousand.

11 Round 286,241 to the nearest ten.

12 Round 3,456,123,765 to the nearest hundred thousand.

Rounding

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Make sure the students can verbalize the strategy they are using when rounding.

Determine the approach and strategy to rounding.

What strategy do you use when rounding? Answers may vary

When do we usually need to round numbers? When we want a quick, but not exact amount--

I can round numbers to a specific place value.Round Whole Numbers

Place Value

The cost of tuition at Cornell University is $43,000 per year when rounded to the

nearest thousand. What is the greatest possible amount the tuition could be before

it was rounded? What is the least possible amount the tuition could be before it was

rounded?

Greatest

Least

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GuidedPractice

GP Name:Name:Round Whole NumbersPlace Value TEKS 4.2D Supporting

1 Mrs. Smith’s class is learning about healthy eating habits. The students learned that the average child should consume about 12,000 calories each week. Kerry consumed 12,748 calories last week. Tyler consumed 11,702 calories last week. Round each to the nearest thousand.

12,748

11,702

2 A pilot wanted to know about how manykilometersheflewonhislast3flights.FromNYCtoLondonheflew5,572 kilometers. Then, from London toBeijingheflew8,147kilometers.Finally,heflew10,996kilometersfromBeijingbacktoNYC.Roundeach number to the nearest hundred kilometers.

3 It takes 39,090 gallons of water to manufacture a new car. Sammy thinks that it should be rounded up to 40,000 gallons. Susie thinks it should be rounded to 39,000 gallons. Who rounded to the nearest thousand, Sammy or Susie?

Explain your answer.

4 Marsha’s brother wanted help with the firstquestiononhishomework.Thequestionaskedthestudentstoround128,902 to the nearest thousand and then to explain the answer. Marsha’s brother thought that the answer was 128,000. Was his answer correct?

A Yes,because128,902roundedtothenearest thousand is 129,000.

B No, because 128,902 rounded to the nearest thousand is 129,000.

C Yes,because128,902roundedtothenearest thousand is 128,000.

D No, because 128,902 rounded to the nearest thousand is 130,000.

5 Louise’s family went on vacation to Disney World. Their vacation cost $5,990. Sophia’s family went on vacation to Niagara Falls. Their vacation cost $4,720. Both families budgeted about $5,000 for their vacation. Round to the nearest thousand, whose family stayed closer to the budget?

A Louise’s family because $5,990 rounded to the nearest thousand is $5,000.

B Louise’s family because $5,990 rounded to the nearest thousand is $6,000.

C Both Louise and Sophia because $4,720 and $5,990 would both be rounded $5,000.

D Sophia’s family because $4,720 rounded to the nearest thousand is $5,000 and $5,990 would be rounded to $6,000.

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Answer Key

AK Round Whole Numbers

Activity1. 270,0002. 2,800,0003. 7,589,0004. 254,6005. 2,600,0006. 473,5807. 970,0008. 78,0009. 1,500,00010. 3,750,00011. 286,24012. 3,500,000

Teaching Model1. 43,499---42,500

Guided Practice1. 13,000--12,0002. 5,600--8,100--11,0003. Susie--39,000 Look at

hundred place4. B5. D

Independent Practice Page 18 SE1. A2. B3. D4. 25,0005. 7,0006. 500,0007. 160,0008. 94,0009. 67,000

TEKS 4.2D Supporting

Activity:Look carefully at the place value being asked to round.

Teaching Model: This problem gives the student the opportunity to explain the range for rounding this number to the nearest thousands.

Guided Practice: Read each answer choice carefully and interpret it fully.

Independent Practice:With rounding, just look at the number before the one being rounded, then make your decision.

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Essential Question(s)

Students should actually use hands-on manipulatives to model decimals. Students are not expected to represent decimals smaller than hundredths.

Concrete and Visual Models

Whatisthevalueofeachsmallsquareintheonelargesquare?How can a model represent a decimal?

Student Expectations - Supporting StandardTEKS 4.2E

Category1


Number and operations. The student applies mathematical process standards to represent, compare, and order whole numbers and decimals and understand relationships related to place value. The student is expected to represent decimals, including tenths and hundredths, using concrete and visual models and money.


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Represent DecimalsDecimals

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EngagingActivity

A

Fill in the grid to show the decimal.

0.8 2 tenths 1 1 and 7 tenths

0.23 1 and 37 hundredths 75 hundredths 0.62

Write the decimal represented by the grid.

Name: TEKS 4.2E Supporting


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The zero is very important. It can change 0.7 (tenths) to 0.07 (hundredths).

Require the students to place the zero in the ones place if there are no whole numbers.

What is the value of each small square in the one large square?

Each small square represents 1

100 of the large square.

How can a model represent a decimal?Decimals using place value of 1/10 or 1/100 can be represented using a 10

grid or a 100 grid model.

Which decimal tells how much is shaded?

A 75 B 7.5 C 0.75 D 0.075

I can represent a decimal from a model.Represent DecimalsDecimals

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GuidedPractice

GP Name: TEKS 4.2E Supporting


1 The model is shaded to show what number?

2 The model is shaded to show what number?

3 Which answer tells how much is shaded?

A 1.06B 1.4C 1.6D 10.4


Caution: Be sure students are counting all of the shaded squares out of 100 total squares.

Caution: Be sure students are counting all of the shaded squares out of 10 total squares.Sa

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Answer Key

AK Represent DecimalsTEKS 4.2D Supporting

Teaching Model: The large square represents the whole number 1. It is then divided into hundredths, so any part would be less than one: 0.01, 0.02, etc. The rows are tenths. The student could count the rows for the tenths place and then the individual boxes for the hundredths place.

Guided Practice: A row represents tenths. A square represents hundredths.

Independent Practice: Page 23: Read carefully. Which grid is shaded to represent a decimal greater than 0.89?

ActivityVisual Evaluation0.501.11.010.700.070.46

Teaching Model1. C

Guided Practice1. 1.02. 0.393. B

Independent Practice Page 21 SE1. D2. Visual Evaluation3. Visual Evaluation

Page 22 SE1. A2. C3. B4. C5. B

Page 23 SE1. D

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Zerosmakeagreatdifferenceinnumbers.Evenifitdoesnothaveavalue,itrepresentsa place. They are really important in decimals. 0.8 and 0.08 are not even close to being equal.Itwouldbelikesayingthat80isequalto800ontheothersideofthedecimalpoint.

Tenths, Hundredths, Decimal, Models

Whatisthedifferenceinthetwodiagramsabove?Each model represents a value .



Number and operations. The student applies mathematical process standards to represent, compare, and order whole numbers and decimals and understand relationships related to place value. The student is expected to compare and order decimals using concrete and visual models to the hundredths.


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5th5.2B compare and order two decimals to thousandths and represent comparisons using the symbols >, <, or =

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

TEKS 4.2F

Category1

Compare and Order DecimalsDecimals

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EngagingActivity

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Convert each model into a decimal, then order the decimals from least to greatest.

1 Convert

Order

2 Convert

Order

Name:TEKS 4.2F Supporting


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Students need to be able to visually compare models to determine order. Hands-on manipulatives should be used in class.

What is the difference in the two diagrams above?The first model shows hundredths and the second model shows tenths.

Each model represents a value less than one.

I can compare and order decimals using models.


Which model represents a greater value: B or C? Explain your thinking.

B C

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GP Name:TEKS 4.2F Supporting


1 Naomi has an amount of money that wold make the comparison below true.

>

Which amount of money would make the comparison true?

A

B

C

D


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UARTER DOLLAR

E PLURIBUS UNUM

L I B E R T Y

P

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A

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UARTER DOLLAR

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L I B E R T Y

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IN GOD WETRUST

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A

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UARTER DOLLAR

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UN

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A

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UARTER DOLLAR

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L I B E R T Y

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IN GOD WETRUST

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UARTER DOLLAR

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L I B E R T Y

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L I B E R T Y

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IN GOD WETRUST

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L I B E R T Y

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L I B E R T Y 1951

IN

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A

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UARTER DOLLAR

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L I B E R T Y 1951

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GuidedPractice

GP Name:TEKS 4.2F Supporting


You must show your work.CBA D

1 List these models in order from least to greatest.

A A, B, C, D

B D, C, B, A

C D, B, C, A

D A, C, B, A

CBA D

Statement 1: A < CStatement 2: D > BStatement 3: C < B

2 Which statements are true?

A Statement 2 only

B Statement 1 & 3 only

C All of the statements

D None of the statements

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Answer Key

AK Compare and Order DecimalsTEKS 4.2F Readiness

Teaching Model: The rows represent tenths. The squares represent hundredths.

Guided Practice: Money represents decimals. Coins represent amounts under a dollar. They are coins that represent 0.10, 0.25, 0.05, 0.01.

There are ten hundredths doing across and ten hundredths going down so it does not matter if the row is across or down.

Independent Practice: Understand that each row that represents a tenth, 0.1, is made up of 10 hundredths, 0.10. 0.1 = 0.10

Read carefully on Page 28 and do what is asked. Analyze the results on the next question.

Activity1. Convert: 0.12, 0.6, 0.04 Order: 0.6, 0.12, 0.042. Convert: 0.61, 0.7, 0.75 Order: 0.75, 0.7, 0.61

Teaching Model1. B B has 0.04 more than C.

Guided Practice1. B

Guided Practice1. B2. B

Independent Practice Page 27 SE1. C2. B3. D4. C5. D6. B

Page 28 SE1. Visual Evaluation2. A3. D

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Essential Question(s)How do fractions and decimals relate? Why is place value important?

Students should have an understanding of place value for decimals and how it relates to a fractional piece of 10 or 100.

Tenths, Hundredths

Student Expectations - Readiness Standard


Category1

TEKS 4.2G

Number and operations. The student applies mathematical process standards to represent, compare, and order whole numbers and decimals and understand relationships related to place value. The student is expected to relate decimals to fractions name tenths and hundredths.


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1st None

2nd2.2Fnamethewholenumberthatcorrespondstoaspecificpointon a number line.

3rd

3.3Arepresentfractionsgreaterthanzeroandlessthanorequaltoone with denominators of 2, 3, 4, 6, and 8 using concrete objects and pictorial models, including strip diagrams and number lines3.3B determine the corresponding fraction greater than zero and lessthanorequaltoonewithdenominatorsof2,3,4,6,and8givenaspecifiedpointonanumberline

5th None

6th

6.2B identify a number, its opposite, and its absolute value6.2C locate, compare, and order integers and rational numbers using a number line6.5Cuseequivalentfractions,decimals,andpercentstoshowequalpartsofthesamewhole

Relate Decimals to FractionsDecimals

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EngagingActivity

A

Describe the shaded portion of each grid as a fraction with a denominator of 100, asasimplifiedfraction,andasadecimalnumber.

Fraction with adenominator of 100:

Simple fraction:

Decimal number:


Simple fraction:

Decimal number:


Simple fraction:

Decimal number:


Simple fraction:

Decimal number:

Name:TEKS 4.2G Readiness


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How do fractions and decimals relate? A fraction is another form of writing a decimal and a decimal is another form of a decimal. Both represent a part of the whole.

Why is place value important? Place value determines the part of the whole needed.

Students should be able to use the beads in the problem above to represent a fraction or a decimal out of the whole necklace. Students should relate these 20 beads to how many out of 100 beads. The understanding of place value should then be used to determine the decimal.

I can relate fractions and decimals to each other.

Susan is making a beaded necklace. She gathered 20 beads for the necklace. She has 5 yellow, 5 red, 3 blue and 7 green beads.

What fraction represents the number of red beads?

What decimal represents the number of red beads?

What fraction represents the number of blue beads?

What decimal represents the number of blue beads?

What fraction represents the number of green beads?

What decimal represents the number of green beads?

What fraction represents the number of yellow beads?

What decimal represents the number of yellow beads?


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GuidedPractice

GP Name:TEKS 4.2G Readiness


1 The models below are shaded to represent four differentfractions.

37100

410

510

68100

Which decimal is not represented by one of these models?

A 0.037B 0.68C 0.5D 0.4

2 The models below are shaded to represent the part of pizzas eaten by the Hernandez family.

Which fraction and decimal represent the part of these pizzas eaten by the Hernandez family?

A 1710 and 0.17

B 1 710 and 1.7

C 1 720 and 1.7

D 1 710 and 1.07


Caution: Make sure students are counting the shaded squares out of the total 10 or 100.

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Answer Key

AK Relate Decimals to FractionsTEKS 4.2G Readiness

Teaching Model: The total beads is 20 so this represents the denominator.

Guided Practice: Read carefully problem 1: not.Read carefully problem 2: Which fraction of the pizza was eaten? The shaded pieces are the eaten pieces.

Independent Practice:Read carefully and analyze each problem before answering.

Activity1. 50/100, 1/2, 0.502. 10/100, 1/10, 0.13. 40/100, 4/10, 0.44. 76/100, 7/10 + 6/100, 0.76

Teaching Model1. 5/202. 0.253. 3/204. 0.155. 7/206. 0.357. 5/208. 0.25

Guided Practice1. A2. B

Independent Practice Page 31 SE1. C2. D3. C4. C5. A6. A

Page 32 SE1. B2. C3. 1.2 > 0.464. A5. Visual Evaluation6. 45/1007. 45 cents

Page 33 SE1. A2. B Sa

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Essential Question(s)How do you represent a tenth on a number line? How do you represent a hundredth on a number line?

Students are expected to determine the corresponding decimal point to the tenths and hundredths place on a number line.

Corresponding,Specified



Number and operations. The student applies mathematical process standards to represent, compare, and order whole numbers and decimals and understand relationships related to place value. The student is expected to determine the corresponding decimal to thetenthsorhundredthsplaceofaspecifiedpointonanumberline.


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3rd3.3Cexplainthattheunitfraction1/brepresentsthequantityformed by one part of a whole that has been partitioned into b equalpartswherebisanon-zerowholenumber

5thNone

6thNone

TEKS 4.2H

Category1

Determine Decimal on Number LineDecimals

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EngagingActivity

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Write the correct letter on the blank line next to each decimal.

0 1 2

a c e g i k

ljhfdb

0.38 c 1.16 1.75 0.54

0.70 1.47 0.02 1.50

1.25 0.25 1.83 0.91

5 6 7

5.2 a b c d

ef

6.75 6.99 5.7

6.3 5.45

1.

11.

10.

9.

8.

7.

6.

5.

4.

3.

2.

12.

1.

2.

3.

4.

5. 6.

Place the letter for the each number on the number line.

0 1 2

a c e g i k

ljhfdb

0.38 c 1.16 1.75 0.54

0.70 1.47 0.02 1.50

1.25 0.25 1.83 0.91

5 6 7

5.2 a b c d

e f

6.75 6.99 5.7

6.3 5.45

A 5.2

B 6.75

C 6.99

D 5.7

E 6.3

F 5.45

Name:TEKS 4.2H Supporting


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Students need to be able to graph on a number representing tenths and hundredths. In looking at the number lines above, students can count by tenths to find the location of U.

How do you represent a tenth on a number line? To represent a tenth, one unit needs to be divided into 10 pieces.

How do you represent a hundredth on a number line? To represent a hundredth, one unit needs to be divided into 100 pieces or the label needs to show each unit.

I can determine the placement of a decimal on a number line.


Point U best represents what number?

30.0 30.3

U

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GP Name:TEKS 4.2H Supporting


0 112

A B C D

1 Which letter best represents 0.2?


0 112

A B C D



5 Which point on the number line best represents 5.3?

P Q R S

4 5 6 7

A P C R

B Q D S


Hint: Additional lines may be added to the number line for more precise fractional pieces.

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Answer Key

AK Determine Decimal on Number LineTEKS 4.2H Supporting

Activity:Watch out for numbers like 0.25 or 0.75. These would be between markers.

Teaching Model: Each marker is a tenth.

Guided Practice: Look for closeness to 0, 1/2, 1 as in question 1, 2, 3 and 4.

Independent Practice:Look for closeness to 0, 1/2, 1 or look at tenths.

Activity1. c2. e3. h4. g5. i6. b7. k8. a9. l10. d11. j12. fA, F, D, E, B, C

Teaching Model1. 30.7

Guided Practice1. A2. B3. D4. C5. C

Independent Practice Page 36 SE1. C2. B3. 9.94. 19.25. U6. A7. B

Page 37 SE1. Visual Evaluation2. A3. C4. A5. D6. C Sa

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When paired with revised SE 4(1)(D), students may represent a/b as a sum offractions 1/b using concrete and pictorial models, which includes improper fractionswhen a>b.

Sum



Number and operations. The student applies mathematical process standards to represent and generate fractions to solve problems. The student is expected to represent a fraction a/b as a sum of fractions 1/b, where a and b are whole numbers and b > 0, including when a > b.


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3rd3.3D compose and decompose a fraction a/b with a numerator greaterthanzeroandlessthanorequaltobasasumofparts1/b

5thNone

6th6.2E extend representations for division to include fraction notation suchasa/brepresentsthesamenumberasa÷bwhereb≠0

TEKS 4.3A

Category1

Represent Sum of FractionsFractions

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EngagingActivity

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Draw a model that represents the given fraction as the sum of its unit fractions. Then write the related addition problem.

Example:

15 +

15 +

15 +

15 =

45

1 23

2 57

3 311

4 512

5 53

Name:TEKS 4.3A Supporting

15

15

15

15

15


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Students need to understand how a fraction can be represented using the sum of its unit fractions. Using models or pictures can reinforce this understanding.

I can represent a fraction a/b using the sum of unit fractions.

How can I represent a fraction using the sum of unit fractions?Models or pictures can be used to demonstrate the decomposition of fractions into the sum of its unit fractions.

Why is a unit fraction important?The unit fraction represents the base unit of a fraction.

What models will I use to represent the sum of a fraction?Fraction strips work well to represent the sum of a fraction.

Look at the strip diagram below.

What is the fraction represented by the shaded area?

What is the fraction that is represented by each piece of the shaded area?

Write an addition problem that represents this shaded area.


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GuidedPractice

GP Name:TEKS 4.3A Supporting


Look at the number line below.

0 1

1 Write the fraction represented by the model.

2 Write the fraction representation for each piece.

3 Write the related addition problem.

Look at the number line below.

0 1

4 Write the fraction represented by the model.

5 Write the fraction representation for each piece.

6 Write the related addition problem.


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Answer Key

AK Represent Sum of FractionsTEKS 4.3A Supporting

Teaching Model: Emphasize unit fractions as in 1/6

Guided Practice: Determine the unit fraction first. (How many sections are between 0 and 1?)On the first problem, recognize that 2/8 is equal to 1/4. Recognize that 2/4 or 4/8 equals 1/2.

Independent PracticeDetermine the unit fraction and interpret each fraction that is being added to find the sum.

ActivityVisual Evaluation

Teaching Model1. 5/6, 1/6,1/6 + 1/6 + 1/6 + 1/6 + 1/6

Guided Practice1. 2/4, or 4/82. 1/4 or 1/83. 1/4 + 1/4 or1/8 + 1/8 + 1/8 + 1/84. 5/65. 1/66. 2/6 + 3/6

Independent Practice Page 40 SE1. B2. A3. C

Page 41 SE1. A

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Vocabulary



This SE focuses on students being expected to express 5/2=3/2+2/2; 5/2=1/2+4/2; 5/2=2/2+2/2+1/2; and 2 ½=1+1+1/2.Students are expected to use concrete models such as fraction strips or fractionsbars and pictorial models such as strip diagrams and to record the appropriatenumber sentences.

Decompose



Number and operations. The student applies mathematical process standards to represent and generate fractions to solve problems. The student is expected to decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations.


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1stNone

2ndNone

3rd3.3D compose and decompose a fraction a/b with a numerator greaterthanzeroandlessthanorequaltobasasumofparts1/b

5thNone

6thNone

TEKS 4.3B

Category1

Decompose a FractionFractions

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Name:

EngagingActivity

A Name:TEKS 4.3B Supporting

1 Decompose 57 inthreedifferentways.

Example: 27 +

37 =

57

17 +

47 =

57

37 +

27 =

57

2 Decompose 712inthreedifferentways.

3 Decompose 5 9 inthreedifferentways.





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Name: Teaching

Model

TM I can ...



Students should draw a model for each number sentence to describe their thinking for a decomposition of a fraction into different parts.

Why would you want to decompose a fraction?By decomposing of fractions, you can recognize equivalent parts of fractions.

How do we know what the sum of a fraction is equal to?You can look at the parts to recognize equivalence.

I can decompose a fraction into the sum of fractions.


Drawapicturetoshowwhytheseequationsaretrue.Explainyourreasoning.

78 = 4

8 + 38

2 14 = 3

4 + 64

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Name:

GuidedPractice

GP Name:TEKS 4.3B Supporting


1 Use the number line below to show 78 +

18 +

38 =

118 .

0 1

2 Which one of these addition sentences represents the fraction 85 ?

A 32 +

53

B 45 +

45

C 23 +

62

D 83 +

82

3 Draw a model to represent the given sum of a fraction problem.

45 = 1

5 + 25 + 1

5


118 = 7

8 + 18 + 3

8


1512 = 8

12 + 312 + 4

12

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Answer Key

AK Decompose a FractionTEKS 4.3B Supporting

Teaching Model: Question 2:The examples from the specifications are both proper and improper fractions as well as mixed numbers. Have the students draw out each fraction into a strip diagram so they may visual see the whole and fractions.

Guided Practice: Question 1: Decompose 5/14 into 2 fractions Question 2:Remember, only the numerators are added.Question 4: What does 1 represent? 15/15

Independent Practice:Recognize that the fractions are coming from different wholes.

Activity1. Example2. 2/12 + 5/12 or 6/12 + 1/12 etc.3.-6. Answers may vary

Teaching Model1. Answer may vary

Guided Practice1. Visual Evaluation 2. B3. Visual Evaluation4. Visual Evaluation5. Visual Evaluation

Independent Practice Page 44 SE1. 2/14 + 3/14, 1/14 + 4/14, 3/14 + 2/14, 4/14 + 1/142. C3. 5/7 + 5/7, 8/7 + 2/7, 6/7 + 4/7, etc.4. C

Page 45 SE1. B2. A

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