AUSD Grade 5 Units 1 - 2 Study Guide - WCCUSD

AUSD Grade 5 Units 1 - 2 Study Guide

of 12 MCC@WCCUSD (AUSD) 09/06/14

= 7 + 98= 14 ÷ 2 + (49)× 2 = 105= 14 ÷ 2 + (49)× 2

1 Evaluate the following expression: 14 ÷ 2 + (7 × 7)× 2

5.OA.1

1´ Evaluate the following expression:

753+ (3+ 2)× (10 − 3)

5.OA.1

Y

ou

Try

!

1´´ Gael says that (4 − 2)× (6 + 4) is 20. Ann says that (4 − 2)× (6 + 4) is 12. Who is correct?

5.OA.1

Y

ou

Try

!

2 Write the numerical expression. Describe the relationship between both values

the quotient of forty-five and the difference of twenty-four and nine

the quotient of forty-five and the difference of twenty-four and nine The values in 45 ÷ (24 − 9) relate to each other in that 45 will be divided by the value of (24 – 9). 5.OA.2

2´ Write the numerical expression.

twice the sum of two and three

5.OA.2

Yo

u T

ry

2´´ Use words to describe the expression

4 × 6 + 8( ) and how the two factors are related.

5.OA.2

Y

ou

Try

÷ = 45 24 − 9( )

14 ÷ 2 + (7 × 7)× 2

= 14 ÷ 2 + (49)× 2= 14 ÷ 2 + (49)× 2 = 7 + 49 × 2= 14 ÷ 2 + (49)× 2 A

D M

G E

S



3 Determine the ordered pairs for the baseball field ( ) and the soccer field( ). If Casey has to go from baseball to soccer practice, how far must he travel?

5.G.1 & 5.G.2

3´ Which ordered pair would come next in the

sequence?

(1 , 3) ; (2 , 6) ; ? Plot the ordered pairs on the coordinate grid below.

5.G.1 & 5.G.2

Yo

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ry!

3´´ Plot the following locations on the

coordinate grid.

S: school (8 , 9) H: home (0 , 5)

P: post office (8 , 5) What is the distance (in units) from school to the home if you must stop at the post office on the way? Explain.

5.G.1 & 5.G.2

Yo

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ry!

x

y

x

y

x

y

The baseball field is located at (7 , 8) and the soccer field is located at (3 , 8). They both share the same y-coordinate so in order to find the distance between the two locations just find the difference in the x-coordinates.

7 − 3= 4 units ∴The distance from baseball to soccer practice is 4 units.



4 Complete the Place Value Chart below.

Thousands Hundreds Tens ONES Tenths Hundredths Thousandths 1,000. 100. 10 1. 0.1 a) 0.001 1,0001

1001

101

11

110

1100

b)

$1,000.00 $100.00 10.00 $1.00 c) $0.01 $0.001 a) 0.01

b) 11000

c) $0.10

5.NBT.1

4´ Match the value in the list below to its

equivalent in the box.

I. 0.02

II. $2.00

III. 2

1000

IV. 200

5.NBT.1

Yo

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ry!

4´´ What is 710 ×10

written in standard form?

Explain your thinking.

5.NBT.1

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PLACE VALUE CHART ÷ by 10 (smaller) × by 10 (larger)

This is in the hundredths place, 2 place values to the right of ones place. That means 1 must be divided by 2 tens or 1

10 ×10= 1100

= 0.01 .

The thousandths place is 3 place values to the right of 1, so 1 must be divided by 3 tens. 1

10 ×10 ×10= 11000

This blank is one spot to the right of the ones place value below 0.1. 0.1 is 1

10, and 1

10of a dollar is one dime or $0.10.

A) 2001

B) 2. C) 2100

D) $0.002

A B C D

A B C D

A B C D

A B C D



5 Express the number in the different representations given. A) Write forty-two thousand, thirty-five in standard form, expanded form, and exponential form.

Standard: 42,035 Expanded: 40,000 + 2,000 + 30 + 5 Exponential: 4 ×104( ) + 2 ×103( ) + 3×10( ) + 5 ×1( )

B) Write 208.305 in word form, expanded form, and expanded (powers of ten) form. Word: two hundred eight and three hundred five thousandths Expanded: 200 + 8 + 0.3 + 0.05

Expanded (powers of ten): (2 ×100)+ (8 ×1)+ 3× 110

⎛⎝⎜

⎞⎠⎟ + 5 × 1

1000⎛⎝⎜

⎞⎠⎟

5.NBT.2/5.NBT.3A

5´ Write 3,521.48 in at least 3 ways.

5.NBT.2/5.NBT.3A

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5´´ How is exponential form related to the expanded (powers of ten) form?

5.NBT.2/5.NBT.3A

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6 Below is a problem from Megan’s homework. Did she complete the inequalities correctly? How do you know? 0.73 0.138 0.17 0.9

ONES Tenths Hundredths Thousandths 0. 7 3 0. 1 3 8

∴No, Megan was only partly correct. When comparing whole numbers she had the correct answers, but she made mistakes with the decimals.

5.NBT.3B

6´ Complete the number sentences listed

below using < , =, >. 0.7 0.700 0.8 0.62 0.475 0.57

5.NBT.3B

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6´´ Describe a method for comparing decimal numbers. Give an example.

5.NBT.3B

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<

17 9 but 0.17 0.9

73 138 but 0.73 0.138

Megan’s Homework

>

<

>

<

>

< = >

< = >

< = >



7 Round to the nearest hundredths. 775.116 “round up” 775.116 775.110 775.115 775.120

5.NBT.4

7´ Mark all the numbers below that can be

rounded to 3.25

5.NBT.4

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7´´ Suppose we round 3.405 to the nearest whole number. Why is the digit in the tenths place important?

5.NBT.4

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A

B

C

D

3.244

3.247

3.253

3.255

775.116

775.110

775.120

∴775.116 rounded to the nearest hundredth is 775.120.



8 Multiply three different ways:

5.NBT.5

8´ Multiply 3 ways: 91× 28

5.NBT.5

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8´´ There are usually 20 school days in a month. Rigo has gymnastics practice every day after school for 75 minutes. How many minutes does he practice every month?

5.NBT.5

Yo

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Standard Algorithm

+2 +1

2881 + 2580

43 x 67

301

40 + 3 2,400 180 280 21

60 + 7

2400 280 180 + 21

2881

Generic Rectangle

2400 280 180 + 21

2881

43 x 67

= 60 x 40 = 7 x 40 = 60 x 3 = 7 x 3

Partial Products

43× 67

1



9 There were 1,426 sheets of paper in Ms. Ruben’s office. She needed to divide them equally between her 46 employees. How many sheets of paper did each employee receive?

5.NBT.6

9´ Divide two ways: 2106÷ 9

5.NBT.6

Yo

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9´´ A farmer collected 1,183 eggs. He will put

them in cartons that will hold a dozen (12) eggs each. How many cartons can he fill? Explain your answer.

5.NBT.6

Yo

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ry!

End of Study Guide

Stacking Method

0 - 46

46

46 1426

30 1 31

- 1380

= 46 ×1

- 460

46 1426 - 460 = 46 ×10

966 - 460 = 46 ×10

506 = 46 ×10

- 46 46

0

31

Partial Quotients

0

46 - 138

- 46

46 1426 3 1

Standard Algorithm

∴Each employee would receive 31 sheets of paper if Ms. Ruben distributed them equally.



You Try Solutions: These are the correct answers with possible student strategies and explanations. Student strategies and explanations may vary; however, strategies should demonstrate a thorough understanding of mathematical concepts and explanations should clearly communicate student thinking. 1´ Evaluate the following expression:

1´´ Gael says that (4 − 2)× (6 + 4) is 20. Ann says that (4 − 2)× (6 + 4) is 12. Who is correct?

2´ Write the numerical expression.

twice the sum of two and three

= 2 × ( 2 + 3)

2´´ Use words to describe the expression 4 × 6 + 8( ) and how the two factors are related. The two factors are 4 and (6+8) they are related in that you have the sum of 4 groups of (6+8). You could also say that you have the sum of 14 fours because (6+8) is 14.

753+ (3+ 2)× (10 − 3)

= 753+ (5)× (7)

= 25 + 5 × 7 = 25 + 35 = 60

A D M

G E

S = (2)× (10)

= 20

(4 − 2)× (6 + 4)

Gael’s Work Ann’s Work

= 4 − (12)+ 4

= 12

(4 − 2)× (6 + 4)

= 4 − (12)+ 4

∴Gael is correct because he followed the order of operations and evaluated the groups first. I think Ann multiplied first and then found an incorrect zero pair. This gives her the incorrect answer. She sees the minus sign going with the second 4 instead of the 12.



3´ The pattern for the x-coordinate is +1 and the pattern for the y-coordinate is +3. ∴ The next ordered pair in the sequence would be (3, 9).

3´´ The distance from school to the post office is 4 units. The distance from the post office to home is 8 units. ∴ The total distance would be 12 units because you would need to combine the two shorter distances.

4´ Match the value in the list below to its

equivalent in the box.

I. 0.02

II. $2.00

III. 2

1000

IV. 200

4´´ What is 710 ×10

written in standard form?

Explain your thinking.

7

10 ×10 = 0.07

7

10 ×10 is 7

100 but with a decomposed

denominator. Two place values to the right of the decimal and is the hundredths place. ∴The fractions are also equivalent to 0.07.

Which ordered pair would come next in the sequence? (1,3) ; (2,6) ; ? Plot the ordered pairs on the coordinate grid.

x

y

0 1 2 3 4 5 6 7 8 9

1

2

3 4

5

6

7

8

9

A) 2001

B) 2. C) 2100

D) $0.002

A B C D

A B C D

A B C D

A B C D

Plot the following locations on the coordinate grid. S: school (8,9) H: home (0,5) P: post office (8,5)

What is the distance (in units) from school to home if you must stop at the post office on the way? Explain.

x

y

0 1 2 3 4 5 6 7 8 9

1

2

3 4

5

6

7

8

9



5´ Write 3,521.48 in at least 3 ways.

Word Form: Three thousand, five hundred twenty-one and forty-eight hundredths Expanded Notation: 3,000 + 500 + 20 + 1 + 0.4 + 0.08 Expanded Form (powers of ten):

5´´ How is exponential form related to the expanded (powers of ten) form?

6´ Complete the number sentences listed below

using < , =, >. 0.7 0.700 0.8 0.62 0.475 0.57

6´´ Describe a method for comparing decimal numbers. Give an example. One method is a number line. Create an open number line. Plot both decimals and then determine which is larger. 0.475 0.57

7´ A number changed to 3.25 after it was

rounded. Mark all of the numbers below that 3.25 could have been originally.

7´´ Suppose we round 3.405 to the nearest whole number. Why is the digit in the tenths place important? The digit in the tenths place is important because that digit tells how many parts of a whole you have. From that digit you can compute how much you need to get to the next whole number. If it is 0.5 or greater, then you change the digit in the ones place to the next digit in ascending order. Because the digit is less than 0.5 the digit in the ones place remains the same.

3×1000( ) + 5 ×100( ) + 2 ×10( ) + 1×1( ) + 4 × 110

⎛⎝⎜

⎞⎠⎟ + 8 × 1

100⎛⎝⎜

⎞⎠⎟

< = >

< = >

< = > 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.9 1

3.244

3.247

3.253

3.255

A

B

C

D

<

Exponential form is the expanded form (powers of ten) represented with exponents. For example 100 is 102 so (3 x 100) is (3 x 102).



8´ Multiply 3 ways: 91× 28

8´´ There are usually 20 school days in a month. Rigo has gymnastics practice every day after school for 75 minutes. How many minutes does he practice every month?

9´ Divide two ways: 2106÷ 9

9´´ A farmer collected 1,183 eggs. He will put them in cartons that will hold a dozen (12) eggs each. How many cartons can he fill? Explain your answer. ∴He will fill 98 cartons. He will have 7 eggs remaining and that is not enough to fill another container and you cannot have a partial container.

728

2548 + 1820

91 x 28

Standard Algorithm

Generic Rectangle

8

1,800 20 720 8

90 + 1 20 +

1800 720 20 + 8

2548

1800

2548

= 20 x 1

Partial Products

= 8 x 1

= 90 x 8 = 90 x 20

720 20 + 8

91 x 28

1500

100 = 20 x 70

= 20 x 5

75 x 20

+ 1400

∴Rigo practices gymnastics 1,500 minutes each month.

Partial Quotients

36

306

0 = 9 × 4 - 36

= 9 × 30 - 270

= 9 × 200 9 2106 - 1800

234

Standard Algorithm

0 - 36

- 27 30

3 9 2106

2

- 18

36

4

12 1183 - 108 103

- 96 7

98

AUSD Grade 5 Units 1 - 2 Study Guide - WCCUSD

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