wccusd grade 5 benchmark 1 study guide · wccusd grade 5 benchmark 1 study guide ... 335.687...

WCCUSD Grade 5 Benchmark 1 Study Guide

of 21 MCC@WCCUSD 10/15/14

1 What are the expressions that are equivalent to 10,000?

5.NBT.2

2 Find the prime factors of 24.

When finding prime factors using a factor tree, circle a prime factor as soon as you write it so you don’t forget to list it at the end. 24 Write the number.

8 x 3 Start with two factors of 24. Circle 3 because it is prime. 8 is composite, so factor it.

4 x 2 Circle 2 because it is prime. 4 is

composite, so factor it.

2 x 2 Circle 2s because they are prime. Since both factors are prime, you don’t need to factor them.

2 x 2 x 2 x 3 List all circled prime factors in order

from least to greatest.

= 4 x 2 x 3 Check your work by multiplying.

= 8 x 3 = 24

5.OA.2.1

1´ You try:

2´ You try:

Find the prime factors of 72 and write as an equation.

The base 10 is multiplied by itself 4 times – it is not 4x10=40

�

10 ×103 or 101 ×103

=10 ×1000=10,000

This expression is incorrect:

This should be multiplied to get 10,000, not added to get 200.

�

A. 10 ×1,000

B. 100 ×1,000

C. 10,000 ×10

D. 10 ×104

E. 102 ×103

F. 103 ×101

Circle the letter of the expressions that are equivalent to 100,000?



3 Decompose 176.842 to expanded form. A number in expanded form is written as the sum of the values of each digit. 1 7 6 . 8 4 2 100 + 70 + 6 + .8 + .04 + .002 = 176.842

�

(1×100) + (7 ×10) + (6 ×1) + (8 × 110) + (4 × 1

100) + (2 × 11000)

The sum written vertically: 100.000 70.000 6.000 0.800 0.040 + 0.002 176.842

5.NBT.3.a

4 Round 335.687 to the nearest hundredth.

The digit 8 is in the hundredths place, so 335.687 will be rounded to 335.68 or 335.69. Draw a number line starting with 335.680 (equivalent to 335.68) and ending with 335.690 (equivalent to 335.69). Add 335.685 as the midpoint between 335.680 and 335.690. 335.687 is closer to 335.690. Therefore, 335.687 rounded to the nearest hundredth is 335.69. 335.687 335.680 335.685 335.690 335.68 (midpoint) 335.69

5.NBT.4

3´ You try: Decompose 241.953 to expanded form.

4´ You try:

Round 687.456 to the nearest hundredth.



5 Find the sum of 17.38 + 48.95 = Decomposition 17.38 + 48.95 = Decompose each addend to expanded notation = (10 + 7 + .3 +.08) + (40 + 8 + .9 + .05) Group like terms (move tens with tens, etc.) = (10 + 40) + (7 + 8) + (.3 + .9) + (.08 + .05) Combine like terms = 50 + 15 + 1.2 + .13 Note: .3 + .9 = 1.2, not 0 .12 Add terms = 66.33 Partial Sums (hundredths first) 17.38 + 48.95 .13 .08 + .05 1.20 .3 + .9 Note: .3 + .9 = 1.2, not 0 .12 15.00 7 + 8 + 50.00 10 + 40 66.33 Partial Sums (tens first) 17.38 + 48.95 50.00 10 + 40 15.00 7 + 8 1.20 .3 + .9 Note: .3 + .9 = 1.2, not 0 .12 + .13 .08 + .05 66.33

5.NBT.7

5´ You try: 53.68 + 21.79 =

Which makes sense when you estimate, because .9 is close to 1.0.



6 Find the difference between 4.73 and 2.36. Open Number Line The difference between two numbers is the distance between them (how far apart they are). Create a number line with the smallest number at the left end and the largest number at the right end. Jump using numbers that make it easy for you. Each person might jump differently. One way to jump: 2.0 .04 .33 2.36 4.36 4.4 4.73 Add the jumps to find the total distance:

2.00 .04

+ .33 2.37 Another way to jump (in opposite direction): .04 .6 1.0 .73 2.36 2.4 3.0 4.0 4.73 Add the jumps to find the total distance:

.04

.60 1.00

+ .73 2.37

5.NBT.7

6´ You try: Find the difference between 6.14 and 3.57.



7 D’asia bought a sandwich for $3.50 and a milk for $1.25. How much change did she get if she gave the lunch clerk $5.00? Bar Model

Whole Part Part Part

Bar models are used to find unknowns. Sometimes the unknown is the whole, and sometimes the unknown is a part. We know two parts: Sandwich is $3.50 and Milk is $1.25 We know the whole: She has $5.00 We don’t know one of the parts: how much change she will get. Let’s draw a bar model that shows this.

The money she started with $5.00

Sandwich

$3.50 Milk

$1.25 Change

? Add the two known parts together, then subtract the sum from the whole of $5.00.

The money she started with $5.00

Sandwich

$3.50 Milk

$1.25 Change

? $3.50 + $1.25 = $4.75 $0.25

Whole – Known Parts = Unknown Part $5.00 – $4.75 = $0.25 Words Math Spent $3.50 & $1.25 $3.50 + $1.25 = $4.75 How much change from $5.00 $5.00 – $4.75 = $0.25 D’asia received $0.25 in change.

5.NBT.7

7´ You try: Alberto had $10.00. He bought a pack of pencils for $1.50, a notebook for $1.25, and an eraser for $0.75. How much change did he get?



8 Find the product of 48 x 57 =

Partial Products

48 x 57 56 (7 x 8) 280 (7 x 40) 400 (50 x 8) +2,000 (50 x 40) 2,736 Generic Rectangle

Decompose factors using expanded notation: (40 + 8) x (50 + 7)

Draw a large rectangle.

Write one of the expanded factors across the top and one down the side. Draw lines separating rows and columns at plus signs. Multiply expanded factors and write products in boxes.

40 8

50

50 x 40 = 2,000

50 x 8 = 400

7 7 x 40 = 280

7 x 8 = 56

Add the partial products from each box.

2,000 400 280 + 56 2,736 Traditional

48 x 57 336 +2,400 2,736

5.NBT.5

8´ You try: Find the product of 98 x 36 =



9 Find the product of 2.3 x 3.2 = Partial Products 2.3 x 3.2

.06 (.2 x .3)

.40 (.2 x 2) .90 (3 x .3) + 6.0 (3 x 2)

7.36 Generic Rectangle Decompose factors using expanded notation: (2 + .3) x (3 + .2)

Draw a large rectangle with expanded notation factors. Include fraction equivalents to help place decimals correctly in partial products.

�

2 or 21

+ 0.3 or 3

10

3 x 2 = 6


6 0.9 0.4 + .06 7.36 Traditional 2.3 1 decimal place in factor tenth x 3.2 + 1 decimal place in factor x tenth 46 2 decimal places in product hundredth + 690 7.36

5.NBT.7

9´ You try: Find the product of 4.2 x 3.4 =

�

3 or 31

+

�

0.2 or 2

10

�

210

×3

10=

6100

= 0.06

�

210

×21

=4

10 = 0.4�

31×

310

=9

10 = 0.9

Does not equal 0.6. Think about multiplying using

fractions.



10 Find the quotient 8,588 ÷ 38 = Traditional 226 38) 8,588 - 7 6 98 - 76 228 - 228 0 Partial Quotients Side Work: List some 38) 8,588 multiples of the divisor - 3,800 100 to help think about 4,788 quotient parts you - 3,800 100 want to use. Multiples 988 must be smaller than - 760 20 the dividend. 228 38 x 1 = 38 - 190 5 38 x 10 = 380 38 38 x 100 = 3,800 - 38 1 38 x 2 = 76 0 226 38 x 20 = 760 38 x 200 = 7,600 38 x 5 = 190 Stacking 6 10 10 200 38) 8,588 - 7,600 988 - 380 608 - 380 228 - 228 0

5.NBT.6

10´ You try: Find the quotient of 9,342 ÷ 27 =

226



11 Find the quotient of 75.25 ÷ 3.5 = Partial Quotients Side Work: List some 3.5) 75.25 multiples of the divisor - 35.00 10 to help think about 40.25 quotient parts you - 35.00 10 want to use. Multiples 5.25 must be smaller than - 3.50 1 than the dividend. 1.75 3.5 x 1 = 3.5 - 1.75 0.5 3.5 x 10 = 35 0 21.5 3.5 x .5 = 1.75 3.5 x 5 = 17.5 Stacking 0.5 1 10 10 3.5) 75.25 - 35.00 40.25 - 35.00 5.25 - 3.50 1.75 - 1.75 0

5.NBT.7

11´ You try: Find the quotient of 53.50 ÷ 2.5 =

21.5



12

5.OA.1

12´ You try: SELECTED RESPONSE Indicate if the expressions have been evaluated correctly. Correct the steps that were done incorrectly.

This is the same expression evaluated incorrectly.

The Order of Operations are rules that tell you what to do first and what to do next. Operations inside Grouping symbols are done first. Parentheses are one type of Grouping Symbol.

This expression has been evaluated correctly by doing the operation inside the parentheses first.

Add what is inside the parentheses first. Multiply the sum by 4.

This expression has been evaluated correctly by doing the operation inside the parentheses first.

This is the same expression evaluated incorrectly.

A) Incorrect Correct

B) Incorrect Correct

C) Incorrect Correct

D) Incorrect Correct

E) Incorrect Correct

F) Incorrect Correct



13 Write the words as numerical expressions.

13´ You try: Write the numerical expressions in words. A)

�

3 6 + 2( ) B)

�

12 − 5 C)

�

9 27) D)

�

27 ÷ 9

E)

�

279

A) twice the sum of seven and nine

twice the sum of seven and nine

17

B) eight less than seventeen

eight less than seventeen

8 –

Think carefully about where the numbers should be placed in a subtraction expression. Ask yourself which number is being taken away from.

C) twelve divided by four

twelve divided by four

12 4

÷

Think carefully about where the numbers should be placed in this type of division expression.



14

5.NBT.3b

14´ You try: Which of the following have a value between 0.5 and 1.5? 1.08, 0.05, 1.005, 5.001, 0.561

Which of the numbers that have a value between 0.7 and 1.7? 7.01, 0.07, 1.007, 0.728, 0.954

Next, write the numbers in order, and you can see that

0.07, 0.728, 0.954, 1.007, 7.01 these are between 0.7 and 1.7

Put in order from least to greatest by looking at each digit.

0.07 is the smallest because it has 0 ones and 0 tenths

0.728 is next because it has 0 ones and 7 tenths

0.954 is next because it has 0 ones and 9 tenths

1.007 is next because it has 1 one

7.01 is next because it has 7 ones



15 Multiply and divide by multiples (or powers) of 10.

5.NBT.2

15´ You try: Which expressions are equivalent to 50.3?

�

A. 0.503×100B. 503÷100C. 5,030÷100D. 10×5.03

Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.

�

42.37×10 = 423.742.37×100 = 4,23742.37×1000 = 42,370

42.37÷10 = 4.23742.37÷100 = 0.423742.37÷1000 = 0.04237

The following equations show patterns when multiplying and dividing by multiples of 10.

100

100

100

30 3 tens _________ _________ _________ hundreds tens ones

�

10 × 30 10 groups of 30 10 of each of the 3 tens _________ _________ _________ hundreds tens ones

�

10 × 30 = 300 10 times 3 tens is 3 hundred _________ _________ _________ hundreds tens ones

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

When each of the 3 tens (30) is multiplied by 10, the 3 in the tens place of 30 is shifted one place to the left to represent 3 hundreds. In 300 divided by 10, the 3 is shifted one place to the right in the quotient to represent 3 tens.



16 Complete the table based on the rule: Some characteristics of the terms in this table: • After 0, terms alternate between odd & even. • After 0, each term is a multiple of 3. Complete the table based on the rule: Some characteristics of the terms in this table: • After 0, terms alternate between odd & even. • After 0, each term is a multiple of 3. Compare pairs of terms from both tables. (0, 0); (3, 9); (6, 18); (9, 27); and (12, 36) are pairs of terms. Some characteristics of the pairs of terms in these tables: • After 0, both terms in a pair are odd or both are even. • After 0, pairs of terms alternate between odd and even. • After 0, each term from Rule B is 3 times the corresponding term in Rule A.

5.OA.3

16´ You try: Complete the table based on the rule: List characteristics of the terms in this table: ____________________________________ ____________________________________ ____________________________________ ____________________________________ Complete the table based on the rule: List characteristics of the terms in this table: ____________________________________ ____________________________________ ____________________________________ ____________________________________ Compare pairs of terms from both tables. List characteristics of the pairs of terms in this table: ____________________________________ ____________________________________ ____________________________________ ____________________________________

Rule A Start at 0, add 3

0 3 6 9

12

Start at 0 Add 0 + 3 = Add 3 + 3 = Add 6 + 3 = Add 9 + 3 =

Rule B Start at 0, add 9

0 9

18 27 36




0 0 3 9 6 18 9 27 12 36







17 Use the pairs of terms from both tables as ordered pairs and plot them on the coordinate plane:

5.OA.3

17´ You try: Use the pairs of terms from both tables as ordered pairs and plot them on the coordinate plane:

End of Study Guide



0 0 3 9 6 18 9 27 12 36

3 6 9

12 15 18 21 24 27 30 33 36 39 42 45 48 51

3 6 9 12 15 18 21 24

Rule A

Rul

e

B



3 6 9

12 15 18 21 24 27 30 33 36 39 42 45 48 51

3 6 9 12 15 18 21 24

Rule A

Rul

e

B



You Try Solutions: 1´ You try:

Circle the letter of the expressions that are equal to 100,000?

2´ You try:

Find the prime factors of 72 and write as an equation. 72 8 x 9 2 x 4 x 3 x 3 2 x 2 2 x 2 x 2 x 3 x 3 = 72

3´ You try:

Decompose 241.953 to expanded notation. 200 + 40 + 1 + .9 + .05 + .003 = 241.953

4´ You try: Round 687.456 to the nearest hundredth. 687.456

687.450 687.455 687.460 687.45 (midpoint) 687.46 687.456 rounded to the nearest hundredth is 687.46.

5´ You try: 53.68 + 21.79 = Decomposition: = (50 + 3 + .6 +.08) + (20 + 1 + .7 + .09) = (50 + 20) + (3 + 1) + (.6 + .7) + (.08 + .09) = 70 + 4 + 1.3 + .17 = 75.47 Partial Sums (hundredths first) 53.68 + 21.79 .17 .08 + .09 1.30 .6 + .7 4.00 3 + 1 + 70.00 50 + 20 75.47 Partial Sums (tens first) 53.68 + 21.79 70.00 50 + 20 4.00 3 + 1 1.30 .6 + .7 + .17 .08 + .09 75.47

�

A. 10 ×1,000

B. 100 ×1,000

C. 10,000 ×10

D. 10 ×104

E. 102 ×103

F. 103 ×101



6´ You try: Find the difference between 6.14 and 3.57. One way to jump on an open number line .03 .4 2.0 .14 3.57 3.6 4.0 6.0 6.14

.03

.40 2.00

+ .14 2.57 Another way to jump (in opposite direction) 2.0 .5 .07 3.57 5.57 6.07 6.14

2.00 .50

+ .07 2.57

7´ You try: Alberto had $10.00. He bought a pack of pencils for $1.50, a notebook for $1.25, and an eraser for $0.75. How much change did he get?

Alberto received $6.50 in change.

$10.00 (Alberto’s money) Pencils $1.50

Notebook $1.25

Eraser $0.75

Change ??

Money spent =1.50+1.25+0.75 =$3.50

$6.50

8´ You try: Find the product of 98 x 36 = Partial Products

98 x 36 48 (6 x 8) 540 (6 x 90) 240 (30 x 8) +2,700 (30 x 90) 3,528 Generic Rectangle 90 8

30

30 x 90 = 2,700

30 x 8 = 240

6 6 x 90 = 540

6 x 8 = 48


2,700 240 540 + 48 3,528

Words Math Spent $1.50, $1.25 $1.50 + $1.25+ 0.75 = $3.50 and $0.75 How much change from $10.00 $10.00 - $3.50 = $6.50



9´ You try: Find the product of 4.2 x 3.4 = Partial Products 4.2 x 3.4 .08 1.60 .60 +12.00 14.28 Generic Rectangle

�

3 or 31

3 x 4 =12

�

31×210

=610

= 0.6

�

0.4 or 4

10

�

410

×41

=1610

=1.6

�

410

×210

=8100

= 0.08

12 0.6 1.6 + .08 14.28 Traditional

10´ You try: Find the quotient of 9,342 ÷ 27 = Traditional 346 27) 9,342 - 8 1 1 24 - 1 08 162 - 162 0 Partial Quotients Side Work: List some 27) 9,342 multiples of the divisor - 5,400 200 to help think about 3,942 quotient parts you - 2,700 100 want to use. Multiples 1,242 must be smaller than - 540 20 the dividend. 702 27 x 1 = 27 - 540 20 27 x 10 = 270 162 27 x 100 = 2,700 - 162 6 27 x 2 = 54 0 346 27 x 20 = 540 27 x 200 = 5,400 27 x 5 = 135 Stacking 6 40 100 200 27) 9,342 - 5,400 3,942 - 2,700 1,242 - 1,080 162 - 162 0

346

�

4 or 41

+ 0.2 or 2

10

4.2 x 3.4 168 + 1260 14.28



11´ You try: Find the quotient of 53.50 ÷ 2.5 = Partial Quotients Side Work: List some 2.5) 53.50 multiples of the divisor - 25.00 10 to help think about 28.50 quotient parts you - 25.00 10 want to use. Multiples 3.50 must be smaller than - 2.50 1 the dividend. 1.00 2.5 x 1 = 2.5 - 1.00 0.4 2.5 x 10 = 25 0 21.4 2.5 x 2 = 5.0 2.5 x 20 = 50 2.5 x .4 = 1.0 2.5 x 4 = 10 Stacking 0.4 1 10 10 2.5) 53.50 - 25.00 28.50 - 25.00 3.50 - 2.50 1.00 - 1.00 0

12´ You try: SELECTED RESPONSE Indicate if the expressions have been evaluated correctly. Correct the steps that were done incorrectly

21.4

Add 3 + 9 first

Subtract 10 – 2 first

Subtract 21 – 10 first

A) Incorrect Correct

B) Incorrect Correct

C) Incorrect Correct

D) Incorrect Correct

E) Incorrect Correct

F) Incorrect Correct



13´ You try: Write the numerical expressions in words. A)

�

3 6 + 2( ) Three times the sum of six and two B)

�

12 − 5 Five less than twelve Five subtracted from twelve Twelve minus five C)

�

9 27) Twenty seven divided by nine D)

�

27 ÷ 9 Twenty seven divided by nine

E)

�

279

Twenty seven divided by nine

14´ You try: Which of the following have a value between 0.5 and 1.5? 1.08, 0.05, 1.005, 5.001, 0.561 the numbers between 0.5 and 1.5 are 0.561, 1.005, and 1.08

15´ You try:

Which expressions are equivalent to 50.3?

�

A. 0.503 ×100 = 50.3 YESB. 503 ÷100 = 5.03 NOC. 5,030 ÷100 = 50.3 YESD. 10 × 5.03 = 50.3 YES



16´ You try: Complete the table based on the rule: List characteristics of the terms in this table: • After 0, all terms are even. • After 0, each term is a multiple of 3 and 6. Complete the table based on the rule: List characteristics of the terms in this table: • After 0, all terms are even. • After 0, each term is a multiple of 3, 6, and 12. Compare pairs of terms from both tables List characteristics of the pairs of terms in this table: • After 0, both terms in a pair are even. • After 0, each term from Rule B is 2 times the corresponding term in Rule A.

17´ You try: Use the pairs of terms from both tables as ordered pairs and plot them on the coordinate plane:


0 6

12 18 24



0 12 24 36 48




0 0 6 12 12 24 18 36 24 48



0 0 6 12 12 24 18 36 24 48

3 6 9

12 15 18 21 24 27 30 33 36 39

42 45 48 51

3 6 9 12 15 18 21 24

Rule A

Rul

e

B

wccusd grade 5 benchmark 1 study guide · wccusd grade 5 benchmark 1 study guide ... 335.687...

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