wccusd grade 5 benchmark 1 study guide · 2013-10-26 · wccusd grade 5 benchmark 1 study guide...

WCCUSD Grade 5 Benchmark 1 Study Guide

of 14 MCC@WCCUSD 10/25/13

1 Find the value of the expression. 24

Base is 2 Exponent is 4 (how many times

the base is multiplied by itself) 24 = 2 x 2 x 2 x 2 24 is not 2 x 4 = 8 = 4 x 2 x 2 24 = 16 = 8 x 2 = 16

NS 1.4

2 Find the prime factors of 24 and write as an

expression in exponential form. 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 for 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 2’s 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

23 x 3 Write prime factors in exponential form.

NS 1.4/5.OA.2.1

1´ You try: Find the value of the expression. 33

2´ You try:

Find the prime factors of 72 and write as an expression in exponential form.



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

NS 1.0/5.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

NS1.1/5.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

NS 2.1/5.NBT.7

5´ You try: 53.68 + 21.79 =



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

NS 2.1/5.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

Part Part Whole

Bar models are used to find unknowns. Sometimes the unknown is the whole, and sometimes the unknown is a part. This word problem has two steps. Step 1 We know the parts: She spent $3.50 and $1.25. The whole is unknown: How much did D’asia

spend? We add the parts to find the unknown whole.

Part: $3.50 Part: $1.25 Whole: $4.75

Part + Part = Unknown Whole $3.50 + $1.25 = $4.75 Step 2: We know the whole: She started with $5.00. We know one of the parts: She spent $4.75. The other part is unknown: How much change did she get? We know the whole and one of the parts, so we subtract the known part from the whole to find the unknown part.

Whole: $5.00 Part: $4.75 Part: $0.25

Whole – Known Part = 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.

NS 2.1/5.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

NS 2.1/5.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) Does not equal 0.6. Think

.40 (.2 x 2) about multiplying using .90 (3 x .3) fractions. !

!" × !!"

= !!""

+ 6.0 (3 x 2) = .06

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 !! 0.3 or !

!"

3 or !! 3 x 2 =

6

!! x !

!" = !

!"

0.9

0.2 or !!"

!!"

x !! = !

!"

0.4

!!"

x !!"

= !!""

0.06 Add the partial products from each box.

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

NS 2.1/5.NBT.7

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



10 Jada has 3 sticker books. Zarrie has 2 sticker books. Each sticker book has 50 stickers. How many stickers do they have in all? Bar Model

50 50 50 50 50 150 100

250 (3 x 50) + (2 x 50) = 150 + 100 = 250 stickers Number Line +50 +50 +50 +50 +50

0 50 100 150 200 250 50 50 50 OR 5 x 50 = 250 stickers 50 + 50 250 stickers They have 250 stickers in all.

AF 1.2

10´ You try: Each package of erasers has 20 erasers. Alonzo has 4 packages. Namon has 3 packages. How many erasers do they have in all?

Jada Zarrie

Jada Zarrie



11 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

NS 2.2/5.NBT.6

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

226



12 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. - 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

NS 2.2/5.NBT.7

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

End of Study Guide

21.5



You Try Solutions: 1´ You try:

Find the value of the expression. 33 = 3 x 3 x 3 = 9 x 3 = 27

2´ You try:

Find the prime factors of 72 and write as an expression in exponential form. 72 8 x 9 2 x 4 x 3 x 3 2 x 2 2 x 2 x 2 x 3 x 3 = 23 x 32 = 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



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? Step 1

$1.50 $1.25 $0.75 $3.50

Step 2:

$10.00 $3.50 $6.50

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

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 x90 = 2,700

30 x 8 = 240

6 6 x 90 = 540

6 x 8 = 48

Add the partial products from each box.

2,700 240 540 + 48 3,528



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 4 or !

! 0.2 or !

!"

3 or !! 3 x 4 =

12

!! x !

!" = !

!"

0.6

0.4 or !!"

!!"

x !! = !"

!"

1.6

!!"

x !!"

= !!""

0.08 12 0.6 1.6 + .08 14.28 Traditional 4.2 x 3.4 168 + 1260 14.28

10´ You try: Each package of erasers has 20 erasers. Alonzo has 4 packages. Namon has 3 packages. How many erasers do they have in all? Bar Model

20 20 20 20 20 20 20 80 60

140 (4 x 20) + (3 x 20) = 80 + 60 = 140 erasers Number Line +20 +20 +20 +20 +20 +20 +20

0 20 40 60 80 100 120 140 20 20 20 20 OR 7 x 20 = 140 erasers 20 20 + 20 140 erasers They have 140 erasers in all.

Alonzo Namon

Alonzo Namon



11´ 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

12´ 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

346

21.4

wccusd grade 5 benchmark 1 study guide · 2013-10-26 · wccusd grade 5 benchmark 1 study guide...

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