ausd 3rd grade benchmark 2 study guide 3rd grade benchmark 2 study guide ... le (one way): 7 another...

AUSD 3rd Grade Benchmark 2 Study Guide

of 14 MCC@WCCUSD (AUSD) 12/26/2013

1

3.OA.5

2

3.OA.5

1´

2´

Group these factors two different ways to get the product. 2 × 4 × 5

40 5 8

5 4) 2(

=×=

××

40 20 2

5) (4 2

=×=

××

Find the product of 4 × 7 by drawing and decomposing an area model.

281216

+

One Way:

16 12

3) (4 4 7 4

+×=×

4

4 + 3

28 12 61

3) (4 4) 4(

=+=

×+×=

∴4 × 7 = 28

2) (5 2) 2( 7 4

+×+=×

28 4 10 4 10

2) (2 )5 (2 2) (2 5) (2

=+++=

×+×+×+×=

Another Way:

281414

+ 2+2

5 + 2

10

10 4

4

You Try: Group these factors two different ways to get the product. 3 × 2 × 4

You try: Find the product of 6 × 9 by drawing and decomposing an area model. If you finish early, draw another area model for 6 × 9 and decompose it a different way.



3 3.OA.5,7

3´

You Try: Find the product of 8 × 9 using the generic rectangle 2 different ways. You may not use your multiplication chart to help you.

1

42121218

+

∴ 6 × 7 = 42

Find the product of 6 × 7 using the generic rectangle. le (One Way):

7

Another Way: Decompose the 6 le (One Way):

21+21 = 42 le (One Way):

21 21

3 + 3

Another Way: Decompose the 6 and 7 le (One Way):

15 6 le (One Way):

15 6 le (One Way):

5 + 2

3 + 3 42

12 30 661515

=+=

+++

le (One Way):

One Way: Decompose the 7 le (One Way):

I’d rather decompose the 7 because 7s are not easy for me.

I know my 3s and 2s, so this is a good choice for me.

Sums of 7 6 + 1 5 + 2 4 + 3 3 + 2+ 2

6

3 + 2 + 2

18 12 12

2)2 (3 67 6

++×=×

42 12 12 18

2) 6( 2) (6 3) 6 (

=++=

×+×+×=



4

3.AO.5

5

3.AO.7

4´

5´

Practice Facts le (One Way):

You’ve learned many strategies to help you multiply. Discuss with your class: Which methods would be good to use for finding the product of 9 × 9? le (One Way): Grouping Number Line Repeated Addition Skip Counting Bar Model Area Model Arrays Area Model (decomposed) Generic Rectangle Distributive Property Other Methods?

You Try: Find the product of 9 × 9. You may not use your multiplication chart to help you.

Practice using the distributive property. Finish the problem below.

=

=

=

+×=

×

)44(6

86

Find the product of 7 × 8 using the distributive property. le (One Way):

56 21 35

)37()57()35(7

8 7

=+=

×+×=+×=

×

le (One Way):

Side Work:

562135

+

∴7 × 8 = 56



6 3.NBT.3

6´

Find the product of 4 × 50. Find the product: 3 × 60

Algebra Proof:

180 1018

10)63( )106(3

=×=

××=××=

603×

I can decompose 60 into 6 × 10.

I can use the associative property to group (3 × 6). 18 × 10 is the same as 18 tens, and 18 tens equals 180.

0 60 120 180

Number Line: + 60 + 60 + 60

Repeated Addition: Bar Model:

60 + 60 + 60

= 120 + 60 = 180

60 60 60

180

OR

3 × 60 = 180

3 × 6 tens = 18 tens

Count by tens: 10, 20, 30… 180

Look for a set of 10 tens to make 100. 100 + 80 = 180

Array: Array:

Number Line: Bar Model:

Repeated Addition:

Algebra Proof:



7

8

3.G.1

7´

8´

3.G.1

A polygon is a closed, flat shape with straight sides.

Polygons: Not Polygons:

some sides are curved

no straight sides

not closed

You Try: Circle all the shapes that are polygons. Explain your choices.

Which polygon does not belong in this group? Justify your answer.

Possible Answers:

This polygon does not belong because it is the only triangle. The other polygons are quadrilaterals.

This polygon does not belong because it is the only one that does not have acute angles.

This polygon does not belong because it is the only one that does not have a right angle.

Sample Selected Response: What is true about both of these shapes? le (One Way):

Both shapes have an even number of sides.

True False 1

Both shapes have parallel sides.

True False 2

Both shapes have acute angles.

True False 3

Both shapes have all congruent sides.

True False 4



9 3.G.1

10

3.G .1

9´

10´

You Try: Use the dot paper to draw at least 3 examples of parallelograms.

You Try: Now draw at least 2 examples of quadrilaterals that are not parallelograms.

You Try: Circle all the rectangles.

Parallelograms are quadrilaterals with 2 sets of parallel sides. Which of the following are parallelograms? Justify your answer.

quadrilateral 2 sets of parallel sides

This is not a parallelogram because it only has 1 set of parallel sides.

2 sets of parallel sides

quadrilateral

This is a parallelogram because it is a quadrilateral with 2 sets of parallel sides.

A rectangle is a quadrilateral with 4 right angles. Is this a rectangle? Justify your answer.

This is a rectangle because it has 4 sides and 4 right angles.

quadrilateral

4 right angles



11 Find the quotient: 18 ÷ 3 continued next page 3.OA.2,6,7

11´ continued next page

You Try: Find the quotient: 32 ÷ 4

Divvy Out:

Bar Model:

Divvy Out:

32 ÷ 4 could mean 32 divided into groups of 4.

32 ÷ 4 could mean 32 divided into 4 equal groups.

Divvy Out (with Numbers)


18 ? ? ?

5, 10, 15 Add more.

16, 17, 18 Done!

5 5 5

1 1 1

Divvy Out (with Numbers)

6 ∴18 ÷ 3 = 6

Divvy Out:

••• ••• ••• ••• ••• •••

There are 6 groups of 3, so 18 ÷ 3 = 6

Bar Model:

6 groups of 3 3 3 3 3 3 3

18

3 Add 3 to make 12.

3 Add 3 to make 15.

3 Add 3 to make 18.

2 groups make 6.

3 3 3 Add 3 to make 9.


18

3 . . . ?

? = how many groups of 3

There are 6 in each group, so 18 ÷ 3 = 6

Divvy Out:

•••••• •••

••• ••••••



11 Find the quotient: 18 ÷ 3 (continued) 3.OA.2,6,7

12

3.OA.4

11´ You Try: Find the quotient: 32 ÷ 4 (continued)

12´

You Try: Write all the equations that could go with these pictures.

0 48

? ? ? ? 48

? ? ? ?

Use the Inverse Operation:

Repeated Subtraction:

Array:

Area:

Write all the equations that could go with these pictures.

0 ?

6 6 6 6 6

6 6 6 6 6

?

5 × 6 = ? ? ÷ 5 = 6

6 × 5 = ? ? ÷ 6 = 5

Other ways to think about 18 ÷ 3


I subtracted 3 six times, so 18 ÷ 3 = 6

0 9 1211111111111111111111112

12 15 18

-3 -3 -3 -3 -3 -3

6 1211111111111111111111112

3 1211111

111111111111111112


18 ÷ 3 = Think: 3 × = 18

18

6 6 6

18

? ? ?

3 × 6 = 18 So, 18 ÷ 3 = 6

Array: 6

3

••••••••••••••••••

?

Area:

?

18 3

6



13 3.OA.3

13´

*Students can check with another method or with the inverse operation. They need to prove their answers, even if they have the fact memorized.

Solve. Show all your work. Showing all your work includes: Set Up Solve Check Sentence

Anthony wants to buy 6 books for $2 each. How much money does he need?

Solve:

2, 4, 6, 8, 10, 12

6 + 6 = 12

*Check:

Possible Sentence: Anthony needs $12.

Possible Ways to Set Up: Use bar model, number line, picture, words, or an equation to show what you are looking for.

6 groups of 2 dollars How much money does he need in all?

0 ?

2 2 2 2 2 2

?

2 2 2 2 2 2 2 × 6 = ? 6 × 2 = ? 2 × 6 = D 6 × 2 = D

You Try:

Tran’s class earned the same number of lunchtime points each day for 7 days. They earned 49 points in all. How many points did they earn each day?

Solve. Show all your work.

Note to Teachers: Benchmark 2 will include one step word problems. Benchmark 3 will include multi-step word problems involving the four operations.



14 3.OA.5

15

3.OA.7,MP.1

16 3.OA.4

End of Study Guide

27 ÷ 3 = ? 3 True False

27 × 3 = ? 2 True False

3 × ? = 27 1 True False

27 ÷ ? = 3 4 True False

Sample Selected Response:

Which of the equations match these pictures? ? ? ?

27

0 27

? ? ?


Which of the expressions below go with the area model? (3 × 5) + (3 × 4)

1 Yes No

3 × 9

2 Yes No

(3 + 5) + (3 + 4)

3 Yes No

3

5 + 4

8

5 + 3 13 11

241113

+


Lisa multiplied 8 × 8 to get 24 , which is incorrect. What went wrong?

She multiplied 8 × 5 wrong. 1 True False


She added 13 + 11 wrong. 3 True False



You Try Solutions: 1´

2´

3´

4´

5´

6´

Algebra Proof:

I can decompose 50 into 5 × 10.

I can use the associative property to group (4 × 5). 20 × 10 is the same as 20 tens, and 20 tens equals 200.

Practice using the distributive property. Finish the problem below.

48

2424 )46()46(

)44(686

=+=

×+×=+×=

×

You Try: Find the product of 9 × 9…. . Example:

9 9 9 9 9 9 9 9 9

81

9 72

9 36 36

9 18 18 18 18

=

+=

++=

++++=

Find the product: 4 × 50

Number Line:

0 50 100 150 200

+ 50 + 50 + 50 +50

Array:

4 × 50 = 200

4 × 5 tens = 20 tens

You Try: Group these factors two different ways to get the product. 3 × 2 × 4

24 4 6 4 2) 3(

=×=××

24

8 3 4) (2 3

=×=××

∴ 8 × 9 = 72

1

722448

+

3) (6 8 9 8

+×=×

8

6 + 3

48 24

3) 3 (3 8 9 8

++×=×

8

3 + 3 + 3

24 24 24 72242424

+

1

You Try: Find the product of 8 × 9 using the generic rectangle 2 different ways….

You Try: Find the product of 6 ×9 by drawing and decomposing an area model…

∴ 6 × 9 = 54

)225( 69 6

++×=×

54 12 12 30

)2 (6 ) 2 (6 )5 6(

=++=

×+×+×=

30 12 12 6

5 + 2 + 2 )27( 6

9 6 +×=

×

54 12 42

) 2 (6 )7 6(

=+=

×+×=

42 12 6

7 + 2



6´ You Try: Find the product of 4 × 50 (continued)

7´

8´

9´


I subtracted 4 eight times, so 32 4 = 8 0 4 8 12 16 20 24 30 32

-4 -4 -4 -4 -4 -4 -4 -4

8

4

?

Array: Area:

?

32 4

8


32

? ? ? ?

32 4 = Think: 4 × = 32

4 × 8 = 32 So, 32 4 = 8

32

8 8 8 8

Divvy Out (Using Numbers):

You Try: Circle all the shapes that are polygons. Explain your choices.

curvy sides open

curvy sides

= 200

50 + 50 + 50 + 50

Repeated Addition: Bar Model:

= 100 + 100

200

50 50 50 50

Algebra Proof:

002 1020

10)54( )105(4

=×=

××=××=

504×

You Try: Use the dot paper to draw at least 3 examples of parallelograms.

You Try: Now draw at least 2 examples of quadrilaterals that are not parallelograms.

Sample Selected Response: What is true about both of these shapes? le (One Way):

Both shapes have an even number of sides.

True False 1

Both shapes have parallel sides.

True False 2

Both shapes have acute angles.

True False 3

Both shapes have all congruent sides.

True False 4



10´

11´ You Try: Find the quotient: 32 ÷ 4

11´ You Try: Find the quotient: 32 ÷ 4 (continued)

12´

4 × ? = 48 48 ÷ 4 = ? ? × 4 = 48 48 ÷ ? = 4

You Try: Write all the equations that could go with these pictures.

0 48

? ? ? ? 48

? ? ? ?


I subtracted 4 eight times, so 32 ÷ 4 = 8

0 4 8 12 16 20 24 28 32

-4 -4 -4 -4 -4 -4 -4 -4

32

4 4 4 4 4 4 4 4

Bar Model:

Array: 8

4

?

••••••••••••••••••••••••••••••••

Area:

?

32 4

8

Think: 4 × = 32


32

? ? ? ? 32 ÷ 4 =

4 × 8 = 32 So, 32 ÷ 4 = 8

32

8 8 8 8

Divvy Out: 8 groups of 4


32

4 . . . ? ? = how many groups of 4

•••• •••• •••• •••• •••• •••• •••• ••••

Divvy Out:

••••••••

••••••••

There are 4 groups of 8, so 32 ÷ 4 = 8


••••••••

••••••••

32

? ? ? ?

2, 4, 6, 8 Add more. 10, 12, 14, 16 Add more. 18, 20, 22, 24 Add more. 26, 28. 30, 32 Done!

Divvy Out (Using Numbers):

∴32 ÷ 4 = 8 8

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

You Try: Circle all the rectangles.



13´

14´

15´

16´

3

5 + 4


(3 × 5) + (3 × 4)

1 Yes No

3 × 9

2 Yes No

(3 + 5) + (3 + 4)

3 Yes No

Which of the expressions below go with the area model?

You Try: Tran’s class earned the same number of lunchtime points each day for 7 days. They earned 49 points in all. How many points did they earn each day?

They earned 7 points each day.

Possible answer including set up, solve, check, and sentence.

49 ÷7 = P

49

? ? ? ? ? ? ?

7

7

7

2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 2 2 2 2 2 2 2 2 2 1 1 1

14 28 42 49

8

5 + 3 13 11

241113

+



She added 13 + 11 wrong. 3 True False


Lisa multiplied 8 × 8 to get 24 , which is incorrect. What went wrong?

? ? ?

27

0 27

? ? ?

27 ÷ 3 = ? 3 True False

27 × 3 = ? 2 True False

3 × ? = 27 1 True False

27 ÷ ? = 3 4 True False


Which of the equations match the pictures?

ausd 3rd grade benchmark 2 study guide 3rd grade benchmark 2 study guide ... le (one way): 7 another...

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