sample - origo education · 2019-05-23 · out in 6 rows. there were 8 chairs in each row. only 5...

STUDENT JOURNAL

Diana Lambdin

Frank Lester, Jr.

Kit Norris

PROGRAM CONSULTANTS

James Burnett

Calvin Irons

SENIOR AUTHORS

Debi DePaul

Beth Lewis

Peter Stowasser

Allan Turton

contributing authorsTE

XA

S

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ORIGO Stepping Stones Texas • Grade 3

6.1

Introducing the Eights Multiplication FactsStep In

Look at this array. What do you see?

What strategy can you use to figure out the product?

Look at the next array. What do you see?

What strategy can you use to figure out the product?

2 × 6 = = 6 × 2

Step Up 1. Look at these pictures. Write the products.

a.

2 × 9 =

double, double, double 9

8 × 9 =

c.b.

double, double 9

4 × 9 =

2 × 6 = = 6 × 2

4 × 6 = = 6 × 4

2 × 6 = = 6 × 2

4 × 6 = = 6 × 4

8 × 6 = = 6 × 8

I used the double, double strategy.

8 sixes is the same as double, double, double 6.

Look at the next array. What do you see?

How can you use the fours fact to help you figure out the product for the eights fact?

Is this an easy strategy to use?

What other eights facts could you solve using this strategy?

double 9

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6.1

2. Write the products for these.

c.

2 × 5 =

4 × 5 =

8 × 5 =

b.

2 × 7 =

4 × 7 =

8 × 7 =

a.

2 × 3 =

4 × 3 =

8 × 3 =

d.

2 × 8 =

4 × 8 =

8 × 8 =

3. Use a doubling strategy to complete this table.

Number Double (×2)

Double Double (×4)

Double Double Double (×8)

6

7

20

36

Step Ahead Write numbers in the squares so that the numbers in each row and column multiply to give the product in the circle.

8 24 5

16

20

1032

56

12

2428

40

36

2072

a. c.b.

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6.2

Reinforcing the Eights Multiplication FactsStep In

Selena bought 8 of these packs of pencils.

How many pencils did she buy in total?

How could you figure it out?

Norton bought 8 different packs of pencils. Each pack had 2 pencils. How many pencils did he buy?

How could you figure it out?

What other problems could you solve using these strategies?

Double 3 is 6, double 6 is 12, and double 12 is 24. So 8 packs of 3 is 24.

Step Up 1. Show how you could use the double, double, double strategy to solve each word problem.

a. Chloe bought 8 packs of stickers. There are 6 stickers in each pack. How many stickers did she buy in total?

double is

double is

double is stickers

b. Noel bought 8 packs of trading cards. There are 9 cards in each pack. How many trading cards did he buy in total?

double is

double is

double is cards

× 2 × 2× 2

What should you write in each of the boxes below to show how many pencils she bought?

It is easier to think double 8 than double, double, double 2.

× 8

3

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6.2

2. Complete each picture.

3. Complete each fact. Then write the turnaround fact for each.

8 × 3 =

× =

a.8 × 6 =

× =

b.8 × 2 =

× =

c.

4. Think about the fours and eights facts. Write the missing number in each equation.

× 2

×

× 2× 2a.

× 2

×

× 2× 2b.

× 2

×

× 2× 2c.

× 2

×

× 2× 2d.

5 7

4 8

Step Ahead

Use repeated doubling to complete the missing numbers.

× 2× 2 × 2 × 2

4

a. 4 × 7 =

d. 24 = × 6

g. 7 ×

= 56

b. 16 = 2 ×

e. × 8 = 64

h. 32 =

× 8

c. × 4 = 36

f. 40 =

× 10

i. 3 × 8 =

×16

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6.3

Exploring Patterns with the Eights Multiplication FactsStep In

Look at this hundred chart.

Color all the numbers above that you know are products of the eights facts.

There are two numbers in the bottom two rows that are the products of 8 × 11 and 8 × 12.

Is there a pattern you can see that could help you figure out the numbers?

Imagine the chart continued to 200. What are some other numbers you would color to continue the pattern?

How do you know?

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

What strategy could you use to check your answer?

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6.3

Step Up Use the hundred chart on page 132 to answer these questions.

1. Look at the color pattern of numbers. Are the numbers odd or even?

2. Look at the numbers in a single column. What do you notice?

3. Look at the numbers that lie along a sloping line. What change happens in the ones digit from one number to the next?

Step Ahead Complete these facts. Then write about the pattern you notice.

8 ×

= 32

4 ×

= 32

2 ×

= 32

4. a. Loop all the numbers in the chart that are products of the fours facts.

b. What pattern do you notice?

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6.4

Introducing the Ones Multiplication FactsStep In

Step Up 1. Complete the picture to match the problem. Then complete the related number fact.

What do you see in this picture?

Write a number sentence to describe your picture.

What number sentence could you write to describe the row of vehicles?

What else might you see in one row? Draw a picture to match.

7 birds sitting on a fence How many birds in total?

× 1 =

a. 6 cookies in a jar How many cookies in total?

× 1 =

b.

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6.4

2. Complete the number fact to match each picture.

3. In each story write a number greater than 1 but less than 10. Then draw a matching picture and write the related number fact.

a.

bananas in a bunchHow many bananas in total?

×

=

b.

stamps in a rowHow many stamps in total?

×

=

c.

muffins on a trayHow many muffins in total?

×

=

d.

flowers in a vaseHow many flowers in total?

×

=

× 1 =

1 ball for each student How many balls in total?

a.

1 ×

=

1 line of ducks How many ducks in total?

b.

Step Ahead Write a rule you can use when you multiply by 1.

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6.5

Introducing the Zeros Multiplication FactsStep In

Step Up 1. Draw the picture. Then write the multiplication fact.

Describe what you see in each row.

What number sentences could you write to describe each row?

Look at Row D. What happens when you multiply by 0?

c. 1 cookie in each jar

3 ×

=

b. 2 cookies in each jar

3 ×

=

a. 3 cookies in each jar

3 ×

=

d. 0 cookies in each jar

3 ×

=

Row A

Row B

Row C

Row D

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6.5

2. Draw rows of 5 stars on the flag to match each multiplication fact.

3. Draw jumps on the number line to show each fact. Then write the products.

4 × 2 =

4 × 1 = 4 × 0 =

10 2 3 4 5 6 7 8 9 10

a.

5 × 2 =

5 × 1 = 5 × 0 =

10 2 3 4 5 6 7 8 9 10

b.

Step Ahead Write a rule you can use when you multiply by 0.

2 × 5 = 10

a. b.3 × 5 = 15

0 × 5 = 0

c.1 × 5 = 5

d.

8

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6.6

Reinforcing the Ones and Zeros Multiplication FactsStep In

Alfredo planted seedlings in one row of 6.

How many seedlings did he plant? How do you know?

Pamela had 6 mushrooms on her plate. She ate none of them.

How many mushrooms did Pamela eat? How do you know?

Emma had 6 pencils on her desk. Then her friend gave her another pencil.

How many pencils did Emma have in total? How do you know?

Madison had 6 packets of stickers. She gave stickers to each of her friends until the packets were empty.

How many stickers did Madison have left? How do you know?

Step Up 1. Read the equation carefully. Then write the answer.

What can you say about the math involved in each story?

a. 5 × 1 =

d. 1 + 7 =

g. 37 × 1 =

b. 9 + 1 =

e. 0 × 4 =

h. 97 + 0 =

c. 8 × 0 =

f. 5 − 0 =

i. 0 × 58 =

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6.6

2. Multiply the two numbers across each row and write the product in the matching circle. Then multiply the two numbers down each column and write the product in the matching circle.

3. Figure out what numbers must be in each row and column to make the product in the matching circle.

Step Ahead Write a story problem to match this fact.

4 4

15

512

2 2

10

102

2 2

18

94

1 1

4

14

5 10

0

00

3 0

1 4

2 6

8 0

2 1

3 5

215

56

a. c.b.

a. c.

d. f.e.

b.

0 0

7

50

1 × 9 = 9

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6.7

Solving Word Problems Involving Multiplication (Eights, Ones, and Zeros)

Step In

Step Up 1. Write an equation to match each story. Then figure out the solution for each word problem.

There are 6 plates on a picnic table.

Each plate has 4 strawberries.

There is also one banana on 2 of the plates.

How many strawberries are there in total? How do you know?

What numbers in the story helped you?

Which numbers would you use to figure out how many pieces of fruit there are in total?

b. Every day Cathy and 2 of her friends jog 3 laps around the athletics track. How many laps will Cathy jog in 8 days?

The teacher has 5 rulers. Each ruler is 1 foot long and 3 of them are plastic. What is the total length of the rulers if they are laid end to end?

×

=

×

=

feet laps

d. Chairs in an auditorium were set out in 6 rows. There were 8 chairs in each row. Only 5 people sat in each row. How many people are there in total?

c. Anoki arranged a bookcase so that each shelf had 9 books. There are 4 shelves of books. 7 of the books are about cats. How many books are there in total?

There are 6 plates with 4 strawberries on each plate.

×

=

×

=

people books

a.

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6.7

2. Figure out the solution to each problem. Show your thinking.

a. Kamen had 4 pieces of ribbon. Each ribbon was 3 feet long. She needed twice the total length that she had. How many feet of ribbon did Kamen need in total?

b. A fruit store sells 3-kilogram bags of apples and oranges. Dad bought 2 bags of oranges and 6 bags of apples. What was the total weight of all the fruit Dad bought?

c. Ruben baked a tray of cookies. The tray held 4 rows of cookies with 7 cookies in each row. He had some cookie dough left over so he baked another tray that had only one row of 7 cookies on it. How many cookies did he bake?

Step Ahead Write a story that matches this number sentence. 4 × 6, then add 3

feet

kg

cookies

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6.8

Exploring Related Partitions (Length Model)Step In

Step Up

Sofia had three strips of paper. The picture shows how she folded two of them into parts of equal size.

The first strip is one whole. What would you label each part of the other strips?

When you write 1 3 what does the 3 tell you?

Look at the folds that made sixths. How are they related to the folds that made thirds?

The 3 tells me that three of the parts are needed to fill the whole.

The paper strips belong to the 1 3 fraction family because you can make sixths by first making thirds.

1. Draw a fold line on the second strip to show halves. Draw fold lines on the last strip to show fourths. Then label each part of the strips.

2. Draw fold lines on the second strip to show thirds. Draw fold lines on the last strip to show ninths. Then label each part of the strips.

1 1

1

The first strip in each of these is one whole.

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6.8

3. Write the fraction that matches the fraction words. Then write how many parts are needed to fill the whole.

Fraction Word Fraction Parts in One Whole

one-third 1 3 3

one-fourth

one-eighth

Step AheadUse paper strips to find a different fraction that belongs in each of the 1

2 and 1 3 fraction families. Draw lines to show the folds

and label each part of the strips.

1 1

4. This strip is one whole.

a. Draw lines to split the strip into sixths. Then shade 4 6 of the strip.

b. What does the 6 tell you?

c. What does the 4 tell you?

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6.9

Introducing Common Fractions as a Sumof Unit Fractions

Step In

Look at this number line.

The distance from 0 to 1 is one whole.

Show how you would mark 1 6 on the number line.

Oscar is making a cake.

He needs 3 4 cup of sugar

but only has a 1 4 measuring cup.

What can he do to measure the correct amount of sugar?

What does this number line show?

0 13 4

2 4

1 4

Step Up1. Look at how each number line has been split up. The distance

from 0 to 1 is one whole. Write the fraction that each arrow is pointing to.

a. b.

I would split the line from 0 to 1 into 6 equal parts. The distance from 0 to the first mark will be 1

6 of the total distance from 0 to 1.

0 1

0 1 0 1

+ 1 4+ 1

4+ 1 4

cup1 4

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6.9

2. For each number line, the distance from 0 to 1 is one whole. Write the answer to each problem. Draw jumps on the number line to show your thinking.

a.Noah has a bottle that holds 1

6 of a gallon of water. How many bottles will he need to make 4 6 of a gallon of water?

b.Athena’s family bought a pizza cut into eighths. Athena ate 3

8 of the whole pizza. How many pieces of pizza did she eat?

3. Write an addition equation to match the jumps on the number line.

0 1

0 1

=

c.

0 1

Step Ahead Complete each equation.

a. 1 4 +

1 4 +

1 4 =

4c.

1 2 +

1 2 =

2b.

1 8 +

1 8 +

1 8 +

1 8 +

1 8 =

8

a.

0 1

+ 1 6 + 1

6

= 6+

1 6

1 6

=

b.

0 1

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6.10

Step Up 1. Draw jumps above the number line to match each common fraction.

Reinforcing Common Fractions as a Sum of Unit Fractions

Step In

Fernando draws jumps above the number line to show 4 6 .

What steps does he follow?

Think about the fraction 4 6 .

What does the 6 mean? What does the 4 mean?

Draw jumps above the number line to match the common fraction.

What equation could you write to match the jumps that you made?

0 13 6

4 6

5 6

2 6

1 6

The 6 tells the number of parts that are needed to fill the whole. The 4 tells the number of parts that were counted.

0 1

5 8

a.

0 1

3 4

b.

0 1

2 3

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6.10

Step Ahead Henry works for the city. It takes him one day to clean 1 4 mile of the

highway. How many days will it take to clean one mile of the highway?

2. Draw jumps above the number line to match each common fraction. Then write an equation to match the jumps that you made.

3. Color the to show the expression that matches the common fraction.

a.

0 13 8 1

8 +1 8 +

1 8 =

3 8

b.

0 15 6

c.

0 14 4

1 8 +

1 8 +

1 8

1 4 +

1 4 +

1 4 +

1 4

1 8 +

1 8 +

1 8 +

1 8

4 8

a.

1 2 +

1 2

1 6 +

1 6 +

1 6

1 6 +

1 6

2 6

b.

3 + 3 + 3

1 3 +

1 3 +

1 3

1 1 +

1 1 +

1 1

3 3

c.

days

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6.11

Step Up 1. Share the pie among each group of friends. Then complete the equation to match.

This pie was shared equally among four friends.

How would you describe the amount of pie that each friend is given? What fraction would you say?

Complete this equation to match.

This pie was cut into eighths. The leftover pie was shared equally among five friends.

Complete this equation to show the amount of pie that each friend was given.

Decomposing Common Fractions (Area Model)Step In

4 4

=

+

+

+

5 8

=

+

+

+

+

Each friend is given 1 4 of the pie.

4 4 =

1 4 +

1 4 +

1 4 +

1 4

a. Share the whole pie among 6 friends.

6 6

=

+

+

+

+

+

3 3

=

+

+

b. Share the whole pie among 3 friends.

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6.11

2. Share the leftover pie equally. Complete the equation to match.

b. Share the leftover pie among 6 friends.

=

+

+

+

+

+

6

8

a. Share the leftover pie among 3 friends.

=

+

+

3

6

3. Write each common fraction as a sum of unit fractions.

a. 3 8

=

b. 4 6

=

c. 2 3

=

b. 2 2

=

Step AheadTwo friends each buy the same-sized pie. Riku cuts her pie into eighths. William cuts his pie into sixths. They each eat two pieces. Who eats the most pie? Explain your thinking.

1 8

+1 8

+1 8

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6.12

Step Up 1. Solve each of these problems. Show your thinking. Then write the answer in the box.

Solving Word Problems Involving Composing and Decomposing Common Fractions

Step In

Wendell is baking a cake. He has these measures in his kitchen.

How can he measure one cup of flour? Which measure should he choose? How many of these will he need?

Wendell decides to put the remaining ingredients in the bowl.

Which measures should he choose? How many times will he need to fill each?

Cake Recipe

6 eggs3 4

cup of milk

1 cup of flour2 3

cup of sugar

3 8

cup of cocoa

1 2 cup

1 4 cup 1

8 cup1 3 cup

Each cup could be used to measure one cup of flour. If you choose the largest cup, you only need to fill it two times.

a. Lily is making a cake. She needs 2 3 cup of sugar, but only has a

1 3

measure. How many times does she need to fill the measure?

b. Alicia bakes a banana bread. She cuts the bread into eighths and then eats three pieces. What fraction of the banana bread does she eat?

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6.12

Step Ahead Use the numbers to complete each problem so that it makes sense.

2. Solve each of these problems. Show your thinking.

a. Morgan has four bottles. Each bottle can hold 1

6 of a gallon. What is the total amount of liquid the bottles can hold?

gal

c. Each morning Grace runs 1 4 of a

mile. What distance will she run in 7 days?

a. 1 8 6 6

8

b. There are 6 pieces of string. Each piece of string is cut in half. How many pieces of string are there now?

pieces

d. It takes 1 3 of a cup of milk for

one cake. How many cups will 7 cakes need?

b. 1 4 4 1

of the cake is left over.

The leftover cake is shared equally

among friends. Each friend is

given

of the cake.

friends enter a swimming

relay. They have to swim a total

distance of mile. Each person

will swim

of a mile.

miles cups

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