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Glossary

Arrays model “2 rows of 8 are I6” and, turned vertically, “8 rows of 2 are I6.” These are turnaround facts.

2 × 8 = 16

8 × 2 = 16

Students look for patterns to develop algebraic thinking and reasoning. “Double 6 ones is I2 ones, so double 6 tens (60) is I2 tens, or I20.”

Double 6 is ___.

Double 60 is ___.

Ideas for Home

• Connect twos facts to familiar situations. E.g. two hands show 2 × 5 = 10 (double 5 is 10); an egg carton shows 2 × 6 = 12 (double 6 is 12), and two weeks on a calendar show 2 × 7 = 14. Extend to fours facts by asking, “How many days are there in 4 weeks?”

• Practice the twos and fours doubling facts. E.g. ask, “What is 4 × 7?” When they answer “28”, ask your child to explain the doubling strategy. E.g. “I know that double 7 is 14 and double 14 is 28, so 4 × 7 is 28.”

Multiplication

• Since Grade 1, students have been practicing doubles facts in addition, so twos multiplication facts are a familiar concept. If they already know 3 + 3, then 2 × 3 or double 3 should be easy.

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ORIGO Stepping Stones 3 • 3.1

Introducing the Twos Multiplication Facts3.1

a. b. c.

Step Up 1. Write a twos number fact and its turnaround for each picture.

What do you see in this picture?

How did you fi gure out the product?

What are some other problems you could solve by doubling?

What multiplication number sentences could you write for this picture of eggs?

I see double 6.

I have used doubling with addition.

×

=

×

=

× =

× =

× =

× =

What do you see in this picture?

Write two related equations to match.

×

=

×

=

In this lesson, students use the doubles strategy to multiply by 2.

• Mastery of multiplication/division facts is the goal in Grade 3. Strategies provide fl exible and effi cient ways to solve problems and extend mental math skills beyond the facts.

• Strategies go beyond basic facts and extend to larger numbers. Knowing that 2 × 3 is 6, for example, means students can extend twos facts to solve problems such as 2 × 30 is 60, or “double 30 is 60”.

• Mentally solving problems such as 2 × 34 follows by pulling apart the tens and ones into 30 + 4, and then thinking (2 × 30) + (2 × 4), so 2 × 34 = 60 + 8 = 68.

• Fours facts build on twos facts. Since twos facts are solved by doubling, then the fours facts relate to double double.

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ORIGO Stepping Stones 3 • 3.4

Introducing the Fours Multiplication Facts3.4

Step Up

How can you fi gure out the total number of jelly beans without counting each one?

What number sentence can you write to describe your thinking?

Two bags of 6 is double 6, so 4 bags of 6 is double, double 6.

Use the same thinking to fi gure out how many cookies are on this tray.

Write a number sentence to match.

What other numbers could you multiply by 4 using this strategy?

a.

4 × 3 =

= 3 × 4

Do

uble

Do

uble

b.

4 × 7 =

= 7 × 4

Do

uble

Do

uble

1. Write the missing products.

In this lesson, students use the pattern of doubling to learn how to effi ciently multiply by four, i.e. doubling and then doubling again.

Core Focus

• Working with twos and fours multiplication facts, and using them to solve problems • Reading and writing times (to the nearest minute, before and past the hour) with

analog and digital clocks• Measuring elapsed time and solving problems involving elapsed time

Grade 3, Module 3

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Grade 3, Module 3

Time

• In earlier grades, students read times on the hour and half hour on analog and digital clocks, as well as reading times on an analog clock such as 2:05 and 4:35 by skip counting by 5s.

• Although digital clocks are easier to read, analog clocks show the key ideas and conventions of time in a clearer way.

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ORIGO Stepping Stones 3 • 3.8

Step Up 1. Draw lines to connect clocks that show the same time.

Relating Analog and Digital Times3.8

What time is showing on the analog clock?

What are some diff erent ways to say the time?

Write numbers on the digital clock to show the same time.

What do the numbers on the left side of the colon tell you?

What do the numbers on the right side of the colon tell you?:

32 minutes past 10. Ten thirty-two.

8:20 6:244:381 1:005:35

In this lesson, students compare and write times shown on analog and digital clocks.

• In Grade 3, students extend to reading and writing times to the nearest minute on both analog and digital clocks, reading and writing times before/past the hour, and working with elapsed time.

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76 ORIGO Stepping Stones 3 • 3.11

Carter’s phone records the length of each call that is made or received.

How could you fi gure out the total amount of time he spent talking to Carmen and Wesley?

Measuring Time Intervals in Minutes3.11

How much longer did Carter spend talking to Felix than to Paige? How do you know?

What are some other call lengths you can add or subtract?

Step Up 1. Draw jumps on the number line to fi gure out the number of minutes.

+4 +13

46 50 63

−10−5

27 32 42

I started at 42 then counted back 10, then counted back 5 more.

18 min + 26 min

minutes

a.

53 min – 18 min

minutes

b.

0utgoing Calls

Felix 42 min

Paige 15 min

Isabelle 8 min

Carmen 1 7 min

Wesley 46 min

I started at 46 then counted on 4 to make 50. Then I added 13 more.

In this lesson, students solve elapsed time problems and compare strategies using the number line.

• The number line is a perfect model to show elapsed time because, when stretched out horizontally, the analog clock face is a number line.

Ideas for Home

• Everyday experience and practice are important for learning to read, write, and make sense of time.

• Look online or in a newspaper for movie schedules. Ask your child to look up a favorite movie and use the time between showings to estimate the movie’s running time.

• Read the TV guide in the newspaper or on the guide channel. Notice how long the programs are and what time they start and end.

• Ask questions that encourage your child to read the channel guide on the television and compare program lengths. E.g. say, “How much longer is _____ than ____?”, “If _______ starts at 6:00 and lasts 90 minutes, what time does it end?”

• Talk about time often during daily activities. E.g. “It’s 7:55. We must leave for school at 8:30. Can you fi gure out how much time until then?” or “The bus will come at 2:30. See how my watch says 2:24. So how many more minutes is it until the bus arrives?”

The trip is minutes long.

Bus Departs Bus Arrives Glossary

Elapsed time is the time that passes while some event is occurring.

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