# Multiplication and Division, Part 1

## Objective

Build fluency with multiplication facts using units of 2, 5, and 10.

## Common Core Standards

### Core Standards

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• 3.OA.A.1 — Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.

• 3.OA.C.7 — Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

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• 2.NBT.A.2

• 2.OA.C.3

• 2.OA.C.4

## Criteria for Success

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1. Skip-count by twos, fives, and tens.
2. Solve multiplication problems involving twos, fives, and tens by skip-counting, keeping track on their papers or on their fingers of how many twos, fives, or tens have been counted, stopping the skip-counting sequence when they reach the number of twos, fives, or tens they intend to count, knowing that the last number said in the skip-counting sequence is the solution.

## Tips for Teachers

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• Students should have mastered counting by 2s, 5s, and 10s in Grade 2 (2.OA.3). If they haven’t, however, you can help students toward mastery of counting by twos with the following process. Instead of having students say all the numbers in the count sequence, have them hum, clap, or make some sort of noise in place of the number names that aren’t part of the count sequence, just thinking about what those numbers are instead. For example, for the skip-count sequence for twos, students would do: <clap> “two!” <clap> “four!” <clap> “six!” <clap> “eight!” etc. Then, they can remove the interspersed sounds and just say the skip-counting sequence. This provides a nice scaffold for students to use a placeholder for those numbers not in the count sequence before removing them entirely.
• Students will only see multiplication problems where 2, 5, and/or 10 is the second factor, i.e., the size of the group. Students will explore the commutative property in Lesson 7, allowing them to solve multiplication problems where 2, 5, and 10 are the first factor, i.e., the number of groups.
• Skip-counting to solve a multiplication problem can be more challenging than skip-counting to solve a division problem. As the OA Progression notes, “for $8\times 3$, you know the number of 3s and count by 3 until you reach 8 of them. For $24\div 3$, you count by 3 until you hear 24, then look at your tracking method to see how many 3s you have. Because listening for 24 is easier than monitoring the tracking method for 8 3s to stop at 8, dividing can be easier than multiplying” (OA Progression, p. 25). Thus, giving students ample time to practice will be greatly beneficial, and practice can be even more targeted in Lesson 7 when students apply the commutative property to solve even more multiplication problems.
• As a supplement to the Problem Set, we recommend 2 additional games you can play with students.
• "Double Up" from Building Conceptual Understanding and Fluency Through Games by the North Carolina Department of Public Instruction to review twos facts. (You'll need to modify it so that students are focusing on their twos facts within $10\times 2$, and you could modify the game so that it instead focuses on fives facts or tens facts.)
• "Charlotte Speedway Race" from Building Conceptual Understanding and Fluency Through Games by the North Carolina Department of Public Instruction to review twos and fives. (The directions can be changed to have students give a multiplication fact using 2, 5, or 10 (instead of just 2 or 5).

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

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How many?

### Problem 2

Solve.

a.   $9\times 2 =$ _____

b.   _____ $= 5 \times 2$

c.   $2\times 5 =$ _____

d.   _____ $= 9\times 5$

e.   $4\times 10 =$ _____

f.   _____ $= 10\times 10$

## Discussion of Problem Set

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• Look at #3d and #6d. What do you notice? What do you wonder?
• Why do you think it is that when you skip-count by twos you say all the even numbers?
• Is Rob’s reasoning correct in #11? Why is place value understanding helpful when multiplying by ten?
• What do you notice about #12a and #12b? What does it make you wonder?
• Look at #12c. Why do you think 4 x 5 is equivalent to 2 x 10?

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### Problem 1

Solve.

1.   $8\times10=$ _____                  2.   _____ $= 9\times 5$               3.   $7\times 2 =$ _____

### Problem 2

Karen counts, “5, 10, 15, 20, 25, 30.” Write a multiplication sentence that corresponds with this count-by.

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