Arithmetic Patterns - Multiply

Examples, solutions, and Videos to help Grade 3 students learn how to identify and use arithmetic patterns to multiply.

Common Core Standards: 3.OA.3, 3.OA.4, 3.OA.5, 3.OA.7, 3.OA.9, 3.OA.1, 3.OA.2, 3.OA.6

New York State Common Core Math Grade 3, Module 3, Lesson 13, Lesson 14

Worksheets for Grade 3

Multiply & Divide by 8 Worksheet Sprint A
Multiply & Divide by 8 Worksheet Sprint B

Lesson 13 Application Problem

Michaela and Gilda read the same book. It takes Michaela about 8 minutes to read a chapter, and Gilda about 10 minutes. There are 9 chapters in the book. How many fewer minutes does Michaela spend reading than Gilda?
Note: This problem comes after the Concept Development so that students have the opportunity to apply some of the strategies they learned in the context of problem solving. Encourage them to check their answers to the nines facts using new learning.

Lesson 13 Concept Development

Part 1: Identify patterns in multiples of 9.
Part 2: Apply strategies to solve nines facts.

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Lesson 13 Problem Set

1. a. Skip-count by nine.
   9, __, __, 36, __, __, __, 72, __, __
   b. Look at the tens place in the count-by. What is the pattern?
   c. Look at the ones place in the count-by. What is the pattern?
2. Complete to make true statements.
   a. 10 more than 0 is ______,
   1 less is _______.
   1 × 9 = _______
   b. 10 more than 9 is _______,
   1 less is _______.
   2 × 9 = _______
   c. 10 more than 18 is _______,
   1 less is _______.
   3 × 9 = _______
   d. 10 more than 27 is _______,
   1 less is _______.
   4 × 9 = _______
   e. 10 more than 36 is _______,
   1 less is _______.
   5 × 9 = _______
   f. 10 more than 45 is _______,
   1 less is _______.
   6 × 9 = _______
   g. 10 more than 54 is _______,
   1 less is _______.
   7 × 9 = _______
   h. 10 more than 63 is _______,
   1 less is _______.
   8 × 9 = _______
   i. 10 more than 72 is _______,
   1 less is _______.
   9 × 9 = _______
   j. 10 more than 81 is _______,
   1 less is _______.
   10 × 9 = _______
3. a. Analyze the equations in Problem 2. What is the pattern?
   b. Use the pattern to find the next 4 facts. Show your work.
   11 × 9, 12 × 9, 13 × 9, 14 × 9
   c. Kent notices another pattern in Problem 2. His work is shown below. He sees that:
   • the tens digit in the product is 1 less than the number of groups
   • the ones digit in the product is 10 minus the number of groups
   Use Kent’s strategy to solve 6 × 9 and 7 × 9.
   d. Show an example of when Kent’s pattern doesn’t work.

Lesson 13 Homework

1. a. Skip-count by nines down from 90.
   b. Look at the tens place in the count-by. What is the pattern?
   c. Look at the ones place in the count-by. What is the pattern?
   
2. Solve.
   a. What is 10 more than 0? ______
   What is 1 less? ______
   1 × 9 = ______
   b. What is 10 more than 9? ______
   What is 1 less? ______
   2 × 9 = ______
   c. What is 10 more than 18? _____
   What is 1 less? _____
   3 × 9 = _____
   d. 10 more than 27? ______
   What is 1 less? ______
   4 × 9 = ______
   e. What is 10 more than 36? _____
   What is 1 less? _____
   5 × 9 = _____
   f. What is 10 more than 45? _____
   What is 1 less? _____
   6 × 9 = _____

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Lesson 14 Concept Development

Part 1: Extend the 9 = 10 – 1 strategy of multiplying with units of 9.
Part 2: Apply strategies for solving nines facts and reason about their effectiveness.

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Techniques to help you remember your nine times table.

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Lesson 14 Homework Sample Solution

2. Thomas calculates 9 × 7 by thinking about it as 70 – 7 = 63. Explain Thomas’ strategy.

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