Multiplication and Division, Part 2

Lesson 23

Math

Unit 3

3rd Grade

Lesson 23 of 23

Objective


Identify arithmetic patterns and explain them using properties of operations.

Common Core Standards


Core Standards

  • 3.OA.D.9 — Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

Foundational Standards

  • 2.OA.C.3

Criteria for Success


  1. Identify the rule of a growing number pattern.
  2. Use the rule of a growing number pattern to extend it to subsequent terms (MP.7).
  3. Use the rule of a growing number pattern to find its nth term (MP.7). 
  4. Identify features of a number pattern that aren’t explicit in the rule itself (such as, in a pattern that starts with 2 and the rule is "add 4," all of the terms in the pattern are even) (MP.7). 
  5. Explain why those embedded features are true (e.g., all of the terms in the sequence are even in the above pattern because the starting number is even and the rule is to add an even number, and an even number plus an even number is even, so all of the subsequent terms will be even) (MP.3).
  6. Determine whether a given number is a term in a given pattern and explain why or why not (MP.3).
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Anchor Tasks


Problem 1

Lisa is making triangle patterns out of toothpicks of all the same length. A triangle is made from three toothpicks. Her first pattern is a single triangle. 

a.   Her second pattern is shown below. How many toothpicks are needed for her second pattern?

b.   Her third pattern is shown below. How many toothpicks are needed for her third pattern? 

c.   If she continued the same pattern, how many toothpicks are needed for the fifth pattern? How many toothpicks are needed for the tenth pattern? 

d.   If you had 24 toothpicks, how many triangles could you make? Explain how you know.

e.   Will there be a pattern in the sequence that uses exactly 37 toothpicks? Why or why not? 

Guiding Questions

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References

Inside Mathematics Problems of the Month Tri-TrianglesLevel A

Tri-Triangles from the Problems of the Month made available by Inside Mathematics under the CC BY-NC-ND 3.0 license. © Noyce Foundation. Accessed Nov. 1, 2018, 12:41 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

Alex made the following pattern by adding the same number each time.

3, 10, 17, 24, 31, …

a.   Find the next two numbers in the pattern.

b.   Why do the values in the pattern alternate between even and odd?

Guiding Questions

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Problem Set


Answer Keys

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Discussion of Problem Set

  • How did you figure out what the rule to Tony’s pattern was in #2? How did you use the same pattern to find the missing values in his new pattern? 
  • How could you change option C in #3 to make it a correct statement? 
  • How do you know all of the values in the pattern in #6 can be divided equally by 7? 

Target Task


Problem 1

Which of these patterns has an odd number as its next term? 

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Problem 2

Jacqueline reads every day over the summer and records the total number of pages she has read. She notices a pattern in the total pages she has read:

4, 8, 12, 16, ______, ______, ______

If her pattern continues, how many pages will she have read the next three days? Fill in the blanks above to extend the pattern.

Student Response

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Additional Practice


The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Extra Practice Problems

Answer Keys

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Word Problems and Fluency Activities

Word Problems and Fluency Activities

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Lesson 22

Lesson Map

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Topic A: Introduction to The Properties of Operations

Topic B: Multiplication and Division by 6 and 7

Topic C: Multiplication and Division by 8 and 9

Topic D: Multiplication and Division by Values Greater than 10

Topic E: Two-Step Word Problems and Patterns in Arithmetic

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