Multi-Digit Division

Lesson 14

Objective

 Identify and extend growing number patterns.

Common Core Standards

Core Standards

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  • 4.OA.C.5 — Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

Foundational Standards

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  • 3.OA.D.9

Criteria for Success

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  1. Identify the rule of a growing number pattern (MP.7, MP.8).
  2. Use the rule of a growing number pattern to extend it to subsequent term (MP.8).
  3. Use the rule of a growing number pattern to find its $${n^{\mathrm{th}}}$$ term (MP.8).
  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, MP.8).
  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, MP.7, MP.8).
  6. Determine whether a given number is a term in a given pattern and explain why or why not (MP.3).

Tips for Teachers

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The Progressions state that “the Standards do not require students to infer or guess the underlying rule for a pattern, but rather ask them to generate a pattern from a given rule and identify features of the given pattern” (OA Progression, p. 31). However, because standardized test items exist in which students are asked to infer the underlying rule, students are asked to do so in this lesson. You might decide to cut or modify tasks that ask students to do so, including changing Anchor Task #2 to include the rule for each given pattern and similarly for corresponding tasks on the Problem Set and Homework. 

Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Task 2 (benefits from worked example). Find more guidance on adapting our math curriculum for remote learning here.

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Anchor Tasks

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Problem 1

Giovanni’s Pizza can seat groups of different sizes at their tables. The square tables at Giovanni’s Pizza seat 4 people each. For bigger groups, square tables can be joined by pushing them together so that they share a side. Two tables pushed together seat 6 people. Three tables pushed together can seat 8 people. 

  1. How many people can sit at four tables pushed together? Five tables pushed together? Six tables pushed together? 
  2. CHALLENGE: How many tables would be needed to seat 20 people?

Guiding Questions

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References

North Carolina Department of Public Instruction 4.OA TasksTable Dilemma

4.OA Tasks from the 3-5 Formative Instructional and Assessment Tasks for the Standards in Mathematics, made available by the North Carolina Department of Public Instruction (NCDPI) Elementary Mathematics Consultants and their public school partners under the CC BY-NC-SA 3.0 license. Accessed March 14, 2019, 2:16 p.m..

Modified by The Match Foundation, Inc.

Problem 2

  1. Find the next two numbers in each of the skip-counting patterns below. 
    1. 4, 8, 12, 16, ____, ____
    2. 97, 91, 85, 79, ____, ____
  2. Will the number 64 be in pattern (a)? What about pattern (b)? How do you know? 

Guiding Questions

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Problem 3

  1. The table below shows a list of numbers. For every number listed in the table, add 7. Record the result on the right.
Number Number plus 7
1  
2  
3  
4  
5  
10  
20  
  1. What happens when we add an odd number to an odd number? An even number to an odd number? Why? 

Guiding Questions

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References

Illustrative Mathematics Double Plus OneIncluding Lesson Plan - Follow the Clues

Double Plus One, accessed on Jan. 18, 2018, 9:25 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by The Match Foundation, Inc.

Problem Set & Homework

Discussion of Problem Set

  • Look at #2. Why do the numbers alternate between even and odd?
  • Look at #3. Was anyone able to determine whether 103 was going to be in the pattern without writing out the pattern all the way up to 103? How did you figure it out?
  • Compare #2 and #3. Which one grows faster? Why?
  • Look at #4. What was the relationship between the row number and the number of cans in the row? What was the relationship between the number of cans in a row and the number of cans in the previous row?
  • Look at #6. Why were all of the numbers odd? 
  • What rule did you create for Juan's pattern in Partc C? How did you know that it decrerases overall?

Target Task

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The first number in a pattern is 3. The pattern rule is to add 4. 

  1. What is the seventh number in the pattern?

3, ___, ___, ___, ___, ___, ___

  1. Explain why all of the terms in the pattern are odd. 

References

PARCC Released Items Math Spring Operational 2016 Grade 4 Released ItemsQuestion #19

Math Spring Operational 2016 Grade 4 Released Items is made available by The Partnership for Assessment of Readiness for College and Careers (PARCC). Copyright © 2017 All Rights Reserved. Accessed Dec. 22, 2017, 1:50 p.m..

Modified by The Match Foundation, Inc.

Mastery Response

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