Multi-Digit Division

Lesson 14

Math

Unit 3

4th Grade

Lesson 14 of 16

Objective


 Identify and extend growing number patterns.

Common Core Standards


Core Standards

  • 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

  • 3.OA.D.9

Criteria for Success


  1. Identify a possible 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


Note that whenever students are given the first few terms in a pattern and asked to identify the rule or to continue the pattern, there are many possible correct answers. For example, say "students are asked to continue the pattern 2, 4, 6, 8, ... Here are some legitimate responses:

  • Cody: I am thinking of a “plus 2 pattern,” so it continues 10, 12, 14, 16, . . . 
  • Ali: I am thinking of a repeating pattern, so it continues 2, 4, 6, 8, 2, 4, 6, 8, . . . 
  • Suri: I am thinking of the units digit in the multiples of 2, so it continues 0, 2, 4, 6, 8, 0, 2, . . .”, among others (CC to RP Progression, p. 40). 

Thus, if students are not told the rule but asked to infer it or to extend a pattern, consider that there may be more than one correct answer, and validate any reasonable response. 

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Anchor Tasks


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. 

a.   How many people can sit at four tables pushed together? Five tables pushed together? Six tables pushed together?

b.   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 Fishtank Learning, Inc.

Problem 2

Here are two patterns:

  • Pattern A: 3, 6, 9, 12, … 
  • Pattern B: 97, 91, 85, 79, …

For each of the patterns above, 

a.   Determine a possible rule for the pattern.

b.   Based on that rule, find the next two steps of the pattern.

c.   Based on that rule, determine whether 54 will be in the pattern.

Guiding Questions

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Problem 3

Bo's class is counting by 10 and then by 9. The left column shows the numbers they say when counting by 10.

counting by 10 counting by 9
10  
20  
30  
40  
50  
60  
70  
80  
90  
100  

a.   Complete the list of the numbers the class will say when counting by 9. What patterns do you notice about the features of the numerical patterns? Make at least two observations about each list. 

b.   For the numbers in the “counting by 10” column, why do you think:

  1. The digits in the tens place change the way they do? 
  2. The digits in the ones place are the way they are?

c.   For the numbers in the “counting by 9” column, why do you think the digits in the ones place change the way they do? Explain your reasoning. 

Guiding Questions

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References

Illustrative Mathematics Count by 10 and by 9Grade 4 Lesson 4 Activity 1

Count by 10 and by 9, accessed on Nov. 24, 2021, 11:17 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 Fishtank Learning, Inc.

Problem Set


Answer Keys

Unlock the answer keys for this lesson's problem set and extra practice problems to save time and support student learning.

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. How did you determine if 8,715 was going to be in the pattern? How did you determine which number term it would be?
  • What rule did you create for Juan's pattern in Part (c)? How did you know that it decreases overall?

Target Task


The first number in a pattern is 5. The pattern rule is to add 6.

a.   Fill in the blanks below to write up to the seventh term in the pattern. 

5, ___, ___, ___, ___, ___, ___

b.   Why are all of the numbers in the pattern in Part (a) odd?

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

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

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Lesson 13

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Lesson 15

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Understanding and Interpreting Remainders

Topic B: Division of up to Four-Digit Whole Numbers by One-Digit Whole Numbers

Topic C: Multi-Step Word Problems and Patterns

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