# Multi-Digit and Fraction Computation

## Objective

Use prime factorization to represent numbers as products of prime factors.

## Common Core Standards

### Core Standards

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• 6.NS.B.4 — Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1—100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).

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• 4.OA.B.4

## Criteria for Success

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1. Understand and define the terms prime number, composite number, multiples, factors, and prime factorization.
2. Understand that every number is composed of prime number factors and that every number can be factored in a way to be represented by these prime factors.
3. Write numbers as products of prime factors in exponential expressions.

## Tips for Teachers

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Anchor Problem #3 is optional and requires some materials preparation. These dominoes cards can be printed so the pictures can be cut out and optionally pasted onto a cardstock or a different colored paper background. See the note for Anchor Problem #3 for more information.

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• Problem Set
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## Anchor Problems

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### Problem 1

Four numbers are shown below. Each number has something unique about it that is unlike the other three numbers. What makes each number different from the others?

 16 6 35 5

#### Guiding Questions

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### Problem 2

For each number below, use a factor tree to write the number as a product of prime factors.

48                                        140

#### Guiding Questions

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### Problem 3

The pictures below represent the numbers 1–7. What do you notice? What patterns do you see? How are these pictures related to the prime factorization of the numbers?

The pictures below represent the numbers 8–14. What do you notice? What patterns do you see? How are these pictures related to the prime factorization of the numbers?

What number does the picture below represent? What would the picture look like for the number 28?

Play factor dominoes using the cards for numbers 1–60.

#### Guiding Questions

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#### References

The Math in Your Feet New Math Game: Factor Dominoes!

New Math Game: Factor Dominoes! by Malke Rosenfeld is made available on The Math in Your Feet Blog under the CC BY-NC-SA 4.0 license. Accessed Sept. 28, 2017, 4:19 p.m..

Modified by The Match Foundation, Inc.

## Problem Set

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With Fishtank Plus, you can download a complete problem set and answer key for this lesson. Download Sample

The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

• Include problems where students reason about prime factorization using the commutative and associative properties; for example: Are the two expressions equivalent? Why or why not? ${2^3 \cdot 3^2 \cdot 5}$ and ${(2 \cdot 3)(2 \cdot 3)(2 \cdot 5)}$
• Have students play additional rounds of the factor dominoes game.