# MathBait™ Multiplication

# Does It Matter?

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In this activity, we get students thinking and warmed up to The Fundamental Theorem of Arithmetic or in other words, all factorizations of a number are equivalent and thus while there are many paths, all roads lead to the same result.

## Details

Resource Type

Warm Up

Primary Topic

Primes & Factoring

Unit

7

Activity

13

of

22

Working with prime numbers is so important, the topic we will introduce in this warm up is called *The Fundamental Theorem of Arithmetic,* which basically says there is exactly one way to build a number.

Circling back to a previous activity, present students with the number 90 and ask them to write 90 as a product of 3 or 4 factors. There are multiple options, here are a few:

90=3×3×10

90=3×6×5

90=15×3×2

90=3×3×2×5

Identify students with different factors and present them to students. Explain each of these looks different, but are they different? Allow students to share their thoughts.

Since every statement is equal to 90, each representation is equivalent - they are all 90. If multiple students figured out four factors, display the different orders (and if possible different methods). Make sure students agree these are all the same. Demonstrate how we can start with 90=9×10, find 9=3×3 and substitute to have 3×3×10 before identifying 10=2×5 and substituting to end up with 3×3×2×5. If we started with a different fact, such as 90=15×6, using substitution we could end up with 3×5×3×2. We know because of the commutative property these are the same, or we can reorder the numbers to make both expressions look the same.

Announce the most factors we can use to write 90 is 4 without using ones. (Circle back to *Centipede* if needed to remind students this would be our max multiplier). Ask students to justify why this claim is true. Students may or may not recall prime numbers, but should be able to conclude that each of the values 2, 3, and 5 don't have any other factors except 1.

Wrap up by telling students in today's lesson, our goal is to find the max multipliers of numbers. That is, to break a number down into the longest possible multiplication statement without using ones. Just as students found different ways to write 90, the order in which we break it down will not matter because we are using substitution and only swapping out equal values. This provides a lot of flexibility! But, in order to know we have reached the max multiplier, we have to identify when a factor cannot be broken down any further. Prompt students to recall what we call this type of number.

Based on student understanding in the warm up, decide if revisiting *Build It* from MathBait™ Multiplication Part 2 would be beneficial as a review. We have included it here if needed.

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