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##### Cross Simplification Lesson

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 Teacherbee_4 Joined: Jul 2011 Posts: 6,027 Senior Member
Teacherbee_4

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Posts: 6,027
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Cross Simplification Lesson
12-04-2017, 07:02 PM
 #1

One of our lessons in math this week is cross-simplifying/cross cancelling when multiplying fractions. While I think the procedure is easy for kids to "get", teaching it conceptually so the kids understand WHY they can do it when they multiply (and not, say, when they are adding), is a challenge. Does anyone have any engaging and/or hands-on lessons to help students see why this works? Thanks!

 NerdTeach Joined: Aug 2017 Posts: 153 Full Member
NerdTeach

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12-05-2017, 04:31 AM
 #2

I teach middle and high school.

I usually start by discussing we can simplify something like 2/2 to just be 1. Once they conceptually understand, then I move on to something like 36/12.

After that, I show them a problem like 3/4 * 12/3. We multiply them first so that it reads 36/12 and simplify. Then, I take a step back, and show them the individual steps on multiplying. (3*12)/(4*3). We look at how the 3's "cancel" just like the first problem did with 2/2.

This leads to a discussion about how this may seem more complicated than just multiplying. But sometimes we have really complicated fractions. Instead of multiplying very large numbers then simplifying, we can simplify then multiply, which is sometimes easier.

I am not sure about anything hands-on, but this is usually how I approach this topic.

 Teddi9192 Joined: Feb 2007 Posts: 4,970 Senior Member
Teddi9192

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12-05-2017, 08:27 AM
 #3

we start with factorization. They list all the prime factors of each number then cross out

6 8
- x -
9 12

6x8
-----
9x12

2x3x2x2x2
-------------
3x3x2x2x3

2x2
----
3x3

4
-
9

 Singvogel Joined: Apr 2014 Posts: 221 Full Member
Singvogel

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12-05-2017, 09:26 PM
 #4

I start this lesson sequence with- "If I multiply [student name] by one, he/she is still [student name]." Continue this silliness, and start to substitute 3 over 3 for the one. Then exaggerate with something like 3,492 over 3,492. This focuses the multiplicative identity concept. Then reverse it with questioning if dividing by one or a form of one has the same result.

When we get to actually multiplying, I introduce "reducing ahead" so that I don't have to do "big arithmetic." Students really buy into it when they see that it saves them a mess at the end of the problem.This "simplifies", pun intended, the work.

This idea also ties in to other topics when we think about what's inside numbers. As PP suggested, seeing the numerators and denominators as their prime factorizations, which lends itself to finding the giant ones (ones in fraction form).

 Teacherbee_4 Joined: Jul 2011 Posts: 6,027 Senior Member
Teacherbee_4

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Thanks
12-06-2017, 06:34 PM
 #5

Thanks for the ideas! I especially like the prime factorization explanation.

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