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Today I had a discussion on how to introduce the basic concept of variables in math using real life examples. We came up with ideas of using boxes containing matches, or M&Ms representing the variables and little piles of the actual items so e.g. 4 boxes with 2 M&Ms would equal a small pile of M&Ms. Problems of giving candy to kids aside, is that a proper way to introduce the concept of a variable? Are there better real life examples which they can perform at school?

Do you have any ideas how to teach this to 13 year olds with a very mixed performance in school (really slow ones to some fast learners).

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    $\begingroup$ A very similar question: When should we first teach variables in school math? And how? $\endgroup$
    – Jasper
    Apr 17, 2017 at 20:00
  • $\begingroup$ This question seems to consist of two parts. The first paragraph is a fine question, while the second might be a duplicate. On Stackexchange sites we only ask one question per question, so maybe remove the second one and ask it as a separate question if the linked one does not provide answers. $\endgroup$
    – Tommi
    Apr 18, 2017 at 4:26
  • $\begingroup$ Perhaps, you may find this helpful. $\endgroup$
    – user 85795
    Apr 18, 2017 at 22:31
  • $\begingroup$ Simple questions like "What number do you add to 5 to get eight" can be written with a box for the missing number, then later the box can be replaced with a variable. At this stage students should be solving simple equations by inspection, not using algebra. $\endgroup$
    – Andrew
    Apr 19, 2017 at 12:21
  • $\begingroup$ You might be interested in reading the progression documents for the Common Core State Standards for K-5and 6-8. Links: commoncoretools.files.wordpress.com/2011/05/… ) commoncoretools.files.wordpress.com/2011/04/… ) $\endgroup$
    – Andrew
    Apr 19, 2017 at 12:24

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I'm sticking with food math here. The "recipe" for cooking rice is a 2:1 ratio of water to rice. You can show that W=2R and start the discussion by telling students that the box says to use, say 2 cups of rice and 4 cups water. But you realize that there are 3 cups of raw rice and you don't want to waste what's left, nor run to the store for more. Since W=2R, you see that W=2*3 = 6, and use all the rice with 6 cups water.

You can create other problems with pizza slices. "Knowing that, on average, boys eat 3 slices and girls, 2 (pls forgive the sexism, this data is pretty accurate) create an equation to show how many slices are needed for the next soccer meet." The 8 to a pie also is great to show fractions. I resort to this with high school students who need help there.

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