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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).

Tommi
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user8046
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    A very similar question: When should we first teach variables in school math? And how? – Jasper Apr 17 '17 at 20:00
  • 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. – Tommi Apr 18 '17 at 04:26
  • Perhaps, you may find this helpful. – user 85795 Apr 18 '17 at 22:31
  • 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. – Andrew Apr 19 '17 at 12:21
  • You might be interested in reading the progression documents for the Common Core State Standards for K-5and 6-8. Links: https://commoncoretools.files.wordpress.com/2011/05/ccss_progression_cc_oa_k5_2011_05_302.pdf ) https://commoncoretools.files.wordpress.com/2011/04/ccss_progression_ee_2011_04_25.pdf ) – Andrew Apr 19 '17 at 12:24
  • One of the difficulties with the concept of "variable" (that is, an indeterminate quantity) is that it is fundamentally abstract. The whole point is to represent a general class of examples without recourse to specific examples, so inherent in the introduction of variables is the observation that two apparently completely different specific problems are representations of a single underlying mathematical equation. It seems therefore that what one has to do is construct parallel real life examples that, although presented in different contexts, give rise to the same algebra problem. – Dan Fox Apr 20 '17 at 07:04

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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.

JTP - Apologise to Monica
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