This post is an extension of the related post, Backwards Math activity, that shows some of the many variations that teachers have created for this activity in their classrooms. The original activity asks students to use four 4’s to create expressions to equal all the integers from 1 to 100.
One of the variations shows 10 different ways to use four 4’s to create expressions equalling one. In doing so we see parentheses, place value, decimals, square roots, exponents, and more. Factorials and the greatest integer function could also be used to give students a richer experience.
As students see these ways to combine fours, their number sense deepens and their creativity increases. The next step extending this activity might be looking for 10 ways to use four 4’s to create expressions equalling two.
As students gain confidence they are willing to explore new and novel combinations of numbers and their numerical flexibility improves. This is great news for teachers as they ask their students to be able to see and explore algebraic expressions. Give this a try and marvel at the amazing expressions your students will create!
- Mr. L
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will you please put more numbers up for 4 4′s like how to get 15 16 17 18 19 20 etc…
thanx
Hello me,
Take a look at this website which contains solutions. Since I use this puzzle in class, I don’t post usually post answers.
http://www.dwheeler.com/fourfours/fourfours-short.txt
Cordially,
Mr. L
[...] Backwards Math Extension- Four Fours Creating Many Equivalent Expressions [...]
dear mr. l
i want to ask you about equations and expressions please answer soon
Hello maya,
You can use the comments section of the blog to leave questions about equations and expressions. Let me know how I may be of assistance.
-Mr. L
can i get the key terms for backwards math on 4
To Anonymous-
I’m not clear what you mean by “key terms” for Backwards Math.
- Mr. L