This post is an extension of the related posts, Backwards Math activity, and Backwards Math Extension, that show 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.
This post shows how to create expressions using the four 5’s. In doing so, the activity provides a great way to transition from number sense to algebra. Students can see the relationships between the numerical expressions using four 4’s and then four 5’s, and thus the underlying algebra that rules all number concepts and operations.
The graphic shows ways to create expressions equalling 1-10 using four 5’s. In doing so we see parentheses, place value, decimals, and exponents.
Below the divider are expressions that equal 1, 2, and 3 using x’s instead of 5’s. These expressions are correct for all values of x not equal to zero, and give teachers the opportunity to show students some algebraic properties.
As students see these ways to combine fives, their algebra sense deepens and their receptivity to new ideas increases. The next step extending this activity might be looking for ways to use four 3’s to create expressions equalling numbers from zero to 100.
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 enjoy the creativity your students show!
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