Squares and Triangles

One day after class, a parent came to me and ask about a question he saw in one of the challenging questions I gave to the students.


He said he would (as would many adults) solve this using simultaneous equations (or System of linear Equations) but would like to know how to teach his kid in 3rd grade without the use of algebra. I invited him to stay for a while to observe the next class.

Students were given Think-Pair-Share to solve that particular question and after minutes of work time, a student raised her hand and this is what she came up with.

“Square is the number in the middle. So, its value is 22+4 divided 2, which is 13.”

“Triangle is difference between the middle number to one of the end numbers, so it is 22-4 divided by 2, which is 9.”


One of my favorite teaching tool is the number line. It can be used for Kindergarten kids right to middle school students. In the above example, 3rd grade students are introduced to early algebraic thinking using a tool they are familiar with. When they finally solve this question using simultaneous equations later on, they would be able to relate to this learning experience. Isn’t that a great way to learn?

Related Resources

Addition Subtraction and Number Sense

For more related resources, please see our Number Sense, Addition and Subtraction page.

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