When are sentence frames helpful? What is the purpose of sentence frames? In this post, I share how sentence frames can be used to help students catch mistakes in their own mathematical claims using sentence frames that include a Claim, Evidence, and Reasoning (CER), which is a structure often used in science classrooms.

In this lesson on whether a relation is a function, I gave teams a Desmos Card Sort (adapted from Sarah Carter, MathEqualsLove) to sort out whether a table, mapping, graph, or list of ordered pairs are functions:

Below were the directions I provided before the teams started: 

I provided the following sentence frames on small cards to each team:

“This relation is a function because every input has exactly one output.”

“This relation is NOT a function because some inputs have more than one output. For example, the input _____ has the outputs of _____ and _____ .” 

As I walked around the classroom, I heard only some (about 50% of) students using the sentence frames. I saw some students reach for the cards when they were stuck, and I also stopped at some teams to encourage them to use the sentence frames. 

After most teams finished the card sort, I asked the whole class to “help” me complete the card sort by using the sentence frames. Here, because students already had a chance to practice with their team, I felt comfortable “cold calling” on students to pick any card to help me sort into the correct pile – “Function” or “Not a Function.” If students started to deviate from the sentence frames, I asked them to read the sentence frame while.

Again, not only were these sentence frames available to students for communicating thoughts, but it was also helpful in supporting students’ understanding of functions. For example, I had a student pick the lower right table (not a function) to sort. These students started off by saying, “This relation is a function because every input has exactly one output. WAIT….” and then pivoted to “…ok wait. This relation is NOT a function because some inputs have more than one output. For example…..um…the input 4 has the outputs of 3 and…..2.”

This was great to see how sentence frames can help students state their claim (this relation is/is not a function), the reason (because every input has exactly one output/some inputs have more than one output), and the evidence (for example, the input ___ has the outputs of__and ___) to further their conceptual understanding of a function in addition to helping them verbally voice their ideas!