Find Regularity in Repeated Reasoning

I have a question…

  • We look for regularity in multiplication in many ways. And one way we learn multiplication is repeated addition.
  • Additionally, we learn how to add together strings of 3 addends (we rarely ask students to add more than 3 addends, unless we’re working on mastery of 2.NBT.6).

It seems like you could develop a lesson that incorporates the 2. I’m thinking of building a lesson based on something like:

2+3+2+3+2+3+2+3

The multiplication in this problem is evident and there are multiple ways to use multiplication to solve. For example, 5×4 as 4(2+3) vs (2×4)+(3×4).

Could students then begin to see larger strings and more complicated combinations in the same way?

Another one:

6+7+4+3

Lends itself to (7×3)-1. You could also use the making tens strategy (6+4)+(7+3).

How would you use repeated reasoning to solve these?

24+8+4+3+9

5+3+5+4+5+2+5+1

(adapted from Number Talks, p. 187)

Back to my question: Are there already lessons like this out there that I don’t know about? Have you ever used Dot Talks in the upper grades to teach this visually?

If you have more ideas for great number sentences or visuals that lend themselves to an exploration of multiplication, post them in the comments below!

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