## Math Picture Book Post #7: Bean Thirteen

A fewÂ ago, I was invited to teach aÂ lesson on division (Grade 3).Â First, I read Bean Thirteen aloud â€“ once just for fun.Â AboutÂ Bean Thirteen, from the author:

Ralph warns Flora not to pick that thirteenth bean. Everyone knows itâ€™s unlucky. Now that theyâ€™re stuck with it, how can they make it disappear? If they each eat half the beans, thereâ€™s still one left over. And if they invite a friend over, they each eat four beans, but thereâ€™s still one left over! And four friends could each eat three beans, but thereâ€™s still one left over! How will they escape the curse of Bean Thirteen?

(A funny story about beans, that may secretly be about . . .Â math!)

Next, we revisited several of the pages. I asked students to write an equation to match the picture. I modelled this using magnetic “bean counters.”Â For the page above, students suggested 2Â Ã— 6 + 1 = 13; I introduced 13Â Ã· 2 = 6 R 1. We discussed and recorded the meaning of this:

In pairs, students then chose their own number of beans (counters) and built different division as sharing stories for this number. They recorded (.doc)Â their stories using pictures, numbers, and words:

I called on students to share their stories with the class. They observed that some numbers gave remainders more so than others; Bean Thirteen can also be used to explore even/odd and prime/composite numbers.

This lesson served as the students’ introduction to division. I wrestled with the decision to introduce remainders at this time. An alternative problem â€“ one consistent with both the prescribed learning outcomesÂ and recommended learning resources â€“ might be toÂ start with 18 beans â€“ a “nice” dividendÂ â€“ and share equally among 2, 3, 6, and 9 bugs â€“ “nice” divisors. NoteÂ 15 Ã· 3 = 4 R 3 (andÂ 15 Ã· 2 = 6 R 3) above. This mistake would not have happened had IÂ not introduced remainders. I wonder if including remainders makes it more difficult for students to understand division and relate division to multiplication.