Last week I asked #MTBoS followers how they would use mental math to solve 36×25.
How would you use mental math to solve 36×25?
— Heather Johnson (@HthrLynnJ) September 2, 2016
Below are a few responses that I received:
— Tina Cardone (@crstn85) September 2, 2016
@HthrLynnJ 3*25=75, but it is really 30, not 3 so it’s 750. 6*25=150. 750+150=(700+100)+(50+50)=800+100=900
— Annie Forest (@mrsforest) September 2, 2016
— Max Goldstein (@maxgoldst) September 2, 2016
Having students use mental math to solve multiplication problems such as 36×25 can provide them with opportunities to informally use mathematical properties that are fundamental to algebraic reasoning.
- Tina’s solution shows a way to use the associative property of multiplication to find the product: 25×36=25x(4×9)=(25×4)x9
- Annie’s solution shows a way to use the distributive property of multiplication over addition to find the product: 25×36=25*30+25*6
- Max’s solution shows a way to use the associative property of multiplication as well as different equivalent expressions to find the product: 25×36=(5×5)x(6×6)=(5×6)x(5×6)=(5×6)^2=30^2=10^2*3^2=100*9
When students talk about their mathematical thinking, they have opportunities to clarify their ideas and to make meaning from symbol sentences. Tina, Annie, and Max all mentioned how they interpreted the symbol sentences they wrote. I think it is especially interesting how Tina said that the first two sentences were how she “thought it through.”
When I investigate students’ reasoning in my own research, I have learned that students may use the same written representation, but think about it very differently. The selection of Tweets that I included here is only a sampling of the interesting ways that #MTBoS followers thought about 36×25.
I wonder what might have changed if I had asked #MTBoS followers how they would use mental math to solve 25×36.
This semester, I am teaching a fully online class – Expanding conceptions of algebra— #MTED5622. In #MTED5622 we are investigating how students in grades K-12 engage in Algebraic Reasoning. One of the resources we are using is from NCTM’s Essential Understanding Series –Developing Essential Understanding of Algebraic Thinking Grades 3-5. This fall, I’ll be working to include blog posts focused on my work in teaching this course.