Last week I made one of my regular visits to the two grades 4&5 classes at Byng Elementary. For this set of number talks, we focused on multiplication facts and strategies the students could use to find other facts if they “knew” one related fact.
For example, we began with 3×8 in one class (and 3X6 in the other) and I asked the students what other x8 facts the students could figure out using what they knew about 3×8. It took some prompting but we got to the ideas of doubling, tripling, adding one more eight, subtracting an eight, doubling and adding, etc.
So for example, if you know 3×8 is 24, you could figure out what 7×8 is by first doubling 24 (which is 6×8) to get 48 and then adding one more 8 (to get to 7×8) to get to 56.
One student realized you could double and double again to figure out 12×8 and the students discussed whether to call that a double double or a quadruple. One wise student noted that if you doubled and then doubled again, then it would be a double double but if you multiplied the product by 4 (or added four times) then it would be a quadruple.
After a group number talk, I put a related fact on the whiteboard and asked the students to show the different ways they could figure out the other facts and using word labels to indicate what strategies they used.
Some students used their own decomposition strategies.
We asked the students to come up and record their strategies and the way they had recorded them.
For both classes, this was the first time the students had recorded their use of strategies like this and many found it challenging to communicate what they did in their head. One teaching and learning opportunity arose when I noticed students were using “run-on” equations to record their mathematical computation process by using two or more “equals” signs in their equations. I asked the students what the symbol meant, and like most students their age, those that spoke up felt it meant “the end” or “you put the answer after it”. This is a huge misconception amongst many students. We discussed how the equals sign was a symbol of equality and meant that both sides of the equation were balanced. One student clearly explained that you had to show each part or each step of the process with its own equation.
I used the example of a teeter totter and we role-played that a bit and then I asked what would happened if we placed two fulcrums under the teeter totter – it just wouldn’t work. Sometimes students need a visual or an analogy of sorts to help them make sense of an abstract concept.
The goal is to have students “fluent” with their multiplication facts by the end of grade 5 and practicing mental mathematics strategies as well as developing students’ number sense as to why those strategies work is a critical piece of developing computational fluency.