Fluency Task

Today I did a fluency task with a colleague’s grade 9 math class. Students are working on their multiplication skills, and today’s task was to use base 10 blocks to build a rectangle. They used 6 of the tens and 12 of the unit blocks.

Groups had to try to build all of the different possible rectangles. We then had a good conversation about how all the rectangles had the same area of 72, but the dimensions are different. We know area is length times width, so we know that each rectangle has a different multiplication represented.

1×72 and 2×36 and 3×24 and 4×18 and 6×12 and 8×9 were all possibilities.

we looked at doubling and halving when exploring the list

1×72, double the 1, halve the 72 and you get 2×36. Double the 2 and halve the 36 and you get 4×18, double the 4 and halve the 18 and you get 8×9.

we looked at how doubling and halving can help us make multiplying easier. Instead of multiplying 15×60 we could double the 15 and halve the 60 to make 30×30 which is 900, the same answer as 15×60.

We tried another question as well, 18×7 we halved the 18 and doubled the 7 to make an equivalent multiplication of 9×14. We know 9 is close to 10, so we can do an overshoot and return to get to the answer of 140-10-4=126.

I was interested to see that many students were attempting to skip count by 18s or by 7s. Hopefully we can show different strategies that can be more efficient than skip counting, so students move into more multiplicative thinking and proportional reasoning.