Bucket of Zeros

Today I had the chance to work with a grade 9 class on integer adding, subtracting and multiplying.

The bucket of zeros includes understanding of zero pairs.

When adding, the tile are all combined, and zero pairs identified, and the answer will be any unpaired tiles at the end.

Subtracting involves using the bucket a bit more. There are animations in my slideshow which show how groups are taken away, including from the bucket, and how by using zero pairs the result is simplified.

The bucket can also be used for questions like -3(2), which can also be written as 0-3(2), which would mean we start with zero, then remove 3 groups of 2. The addition of the 0 in the front of the questions helps to ground us with our original bucket of zero.

It is with this type of task that I can explain to people why a negative times a negative is a positive, or why a negative times a positive is a negative. It brings conceptual understanding rather than just memorizing some rules.

It was great to see students engaging with manipulative tiles at their desks and building confidence with this new thinking routine.