Bucket of Zeros

Today in grade 9 I was in a class where students were working on integers and using the bucket of zeros to show that a negative times a negative will be a positive number. Many times we have been told the rule, but it is important to be able to show why it makes sense.

Students started out by making a bucket of zeros with many zero pairs on their desk.

The next step is to decode the question. This question was -7(-4), which we can be viewed as removing 7 groups of (-4).

Once the 7 groups of (-4) are removed, we look at what’s left.

We have some zero pairs, and also 28 red tiles. So we have proven that -7(-4)=28.

To consolidate, students were doing questions on the board, showing their work with the bucket of zeros.

They then consolidated with a 4 quadrant meaningful note.