Patterns in the tables of integers

Mathematics is said to be the science of patterns. Activities that involve pattern searching is a great way to engage students in mathematical thinking. Here are some of my favorites for teaching positive and negative integers. If you are wondering why most of my posts are about integers it’s because I’m doing a Lesson Study with a group of Mathematics I (Year 7) teachers about this topic. Last week we concluded the first cycle of our research lessons on teaching subtraction of integers.

The first task students need to do with the tables is to list 3-5 observations. From there you can start asking the ‘whys’ for each observation. Sample questions are provided for each table below:

1. Adding integers

Sample questions for discussion:

a) Under what conditions will the sum be positive? negative? zero?

b) Why are there the same numbers in a diagonal?

c) How come that the sum is increasing from left to right, from bottom to top?

2. Taking away integers

Sample questions for discussion:

a) Under what conditions will the difference be positive? negative? zero?

b) Why are there the same number in a diagonal?

c) How come that for each row/column, the difference is decreasing?

3. Multiplying integers

Sample question for discussion:

a) Under what conditions will the sum be positive? negative? zero?

4. Dividing Integers

Sample question for discussion:

a) Under what conditions will the difference be positive? negative? zero?

       b) Does dividing integers still results to an integer? What do we call these new numbers?

Feel free to share your ideas/questions for discussion.

You may also want to share other  math concepts that students can learn with these tables.