# Odd & Even Numbers – Additive Structure

This task is designed for my class working on First Level. They have a lot of gaps in their basic knowledge. We’ll be talking about odd and even numbers this week, looking at the hundred square and getting a sense of these numbers.

This task is about getting to some of the general properties, namely:

• Odd + odd = even
• Even + even = even
• Odd + even = odd

That set of results strikes me as being quite familiar. Think of multiplication or division of negative numbers. When the signs are the same the answer is positive. When they differ it is odd.

The first 2 questions are to make sure pupils understand the task itself. After that we do some variations of 10 and 16, looking at how they can be arrived at with various additions and subtractions. There are obviously A LOT of different ways of answering some of these questions. I intend to intro the lesson by doing some questioning along the line of “give me an odd and even number which add to 9, and another, and another”, inspired by Questions and Prompts. Another follow up might be “give me an even number minus an odd number that gives 9, that nobody else is thinking of”.

The task opens up a little creativity to pupils, there are correct answers, but not only 1 correct answer. This sort of freedom within constraints might be new to some of the class.

Question 12 and 13 are simply just to increase the mental complexity a little.

Questions 14, 15 and 16 are the key. This is where we draw the conclusions. I tried the task with my own kids, who are P5 and they wanted to write specifics in the boxes to prove or disprove the statements. This is fine. Of course, it is not a proof, but I think we are a bit away from that with this class. There is potential to do a nice geometric proof using Cuisenaire etc.