Developing Maths Langugae

 Over the past 2 weeks we have been focusing on how to recognise and work out if a number is odd or even. During this time we have made baskets to collect the numbers that are odd and even both physically and digitally.

We looked at how we can look at the last digit of a number to see if the number is odd or even. During our sharing time myself or one of the students would re-voice what a student said for example:

Student A: 38 is an even number because of the 8

Teacher: So are you saying because the last digit is an 8 it is an even number?

Student A: Yes, that last number is 8 and I know that the numbers that end with, 2, 4, 6, 8 or 0 are even numbers.

Student C: I know that numbers that end with a 1, 3, 5, 7 or 9 are odd numbers.

Teacher: Yes that last number or digit helps us to see or decide if it's an odd or even number.

I then explained to the students that we would also be able to share the number between 2 and if both people got the same or equal amount for example: 7 and 7 it would be an even number, but if the people got different for example: 7 and 8 it would be an odd number.

I then set a task for students to work out odd and even numbers through sharing. I assumed, in error, that my students understood sharing as we share our scissors, we share games, and we had talked about what sharing looked like and even did an example on the mat of sharing the marbles between 5 people.

When students worked independently working out if a number was odd or even by sharing we ended up with all sorts of results.

Student A: 10 + 8 =18 this is an even number because they both end in an even number (meaning the 10 and the 8).

Student B: 10 + 15 = 25 this is odd because the total ends in a 5

Student C: 9 + 7 = 16 this is odd because the two numbers are different (the 9 and 7 are not the same).

I stopped the session and decided to try again the next day with a different approach. We begun our session by making groups of 5 or 6 and placing counters in the middle, for the students to share among themselves. After a short amount of time I stopped the students and asked them to count how many counters they each had. Not one of the groups had the same amount as each other we had 9,12,11 all from the same group.

I then asked the students if we share equally what would that look like. After much discussion one student stated that thinking about the word equal we should all have the same. Other students agreed with, yes that's right, Yea equal means the same. We then tried the process of sharing again. This time we had a little more success in that 2 groups were successful at sharing equally. I then asked these groups to share what they had done to be successful.

They shared with the class that they took turns I re-voiced this and said so you are saying that each person had to take a turn in the correct order is that correct because I know some of the other groups took turns but they didn't end up with equal or the same amount of counters.

Student A: Yes Ms that is right you can't take your turn until the person beside you has had their turn.

Teacher: Ok let's try that again.

Here are some images of us sharing equally so that we all have the same.

Now that we can equally share in a large group we are going back to having a partner to see if the number is odd or even.

Teacher: When we are sharing our number how will we know if the number ends up being an odd or even number?

Student A: I think there will be a counter left over in the middle because we both have to have the same for it to be an even number.

Student B: Yes if one person has 1 more than the other it is an odd number.

Teacher: So if we lined up outside and I said that I wanted two equal lines would that be an odd or even number?

Student C: I think if the numbers were both the same the number would be an even number.

We then proceeded to line up outside, we had 13 in one line and 14 in the other line.

Student D: Ms if we turn to our partner and hold hands if everyone can hold hands with someone we will have an even number.

Student E: Ms I don't have a partner, I'm the odd one out. Our number must be odd.

The next few days whenever we lined up to go somewhere my students wanted to work out if they had an odd or even number. I have since set an odd and even task where students used both the strategies of working out an odd or even number (last digit and equal sharing). Although most students prefer to use the last digit strategy (because they have realised they can work out if a number is odd or even whatever the size of the number) I knew that it was important for them to have the knowledge and understanding of equal sharing, especially as we move on to multiplication and arrays.