Maths on the move

1. Maths on the move Cookie Count Room 13 – Year 2 Class 2007

2. Overview of Unit Topic: Cookie Count and more… Learning Area: Mathematics Strand: Number Key Ideas: Children generate and explore a variety of computational strategies to use numbers in daily activities when they need to estimate and quantify. Id T C KC1 KC6 Outcomes:1.7 Describes, represents and uses a variety of counting strategies and the four number operations to estimate and quantify collections of objects, units of comparison and amounts of money. In T C KC2 1.8 Uses counting strategies to answer questions about situations that involve number operations, use of a calculator, and informal and standard algorithms. Id T C KC7 Other Learning Areas integrated into this unit: ICT and Visual Arts

3. Overview of lessons Lesson 1 Cookie Count – small groups Lesson 2 Dividing into 2 groups a different way. Then into 4 groups – whole class. Lesson 3 Doing it all again and recording – whole class. Lesson 4 Monster Share – individual and small groups Lesson 5 How many cookies can I make? Lesson 6 Sharing the play dough cookies. How many is there altogether? How many will I get?

4. Lesson 1: Cookie Count MaterialsAbout eighty (80) counters. These are the cookies.One (1) paper plate. From Maths 300 This problem was inspired by The Doorbell Rang, Pat Hutchins, Puffin, 1988. • Make your own tray with this number of cookies. • 1. Two friends are about to share the cookies. How many do they get each? • Two more friends arrive before any are eaten. How many do they each get now? • 3. Then another two friends arrive. How many now? • 4. Finally another six friends arrive! How many does each person get?

5. Lesson 1 Cookie countI introduced the lesson by reading through the instructions and explaining the task.Students worked in small groups and only did the first question.80 cookies shared between two friends. How many do they each get?A lot of students knew the answer but found it hard to explain how they worked it out.It took some time for students to ‘work together’ instead of all wanting to be ‘the leader’. • This group had several goes at dividing their 80 cookies into 2 groups. In the end they decided to take it in turns to take one each and ended up with three piles. • Then they divided the 3rd pile in half again, adding half to the 1st pile and the other half to the 2nd pile.

6. This group worked really well together. Most of them knew the answer before they began the task. • They put their cookies into groups of 5 so each person had four groups of 5. Then they took it in turns to put groups of 5 cookies onto the 2 plates. • They recorded it as • 40 + 40 = 80

7. This group put the 80 cookies in a circle on the floor. Split the circle in half (by estimating where ½ was), put each half onto a plate and then counted each pile to make sure there were 40 on each plate. • They were pretty close. 39 on 1 plate and 41 on the other. • The fourth group put their cookies into groups of 10, counted by 10s to check there were 80 counters. Then they took it in turns to put groups of 10 onto each plate until all the cookies were gone.

8. Lesson 2 – Dividing 80 cookies into 2 groups a different way and then into 4 groups – whole class The second time we did this lesson we did it as a whole class using students as the ‘friends’ sitting in the middle of the mat with the rest of the class sitting around the outside. This was much better. Most students remembered from the first lesson that 40 + 40 = 80 and that we could just count out 40 counters for each ‘friend’. They did this and there were no cookies left over. Two more students joined the middle making 4 friends altogether. • Some of the ideas students had to divide the cookies into 4 groups were: • Put them all into one pile again and each person take it in turns to take 1 cookie each until they were all gone. • One student suggested that they divide their pile of 40 cookies into 2 equal groups, and give one to the ‘new friend' and the other student do the same. • Another student suggested we put them all back into the middle and put them into groups of 10. Then each student take a group of 10 cookies until they are all gone. Then count your pile to make sure everyone has the same amount.

9. Lesson 3 – Doing it all again and recording – whole class • During this lesson we tackled question 3 which was… another 2 friends arrive. How many each? • This means there are 6 friends. We had 6 students in the middle and the others around the outside. This lesson all students were engaged in the problem for a fair while, but in the end there were only a handful who were determined to solve the problem. • The problem was… 80 cookies shared between 6 students. • Students took 10 counters each, but there wasn’t enough for another 10 each. There were lots of ideas on what to do next, such as, take one each, take two each, count how many are left on the plate. Students decided to take 2 more each and then 1 more each until there were only 2 cookies left. • After further discussions students decided that they could break the 2 cookies into 1/3s, then every one would get a share of the last two cookies. They didn’t like the idea of having any cookies ‘left over’. • In total all 6 students got 13 and a 1/3 cookies each. That was an ‘ah’ moment, when they decided to divide the 2 cookies into thirds so there would be no ‘left overs!’

10. Students copied this into their books. It is exactly how a few students explained what we did. ÷ into 6 groups = 13 and 1/3 cookies each

11. Lesson 4 – Monster Share Materials: Maths Lab 1 or 2 CD Rom Students played this sharing game on their own or with a couple of other students at the computer with them. It is better when there are 2 or 3 students at one computer because there is more interaction, talking and helping each other work out the problems. Students have to share the food equally with the monsters. Every game has a different amount of monsters and/or food.

12. Lesson 5 – How many cookies can I make? Each student was given a lump of play dough and asked to estimate and then make some cookies about the same size as a 20c coin. Jesse recorded her estimate, then made her cookies. She made 23 and recorded that too. Lesson 6 – Sharing the play dough cookies. How many is there altogether? How many will I get? • Before dividing the cookies the class manager recorded every students prediction of how many cookies were made altogether. Some of them were 60, 45, 100, 80, 200, 78, 167 • We discussed how to divide them. E.g. taking 1 at a time, 10 at a time etc.

13. After asking questions like… is there another way or a quicker way of dividing them up…students decided to take 10 cookies each and sit on the mat. The remaining cookies were put into the centre of the circle. It was interesting to see the different ways students arranged their 10 cookies.

14. 28 cookies left over 8 cookies left over After more discussions students all took 1 more cookie each, which left only 8. We discussed how to divide the 8 cookies. E.g. break each one in half (=16 pieces), but that still wouldn’t be enough. Another idea was to break each cookie into 1/3s (= 24 pieces, 1 piece for each student and still there would be 4 left over) And that’s as far as we got.

15. THE END