Take A Score Years 1 - 6

Summary Negative numbers turn up naturally when children have free access to calculators. The problem isn't that they do, after all many children have, for example, experienced negative temperatures, it's how to help children interpret them. If we were to say something like "0 - 5, oh you can't do that", it would be counter-productive to developing the 'can do' attitude that characterises independent learners. Taken from page 17, Calculators, Children and Mathematics, the report of the Calculator Aware Number project, this calculator game practises number skills in a way that allows negative numbers to occur sometimes. As shown in the example below, those times challenge teachers to support children's learning a little more closely. Suitable for threading. Materials One calculator per person One dice per pair

Figure 3.7, page 17, Calculators, Children and Mathematics

Procedure Another teacher devised a game called 'Take a Score'. Each child had a record sheet, as shown in Figure 3.7. Each child threw a die four times; after each throw the score was written in one of the boxes. The calculations were then made, and the total score was the sum of the two answers. Negative answers might arise in the subtractions, and the addition of both positive and negative numbers might be needed to find the total score. In this classroom ... it was possible to input negative numbers when checking on the calculator. The Teacher wrote: Jamie and Allen were playing a variation on the 'Take a Score' game. Jamie's book looked like this when I spoke to him: 0 - 8 = 8 0 - 5 = 5 My score is 13.

Content addition facts beyond 10 addition facts to 10 counting equations: creating/solving mathematical conversation negative numbers number line - ordering, operations operations - whole number problem solving properties of number properties of zero recording - calculator recording - written subtraction

The conversation between Jamie and his teacher went as follows:

Teacher:	Do you think those two are right?
Jamie:	Yes.
Teacher:	Will you check them with the Unifix please?
Jamie:	Is it -8?
Teacher:	What can you use to check it? [Jamie used a calculator, and corrected the subtractions.]
Teacher:	What do you think your score is?
Jamie:	[Using fingers and speaking to himself.] Minus four.
Teacher:	How do you get that?
Jamie:	Well, I said my thumb was -8, and then I counted -7, -6, -5, -4. Oh, I should have said -7, -6, -5, -4, -3. It's -3.
Teacher:	Do you want to check it?
Jamie:	[Enters -8 + -5 = on the calculator.] Oh it's -13.
Teacher:	Is the calculator right? Why does it say -13?
Jamie:	'Cos -8 and -5 is -13.

Comments, Variations, Extensions

1. Check your calculator before you introduce this game. If they have a ⁺/_- button you can enter positive and negative numbers. Also if they have this button it is almost certain they will correctly evaluate the addition and subtraction of positive and negative numbers.

2. To enter negative numbers, enter the size of the number first by pressing a digit. The calculator will assume you mean positive. Use the ⁺/_- button to make it negative.

3. Remember positive and negative are types of numbers and subtraction is an operation between two numbers. Subtraction and negative are not the same.

4. Some teachers may like to put the activity in a problem solving context by starting with a scoreboard showing addition rather than subtraction. When the children are confident with that game you can, over time, ask:
   • What happens if we subtract the two scores to get our final score?
   • What happens if the score board has subtractions instead of additions?
   • What happens if the score board has subtractions and we subtract the two scores to get our final score?

5. See the activity Smarties for another game in which negative numbers occur naturally.

6. See Children's Methods of Calculation in the From CAN section to develop a sense of how working with negative numbers can lead to a powerful alternative approach to subtraction.

7. Task 47, Red & Black Card Game, from the Mathematics Task Centre, and the extended form of it in Lesson 89 Maths300 also provide situations where negative numbers come up naturally.

8. See Integers to see how Poly Plug can be used as a concrete model of the arithmetic of positive and negative numbers (integers). This concept is also explored in Task 130, Protons & Anti-Protons from the Mathematics Task Centre and in the extended form of it in Lesson 76 from Maths300.

9. For a number line model see Task 131, Walk The Plank, from the Mathematics Task Centre Project, and the extended form of it in Lesson 32 Maths300.

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