Teachers’ Notes Key Stage 2

Mrs Jessop And the Maths Lesson Of Doom

This play has been developed to support the teaching of numeracy in schools at Key Stage Two and to reinforce much of the number work tested in the SATS for year 6.

The main focus of the play is on number patterns, mental arithmetic and approaches to the four functions, including work with the number line, number patterns, decimals and fractions, and multiplication tables.

Each mathematical idea is built upon throughout the play involving the audience directly in both the calculations and the methodology employed in problem solving and encouraging them to use a variety of approaches to achieve a single answer. Throughout the play the work is put into a number of everyday contexts through which the problems are explored.

The following pages provide a summary of the work covered and examples of how it is put into practice in the play. At the back of this booklet you will find a pupils’ worksheets designed to tie in with the mathematical concepts covered in the play, which can be photocopied for use in the classroom.

ORDERING NUMBERS

The order of numbers is all important, giving them a value specific to their position. The ten digits are introduced and four of them are selected at random. These four are then used to illustrate how the position of each digit matters.

3,4, 8 and 9 are chosen and in that order we see that there are 9 thousands, 8 hundreds, 4 tens and 3 units and we are told that the units can also be split up into tenths, like pieces of cake.

PLACE VALUE

The position of a digit in a number gives its value and each position is worth ten times more than the position on its right.

Using this idea we set up a human calculator using the 9, 8 and 1. Starting with the number 981 we multiply by 10. The numbers all move one place to the left, giving us 9, 810 and a zero is added to the number to keep the numbers in their new position. The numbers are reshuffled to create 8,190. This time we divide by 10 and the digits move one place to the right giving us 819. Now a decimal point is introduced and starting with the number 90.18 the audience multiply by 100. The digits move two places to the left, past the decimal point and we get 9018. Finally 1,098 is divided by 100 giving us 10.98. we see the decimal point stays in its position as the digits move to the left and right. If there are any zeros then they must move also as they are part of the number.

FRACTIONS

A fraction is part of a whole number and has two parts. The top number is the numerator and the bottom is the denominator.

We start by finding ¼ of 100 and see it to be 25 by splitting 100 into 4 equal parts. We see that to simplify a fraction the numerator and denominator must be divided by the same number thus the fraction 2/4 can be simplified to ½ by dividing top and bottom by 2. Using this knowledge the audience are asked to simplify 2/6: divide top and bottom by 2 to get 1/3, 6/10 is simplified to 3/5 and 6/9 to 2/3.

PERCENTAGES

A percentage can be described as ‘out of 100’ and can be written as a fraction with a denominator of 100. In order to represent a fraction as a percentage its is necessary to find the equivalent fraction.

The children see that to change 7/10 into a percentage you must first find the equivalent fraction with a denominator of 100. Thus top and bottom must be multiplied by 10, giving us 70%. They help find the equivalent percentages for 7/25 and 2/5. We show that the reverse is true, changing 50% into 50/100 and simplify it down to 1/2.

THE FOUR OPERATIONS

With addition, subtraction, multiplication and division we look at the method employed to solve the problem and how to choose the most appropriate way of tackling the question. The audience learn this song:

When you see a problem

It’s easy to overcome

Read the instructions carefully

Then organise the sum

Answer the calculation

Then answer the problem too

Then the world of mathamtics

Will be easy for you.

Estimate, Count on, count back,

Round and then adjust

Learn your tables, know your bonds

Break your numbers up

With every problem we see the children must read the instructions carefully, organise the sum, answer the calculation then answer the problem.

ADDITION

Addition is approached using two methods: breaking numbers up and rounding and adjusting.

The problem is set up: how much does Johnnie spend if he buys Millions for 45p and a Mars Bar for 49p and is tackled in two ways. Firstly the numbers are broken up into tens and units:

Next we approach the same problem using rounding to reach the answer:

The audience are then given two more problems. They must choose the best method to use to solve them and then that method is used to find the answer.

SUBTRACTION

The main method used to solve subtraction problems is to find the difference by counting on. A number line is used to illustrate the method.

We are given the problem: Johnnie has 72p. How much change does he get if he spends 35p? We start with a number line and put 35 on one end with 72 on the other. We count on 5 to 40, hold the 5 in our heads and count on from 40 to 72, giving us 32. We add the 5, giving us the answer 37p.

Here the methods used for addition problems are revised and the children are instrumental in solving the next three problems, using either counting on, breaking numbers up or rounding. In each case the problem is worked through using the technique suggested by the audience.

MULTIPLICATION

Throughout the play the audience joins in Mrs Jessop’s mental warm ups by chanting multiples of 3, 4, 7 and 8, and by doubling and halving numbers given. Multiplying a two digit number by a single digit is approached in a similar way to addition and subtraction; by breaking numbers up or by rounding. To this we add doubling and halving as a useful tool.

BREAKING NUMBERS UP. We set up the problem 23 x 7 and see that we can break it up into two sections: 20 x 7 + 3 x 7.

If we know our tables well we can follow these steps to answer the calculation

ROUNDING. The next problem is 49 x5. Here we see that the simplest method is to round; 49 x 5 = 50 x 5—1 x 5 thus we round the 49 up to 50 and then adjust by taking away the one lot of 5.

DIVIDING

As division is the inverse operation of multiplication a good working knowledge of the multiplication tables is a necessary. It is also very useful to know the rules of divisibility and the audience learn the following:

The audience are then given a series of different numbers and by using the rules of divisibility they work out whether a given digit will divide into it or not eg. Is 117 divisible by 9? Yes, because the sum of its digits is divisible by 9. Is 148 divisible by 4? Yes, because the last two digits divide exactly by 4. Is 102 divisible by 3? Yes, because the sum of the digits divides by 3. Is 11 divisible by 2? No, because it is not an even number.

NUMBER SEQUENCES

A series of numbers linked by a pattern or rule is a number sequence. There are several famous sequences: the Fibonacci sequence, prime numbers, square numbers as well as a sequences of multiples or those with a regular number difference.

THE FIBONACCI SEQUENCE. We show this to be a sequence of numbers created by totalling the last two numbers in the sequence to find the next number.

Ie. 1 1 2 3 5 8 13 21 34 etc.

PRIME NUMBERS. The sequence of numbers that have factors of only 1 and themselves are called Prime Numbers and the first ten numbers in this sequence are 2 3 5 7 11 13 17 19 23 29. It is a useful sequence to know and recognise

SQUARE NUMBERS. Numbers multiplied by themselves make square numbers and can be shown as squares. Here are the square numbers upto and including 12x12: 1 4 9 16 25 36 49 64 81 100 121 144

Factors and multiples are touched upon and we see that the 8 times table is also a number sequence where the difference between each number is 8.