Maths Information Evening

Maths Information Evening

Tuesday 6th November 2012

Outline of the Evening

Teaching methods for the 4 operationsWays to help your child at home Maths vocabularyUseful websites

Addition

Stage 1: The empty number line The empty number line helps to record

the steps on the way to calculating the total.

48 + 36 = 84   

Stage 2: Partitioning

 The next stage is to record mental methods using partitioning. Add the tens and then the ones to form partial sums and then add these partial sums. 

Record steps in addition using partitioning:

47 + 76 = 40 + 7 + 70 + 6

Rearrange the sum:

40 + 70 + 7 + 6 = 110 + 13 = 123

Stage 3: Expanded method in columns

Move on to a layout showing the addition of the tens to the tens and the ones to the ones.

4776

13 110

123

Stage 4: Column method 

In this method, recording is reduced further. Carry digits are recorded below the line.

1 1

366458824

1

4776

123

Subtraction

Stage 1: Using the empty number line The empty number line helps to record or explain the steps in mental subtraction. A calculation like 74 – 27 can be recorded by counting back 27 from 74 to reach 47. 

The counting-up method

The mental method of counting up from the smaller to the larger number can be recorded using number. 74 – 27 = 47

Stage 2: Partitioning

 Subtraction can be recorded using partitioning:

74 – 27 = 74 – 20 = 54 

54 – 7 =  47  

Stage 3: Expanded layout, leading to column method 

Example: 98 – 36 Example: 74 - 27

90 + 8 98

- 30 + 6 36

60 + 2 62

Stage 4: Column Subtraction

Recording is reduced further. When decomposition is necessary the altered numbers are shown above the actual numbers.

Example: 74 – 27 6 1 7 4 - 2 7 4 7

Multiplication

Stage 1: Mental multiplication using partitioning

14 x 3 = (10 + 4) x 3 = (10 x 3) + ( 4 x 3) = 30 + 12 = 42  

43 x 6 = (40 + 3) x 6 = (40 x 6) + (3 x 6) = 240 + 18 = 258  

Stage 2: The grid method 

An expanded method which uses a grid can be used. It is an alternative way of recording the same steps e.g. 38 x 7 =

Stage 3: Expanded short multiplication 

The next step is to represent the method of recording in a column format, but showing the working. Draw attention to the links with the grid method.

38X 7 56 210 266

Stage 4: Short Multiplication

The recording is reduced further, with carry digits recorded below the line.

If, after practice, children cannot use the compact method without making errors, they should return to the expanded format of stage 3.

Stage 5: Two digit by two digit - Grid Method T U X T U

Extend to TU × TU asking children to estimate first. Start with the grid method.

Stage 5: Two-digit by two-digit products

Reduce the recording, showing the links to the grid method. (Some children may need this step)

56 × 27 is approximately 60 × 30 = 1800.

56 X 27 42 6 x 7 350 50 x 7 120 6 x 20 1000 50 x 20 1512 1

Stage 5: Long Multiplication 

Move onto formal written methods of multiplication.

56

4X 27

1 392

1120

1512 1

56 x 7

56 x 20

Stage 6: Three-digit by two-digit products

•Extend to HTU × TU asking children to estimate first. Start with the grid method.

•286 × 29 is approximately 300 × 30 = 9000.

Stage 6: Three-digit by two-digit products

•Children who are already secure with multiplication for TU × U and TU × TU should have little difficulty in using the same method for HTU × TU.

•Again, the carry digits in the partial products are usually carried mentally.

286 x 29 2574 286 x 9

5720 286 x 20 8294

1

Division

Stage 1: Mental division using partitioning e.g. 84 ÷ 7 =

Stage 2: Short division of TU ÷ U 

20 73 60 21

2

2 7

3 8 1

81 ÷ 3 = (60 + 21) ÷ 3 = (60 ÷ 3) + ( 21 ÷ 3)

= 20 + 7 = 27

Stage 3: ‘Expanded’ method for HTU ÷ U  This method is often referred to as

‘chunking’.

6 196

180 6 3016

12 6 24 32

Answer: 32R 4

Stage 4: Short division of HTU ÷ U

2

9 73 2 9 1

Stage 5: Long division 

2324 560

48080728

Answer: 23 R 8

20 x 24

3 x 24

The next step is to tackle HTU ÷ TU, which for most children will be in Year 6.

Helping at Home

A major key to success in maths at KS2 is to learn times tables.

This can be made fun in lots of different ways and there are lots of good resources available on the market to help, for example books, posters and CDs.

Maths Problems

Not all the maths that we do in school is about calculations. The maths curriculum has a wide variety of topic areas in which the children acquire knowledge which will help them in every day life.

There are many ways that you can help your child to learn at home by asking them questions and doing practical activities in the following areas;

Maths Problems

Measures (weight, length, capacity)MoneyTimeFractions, decimals, percentages

Measures – Weight

Any practical use of weighing objects and using scales. This could be linked to making a recipe for 4 people and ask what quantities would be needed to make the recipe for 8 or 2 people?

Estimate the mass of this bag of carrots. Weigh the bag to see how close you are.

A sack of rice weighs 5 kg. How many grams is this? Weigh this apple to the nearest 10 grams. Approximately how

many apples of a similar size together would weigh 1kg? How did you get your answer?

Three parcels weigh 785g, 55g and 0.25kg. How much do they weigh altogether?

Measures – Length

What would you measure using a ruler? a tape measure? a surveyor's tape? trundle wheel? Have a go at measuring the length of things.

A bench is 2 metres and 40 centimetres long. How many centimetres is this? Explain how you worked this out.

Which of these measurements is equivalent to 2.07 metres: 270cm, 2007cm, 207cm or 270cm? How did you know?

Draw these lines accurately using a 300mm ruler marked in cm: 5.2cm 0.7cm 83mm 7mm

Measures – Capacity

Suggest some objects whose capacity could be measured using a 1 litre measuring jug.

Test suggestions and discuss accuracy. Choose the correct answer. A drinking glass

holds about...0.2litres,  2litres,  20litres, 200 litres?

Which measurement is equivalent to 1.3 litres: 130ml, 1003ml, 1300ml or 103ml?How do you know?

Money

Using shopping as a way to help children calculate costs of several items and how much change they will get. When sales are on, calculate how much they will get off etc. Link to percentages and decimals.

If Ella buys one toy costing 35p and another costing 48p. She pays with a £5 note. How much change does she get?

Parveen buys 3 small bags of peanuts. She gives the shop keeper £2 and gets 80p change. What is the cost in pence of one bag of peanuts?

185 people go to the school concert.They pay £1.35 each.How much ticket money is collected?

Time

How would a digital clock show the time twenty minutes to six ?

The car journey to work takes Rob 20 minutes. He needs to be at work at 9 O'Clock. What time should he set off to work?

How would quarter past four in the afternoon be shown on a 24-hour digital clock?

A plane takes off on Tuesday at 22:47. It lands on Wednesday at 07:05. How long in hours and minutes is the flight?

Use calendars, timetables, digital and analogue clocks to create problems for your children to solve.

Fractions, decimals, percentages

I ate more than half a pizza but less than three quarters. What fraction could I have eaten?

What would you prefer: 3 pizzas shared between 4 people or 6 pizzas shared between 10 people? Explain why.

Which of these decimals means 7/10?a. 70, b. 7, c. 0.7, d. 0.07.

What fractions is the same as nought point four? What percentage of £8 is £2?

What percentage of £100 is £20?

Games

A key to success in maths is to make it fun and entertaining for the children. This can involve playing maths games or using interactive maths resources which are available on the internet.

Mathematical Language

The language used in maths can be quite confusing for children for example, the words product, sum and factor have meanings which are nothing to do with maths.

Try to talk to your child at home about what they have been learning in maths and if possible question them about their understanding of the language.

A children’s maths dictionary is a useful tool.

Useful websites

www.samlearning.com

www.amathsdictionaryforkids.com  www.coolmath4kids.com  www.bbc.co.uk/schools/websites/4_11/site/numeracy   www.woodlands-junior.kent.sch.uk/maths

www.sumdog.com

www.mymaths.co.uk