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**Maths Information Evening**

Tuesday 6th November 2012

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**Outline of the Evening Teaching methods for the 4 operations**

Ways to help your child at home Maths vocabulary Useful websites

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**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

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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: = Rearrange the sum: = = 123

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**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. 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 separately. The addition of the tens in the calculation 47 + 76 is described in the words ‘forty plus seventy equals one hundred and ten’, stressing the link to the related fact ‘four plus seven equals eleven’. The expanded method leads children to the more compact method so that they understand its structure and efficiency.

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Stage 4: Column method In this method, recording is reduced further. Carry digits are recorded below the line. 1 4 7 6 2 3 +

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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.

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**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

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**Stage 2: Partitioning Subtraction can be recorded using partitioning:**

74 – 27 = 74 – 20 = 54 54 – 7 = 47

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**Stage 3: Expanded layout, leading to column method **

Example: 98 – Example:

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**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

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**Multiplication Stage 1: Mental multiplication using partitioning**

14 x 3 = (10 + 4) x 3 = (10 x 3) + ( 4 x 3) = = 42 43 x 6 = (40 + 3) x 6 = (40 x 6) + (3 x 6) = = 258

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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 =

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**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. 38 X 7 56 210 266

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**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.

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**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.

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**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 x 7 x 7 x 20 x 20 1512 1

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**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

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**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.

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**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 x 9 x 20 8294 1

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

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**Stage 2: Short division of TU ÷ U **

81 ÷ 3 = ( ) ÷ 3 = (60 ÷ 3) + ( 21 ÷ 3) = = 27

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**Stage 3: ‘Expanded’ method for HTU ÷ U **

This method is often referred to as ‘chunking’.

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**Stage 4: Short division of HTU ÷ U**

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Stage 5: Long division The next step is to tackle HTU ÷ TU, which for most children will be in Year 6. 20 x 24 3 x 24

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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.

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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;

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**Maths Problems Measures (weight, length, capacity) Money Time**

Fractions, decimals, percentages

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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?

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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

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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?

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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?

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**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.

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**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 What fractions is the same as nought point four? What percentage of £8 is £2? What percentage of £100 is £20?

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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.

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**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.

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**Useful websites www.samlearning.com www.amathsdictionaryforkids.com **

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