Transcript Maths Information Evening

Maths Information Evening
Tuesday 6th November 2012
Outline of the Evening
Teaching methods for the 4 operations
 Ways to help your child at home
 Maths vocabulary
 Useful 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.
47
 76
13
110
123
Stage 4: Column method

In this method, recording is reduced
further. Carry digits are recorded below
the line.
47
 76
123
1
366
 458
824
11
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
90 + 8
- 30 + 6
60 + 2
Example: 74 - 27
98
36
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
74
-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.
38
X 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
350
120
1000
1512
1
6x7
50 x 7
6 x 20
50 x 20
Stage 5: Long Multiplication
Move onto formal written methods of
multiplication.
56
X 27
392 56 x 7
1120 56 x 20
1512

4
1
1
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
5720
8294
1
286 x 9
286 x 20
Division

Stage 1: Mental division using
partitioning e.g. 84 ÷ 7 =
Stage 2: Short division of TU ÷ U
81 ÷ 3 = (60 + 21) ÷ 3 = (60 ÷ 3) + ( 21 ÷
3)
= 20 + 7 = 27
20  7
3 60  21
27
2
38 1
Stage 3: ‘Expanded’ method for
HTU ÷ U

This method is often referred to as
‘chunking’.
6 196
 180 6  30
16
 12 6  2
4
32
Answer:
32 R 4
Stage 4: Short division of
HTU ÷ U
97
2
329 1
Stage 5: Long division
The next step is to tackle HTU ÷ TU, which for most children will be in
Year 6.
23
24 560
20 x 24
 480
80
3 x 24
72
8
Answer: 23 R 8
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)
 Money
 Time
 Fractions, decimals, percentages

Measures – Weight

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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

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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

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

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
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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
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www.bbc.co.uk/schools/websites/4_11/site/numeracy

www.woodlands-junior.kent.sch.uk/maths
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www.sumdog.com

www.mymaths.co.uk