Transcript parentworkshop2013 - Chaddlewood Primary School

Mathematics
Workshop
2013
www.chaddlewood-primary.plymouth.sch.uk/maths
What we’ve learnt,
and why we’ve changed some things
How we found out..
As part of our regular assessments within mathematics
we identify;
- Children making ‘above’ expected progress within a
particular mathematical area
This helps us to identify how we can stretch their knowledge and understanding (for
example, the child might have mastered a concept and be able to apply the skill. We
then move the child carefully on to the next step).
-Children making ‘average’ progress within a particular
mathematical area
-Children making ‘below’ expected progress within a
particular mathematical area
We can then investigate the cause of this and, as appropriate, alter how these
strategies are addressed
How we found out..
To find this out we….
Carry out informal assessments by;
- observing what children do without our help
- question them to identify how far their understanding reaches
- ask ‘how’ they know
Through;
- what they normally do in class
- monitoring by myself and external organisations/people
- the recording within their books
We identified...
- That some children answer questions literally
- That some children struggle with
understanding a lot of different approaches to
a problem
- That some children were slow at calculating
mentally
What you do,
and what children do too
Question 1
I have 28 apples in one hand and 57 apples
in the other. What have I got..?
Big hands
Question 2
Find x.
Here it is!
x
3cm
4cm
Answer 3
Write the number
one hundred and two
in digits.
1002
Place Value
Simply – recognizing that the value of a digit is
determined by its place in a number.
TH
H
T
U
1
3
2
5
3
2
5
1
3
2
5
4
. Tenths
.1
Hundredths
Common mistakes…
- Writing ‘one hundred and thirty six’ as 10036.
- Thinking that 6,000 is one more than 5099.
- Thinking that 3.153 must be larger than 3.35
because it has more digits in it.
- Thinking that 0.75 is smaller than 0.203 because 75
is smaller than 203.
Question 4
Sam has £1 in his pocket and apples
cost 30p each.
How many apples can Sam buy?
Show how you got your answer.
3.
Sam told me.
What we’ve changed,
and what we haven’t
Some problems...
How can you prove to someone that
the answer to 9+6 is 15?
Which is bigger… 23 or 32?
How do you know?
What is 149+353?
How things develop across the school
Addition
Addition
 Counting using objects.
 Jumping on a number line (of increasing size).
… 3 4 5 6 7 8
9 10 11 12 13 14 15 16 17 18 19 20 21 22
 Using a hundred square to add 10.
Addition
 Partitioning two digit numbers
 Adding two digit numbers together (using any equipment, normally
hundred squares)
 Adding two digit numbers together (without equipment)
Adding three digit numbers together using above strategy.
Addition
 Using ‘empty’ number lines.
More formal methods of addition.
23 + 12…
20 + 10 = 30
3+ 2 = 5
= 35
Addition
 Problems which do NOT involve the need to ‘carry’.
 Problems which do involve ‘carrying’.
358
+ 31
=
9
80
300
(8 + 1)
(50 + 30)
(300 + 0)
300 + 80 + 9 = 389
358
+138
= 16
80
400
(8 + 8)
(50 + 30)
(300 + 100)
400 + 80 + 16 = 496
Addition
 Further condensation of method.
Addition
 Adding decimals.
Adding problems including brackets.
 Algebra.
(4 + 7) x 3 =
Addition
 Condensing algebra.
4f + 7 = f + 16
4f + 7 – 7 = f + 16 – 7
take 7 off both sides
4f = f + 94f – f = f + 9 – f
take f off both sides
3f = 9f = 3
divide both sides by 3
Subtraction
Subtraction
 Using songs and rhymes.
 Using pictures to take away.
 Using number lines: ‘11 take away 7 is…’
 Finding the difference between quantities.
 Using number lines: ‘What is the difference between 11 and 7?’
Subtraction
 Using hundred squares.
Subtraction as the inverse to addition.
 Finding missing numbers, e.g.
2+7 =
2+
=9
2+7
7+2
9–7
9–2
=
=
=
=
9
9
2
7
Subtraction
 Taking away using tens and units.
23 – 12 =
 Using number lines.
47 – 11 =
22 – 7 =
16 – 9 =
Subtraction
 More formal representations.
87 – 32 = 55 because
87 – 30 = 57
57 – 2 = 55
 Formal written methods.
 ‘Borrowing’.
Subtraction
 Decimal numbers
34.8 – 26.4 =
Multiplication
Multiplication
 Adding groups of equipment.
 Understanding X as ‘lots of’.
5
 Arrays.
+
5
+
5
Multiplication
 Partitioning numbers.
 Grid method.
6 x 124 =
124 books were sold. Each book cost £6.
How much money was taken?
Multiplication
 Vertical method
124
x6
24 (6 x4)
120 (6 x 20)
600 (6 x100)
744
 Grid method for larger numbers.
Multiplication
 ‘Short’ multiplication.
4
6
x
9
4 1 4
4
5
Multiplication
 ‘Long’ multiplication
 Making it shorter…
Using multiplication facts
·It
is vital that children know their times tables as all the work higher up the school relie
on them knowing their tables.
·Tables should be learned at least 2-3 times a week.
What is expected
Year 2
2 times table
5 times table
10 times table
Year 3
2 times table
3 times table
4 times table
5 times table
6 times table
10 times table
Year 4
Derive and recall all multiplication facts up to 10 x 10 (5 second recall)
Years 5 & 6
Derive and recall quickly all multiplication facts up to 10 x 10 (5 second recal
Division
Division
 Practical sharing.
 Counting on in ‘groups’.
Division
 Introducing sharing.
Division
 More complex grouping. and sharing.
Division
 Using number lines.
 Knowing division as the inverse of multiplication.
Division
 Remainders.
 Using number lines confidently.
Division
 Formal method.
Division
 Remainders as a fraction.
 Division of larger numbers.
Division
 Division including decimals.
 ‘Bus Shelter’ method.
The models that we use, and why we
use them
Partitioning
Children need to understand that in 102
there is one lot of one hundred, zero lots of
ten and two units. Zero ‘holds’ the place of
the tens.
Partitioning
Breaking a number up according to its place value.
(typically to make addition and multiplication easier).
3276
3000+200+70+6
So 52 x 3 becomes 50+50+50 and
2+2+2 …
How you can support mathematics
learning at home
What can I do at home?
As well as looking at these strategies at home (in this order), you could…
 Play number games.
Recognise numbers around shops and the environment.
Ask for an amount of something.
Make number patterns (e.g. one apple, two oranges, three
bananas)
Use dice – count the dots quickly, predict bottom number on die,
difference between two rolls…
Which number is missing?
Guess the number (it’s one more than 5, it’s between 100 and 150)
Share an amount between 2, 3, 4 people.
Count backwards and forwards from a given two-digit number.
Estimate total of something by rounding to 10, 100, etc.
 Experiment with shapes through painting, ‘spot the shape’,
patterns
What can I do at home?
 Measures.
Cooking!
Count up money to find a total. Work out change from shop.
 Telling the time.
What time will it be one hour from now?
How long have you spent doing something?
What can you do in one minute?
 Times tables!
What can I do at home?
A prominent clock in the kitchen – ideally analogue and digital.
Display a traditional calendar, and refer to it.
Board games that involve dice and spinners – helps not only with
counting but with the concepts of chance.
Traditional playing cards – simple games such as snap are a natural way
of learning about sorting and chance.
Dominoes – to help with number combinations.
Using a calculator, for example when shopping. This shouldn’t be seen as
a way of ‘cheating’ – just a way to save time. We use these in class to
save time to focus on what is really happening.
Measuring jugs with scales / kitchen scales.
Dried pasta…or Smarties! – useful for counting large collections to
investigate remainders etc.
Tape measure and ruler – involve your child in ‘real life’ situations.
An indoor / outdoor thermometer.
What can I do at home?
General websites:
www.mathletics.co.uk
www.chaddlewood-primary.plymouth.sch.uk/maths
www.mathszone.co.uk
www.woodlands-junior.kent.sch.uk/maths
www.funbrain.com
www.nrich.maths.org
Lots of problem solving activities
www.puzzlemaker.com
A tool for making and customising maths puzzles
www.coolmath.com
Fun maths games
www.4learning.co.uk/numbercrew
Good KS1 maths site
www.thinkquest.org/25459
Maths games, quizzes ,and problem solving activities
www.funwithspot.com
Great interactive maths
games for KS1
www.ladybird.co.uk
Counting, matching etc for
KS1
www.bobthebuilder.com
Challenging activities for
KS1
www.teachingtime.co.uk
Great site for learning time,
includes an interactive clock
www.ricksmath.com
Learning basic maths skills
www.mathsisfun.com
Maths games, puzzles and
activities
Any questions?