2. What is progress in Maths?What is progress in Maths?
At all levels learning maths is about solving problems
using key processes such as:
Looking for patterns and relationships between
numbers.
Making sense of and checking information.
Communicating and presenting maths using words and
diagrams (symbols and pictures).
Reasoning and developing mathematical arguments.
Calculating
Comparing
Manipulating, organising and interpreting information.
Reasoning
3. Maths in Key Stage 1Maths in Key Stage 1
In Year 1 Autumn term I – taught
twice a week with provision activities
available
Year 1 – till Summer term – taught 5
times a week
Year 2 – taught 5 times a week
Taught across the curriculum where
possible
7. The ‘fiveness’ of fiveThe ‘fiveness’ of five
We encourage the children to explore
numbers and how they are made up as
well as what they look like (numerals).
Use the red and yellow counters on your
tables to explore the different ways you
could show the number 10.
9. Exhibition of a NumberExhibition of a Number
Can you make an exhibition of the
number 12 using as much of the
equipment as you can?
Can you show it in different jumps?
As a fraction of a number?
Using measurements or money?
10. What numbers are being shown here?What numbers are being shown here?
15. Place ValuePlace Value
The position (place) of a digit in a
number determines its value. Hence
the term place value.
Children have to be really
comfortable with their understanding of
the value of number to be able to apply
it in calculations.
18. Abacus CountersAbacus Counters
Tens Ones
If you had three counters, you could make the numbers 30, 21, 12 or
3. What numbers could you make with 4, 5 or 6 counters?
19. Addition and SubtractionAddition and Subtraction
Year 1Year 1
Using pictures of objects – cubes,
counters
Using number lines to add/subtract
one-digit from a two-digit number to 20
Bead strings.
Number bonds to 10 and 20.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
15
20. Finding the DifferenceFinding the Difference
7
6
5
4
3
2
1
3
2
1
Using cubes to physically show the
difference between two amounts.
They both have 3 – what’s the difference?
34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
When the 2 numbers in a calculation are close in value, we count up from
the smallest number.
1 2 3 4 5
43 – 38 = 5
(The difference between 43 and 38 is 5)
21. Addition and SubtractionAddition and Subtraction
Year 2Year 2
When children are confident with using empty
number lines, they will use their knowledge
of tens and ones to add:
Two-digit numbers and ones - 34 + 9
Two-digit numbers and tens - 34 + 40
2 two-digit numbers - 34 + 23
23. Using a Number LineUsing a Number Line
48 + 36 = 84
48 58 68 78 79 80 81 82 83 84
+10 +10 +10
+1 +1+1+1+1+1
Tens and ones can then be done in one jump or by bridging to
the next ten.
24. Addition – Year 2Addition – Year 2
Children will begin to use informal pencil and
paper methods (jottings) to support, record and
explain partial mental methods building on
existing mental strategies.
Partitioning – tens and ones
35 + 52 = ?
(t) 30 + 50 = 80
(o) 5 + 2 = 7
(r) 80 + 7 = 87
25. Addition – Year 2Addition – Year 2
Estimating calculations:
49 + 52 = ?
What estimation could I make here?
“I know that 49 and 52 are both close to
50 so the answer should be somewhere
near 100.”
26. Your Turn!Your Turn!
Think about the methods we’ve just
shown you. Use some of them to
complete these calculations.
53 + 24 =
37 + 56 =
27. Subtraction – Year 2Subtraction – Year 2
Partitioning:
This is trickier to show children when subtracting as
there will be some situations where the children
need to take away too many ones.
77 – 42 =
(t) 70 – 40 = 30
(o) 7 – 2 = 5
(r) 30 + 5 = 35
If there are more ones in
the second number then
you only partition that
number (or use a number
line!)
77– 49 =
(t) 77 – 40 = 37
(o) 37 – 9 = 28
Because we have separated
the tens and ones we must
recombine them by ADDING!
28. Missing NumbersMissing Numbers
We teach the children to use the inverse
(opposite) of the given calculation
Addition/subtraction
Multiplication/division
15 + = 26
We would either:
Find the difference between 15 and 26 by
counting up
Work out what 26 – 15 was
29. Your Turn!Your Turn!
Use the inverse to solve these calculations.
- 23 = 12
14 + = 35
5 x = 25
÷ 7 = 10
31. Using bead strings to show ‘lots of’ or
‘groups of’:
3 x 5 = 15
Multiplication and DivisionMultiplication and Division
Year 1Year 1
We use lots of different words to show
multiplication – it’s important to not just call
them the ‘Times Tables’.
32. Using ArraysUsing Arrays
An array can be used to help solve multiplication or
division calculations.
3 x 5 = 15
15 ÷ 5 = 3
5 x 3 = 15
15 ÷ 3 = 5
We often do
this using
edible objects!
33. Repeated AdditionRepeated Addition
3 times 5 is 5 + 5 + 5 = 15 or
3 lots of 5 or 3 x 5 = 15
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
+5 +5 +5
+5 +5 +5
34. Repeated SubtractionRepeated Subtraction
Repeated subtraction to divide using an empty
number line:
24 ÷ 4 = 6
We also use multiplication and counting in
‘lots of’:
30 ÷ 5 = ? How many 5’s are in 30?
0 4 8 12 16 20 24
-4 -4 -4 -4 -4 -4
35. CommutativityCommutativity
Children should know that 3 x 5 has the same
answer as 5 x 3. This can also be shown on the
number line.
We also learn that division is NOT commutative!
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
+5 +5 +5
+3 +3 +3 +3 +3
36. Which multiplication and division calculations
does this array show? Can you show the
repeated addition for it? Can you show the
commutativity on a blank number line?
Your Turn!Your Turn!
37. Using and ApplyingUsing and Applying
After they have learnt a calculation skill,
we give the children opportunities to
use and apply their knowledge.
This is a great chance to get the
children to talk about the strategies they
are using and check that they are
applying the most appropriate strategy
– although as long as it works for them
it can be any strategy!
38. Word ProblemsWord Problems
A word problem gives the children a
question.
They have to look at the words and
numbers used in the word problem to
decide which calculation they need to
write.
We would also encourage them to use
pictorial representations to find the
answers.
39. One-Step Problems
There are 5 lily pads in the pond. They each
have 3 frogs on. How many frogs are there
altogether?
5 x 3 = 15
40. Two Step Problems
Matt has 25 bags of plain crisps and 31
packets of flavoured crisps. There are 52
children in the class and they have one packet
each. How many packets are left?
• What are the steps needed to solve this
problem?
• What calculations will you need to write?
• What methods would you use to solve these
problems?
• Would a pictorial representation be the best
method?
41. Problem SolvingProblem Solving
Solving a problem is more open-ended.
There’s usually more than one answer.
Problem solving helps children to:
Think
Apply
Communicate
Reason
42. Problem SolvingProblem Solving
There are a few problems on each
table.
Have a go at finding as many solutions
as you can with your group.
Feel free to move around to the other
tables to look at theirs!
43. Helping Your Child At Home
Don’t!
• Push a skill, especially if a child is becoming confused or is feeling
pressured. It always pays to talk to the teacher if you feel your child is not
understanding something, rather than confuse them further by teaching
them in a different way.
• Force workbooks on your child. They will do plenty of writing in
their maths books at school. At home, you have the opportunity to help
them memorise their number facts and perform mathematical calculations
in their heads.
• Stress written sums laid out as you used to do them! Nowadays
it is the development of what we call ‘numerical fluency’ that counts.
Children need to be comfortable with numbers, to understand how they
work and to be confident in doing mental calculations.
• Just give them bigger numbers to work with.
Consider the ways that you could challenge them
to deepen their understanding of that concept.
44. Helping Your Child At Home
Do!
• ‘Little and often’! Counting sultanas as you eat them or stairs when
going up to a first floor flat is a much better way of rehearsing counting
than sitting over a workbook.
• Give LOTS of praise. Resist the temptation to say, ‘but’ or to point
out mistakes every time. Children need encouragement and positive
reinforcement to be confident, and a confident child makes a better
learner.
• Play games! Dice, dominoes, track games and cards all make
excellent
excuses for using and applying our number skills. And at the same time
your child is learning the important skills of losing with grace and
winning with style!
• Remember that your focussed attention is a far more
important and pleasurable commodity for any child than
any amount of TV or video game activity. Every child
wants to be doing things one-on-one with someone they
love and trust.
