Maths INSET

1. Maths Inset
16th June 2015
Rachel Cowen

2.  To reflect on how we presently teach & record
multiplication methods.
 To agree on progression of calculation methods to be
used across the school.
 To briefly consider the impact of daily Times Table
challenges.
Aims

3.  Problem solving & Mathematical reasoning are embedded into all
parts of the Maths curriculum & not viewed as a separate entity.
 Children are discussing Maths & methods & making connections for
themselves.
 Everyone is teaching for understanding.
 Practical resources, visual images & ICT foster pupils’ deeper
understanding. All children are encouraged to use practical
equipment, there is evidence this has real benefits in terms of
developing mental imagery.
 Teachers work & plan together to support consistency &
improvement.
 There is timely intervention which overcomes gaps & builds a firm
foundation for future learning.
What does OUTSTANDING Maths
look like?

4.  How can we develop consistency in our teaching in terms
of subject knowledge and language choices?
 How can we ensure our calculation policy reflects the
changes in the New Curriculum and the needs of the
children in our school?
 How can our policy build effectively on prior learning?
 How can we improve the accuracy of children’s
multiplication work across the school?
 How can we support the children to effectively record
their mathematical thinking?
Key Questions

5.  What mental images do you have when you think of
multiplication?
 What mental images would your pupils have when
they think about multiplication?
Task 1

6. Understanding the meaning of multiplication is often difficult
for children as they relate answers to multiplication
equations as basic facts to be recalled rather than addressing
the equations in terms of structure and patterns. It is
important to support pupils to develop a deep connected
understanding of multiplication and division. As structure and
patterns are fundamental to multiplication it is essential that
children’s awareness of this is facilitated by classroom
experiences. Using concrete representations is a powerful
way to develop children’s understanding of the structure of
multiplication.
Concepts of Multiplication

7.  Students’ learning starts out with visual, tangible, and
kinesthetic experiences to establish basic understanding, and
then students are able to extend their knowledge through
pictorial representations (drawings, diagrams, or sketches) and
then finally are able to move to the abstract level of thinking,
where students are exclusively using mathematical symbols to
represent and model problems (Hauser).
 Studies have shown that “students who use concrete materials
develop more precise and more comprehensive mental
representations, often show more motivation and on-task
behavior, understand mathematical ideas, and better apply
these ideas to life situations,” (Hauser).
Why?

8.  Multiplication is a description of repeated addition.
 Multiplication is commutative, i.e 4 x 6 = 24 and 6 x 4
= 24
Key concepts of Multiplication

9.  Multiple Representations
 Representing multiplication in Key Stage 1
 The commutative law for multiplication
 Grid multiplication as an interim step
 Moving from grid to a column method
Areas to address

10. Stage 1
Children are encouraged to develop a mental image of the size of numbers.
They learn to think about equal groups or sets of objects in practical, real life
situations.
They begin to record these situations using pictures.
A child’s jotting showing fingers on each
hand as a double.
A child’s jotting showing double
three as three cookies on each
plate

11.  Pupils should be taught to:
 solve one-step problems involving multiplication by
calculating the answer using concrete objects, pictorial
representations and arrays with the support of the
teacher.
Year 1- Statutory Requirements

12.  Children understand that multiplication is repeated
addition and that can be done by counting in equal
steps/groups.
Stage 2
or

13.  Children can then be introduced to
the image of a rectangular array, initially
through real items such as egg boxes,
baking trays, ice cube trays, wrapping paper
etc. and using these to show that counting up in equal groups
can be a quicker way of finding a total.
 Children to also understand that 3 x 5 is the same as 5 x 3

14.  Pupils should be taught to:
 recall and use multiplication facts for the 2, 5 and 10
multiplication tables, including recognising odd and even
numbers
 calculate mathematical statements for multiplication within the
multiplication tables and write them using the multiplication (×)
and equals (=) signs
 show that multiplication of two numbers can be done in any
order (commutative)
 solve problems involving multiplication, using materials, arrays,
repeated addition, mental methods, and multiplication facts,
including problems in contexts.
Year 2-Statutory requirements

15.  Children continue to use arrays and create their own
to represent multiplication calculations
Stage 3

16.  The children are confident in using the equals sign at
the start of the number sentence and are developing
fluency and flexibility.
10 = 5 x 2 20 = 5 x 4
10 = 2 x 5 20 = 4 x 5
Position of = sign

17.  Pupils should be taught to:
 recall and use multiplication facts for the 3, 4 and 8 multiplication
tables
 write and calculate mathematical statements for multiplication and
division using the multiplication tables that they know, including for
two-digit numbers times one-digit numbers, using mental and
progressing to formal written methods
 solve problems, including missing number problems, involving
multiplication and division, including positive integer scaling
problems and correspondence problems in which n objects are
connected to m objects.
Year 3 Statutory Guidance

18.  Pupils should be taught to:
 recall multiplication facts for multiplication tables up to 12 × 12
 use place value, known and derived facts to multiply mentally, including:
multiplying by 0 and 1; multiplying together three numbers
 recognise and use factor pairs and commutativity in mental calculations
 multiply two-digit and three-digit numbers by a one-digit number using formal
written layout
 solve problems involving multiplying and adding, including using the distributive
law to multiply two digit numbers by one digit, integer scaling problems and
harder correspondence problems such as n objects are connected to m objects.
 Pupils continue to practise recalling and using multiplication tables facts to aid
fluency.
 Pupils practise mental methods and extend this to three-digit numbers to derive
facts,
(for example 600 ÷ 3 = 200 can be derived from 2 x 3 = 6).
Year 4 Statutory Guidance

19. As they progress to multiplying a two-digit number by a
single digit number, children should use their knowledge of
partitioning two digit numbers into tens and units/ones to
help them.
For example, when calculating 14 x 6, children should set out
the array, then partition the array so that one array has ten
columns and the other four.
Stage 4

20. Children will continue to use arrays to lead into the
grid method of multiplication.
14 x 6
The 14 is partitioned (split) into 10 and 4.
The answer to 6 x 10 is found = 60
The answer to 6 x 4 is found = 24
The two answers are added together 60 + 24 = 84
Stage 4

21.  Notice how the place value counters:
 Enable the children to represent 34
 Support construction of the array
 Support understanding the grid method.
Place value counters

22. Stage 5
This is the final stage, the array is removed and
children use the grid method.

23. Pupils should be taught to:
 multiply numbers up to 4 digits by a one- or two-digit
number using a formal written method, including long
multiplication for two-digit numbers
 multiply numbers mentally drawing upon known
facts
 multiply whole numbers and those involving decimals
by 10, 100 and 1000
Year 5

24.  solve problems involving multiplication including using their
knowledge of factors and multiples, squares and cubes
 solve problems involving multiplication including
understanding the meaning of the equals sign
 solve problems involving multiplication including scaling by
simple fractions and problems involving simple rates.

25.  multiply multi-digit numbers up to 4 digits by a two-
digit whole number using the formal written method
of long multiplication
Year 6

26. The grid method can be used for multiplying any numbers,
including long multiplication and multiplication involving
decimals.
Stage 6

27. 2741 x 6 becomes
2 7 4 1
x 6
1 6 4 4 6
4 2
Short Multiplication

28. 124 x 26 becomes
1 2
1 2 4
x 2 6
7 4 4
2 4 8 0
3 2 2 4
1 1
Long Multiplication

29. How does asking the question “What’s the same,
what’s different?” support children in moving from the
grid to the column method?
Notice also the choice of numbers: there is no repetition
in the digits in order that children can match the same
numbers in the grid method and formal algorithm.
What’s the same?
What’s different ?

30.  Children should not be made to go onto the next
stage if:
1) they are not ready.
2) they are not confident.
 Children should be encouraged to consider if a mental
calculation would be appropriate before using written
methods.
Important Points

31. Times Tables Club
How are we finding this?
Is it benefitting the children & are they making
progress?
Do we want it to continue?
Do we need to all use the same Times Tables
club from September?

32.  https://www.flocabulary.com/do-you-know-your-2s/
Flocabulary

33.  http://www.topmarks.co.uk/maths-games/7-11-
years/multiplication-and-division
 http://www.everyschool.co.uk/maths-key-stage-1-
multiplication.html
 http://nrich.maths.org/8938
 http://resources.woodlands-
junior.kent.sch.uk/maths/timestable/interactive.htm
Multiplication Games

34.  Can you work in pairs or small groups to solve these
problems?
 Can you come up with two different ways to solve
each problem and decide in your groups which are
the most efficient ways?
Multiplication Problems

35. • Jason is paid £5 per hour to deliver newspapers. If he works
for 18 hours per week, how much money would he earn?
• Sarah is planting some seeds in the garden. She has 19
packets which have 26 seeds in each of them. How many
seeds is she planting altogether?
• The concert hall has 224 seats in each row. If there are 56
rows on the ground floor, how many people can be seated?
Multiplication Problems