Maths Inset16th June 2015Rachel Cowen

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

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?

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

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

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

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?

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

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

Stage 1Children 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

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

Children understand that multiplication is repeated addition and that can be done by counting in equal steps/groups.

Stage 2

or

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

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

Children continue to use arrays and create their own to represent multiplication calculations

Stage 3

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 410 = 2 x 5 20 = 4 x 5

Position of = sign

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

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

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

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

Stage 4

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

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

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

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.

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

Year 6

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

Stage 6

2741 x 6 becomes

2 7 4 1 x 6

1 6 4 4 6 4 2

Short Multiplication

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

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 ?

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

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?

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

Flocabulary

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

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

• 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