Backwell JuniorSchool

Maths Parent Workshop

Tuesday 14th October 2014Before we begin, please try to solve the

calculations on your table…..

Aims

• To explain how we teach your children +, -, x, ÷ and Times Tables

• To discuss our school focus of Conceptual Understanding

• To give you ideas of how you can help your children at home.

How did you solve these?

• 157+65=

• 245-152=

• 46x22=

• 154÷7=

• 278÷19=

How did you solve these?

• 157+65= 222

• 245-152= 93

• 46x22= 1012

• 154÷7= 22

• 278÷19= 14.63

Maths lessons

• Emphasis on mental calculation• Children are encouraged to work

mentally, using jottings to support their thinking

• Encouraged to use more formal written methods only for calculations they can not solve in their heads

• Maths through problem solving/conceptual understanding

By the end of Key Stage 2 we want your children to…

• Have good understanding of the 4 operations

• Have an efficient, reliable method of written calculation for each operation

• Be confident with mental calculations and times tables

• Apply what they know to problems• Be happy and confident

mathematicians

Addition

Use of a number line

1 2 3 4 5 6 7 8 9 10 11 12 13

Addition

6+5=

Use of a 100 square

34+12=

Addition by partitioning25 + 16 =

(20+5)+(10+6) 20+10=30 5+6=11 30+11=41

Addition – Column Method

126+19=145

1 2 6+ 1 91 4 5

1

Addition – Column Method Development

12476+7369

12476+ 7369 19847

1 1 Extension through Decimals

Addition – Column Method Development

Your turn:

67.75 + 21.50=89.25

Subtraction

Subtraction

3-2=

Taking away practically.

Use of a number line/100 square

12-6=6

1 2 3 4 5 6 7 8 9 10 11 12 13

Subtraction- Column Method

204-65= 139

129014 - 65 139Your turn:708-89= 619

Multiplication

Multiplication- repeated addition

xxxxx

3x5= (3 groups of 5)

xxxxx

xxxxx

5 + 5 + 5 = 15

Multiplication using a blank number line

4x3= 12_____________________0 3 6 9 12

Multiplication by Partitioning

32x3= 96

Your turn: 45x6= 270

x 30 23 90 6 = 96

Multiplication - Written Method

Short Multiplication

347 x 7

347 x7

2429 3 4

Your turn: 2746x 6 = 16,446

Multiplication - Written Method

Long Multiplication33x28

33 x28 264 2

660 924

Multiplication - Written Method

Your turn:

36x57 =2052

Times Tables Awards

• Carrying out mental maths calculations quickly and accurately continues to be an important part of the maths curriculum.

• Times Tables tests are carried out each week (some children may begin on Number Bonds rather than Times Tables).

• Children progress through Bronze, Silver and Gold Awards.

• Children now need to know facts for 11 and 12 times tables as well (our new tests are out of 26).

Bronze Times Tables AwardsChildren know their times tables facts in order:

Children need to achieve 26 out of 26 twice

before they move onto the next times table.

Class teachers will the children know which times tables they’re

working on each week.

Silver Times Tables AwardsChildren know their times tables facts in random order:

Gold Times Tables AwardsChildren know their multiplication and division facts:

Next Steps…

• If children achieve all of their awards, they will move onto our Extension Challenges.

• These involve revising all times tables facts (45 Golden Facts and 75 Facts)

• They then move onto working with Fractions and Percentages..

Division

DivisionSharingThe children are sharing out into a known number ofgroups but how many in each group is unknown,

12÷3=

12 apples are shared into 3 baskets.How many apples are in each basket?

DivisionGroupingIt is known how many are in a group but the number of groups is not known.

12÷3=How many groups of 3 are there in 12?

There are 12 apples. How many horseswill get 3?

Division using a blank number line

25÷5= 5

_______________________0 5 10 15 20

25

(How many groups of 5 are there in 25?)

DivisionShort Division

98÷7=14

1 4 7 92 8Your turn: 98÷6 With a decimal remainder

=16.33

Remainders

99÷7=14r1 or 1 4.142 7 92 9103020

Long Division

432÷15

432 ÷ 15

Long Division

becomes

15 ) 432

432 ÷ 15

Long Division

15 ) 4 3 2

Calculate 4 ÷ 15

432 ÷ 15

Long Division

15 ) 4 3 2

We can’t do it, so we write the answer 0 here

0

432 ÷ 15

Long Division

15 ) 4 3 2

So we next look at 43 ÷ 15

0

Use repeated subtraction here if this helps

432 ÷ 15

Long Division

15 ) 4 3 20

2 x 15 = 30

3 x 15 = 45

2

432 ÷ 15

Long Division

15 ) 4 3 20

2 x 15 = 30

2

- 30

13

We need to take off 13 from the 43 to get the remainder

432 ÷ 15

Long Division

15 ) 4 3 20 2 8

- 30

1 3 2

Now we are going to do 132 ÷ 15 and put the answer here

432 ÷ 15

Long Division

15) 4 3 20 2 8

-3 0 1 3 2

Now we are going to do 132 - 120 to get the remainder

1 2 0 1 2

432 ÷ 15

Long Division

15 ) 4 3 2120

0 2 8.8

- 3 0

1 3 21 2 0

1 2

432 ÷ 15

Long Division

= 28 r 12

or 28.8

Long Division

Your turn:

496 ÷ 11= 45 r1 or 45.09

Conceptual Understanding

Presenting problems and questions in different ways to deepen children’s understanding and reasoning in maths.

Different to procedural teaching methods which practice processes – lists of calculations etc.

Conceptual Understanding

Problems can be adapted by:•removing intermediate steps •reversing the problem•making the problem more open•asking for all possible solutions•asking why, so that pupils explain their reasoning•asking directly about a mathematical relationship.

Conceptual Understanding

Which version involves deeper problem-solving skills and why?

Version 1

Version 2

Conceptual Understanding

Question 1 Jeans cost £13.95. They are reduced by 1/3 in a sale.What is their price in the sale?Dan buys the jeans. He pays with a £10 note. How much change does he get?

Question 2 Jeans cost £13.95. They are reduced by 1/3 in a sale.Dan buys the jeans. He pays with a £10 note. How much change does he get?

Conceptual Understanding

Jeans cost £13.95. They are reduced by 1/3 in a sale.

Dan has £10. Does he have enough money to buy the jeans? Explain why.

Deepening a Problem

What is the area of this rectangle?

How could we ask a different question to deepen the children’s learning…?The problem you devise should be based on the same 20cm by 5cm rectangle.

Two and Twonrich.maths.orgHow many solutions can you findto these two additions?Each of the different lettersstands for a different number.

O N E T W O O N E T W O T W O F O U R

How you can support your child

• Look for and talk about numbers in the environment

• Play games• Shopping• Number bonds• Doubles/Halves• Times tables• Division facts• Problem solving

Websites

• http://nrich.maths.org/public/• http://www.bbc.co.uk/schools/ks2bitesize/maths/n

umber.shtml• http://www.teachingtime.co.uk/• http://www.teachingtables.co.uk• http://www.bbc.co.uk/schools/laac/menu.shtml• http://www.woodlands-junior.kent.sch.uk/interacti

ve/literacy/index.htm• http://www.coxhoe.durham.sch.uk/

Thanks for coming!