Download - Backwell JuniorSchool
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Backwell JuniorSchool
Maths Parent Workshop
Tuesday 14th October 2014Before we begin, please try to solve the
calculations on your table…..
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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.
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How did you solve these?
• 157+65=
• 245-152=
• 46x22=
• 154÷7=
• 278÷19=
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How did you solve these?
• 157+65= 222
• 245-152= 93
• 46x22= 1012
• 154÷7= 22
• 278÷19= 14.63
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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
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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
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Addition
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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=
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Addition by partitioning25 + 16 =
(20+5)+(10+6) 20+10=30 5+6=11 30+11=41
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Addition – Column Method
126+19=145
1 2 6+ 1 91 4 5
1
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Addition – Column Method Development
12476+7369
12476+ 7369 19847
1 1 Extension through Decimals
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Addition – Column Method Development
Your turn:
67.75 + 21.50=89.25
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Subtraction
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Subtraction
3-2=
Taking away practically.
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Use of a number line/100 square
12-6=6
1 2 3 4 5 6 7 8 9 10 11 12 13
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Subtraction- Column Method
204-65= 139
129014 - 65 139Your turn:708-89= 619
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Multiplication
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Multiplication- repeated addition
xxxxx
3x5= (3 groups of 5)
xxxxx
xxxxx
5 + 5 + 5 = 15
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Multiplication using a blank number line
4x3= 12_____________________0 3 6 9 12
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Multiplication by Partitioning
32x3= 96
Your turn: 45x6= 270
x 30 23 90 6 = 96
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Multiplication - Written Method
Short Multiplication
347 x 7
347 x7
2429 3 4
Your turn: 2746x 6 = 16,446
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Multiplication - Written Method
Long Multiplication33x28
33 x28 264 2
660 924
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Multiplication - Written Method
Your turn:
36x57 =2052
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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).
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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.
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Silver Times Tables AwardsChildren know their times tables facts in random order:
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Gold Times Tables AwardsChildren know their multiplication and division facts:
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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..
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Division
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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?
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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?
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Division using a blank number line
25÷5= 5
_______________________0 5 10 15 20
25
(How many groups of 5 are there in 25?)
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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
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Long Division
432÷15
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432 ÷ 15
Long Division
becomes
15 ) 432
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432 ÷ 15
Long Division
15 ) 4 3 2
Calculate 4 ÷ 15
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432 ÷ 15
Long Division
15 ) 4 3 2
We can’t do it, so we write the answer 0 here
0
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432 ÷ 15
Long Division
15 ) 4 3 2
So we next look at 43 ÷ 15
0
Use repeated subtraction here if this helps
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432 ÷ 15
Long Division
15 ) 4 3 20
2 x 15 = 30
3 x 15 = 45
2
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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
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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
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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
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432 ÷ 15
Long Division
15 ) 4 3 2120
0 2 8.8
- 3 0
1 3 21 2 0
1 2
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432 ÷ 15
Long Division
= 28 r 12
or 28.8
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Long Division
Your turn:
496 ÷ 11= 45 r1 or 45.09
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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.
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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.
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Conceptual Understanding
Which version involves deeper problem-solving skills and why?
Version 1
Version 2
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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?
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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.
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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.
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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
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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
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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/
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Thanks for coming!