Mathematics

6 November 2013

Areas of mathematics

• Numbers and the number system, including calculating and, eventually, algebra

• Using and applying mathematics

• Shape, space and measure

• Data handling

Early number

• Patterns

• Object counting

• Reading symbols

• Vocabulary

• Number games

• Discovery

• Fun!

Count the teddies. Count the cups.

Does each teddy have a drink?

How many more cups do we need?

Key number knowledge

• Secure place value• Halves and doubles• Number bonds within 10, 20, 100 …• Understanding inverse (+ - x ÷)• Times tables• Related division facts• Partition and recombine

Supporting mental calculation

• Near doubles, eg: 6 + 7 = 6 + 6 + 1

• Step counting, eg: 2, 4, 6, 8, 10

• Bridging up through 10, eg: 28 + 5

• Bridging down through 10, eg: 46 - 8

• Inverse properties, relationshipseg: 36 + 12, 48 – 36, 48 – 12

7 x 8 = 56, 56 8 = 7, 56 7 = 8

Number LinesNumbered line

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Partly numbered line

5 10 15

Empty number lines

63 – 27

63 – 27 = ?

-20 -3 -4

63 43 40 36

-10 -10 -10

10 20 30 33 36 40 50 60 63 70 +3

+3 +10 +10 +10 +3

27 30 40 50 60 63

The importance of ‘value’(and ‘place value’)

The importance of thePlace Holder

0… a most important

digit?

Why?

Partitioning8 = 5 + 3 or 6 + 2 or 4 + 4 17 63

10 + 7 3 + 60 20 + 43

25 + 42

20 + 40 = 60 5 + 2 = 7

60 + 7 = 67

Partitioning

73 – 31

70 - 30 3 - 1

70 – 30 = 40 3 – 1 = 2

so the answer is ?

1028 + 6493

th h t u th h t u 1 0 2 8 1000 000 20 8+6 4 9 3 6000 400 90 3 7000 + 400+110 +11 = 7521

Partitioning to add(expanded addition)

and Subtract(expanded decomposition)

Compact Addition and Subtraction

th h t u 1 0 2 8+6 4 9 3 7 5 2 1 1 1

1028 + 6493 = 6493 – 1028 =

Division and multiplicationDivision and multiplication are inverse operations, so if

you know your times-tables, division is not that hard.

72 ÷ 3 means how many groups of 3 are there in 72?

The answer can be found by chunking along a number line:

0 30 60 63 66 69 72

10x3 10x3 3 3 3 3

All together, it took 24 jumps of 3 to get to 72 so 72 ÷ 3 =24

So, 24 x 3 = ? 3 x 24 = ?

Compact chunking (2 steps)172 4 The Key: 2 x 4 = 8 172 5 x 4 = 20- 140 (35 groups of 4) 10 x 4 = 40 32 20 x 4 = 80- 32 ( 8 groups of 4) 30 x 4 = 120 0 43 35 x 4 = 140 8 x 4 = 32 We needed 43 lots of 4 to get to 0, so 172 4 = 43

We also now know that 4 x 43 = 172 and 43 x 4 = 172

Leading to short division

5 9 r36 3 5 57

Grid mutiplication

342 x 7x 7

300 2100 40 280 2 14 = 2394

Maths at homeFun games to reinforce key skills, problem solving,

strategic thinking and quick mental maths:

• Snakes and ladders

• Rummikub• Yahtzee• Triominoes• Playing cards• Monopoly• Mancala

• Math magic• Tantrix• Blokus• Shut the box• Chess• Smath• Mathdice Jr.

Also, ask your teacher if they have maths games you can borrow,

or simply search Amazon etc for ‘maths games for children’.

Useful websiteswww.topmarks.co.uk/parents/numbers.aspx

http://www.bbc.co.uk/schools/parents/helping_at_home/

http://nrich.maths.org/public/index.php

http://www.ictgames.com/

http://www.primarycorner.com/downloads

http://www.primarygames.com/math.htm

http://www.mad4maths.com/

http://www.sheppardsoftware.com/math.htm

http://www.mathsisfun.com/