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 Count the teddies. Count the cups. Does each teddy have a drink? How many more cups do we need? Patterns Object counting Reading symbols Vocabulary Number games Discovery Fun!

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, relationships eg: 36 + 12, 48 – 36, 48 – 12 7 x 8 = 56, 56 ¸ 8 = 7, 56 ¸ 7 = 8

Number Lines Numbered line Partly numbered line Empty number lines 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 the Place Holder … a most important digit? Why?

Partitioning 8 = 5 + 3 or 6 + 2 or 4 + 4 17 63 10 + 7 3 + 60 20 + 43 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 ?

Partitioning to add (expanded addition) 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

and Subtract (expanded decomposition) 6493 – 1028 th h t u th h t u 6 4 9 3 6000 400 890 13 - 1 0 2 8 1000 000 20 8 + 5000 + 400+ 60 + 5 = 5465

Compact Addition and Subtraction 1028 + 6493 = 6493 – 1028 = th h t u 6 48913 - 1 0 2 8 5 4 6 5 th h t u 1 0 2 8 +6 4 9 3 7 5 2 1 1 1

Division and multiplication Division 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 6 3 5 57

Grid mutiplication 342 x 7

Maths at home Fun 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 websites www.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/