Transcript Mathematics for parents Wednesday 6 November 2013

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
Count the teddies. Count the cups.
Does each teddy have a drink?
• Reading symbols
• Vocabulary
• Number games
• Discovery
• Fun!
How many more cups do we need?
Key number knowledge
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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
1
2
3
4
5
6
7
8
9
10
11
Partly numbered line
5
Empty number lines
10
15
12
13
14
15
63 – 27
63 – 27 = ?
-20
-3
63
43
-10
10
+3
27 30
-4
20
40
-10
30 33 36 40
+3
+10
40
-10
50
+10
36
60 63
+10
50
+3
60
63
70
The importance of ‘value’
(and ‘place value’)
The importance of the
Place Holder
0
… a most important digit?
Why?
Partitioning
8 = 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
70 – 30 = 40
3–1=2
so the answer is
?
-
1
Partitioning to add
(expanded addition)
1028 + 6493
th h t u th
h
t u
1028
+6 4 9 3
1000 000 20 8
6000 400 90 3
7000 + 400+110 +11 = 7521
and Subtract
(expanded decomposition)
6493 – 1028
th h t u th
6493
- 1028
+
h
t u
6000 400 890 13
1000 000 20 8
5000 + 400+ 60 + 5 = 5465
Compact Addition and Subtraction
1028 + 6493 =
th h t u
1028
+6 4 9 3
7521
11
6493 – 1028 =
th h t u
6 48913
-1028
5465
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
10x3
10x3
60
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 = ?
63 66 69 72
Compact chunking (2 steps)
172 4
172
- 140 (35 groups of 4)
32
- 32 ( 8 groups of 4)
0 43
The Key:
2x4=8
5 x 4 = 20
10 x 4 = 40
20 x 4 = 80
30 x 4 = 120
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 r3
6 3 5 57
Grid mutiplication
342 x 7
x
300
40
2
=
7
2100
280
14
2394
Maths at home
Fun games to reinforce key skills, problem solving,
strategic thinking and quick mental maths:
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Snakes and ladders
Rummikub
Yahtzee
Triominoes
Playing cards
Monopoly
Mancala
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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/