routes through calculation
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Routes through Calculation. Friday, 21 March 2014. What you say counts. Addition:. Number lines: Addition can be done in any order, but encourage pupils to begin with the largest number. e.g. 5+8 is the same as 8+5. - PowerPoint PPT PresentationTRANSCRIPT
Routes through Calculation
Friday, 21 March 2014
What you say counts.
Addition:
8 9 10 11 12 13
Number lines: Addition can be done in any order, but encourage pupils to begin with the largest numbere.g. 5+8 is the same as 8+5
+1 +1 +1 +1 +1
Addition:
86 136 140 143
The number line can be extended to larger numbers, and used For counting on in GROUPS of tens and ones/units. PARTITIONING can now be into larger groups.
e.g. 86+57
+50 +4 +3
Addition:Partitioning can be used to build on the knowledge used from number lines
35+2630+20=505+6=1150+11=61
Addition:This leads on to the informal and formal written method!
86+ 57 --------------- 13 (6+7) 130 (80+50) --------------- 143
86+ 57 --------------- 143 --------------- 1
Subtraction:
14 15 16 17 18 19
The number line can be used for subtraction, but going the other way.
e.g. 19-5
-1 -1 -1 -1 -1
Subtraction:
182 189 219
And with larger numbers too!
e.g. 219-37
-7 -30
Subtraction:By partitioning.
74-2774-20= 5454-7 = 47
74-27
70+4 - 60+14-20+7 20 + 7--------- ---------- 40 + 7* Introduces the concept of EXCHANGING (not BORROWING)
Subtraction:This leads to a better understanding of the formal method!
MultiplicationBegins with simple dot arrays and groupings
* * *
4 lots of 34 X 3
3+3+3+3 (Solve with a number line beginning at 0)Multiplication is simply repeated ADDITION!
* * *
* * *
* * *
* * *
OOOOOO
Is either 3 lots of 2, or 2 lots of 3 OO
OO
OO
oooooo
Multiplication:Partitioning again.
12 X 6 (10+2) X 6
10 X 6 = 602X 6 = 12
60 +12 = 72
Multiplication:The GRID method, using partitioning. E.g.9 X 46
40 6
9 360 54
360 + 54 = 414
Multiplication:And larger numbers… 72 X38
70 2
30 2100 60 =2160
8 560 16 = 576
2160 + 576 = 2736
MultiplicationLeading to the expanded methods:
46 x 9 -------- 54 (6X9) 360 (40X9) -------- 414
72 x 38 -------- 16 (2X8) 560 (70X8) 60 (2X30) 2100 (70X30) -------- 2736
MultiplicationAnd finally the formal written methods:
46 x 9 -------- 414 -------- 5
72 x 38 -------- 576 1
2160 -------- 2736
Division:Like multiplication, begins with dot arrays and groupings.
OOOOOO
Is either 6 shared between 2, or 6 shared between 3
OO
OO
OO
oooooo
* * *
* * *
* * *
* * *
* * *
12 ÷ 4 = 3
Division:Division is simply repeated SUBTRACTION!
Using a number line. E.g. 35 ÷ 7
0 7 14 21 28 35
-7 -7 -7 -7 -7
35 ÷ 7 = 5 There are 5 “jumps”
Division:With remainders. E.g. 38 ÷ 7
3 10 17 24 31 38
-1 -1 -1-7 -7 -7 -7 -7
38 ÷ 7 = 5 “jumps” – 3 38 ÷ 7 = 5 r 3
Division:Chunking!
Simple
With remainders
What have you got to help you and your child with maths?
Conker Maths/ KIRFShttp://www.conkermaths.org/cmweb.nsf/pages/kirfs.html
RMEasimathshttp://www.rmeasimaths.com/
Mathleticshttp://www.mathletics.co.uk/