| Mathematics at Somerhill : Mathematics at Somerhill “This is the way we do it.” |
| When do children need to start recording? : When do children need to start recording? |
| Addition : Addition Number Line Method
TU + TU
86+57 Start at 86 (the larger number) on the number line.
Partition the smaller number 57 into tens and units and count on the multiples of 10 first and then the units. 86 136 140 143 +50 +4 +3 86+57=143 |
| Addition: Using a number line to add too much and then subtract (compensate) : Addition: Using a number line to add too much and then subtract (compensate) Start with the larger number 754. Add on 100 and then subtract 4
HTU + TU
754 + 96 754 850 854 +100 -4 754+96=850 |
| Addition: Expanded method ~ moving on from adding the most significant digits first to adding the least significant digits first. : Addition: Expanded method ~ moving on from adding the most significant digits first to adding the least significant digits first. HTU + HTU
625 + 148 Add most significant digits first:
(in this example, hundreds) Add least significant digits first:
(in this example, units) 625
+ 148
700
60
13
773 600 + 100
20 + 40
5 + 8 625
+ 148
13
60
700
773 5 + 8
20 + 40
600 + 100 625+148=773 |
| Addition: Using a standard Method : Addition: Using a standard Method HTU + HTU
587 + 475 587
+475
1062 1 1 7 + 5 = 12
Place the 2 in the units column and carry the 10 forward to the tens column. 80 + 70 = 150 then + 10 (carried forward) which totals 160. Place 60 in the tens column and carry the 100 forward to the hundreds column. 500 + 400 = 900 then + 100 which totals 1000. Place this in the thousands column. |
| Subtraction: counting on : Subtraction: counting on TU - TU
84 56 0 56 60 80 84 Start Here
Start by taking away (crossing out) the 56 Find the difference between the two numbers. Count on from 56 to 84.
20 + 4 + 4 = 28 + 4 + 20 + 4 84 – 56 = 28 |
| Subtraction: Complementary addition : Subtraction: Complementary addition HTU – HTU
954 - 586 954
- 586
4 To make 590
10 To make 600
300 To make 900
50 To make 950
4 To make 954
368 954 – 586 = 368 Start Here Count on to the next multiple of 10 Count on to the next multiple of 100 Count on in 100s. Count on to the larger number in the calculation which is 954 |
| Subtraction: Standard method (decomposition) : Subtraction: Standard method (decomposition) 754
- 286
468 6 4 1 1 You cannot subtraction 6 from 4 so you must take a 10 from 50 to make 14 (and 40 in the tens column) You cannot subtraction 40 from 80 so you must take a 100 from 700 to make 140 (and 600 in the hundreds column). |
| Multiplication: Introducing multiplication on a number line : Multiplication: Introducing multiplication on a number line TU x U
14 x 5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 0 50 70 5 x 10 5 x 4 Multiplication is repeated addition Using table facts to make bigger jumps is more efficient. 14 x 5 = 70 |
| Multiplication: Grid method : Multiplication: Grid method 14 x 5 = 70 46 x 32 1380
92
1472 |
| Multiplication: Expanded method and Compact method : Multiplication: Expanded method and Compact method Expanded Method Compact Method HTU
23
X 8
160 (20 x 8)
24 (3 x 8)
184 20 multiplied by 8 equals 160
3 multiplied by 8 equals 24 Final product from totalling the part products HTU
23
X 8
184
2 3 multiplied by 8 equals 24 2 is the 2 tens that need to be carried forward and added to the next part product |
| Division: Introducing division on a number line : Division: Introducing division on a number line TU ÷ U
29 ÷ 3 0 3 6 9 12 15 18 21 24 27 29 Start Here Counting on in
groups of 3 9 groups of 3 2 left over 29 ÷ 3 = 9 remainder 2 |
| Division: Chunking on a number line : Division: Chunking on a number line TU ÷ U
72 ÷ 5 0 50 20 72 5 x 10 5 x 4 r 2 5 x 10 is ten groups of 5 5 x 4 is 4 groups of 5 There is a remainder of 2 left 72 ÷ 5 = 14 r 2 Add these two groups to make 14 remainder 2 |
| Division: Chunking : Division: Chunking HTU ÷ U
256 ÷ 7 A
256
- 70 (7 x 10)
186
- 70 (7 x 10)
116
- 70 (7 x 10)
46
- 42 (7 x 6)
4 Subtract chunks of 70 (7 x 10) How many groups of 7 in 46? 10 + 10 + 10 + 6 = 36 r 4 B
256
- 210 (7 x 30)
46
- 42 (7 x 6)
4 Subtract one large chunk of 210 256 ÷ 7 = 36 r 4 |
| Division: Short and compact method ~(Bus Shelter) : Division: Short and compact method ~(Bus Shelter) HTU ÷ U
471 ÷ 3 3 4 7 1 1 1 3 4 7 1 3 4 7 1 1 1 2 2 1 5 1 5 7 Q: What is the largest number of hundreds that will divide exactly by 3?
A: 300 divided by 3 = 100. this leaves 100 which is exchanged for 10 tens in the tens column. Q: What is the largest number of tens that will divide exactly by 3?
A: 150 divided by 3 = 50. this leaves 20 which is exchanged for 20 units in the units column. Q: What is the largest number of units that will divide exactly by 3?
A: 21 divided by 3 = 7 471 ÷ 3 = 157 |