maths workshop ks1. aims in ks1 to have a secure knowledge of number facts and a clear understanding...
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Maths WorkshopKS1
Aims in KS1
• To have a secure knowledge of number facts and a clear understanding of the four operations.
• To be able to use their knowledge and understanding to carry out calculations mentally and to apply appropriate strategies when using larger numbers.
• To have an efficient, reliable written method of calculation for each operation that can applied with confidence.
Strategies for Mental Calculations
• Number bonds to 10 and 20• Counting forwards and backwards in
1s and 10s• Doubles and near doubles• Partitioning and recombining
numbers• Adjusting near multiples of 10 • Bridging through 10• Inverse relationships
Addition
Progression in Addition
Recording calculations in pictures
4 + 2 = 6 3 + 3 = 6
Bead strings or beads / counters to illustrate addition
8 + 2 = 10
Using a number line to count on in units
12 + 6
+1 +1 +1 +1 +1 +1
12 18 12 + 6 = 18
12 + 6 =
12 + 6 = 18
+
1
+
1
+
1
+
1
+
1
+
1
1812
Using a number line to count on in tens
+ 10 + 10 + 10
24 + 30 =
24 + 30 = 54
+
10
+
10
+
10
24 34 44 54
Partition a number to bridge through a multiple of ten
I can partition a number to bridge through a multiple of ten 16 + 7
+ 4 + 3
16 20 23
16 + 7 = 23
15 + 8 =
+ 5
15 20 23
+ 3
15 + 8 = 23
Use a number line to count on in tens and units by partitioning
I can partition a number to bridge through a multiple of ten 16 + 7
+ 4 + 3
16 20 23
16 + 7 = 23 48 + 14 =
62
48 + 14 =
+
10
48 58 62
+ 4
Adding near multiples of ten by adding in tens and adjusting
+ 20
35 54 55
-1
25 + 19 =
25 + 19 = 44
+ 20
454425
Partitioning to solve more complex addition
265 + 177 =
265 = 200 + 60 + 5177 = 100 + 70 + 7 __________ 300 + 130 + 12 = 442
Using the partitioned method to add in columns
215 + 176 11 ( 5 + 6) 80 (10 + 70) 300 (200 + 100) 391
215 + 176 =
215 + 176 = 391
Column method including carrying digits
217 + 179 =
2 1 71 7 9
217 + 179 = 396
1
3 9 6
Bead strings or beads / counters to illustrate subtraction
10 – 2 = 8
Using a number line to count back in units 12 + 6
+1 +1 +1 +1 +1 +1
12 18 12 + 6 = 18
18 - 6 =
18 – 6 = 12
-1-1-1-1-1-1
12 18
Progression in Subtraction
Recording calculations in pictures
9 – 5 = 4
To find the difference by counting on the number line
+ 10 + 10 + 10
32 - 18 =
2 + 10 + 2 = 14
+ 2 +
10
+ 2
18 20 30 32
32 - 18 = 14
To bridge through a multiples of ten when counting back
42 – 25 =
+ 10 + 10 + 10
42 – 25 = 17
- 3
17 20 22 42
- 2 - 20
To subtract near multiples of ten by subtracting in tens and adjusting
I can subtract near multiples of ten by subtracting in tens and adjusting 45 - 19
-20
+1
25 26 45
45 – 19 = 26
- 20
35 36 55
55 – 19 =
55 – 19 = 36
To partition numbers and subtract using decomposition
81 – 57 =
81 – 57 = 24
50 780 1
70 1
420
To partition numbers and subtract using decomposition
534 - 218 =
534 - 218 = 316
218 = 200 10 8
534 = 500 30 4
20 1
300 10
6
To use a number line to find the difference between decimals
+ 10 + 10 + 10
6.2 – 1.6 =
6.2 – 1.6 = 4.6
+ 0.4 + 4 + 0.2
1.6 2.0 6.0 6.2
0.4 + 4 + 0.2 = 4.6
Subtraction using the column method
561 – 146 =
561 – 146 = 415
561
146
15
4 15
Counting objects in equal groups
Count how many in each group
3 groups /lots of 5
To understand multiplication as repeated addition
5 x 2
2 + 2 + 2 + 2 + 2
5 x 2 = 10
5 lots of 2 =
2 + 2 + 2 + 2 + 2 =
5 x 2 = 10
Multiplication as arrays(arranging the counters in equal
rows – an array)
Repeated addition on a number line
4 x 5
+5 +5 +5 +5
0 5 10 15 20 4 x 5 = 20
4 lots of 5 =
4 lots of 5 or 4 x 5 = 20
5 + 5 + 5 + 5 = 20
To count in 2s, 5s and 10s
2s 5s 10s
To simplify multiplication by partitioning
14 x 3 = (14 = 10 + 4)
10 x 3 = 30
4 x 3 = 12
14 x 3 = 42
(30 + 12 = 42)
To multiply by 10, 100 and 100 using place value (Y3)
Th H T U
1 2
1 2 0
1 2 0 0
1 2 0 0 0
12 x 10 = 120
12 x 100 = 1200
12 x 1000 = 12000
To multiply using multiples of 10, 100, 1000
3 x 20 = 3 x 2 x 10 = 60
7 x 300 = 7 x 3 x 100 = 2100
To multiply using grid method (Y4)
24 x 6 =
x
6 120
24
420
24 x 6 = 144
120 + 24 = 144
Multiply by expanded multiplication
42 x 8 16 (2 x 8) 320 (40 x 8) 336
42 x 8 =
42 x 8 = 336
Multiplication using column method (Y5)
24 x 37 =
24 x 37 = 888
24 x 37
168
720
888
Sharing items into groups
6 shared between 2 is 3
Division by repeated subtraction
4 x 5
+5 +5 +5 +5
0 5 10 15 20 4 x 5 = 20
20 ÷ 5 =
20 ÷ 5 = 4
-5 -5 -5 -5
Division by chunking (Y4-5)
63 ÷ 5 =
6350 (10 X 5)
13 ( 2 x 5 ) 10 3
63 ÷ 5 = 12 r 3
Division by semi-compact division (Y6)
357 ÷ 6 =
357 ÷ 6 = 59 r 3
6 3 5 7
5
30
57
54
9
3
Division by compact method (Y6)
357 ÷ 6 =
5
6 3 5 759 r 3
357 ÷ 6 = 59 r 3
Questions