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Maths Workshop KS1 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 +1 +1 +1 +1 +1 +1 12 12 + 6 = 18 12 + 6 12 = 18 18 18 Using a number line to count on in tens 24 + 30 = + 10 + 10 24 10 ++10 34 ++ 10 10 44 24 + 30 = 54 54 Partition a number to bridge through a multiple of ten I can partition a number to bridge through a multiple of ten 16++87 = 15 + 5+ 4 16 15 ++33 20 20 23 23 15 + 8 = 23 rtition a number to bridge through a multipl Use a number line to count on in 16 + 7 tens and units by partitioning 48 + 14 = ++ 43 ++ 10 4 48 16 58 20 48 + 14 = 62 62 23 Adding near multiples of ten by adding in tens and adjusting 25 + 19 = + 20 -1 35 25 54 44 5545 25 + 19 = 44 Partitioning to solve more complex addition 265 + 177 = 265 = 200 + 60 + 5 177 = 100 + 70 + 7 __________ 300 + 130 + 12 = 442 Using the partitioned method to add in columns 215 + 176 = 215 + 176 11 ( 5 + 6) 80 (10 + 70) 300 (200 + 100) 391 215 + 176 = 391 Column method including carrying digits 217 + 179 = 217 179 39 6 1 217 + 179 = 396 Bead strings or beads / counters to illustrate subtraction 10 – 2 = 8 Using a number line to count back in units 18 - 6 = +1 -1 +1 -1 +1 -1 +1 -1 +1 -1 +1 -1 12 12 12 + 6 =1818 – 6 = 12 1818 Progression in Subtraction Recording calculations in pictures 9–5=4 To find the difference by counting on the number line 32 - 18 = + 10 ++ 10 2 + 210 ++10 2 + 10 + 2 = 14 18 20 30 32 - 18 = 14 32 To bridge through a multiples of ten when counting back 42 – 25 = + 10 +- 10 2 -3 17 20 +- 20 10 22 42 – 25 = 17 42 To subtract near multiples of ten by subtracting in tens and adjusting 55 – 19 = - 20 +1 35 36 55 – 19 = 36 55 Ic To partition numbers and subtract using decomposition 81 – 57 = 70 1 80 1 50 7 20 4 81 – 57 = 24 To partition numbers and subtract using decomposition 534 - 218 = 20 1 534 = 500 30 4 218 = 200 10 8 300 10 6 534 - 218 = 316 To use a number line to find the difference between decimals 6.2 – 1.6 = 10 ++ 0.4 1.6 ++410 2.0 ++ 10 0.2 6.0 6.2 – 1.6 = 4.6 0.4 + 4 + 0.2 = 4.6 6.2 Subtraction using the column method 561 – 146 = 51 561 146 415 561 – 146 = 415 Counting objects in equal groups Count how many in each group 3 groups /lots of 5 To understand multiplication as repeated addition 5 lots of 2 = 2+2+2+2+2= 5 x 2 = 10 5 x 2 = 10 Multiplication as arrays (arranging the counters in equal rows – an array) Repeated addition on a number line 4 lots of 5 = 0 5 10 15 20 4 x55+=520 + 5 + 5 = 20 4 lots of 5 or 4 x 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 1 H T U 1 2 1 2 0 12 x 10 = 120 1 2 0 0 12 x 100 = 1200 2 0 0 0 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 20 4 6 120 24 120 + 24 = 144 24 x 6 = 144 Multiply by expanded multiplication 42 x 8 = 42 x 8 16 (2 x 8) 320 (40 x 8) 336 42 x 8 = 336 Multiplication using column method (Y5) 24 x 37 = 24 x 37 168 720 888 24 x 37 = 888 Sharing items into groups 6 shared between 2 is 3 Division by repeated subtraction 20 ÷ 5 = -5 0 -5 5 -5 10 -5 15 4 x 5 = 20 20 ÷ 5 = 4 20 Division by chunking (Y4-5) 63 ÷ 5 = 63 50 (10 X 5) 13 ( 2 x 5 ) 10 3 63 ÷ 5 = 12 r 3 Division by semi-compact division (Y6) 357 ÷ 6 = 59 6 357 30 57 54 3 357 ÷ 6 = 59 r 3 Division by compact method (Y6) 357 ÷ 6 = 5 9 6 3 5 57 r3 357 ÷ 6 = 59 r 3 Questions