Addition Count objects to 20, moving objects whilst counting • Say one more than a number to 10 e.g. one more than 7 • Compare two numbers under 10– which is more? • Adding by combining groups– use pictures and drawings Foundation stage • Subtraction Count objects to 20, moving objects whilst counting • Say one less than a number to 10 e.g. one less than 7 • Compare two numbers under 10– which is less? • Subtraction as taking away • • • • Begin to count in 2s to 20 Begin to count in 10s to 100 They will work on putting objects in equal groups and counting them Division • • • • Begin to count in 2s to 20 Begin to count in 10s to 100 Halving Division as sharing Share the pears equally between three people • • • • • Count objects to 20, moving objects whilst counting Read, write and order numbers to 20 Say one more than a number to 30 e.g. one more than 27 Adding by combining groups– use pictures and drawings Use of + and = signs to write number sentences How many cherries are there? 2, 4, 6 There are four bananas and I eat two. How many are left? Count one group, then start counting from that total when adding on e.g. 1,2 then 3,4,5 Level One Multiplication • • • • • Count objects to 20, moving objects whilst counting Read, write and order numbers to 20 Say one less than a number to 30 e.g. one less than 27 Subtraction as taking away Subtraction as finding the difference • • • • Count in 2s to 20 Count in 5s to 50 Count in 10s to 100 They will work on putting objects in equal groups and counting them 9-4 = 5 This can also be used to illustrate that the difference between 9 and 5 is 4 (4 hops back) Use a number line to count in hops of 2, 5s and 10s • • • • • Begin to count in 2s to 20 Begin to count in 10s to 100 Halving Division as sharing Division as grouping Use a number line to count the number of hops taken e.g. how many 2s are in 10? (how many hops have you taken) Addition Read, write and order numbers to 100 • Be able to say one more to 100 e.g. one more than 58 • Addition by partitioning and recombining (TU) Level Two • Children will use tens and units equipment– make both numbers then add the tens together, then the units. The children will move onto drawing the equipment. Children will move onto an expanded written method– layout is crucial. Subtraction Read, write and order numbers to 100 • Be able to say one less to 100 e.g. one more than 58 • Subtraction by partitioning and recombining (TU) • 32 - 11 Children will use tens and units equipment to subtract. Make the first number then take away the second. Read, write and order numbers • Read, write and order numbers to 1000 to 1000, be able to say one less • Be able to say one more to to 1000 e.g. one less than 348 1000 e.g. one more than 348 • Subtraction by partitioning • Addition by partitioning and and recombining (HTU, recombining (HTU, decimals) decimals) Introduction of decomposition Level Three Decomposition. In this example breaking down 50 into 40+10 and moving the ten into the units because 3-8 does not work 3.9 Subtraction can be done by finding the difference– counting on from the smaller number to the bigger one Division • Know 2, 5 and 10 times tables • • • • Children will move onto an expanded written method– layout is crucial. • The layout is crucial– hundreds, tens and units needs to be carefully lined up Multiplication • Know 2, 5 and 10 times tables off by heart. Begin to learn 3 off by heart. Begin to learn 3 times table times table Count in 2s to 20, 5s to 50 and • Know halves of even numbers 10s to 100 to 20 off by heart e.g. half of 14 Know doubles of numbers to 10 • Division as sharing off by heart e.g. double of 4 • Division as grouping Multiplication as repeated addition Use of x and = signs to write 15 ÷ 3 number sentences Division by grouping becomes the main way to divide. Use equipment to do this. Children will learn what a remainder is. In this example there are 5 groups of 3 in 15. Children use their own pictures too as well as equipment to multiply using repeated addition. They do not count in 1s, but count in 2s, 5s, 10s as appropriate. Know 2, 3, 5, 6 and 10 times tables off by heart • Multiply numbers by 10 or 100 • Multiply two digit numbers using the grid method • 16 x 4 X 10 6 4 24 40 Know 2, 3, 5, 6 and 10 times tables off by heart • Find a quarter of a number by halving and halving again • Dividing by 10 • Introducing written methods of division (chunking on a numberline) • 40 + 24 = 64 Partition the two digit number into tens and units. Multiply each part by the single digit. Then add each part to work out the answer (mentally is possible). At this level only numbers with one ten will be used. It is important to keep the numbers lined up. This example shows children counting how many groups of 5 there are in 55. Start at 0 and think of counting in more than one group at a time. Here they have counted on 10 groups of 5 and then another 5. the answer is how many groups there are, in this case 11. Addition Subtraction Multiplication Read, write and order numbers • Read, write and order numbers • Know times tables off by heart to 10 000 and know the value of to 10 000 and know the value of to 10x10 • Multiply whole and decimal each digit each digit numbers by 10 and 100 • Add mentally two digit • Subtract mentally two digit • Use efficient written methods numbers numbers • Use efficient written methods • Use efficient written methods Level Four • Contracted method of addition. Layout is crucial. The number of digits in a number may not be the same. 2?8 +3? 251 Missing number problems extend children’s thinking Add numbers to 10 000 Read, write an order numbers to two decimal places, say which is more e.g. which is more 2.36 or 2.64? How do you know? • Use simple algebra • Use written methods to add numbers where the number of digits is not the same • • Level Five Decomposition– contracted method Layout is crucial. The number of digits in a number may not be the same. Children will be able to chunk on a number line confidently, with remainders Children will use the grid method to multiply numbers with different numbers of digits, including decimals Use written method of chunking Subtract numbers to 10 000 • Know times tables off by heart Read, write an order numbers to to 12x12 two decimal places, say which • Multiply whole and decimal is less e.g. which is less 2.36 or numbers by 10, 100 and 1000 2.64? How do you know? • Use efficient written methods • Use simple algebra 36.21 x 8 • Use written methods to subtract numbers where the number of digits is not the same • • Decomposition more than once! Partition the number into tens, units, tenths and hundredths. Multiply each part and then recombine. Calculate 1.2 x (1.3 + 1.4) x 1.5 Children will learn how to use simple algebra Know times tables off by heart to 10x10 • Divide whole and decimal numbers by 10 and 100 • Use efficient written methods • Children will subtract decimals using a written method The number of digits may not be the same! 2n + 2n = 4n Division 2n - 1n = n Children will learn how to use simple algebra Children will use brackets Know times tables off by heart to 12x12 • Divide whole and decimal numbers by 10, 100 and 1000 • Use efficient written methods • Continue to use written method of chunking Begin to use the bus stop method