Glendale high achievers expectations for Maths number teaching: By year group.
Two initial aims on entry:
• To recognise, say in order and write correctly numbers to 10;
• To accurately count to 5, then 10, practically, including understanding 0 as being ‘none’.
Further skills to include:
Ordinal numbers – 1st, 2nd, etc
Matching sets that have the same number, using language including ‘equal’ ‘more’ and ‘less’ when comparing sets and introducing the = sign.
Estimate objects up to 6 (Use dice or domino patterns.)(Learn the patterns)
Finding numbers on a number line to 10
Once secure with the above:
Introduce the number square and use to count in 1s, 2s, 10s, numbers to 100. Left to right count to be emphasised (linked to reading ability).
Introduce counting backwards on the number square in 1s, 2s, 10s.
Cover what comes next, forwards and backwards, for known sequences – 1s, 2s, 10s, using ‘what is 1more than ..?’ or ‘what is 2 less than..?’etc.
Introduce ‘If I’ve got 7, how many more do I need to get to 10? (Addition by counting on.) Demonstrate recording as ‘7 and (or +) * * = 10
Compare and order numbers over 10, reinforcing ‘equal’, ‘more’, ‘less’.
Copy and construct patterns of beads, pegs, cubes, shapes etc, and begin to show number patterns on the number square by colouring, blanking, looking at unit patterns e.g. the unit number when counting in 10s, etc.
Introduce totalling, by putting 2 sets together and counting them all.
Use the + sign., and language of addition.
Reverse the sum to use counting on to get to the answer. 3+2=… , 5= 2+… . (Addition numbers equal the same whichever way round you write them.)
Make own addition sums to a given number – discuss and demonstrate pattern. Practical pattern work with recording. (Number bonds – 5= 5+0, 4+1, 3+2 etc)
Introduce subtraction as’ take away’.
Secure number recognition and 1:1 correspondence to 20 and beyond through practical object counting and use of number square.
Estimate objects to 10 without counting, including ‘more than 10’ as an option. (Using dice or dominoes as an initial basis of instant recognition)
Check understanding of conservation of number – that a pattern of 8 has the same amount as a random mix of 8.
Introduce simple problem solving as soon as children can count 1:1 and recognise numbers. (Which is more, 7 or 3? What comes between 6 and 4? What number should be on the red door if either side is a 4 and an 8?)
Apply skills to measuring including using standard measures, money, shapes and data handling.
Further clarification, and identification of potential difficulties: Numbers and Patterns – Steps in Learning.
For classroom ideas: Numbers and Patterns – the role of the adult.
For outside play ideas: Numbers and patterns- Supporting Resources.
Ensure activities allow all children to be involved, not sitting waiting.
Moving on: Into Y1
Using the number square and Unifix/Deines demonstrate 12 = 1 ten and 2 units, and explain how the pattern extends through to 100.
Demonstrate jottings as lines for 10s and small circles in dice/domino/paired pattern for units. Introduce square as jotting for 100.
Practise and secure number bonds to 10, addition and subtraction, emphasising pattern and logical coverage. (Include practical and pattern opportunities, and use of the hundred square.)
Explore doubles and halves to 30, then 40, and then in patterns of 5 (half of 70, double of 25 etc)
Add and subtract 10 from any digit, showing pattern on number square.
Investigate the pattern of counting in 5s, forwards and backwards; consolidate 2s and 10s into times tables.
Count repeated sets of the same size, based on simple problem sums. (How many legs on 3 chairs?)
Mentally add a single digit to a double digit, using the number square to show the relationship to single digit addition. 8+6=14, 18+6=24, moving to 18+16=34. Jottings encouraged using vertical grouping.
Regularly use known facts to investigate a number: 35 = 30+5 = 5×7= half of 70= 105-70 etc. Can be part of problem solving. Play with sums, contracting and extending them.
Find the difference by counting on and subtraction.
Develop mental subtraction strategies, including relating single digit subtraction patterns to single digit from a double digit subtraction, and subtraction from a multiple of 10. Jottings encouraged, using lines and circles. 7 – 4 = 3, 27 – 4 = 23; 10 – 4 = 6, 70 – 4 = 66; 8 – 2 = 6, 58 – 22 = 36. Develop through the 10.
Share numbers to 30 between varied numbers of people as part of simple problem solving. (20 sweets shared between 6 children. How many each? And how many left over? (Practical and jottings by grouping.)
Use jottings in arrays to show patterns of multiplication are the same whichever way round the multiplication is written. Use this information to check answers. 5 x 3 = 15 = 3 x 5
Use jottings in arrays to link multiplication with division. 4×6 (set out in 4 lines of 6) = 6×4 (turn array to show 6 lines of 4) = 24. 24 -:- 6 = 4 (work out and show array), 24-:- 4 = 6 (Demonstrate pattern of array, and compare to previous array.) (Arrays can be very useful jottings for multiplication and division.)
Introduce numbers up to 200, including use of 0 as a place holder. (204)
Apply number to problem solving every week. Include calculation applied to measures, shape, money, and data handling problems.
Through to Y2
Develop number recognition, place value and order through to 1000. Add and subtract 1, 10, 100 from any integer (whole number) to 1000
Add 9 (19, 29) and 11 (21, 31) and subtract 9/11 using knowledge of addition and subtraction of 10.
Extend recall of number bonds to include numbers to 100. Use mental strategies to partner 68 to make 100. (Formal jottings could be used)
Introduce vertical addition as a strategy for working out tu and htu calculations.
Develop formal subtraction jottings into vertical subtraction sums.
Extend doubles and halves/ odd and evens to follow patterns previously established. (Half of 10, half of 100, half of 1000 etc.)
Count forwards and back in 10s, 25s, 50s and 100s up to 1000, from a variety of starting points.
Round numbers up or down to 10.
Develop mental strategies, including adding more than 2 numbers using the largest first; finding the difference by counting on.
Extend discovery of facts about a number to include more than one operation : 25 = 20 + 5 = (4 x 5) + 5; half of 60 – 5; 10 + 10 + 5; 30 – 5 ->15 + 15 – 5 etc.
Multiplication as extension of known facts – 5×10, 50 x 10, 5 x 100;
Count in 3s and 4s, observing the patterns on the number square, and transfer to times tables. Divide by 3 or 4 up to 30/40, then using multiples of 10, using other key facts. 8-:- 4 = 2, 80 -:- 4 = 20, 800 -:- 4 = 200 etc. Note the link between multiplication and division. 20-:- 4 = 5; 5 x 4 =20 etc.
Use simple fractions as a means of sharing, eg 1/8 of 16, 2/5 of 20 etc; to count in up to 10; to recognise equivalence.
To add and subtract 1 or 2 digit numbers mentally, from a 2 or 3 digit number; to add and subtract larger numbers (to 100, to 1,000) using jottings or vertical calculations.
Use known facts to check answers: 27 – 6 = 21, 21 + 6 =27; 18 -:- 6 = 3, 3 x 6 = 18; half of 18 = 9, because 2 x 9 =18 etc.
Apply number to problem solving, including 2 or 3 step problems, every week. Include calculations related to measures, shapes, money, time and data handling regularly.