Grouping and Place Value Grouping and Place Value Grouping and Place Value Be able to see at a glance how many there are in a small collection and attach number names yet may not be able to say the number names in order. This is called SUBITISING. Subitising (‘seeing’ without counting) small collections (e.g.... 1 - 5) using concrete materials. Explain flashed domino patterns up to 6 and explain what they see and describe it in another way. Recognise quantities from domino/pair/irregular patterns (subitising). Start to recognise numbers up to 10 and beyond when combining two or more patterns. Count and copy a sequence of individual sounds, up to 3 claps, beats (this is known as a temporal sequence). Count and copy a sequence of individual sounds, up to 5 claps, beats (temporal sequences). Count and copy a temporal sequence of claps, beats up to at least 10 - individual and groups of claps. Use fingers and beats to represent numbers in stories and songs. Use finger patterns to keep track of temporal sequences (like beats of a drum or jumps) e.g. Use your fingers to count how many beats are made on this drum. Use finger patterns to show patterns of 0-10, doubles Make finger patterns up to 5 by looking at their fingers. Make finger patterns up to 5 and beyond in different ways by looking at their fingers. e.g. Put I finger up on one hand and 4 on the other, 2 fingers up on one hand and 3 on the other, 0 fingers up on one hand and 5 on the other. Make finger patterns up to 10 in different ways without looking at their fingers. e.g. make different combinations of ten.
Strategy See the for Early level on the Highland Numeracy Blog Early addition and subtraction Early addition and subtraction Early addition and subtraction Find groups of the same theme within a collection, e.g. pigs in farmyard toys, or from box of plastic fruit find 5 bananas, 5 apples, 5 lemons. Match objects in a collection to see which group has the most or the fewest. Estimate the number of objects in a group of up to 20 objects and count to check. Use vocabulary such as bigger, smaller and ‘the same’ to compare groups of items. Find and describe items that are the same and different within a collection, e.g. ‘horses’ and ‘not horses’. Count the different groups in a collection to decide which has the most or fewest, within 20. Sort objects using familiar or given criteria, e.g. colour, size, family, etc. Sort objects into groups using simple given criteria and be able to explain how they did this, e.g. colour, size, family, etc. Compare and order groups of numbers by deciding the criteria for themselves and be able to articulate their criteria for sorting, e.g.... bigger than 5, less than 10 (within 20). Compare two groups of objects and identify which is the smallest/largest group. Compare two groups of objects to determine ‘how many more’ and use appropriate vocabulary: altogether (within 10). Show an awareness of counting a collection using some number names but not always reliably. (Staff model touching and moving an object to count it). Count up to 10 visible items by touching each item in turn, count becoming more reliable/stable Understand that ten ones can be bundled up and become one ten. Pupils can also connect symbols and words to recognise tens and ones e.g. understand that 17 sweets packaged into bags of ten means one bag of sweets and 7 left over or can be represented as below. Show an awareness of counting a collection using some number names but not always reliably. (Staff model touching and moving an object to Can count items in a collection and know that if items are added to a collection there will be a change in the size of the set. Can combine two or more groups of objects to model and solve addition and use appropriate vocabulary; makes, join, altogether. (They may start to count by counting both groups
Use known facts to solve an unknown fact Begin to solve multiplication facts about the five times table from their knowledge of place value. e.g. Understand that four tens is the same as eight fives. 4 x 10 =40 so 8 x 5 = 40 Use repeated addition and known facts to work out multiplication problems Rounding and Estimating Rounding and Estimating Rounding and Estimating Describe whether a number is closer to zero, ten or twenty by using a tool such as a tens frame or a number line. 8 is closer to ten than zero 7 is closer to ten than zero Round numbers to the nearest ten when estimating. e.g. 32 to 30 and 57 to 60 and explain their answer. Round numbers to the nearest ten or hundred when estimating. e.g. 345 to 350 or 300 875 to 880 or 900 Patterns and Relationships Patterns and Relationships Patterns and Relationships Describe and explain number sequences and patterns, understanding the pattern for the ‘teen’ numbers and then extending this to other multiples of 10. e.g. 11, 12, 13, 14, 15 etc. 1-9 is being repeated. Look on a number line/ hundred square and predict which number will come next. Understand repeating patterns in the tens and ones columns and use this to explain patterns in the decades. (0-9 numbers are repeated). e.g. 21, 22, 23, 24…. and 31, 32, 33, 34…. 20, 30, 40, 50, 60 … Understand repeating patterns in the hundreds, tens and ones columns and use this to explain patterns in the hundreds and thousands. Understand that the next number in a sequence of Understand that the next number in a sequence of multiples is adding that multiple and the number
Record multiplication problems using the terms ‘groups of’, ‘lots of’, ‘sets of’, ‘shared equally’ and ‘remainders’. Begin to use symbols (x, ÷) to represent the operations of multiplication and division. Confidently use the symbols (x, ÷) to represent the operations of multiplication and division. Experiences and outcomes
Mental and semi-formal calculations for multiplication and division. Mental methods should always be used in preference to formal algorithms. If a pupil cannot use mental strategies to solve a problem, they should not be asked to record solutions using formal algorithms as this will simply take them through a process rather than truly demonstrate their understanding of the given task. Subtract – change the numbers by adding or subtracting the same amount e.g. 22 – 17 becomes 20 – 15 = 5 72 – 27 becomes 75 – 30 = 35 507 – 296 becomes 511 - 300 = 211 Start to use arrow notation to record thinking. ‘Instead of 53 take 19, I did 54 take 20’ 53 – 19 = 54 – 20 = 34 Pupils should explore the effect of carrying out operations on an existing equation, e.g. if they know (and write down) 20+15=35 then what is the effect of (say) doubling both sides? What happens if we add 5 to one side but not the other? What happens if we carry out different operations to both sides of the equation? Use a known fact to work out an unknown fact e.g. Number bonds to 10: 40 + 70 40 + 60 = 100 so 40 + 70 is ten more = 110. Near doubles: e.g. 31 + 31 is double 3 tens add 2 69 + 69 is double 7 tens take 2 away Doubles, up to 40: 139 + 139 is double 14 tens – 2 [ 280 -2] 142 + 144 is double 14 tens add 6 [ 280 + 6] Can express their understanding of a particular calculation using stories, symbols pictures and real life situations. e.g. use a think board to record their understanding of a multiplication sum and give valuable insight into the connections they have made between concrete objects, pictures and diagrams and words and symbols See this think board in more detail at Write number sentences using the terms ‘change’, ‘combine’ and ‘compare situations’, using diagrams and addition and subtraction number sentences. e.g.
Solve multiplication problems by using a rounding and compensation method (tidy numbers) e.g. 5 x 19 5 x 20 and then subtract 5 100 – 5 = 95 5 x 21 5 x 20 and then add 5 100 + 5 = 105 Children should be presented with daily opportunities to solve a mix of calculations in the form of equations and word problems where children choose the strategy from * and ** and discuss confidently the most efficient method chosen. Begin to solve multiplication or division problems involving a 3 - digit number by a 1-digit number by a short written algorithm – see ‘Suggested Written Recording’ Solve division problems by using standard place value. e.g. 92 ÷ 4 = (80 ÷4) + (12 ÷ 4) = 20 + 3 = 23 186 ÷ 3 = (180 ÷ 3) + (6 ÷ 3) = 60 + 2 = 62 Solve division problems using known addition, subtraction and multiplication facts within the 2, 3, 4, 5 and 10 times table. E.g. How many threes are there in 15? 15 ÷ 3 = 5 5 threes makes 15 How many equal sets of 3 makes 15 15 – 3 – 3 – 3 – 3 – 3 = 0 3 + 3 + 3 + 3 + 3 = 15 Begin to solve division problems by using a rounding and compensation method (tidy numbers) e.g. 248 ÷ 7 How many 7s are there in 280? 7 x 40 = 280 280 – 248 = 42 42 ÷7 = 6 so 40 sevens subtract 7 sevens equals 33 sevens. Solve division problems by using a multiplication strategy and by using the inverse rule. Children should be presented with daily opportunities to solve a mix of calculations in the form of Begin to split a number to reveal its factors to help solve a multiplication and division problem e.g. 4 x 32 = 2 x 2 x 32 = 2 x 64 = 128 8 x 57 = 2 x 2 x 2 x 57 = 2 x 2 x Represent multiplication/ division stories using a variety of ways, including story, pictorial, concrete and abstract. e.g. Tommy arranged his 15 football trophies evenly on three shelves. How many trophies were on each shelf? Fiona distributed 650 flyers for her new restaurant evenly amongst 13 streets. To how many houses did she deliver the