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1 + Addition + We encourage children to use mental methods whenever possible Children may not need to be taught every step STEP Tips for mental / oral session Counting Concept & images Comments Early addition Combining groups of objects to find the total Put all objects together and count Find total of 2 groups using objects Then total of 2 groups using objects and numerals Then total of 2 groups using objects and recording as a number sentence EARLY MATHS CHALLENGES SUPPORT THIS STEP Then adding on to a set, one by one Requires fluency with counting from any number! Use fingers (but avoid counting from one each time!) NUMICON very useful here 2 Relating groups of objects to number line Finding numbers Informal number line / number sentences As above, alongside a calculation Look at number sentences. Then Look at number sentences use objects provided to find the answer Look at number sentences: what do we have to do? Use objects to find an answer 3 Locating numbers on a number line / track & adding one more. Counting to ten and back Locating numbers Add one onto a number Find 5 on number track, then add one Encourage children to locate the first number and count on from there, rather than starting at zero.

2 4 Number bonds up to 0 i.e. number bonds for all numbers up to 0, not just 0 itself 5 Using number bonds to add on the number line. Pegs on a coat hanger (turn round to show inverse) Write all the ways to make 2,3,4,5,6,7,8,9,0 Adding to a ten mentally (0 + 2 = 2, = = 4 ) How many ways of splitting up a number? 0 =? +? 9 =? +? 8 =? +? Etc Bridge 0 (e.g =3) Include use of bead Add a 2digit number number bar and a digit Model with numicon In order to calculate effectively children must know all the bonds for numbers up to ten. This will enable them to jump on the number line rather than count. Children need to understand = as balance Using a bead bar is also an effective way to showing how to split smaller numbers up MATHS CHALLENGES SUPPORT THIS STEP Emphasise JUMP on number line, NOT counting! Use number bonds to jump to the next ten on the number line. Then add what is left in one jump.4 THIS IS AN IMPORTANT STEP AND IT OFTEN REQUIRES A LOT OF PRACTISE 6 TU + TU Working towards the compact standard method (so child can choose) Counting on in tens Focus on tricky parts: counting over 00, counting back past 20 in the teen numbers. TU + TU Use bundles of straws first as these help children to develop an understanding of the size of a number then Use diennes first and finally move on to place value counters. Children should be working on these methods during Year2/3 2 5 Move all the ones together and EXCHANGE ten ones for a ten counter

3 Then 347 Then, with carrying AGAIN, use PLACE VALUE COUNTERS to model CARRYING if needed 7 Compact Column addition HTU+HTU Practice partitioning Number bonds up to ten (to avoid counting in ones when adding up columns) As the children become more confident in column addition they can gradually start to use the compact method for speed. It is vital that they still understand that the small represents tens or hundreds (if they don t, use place value counters) 8 Compact Column addition with decimals Moving digits ITP to investigate decimals. Practice partitioning Number bonds up to ten (to avoid counting in ones when adding up columns) Same number of decimal places 78.5 km km 33. km Then, different number of decimal places As with the compact column addition strategy it is vital that children understand what each column represents in terms of value.

4 Subtraction We encourage children to use mental methods whenever possible Children may not need to be taught every step STEP Tips for mental / oral session Counting Early subtraction Concept & images Take away a number of objects from the group, count what s left Introduce and = symbols Comments Then start with group of objects and record the numeral. Take some away, record and count what s left (record) 6 take away 3 is 3 OR 3 less than 6 is 3 2 Relating groups of objects to number lines Finding numbers Include vocabulary: difference Relate to number line Emphasise JUMPING on number line, not counting Then look at a number line: what do we need to do? 3 Locating numbers on a number line and finding one less. Counting to ten and back Locating numbers Take away one from a number Find 5 on number track, then SUBTRACT one Encourage children to locate the first number and count back from there, rather than starting at zero. 4 Number bonds up to 0. Use pegs on washing line (reverse to show inverse) Inverse use of number bonds(the opposite of step 3 for addition) Model with numicon In order to calculate effectively children must know all the bonds for numbers up to ten. This will enable them to jump back on the number line rather than count. Using a bead bar is also an effective way to showing how to split smaller numbers up. KS children to also model this using jumps on a number line in order to lead to step 5. Emphasise JUMP on number line, NOT counting! Use number bonds to jump back to the previous ten on the number line. Then subtract what is left in one jump. Use number bonds/love hearts 5 Using number bonds to jump back on the number line / begin to find Place value partitioning Children need to know number bonds to 20 AND to all the Jumping back (Bridging 0)

5 differences by comparing numbers up to 20 N.B. BUNDLES of 0 STRAWS ARE BETTER THAN DIENNES TENS in aiding understanding Comparing two sets (comparison or difference 2-5 =7 Seeing one set as partitioned Useful when two numbers are close together, where take-away image can be cumbersome Helps to see the related calculations; 5+7=2, 7+5=2, 2-7 = 5 and 2-5=7 as all in the same diagram 6 TU - TU Subtracting on the number line (finding the difference) Counting on and back in tens Focus on tricky parts: counting over 00, counting back past 20 in the teen numbers. Seeing 2 as 5 and 7 TU TU start with multiples of 0 i.e , count up from 40 COUNTING ON (on a numberline) Emphasise looking at HOW CLOSE NUMBERS ARE before diving into use of a number line. Can this be done mentally by counting on from the lower number? THE NUMBER LINE REPRESENTS THE JUMPS IN YOUR HEAD, SO ADD THE JUMPS! 7 Column subtraction without exchange Practice partitioning Number bonds up to ten (to avoid counting in ones when subtracting columns) Easy column subtraction to practise layout. USE DIENNES AND THEN PLACE VALUE COUNTERS TO SUPPORT THIS STEP 73 Then If subtracting near multiples of ten, more confident pupils can do subtracting a ten and adjusting: 43 9 can be done by = 23 Add one back on = 24 MATHS CHALLENGES SUPPORT THIS STEP Don t use number line for HTU HTU (only exception is something like, , which would involve too many exchanges) 8 Column subtraction with exchange Practice partitioning Number bonds up to ten (to avoid counting in ones subtracting columns) Compact column subtraction with EXCHANGE(S) Then If child struggles, use PLACE VALUE COUNTERS to SHOW THE EXCHANGING e.g As the children become more confident in column subtraction they can gradually start to use the compact method for speed. It is vital that they still understand that the small represents tens or hundreds ~ if they don t use PLACE VALUE COUNTERS

6 Start off with 7 tens and 2 ones. EXCHANGE one of the tens for ten ones Note how the answer is clearly shown on the top row (it s literally what you re left with. The amount taken away is on the bottom: helps with checking). 9 Compact column subtraction with decimals. Moving digits ITP to investigate decimals. Practice partitioning Number bonds up to ten (to avoid counting in ones subtracting columns) km km km Then, subtractions with different numbers of decimal places As with the compact column subtraction strategy it is vital that children understand what each column represents in terms of value.

7 X Multiplication X We encourage children to use mental methods whenever possible Children may not need to be taught every step they may be comfortable with using standard method if their times tables knowledge / understanding of place value is secure STEP Tips for mental / oral session Repeated addition Counting in steps of Times tables songs Counting forwards and backwards Concept & images 5 x 3 = 5 is the same as = Comments Repeatedly adding the same number again and again. Counters can be used to illustrate OR BEAD BARS Good to say How many 5s are there in 5?, not just 5 x 3 =5 2 Simple Multiplication Counting in steps of Times tables songs Times Tables bingo Interactive maths games. Array Number line Read out the calculations as: 3x4 3, multiplied 4 times Understand that this is a group of 3, repeated 4 times. Use an array to model the concept. Emphasise that children don t count individual dots, but count up rows / columns This can lead onto children representing their counting on a number line. Use language of twice as big 3 Doubling (to help learn times tables) SCALING Interactive maths games. Doubling & Halving rapid recall To do 8 x 8 8 x 2 = 6 (double or x2) 8 x 4 = 32 (double, then double again or x4) 8 x 8 = 64 (double once more, x8)

8 X means SCALE UP OR DOWN Images like this will help younger children to understand fractions better (and fraction walls will too) 9 x /3 = 3 OR 3 is /3 of 9 3 times shorter 4 Moving digits Moving digits ITP PLACE VALUE CHARTS are valuable for whole numbers and decimals Similar to doubling, children should be able to multiply by ten mentally. They need to do this in order to solve larger multiplication calculations effectively. Multiply by 0 / 00 etc. 7.9 x 00 = 790 H T U. tenths x 0 (digits move one column to left) x 00 (digits move two columns to left) Use MOVING DIGITS ITP / place value chart: Emphasise the DIGITS MOVE Saying add on a zero when x by 0 / two zeros when x by 00 etc. is fine so long as it s emphasised that this ONLY WORKS FOR WHOLE NUMBERS. Or children will put.75 x 0 =.750!!!)

9 5 Grid Method TU x U & Working towards Standard Method Times Tables bingo Interactive maths games. Partitioning works well as a mental method, but children often make mistakes when using it as a written method, so avoid it (especially with TU x TU e.g. 4 x 2 they will put 08, because they think 0 tens are one hundred, 4 x 2 is 8, add that together. They need to think what TEN TIMES 4 is first ) 3 x 6 is the same as 0 x 6 and 3 x 6 (60 + 8) = 78 is fine. So use Grid Method if not absolutely sure of the answer x = The grid method allows children to use known number facts to solve multiplication problems. Work towards standard method 2 4 X 3 2 (x3) 6 0 (x20) Compact Standard Method 7 Grid Method (Or standard method if children are confident) for TU X TU Times Tables bingo Interactive maths games. Times Tables bingo Interactive maths games. Compact (standard method) 2 4 X x 4 = 336 X Children can begin to use the compact methods when they are comfortable with solving the multiplications mentally. The grid method allows children to break up large multiplication calculations into easier calculations. Being able to multiply digits by ten and multiples of ten is a necessity.

10 24 X 4 96 (4 x 4 = 6, plus 4 x 20 = 80) 240 (0 x 24= 240) 336 Grid Method (Or standard method if children are confident) for HTU X U Then 242 x 7 = 694 X Multiplying Decimals Times Tables bingo Interactive maths games. 242 X x 4 = X N.B. Grid Method is best avoided with decimals, because identifying the value of each digit beyond the decimal point is tricky for children Continue to use 0 as place holder if necessary.

11 Division Remember, children should think about whether a calculation can be done mentally first. STEP Tips for mental / oral session Sharing 2 Grouping (and use of arrays) Counting in groups. Times tables facts. Times table bingo SHARING Is it fair? Concept & images As GROUPING link to REPEATED ADDITION/x tables 9 3 = 3 (groups) Arrays are useful to explain RELATED FACTS: 3 x 4 = 2 4 x 3 = 2 So 2 4 = 3 Comments USE COUNTERS OF DIFFERENT COLOURS When sharing you know how many groups you will have; you are working out how many will be in each group. Don t over teach sharing! Focus more on grouping As this relies more on times tables knowledge, it is better to use this strategy than sharing. Children should understand that even when solving a sharing problem, they can solve it quicker through grouping. MULTIPLICATION AWARDS SUPPORT THIS WORK And 2 3 = 4 Grouping using number line 5 5 = 3 3 Grouping on the number line Then with remainders Times tables facts. Times table bingo Primary resources interactive games Finding a remainder 7 5 = 3 r 2 Encourage children to read the question as: I have 5, how many 5s? They can then use times tables knowledge to solve the problem, using number lines to record their thinking. Encourage children to read the question as: I have 7, how many 5s?

12 How many WHOLE groups of 5 can they count in 7? What s left over? This is the remainder. 4 Begin to link to SCALING HALVING (use Numicon / Bead Bars / counters) 8 2 is the same as 8 x ½ (or 8/2) = 4 SCALING is linked with SHARING: The new 204 Curriculum states that children should be introduced to fractions at an early age (around Year 2) LINK WITH DIVISION e.g. show 9 3 is 9 x /3 Also show 2 4 as 2 so that they are introduced to improper fractions. 4 This introduction to improper fractions with simplifying when they get older, e.g = = 3 = 8 Using the standard goes into method allows children to use known multiplication facts mentally and reduce the jottings needed to record their thoughts. 5 TU U Standard method (move onto HTU TU too) Times tables rapid recall Standard Goes Into Method 4 r Then 6 4 r = Then HTU U 6 Decimal AND FRACTION Divisions Decimal place value Times tables rapid recall With decimals: Use standard method 2 r = = 3 X 3 = 9 Flip the 2 nd fraction, then multiply More able could put answer to calculation on left as 2.5, because they d notice that 3.5 is half of 7

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