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+ Addition + This shows the progression of teaching addition at Parrett and Axe. Each method is designed to lead on to the next gradually building up children’s understanding of number. Remember, children should think about whether a calculation can be done mentally first. STEP Tips for mental / Concept & images Comments oral session 1 Counting Early addition Combining groups of objects to find the total using fingers to make number sentences eg4 (on one hand) and 1 (on the other) + counting on from any number eg. Start at 7 onto 20 Put all objects together and count… Find total of 2 groups using objects in hoops… Then total of 2 groups using objects and numerals in hoops… Then… total of 2 groups using objects and hoops and recording as a number sentence… Then without hoops, with objects and record as a number sentence counting on and back on a number line, pointing as you go 2 Finding numbers Relating ‘Informal number line’ / number sentences groups of As above, alongside a calculation 3 Counting to ten and Add one onto a number Locating back numbers on a Locating numbers more. Then… Look at number sentences – use objects provided Look at number sentences: what do we have to do? Use number line & adding one answer to find the answer objects to number line Look at number sentences. Use objects on sheets to find objects to find an answer 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. 4 Number bonds up to 10. play “pingpong” for bonds to 10 Pegs on a coat hanger (turn round to show inverse) Write all the ways to make 2,3,4,5,6,7,8,9,10 How many ways of splitting up a number? rapid recall Using number Adding to a ten bonds to add mentally on the (10 + 2 = 12, number line. on the number line rather than count. 10 = ? + ? 9 = ?+? 20 = ? +? 8 = ? + ? 100 = 20+80 100 = 24 + 76 Using counters and 2 plates + show me ways to make 9 Bridge 10 (e.g. 8 + 5 =13) Include use of bead bar 10 + 3 = 13 10 + 4 = 14…) In order to calculate effectively children must know all the bonds for numbers up to ten. This will enable them to jump etc. Domino pairs 5 Model with numicon Doubling and repeated addition Using a bead bar is also an effective way to showing how to split smaller numbers up KS1 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 to the next ten on the number line. Then add what is left in one jump. Vocab – add, sum, total etc Link to subtraction – sum families 8+5=13 13-5=8 5+8=13 13-8 =5 6 Counting on and Adding multiples of 10 Using number back in steps of Addin near multiples of 10 – (9 19 29) line to jump ten. rounding and readjusting jump in steps of ten. Focus on what happens to the tens and units as you count. Focus on tricky parts: counting over 100, counting back past 20 in the teen numbers. in tens from any 2-digit number. Starting from any 2-digit number children must be able to Adding multiples of 100 using number grids as well as number lines 7 Adding on the number line. Counting on in tens Adding to a ten mentally This puts together the two previous ways of adding on a TU + TU number line. THE NUMBER LINE REPRESENTS THE JUMPS IN YOUR Adding by partitioning HEAD! If adding near multiples of ten, more confident pupils can 38+26=64 do adding a ten and adjusting: 30+20=50 8+6=14 50+14=64 8 Practice partitioning Column Number bonds up addition for to ten (to avoid adding pairs counting in ones when of 3 digit 43 + 19, = 43 + 20 = 63 -1 = 62 HTU + HTU using partitioning Start by partitioning the numbers so the children understand 347 + 122 = what each column represents. 300 +100 40 20 400 60 7 347 2 122 9 = 469 Children should only use this when adding together 3-digit 9 numbers and preferably when the units add to more than 60 adding up columns) ten. (Although to introduce concept using simpler numbers 400 numbers. is a good idea) 469 THEN, GO BEYOND 10 in U column etc. 159 + 264 = 100 50 9 +200 60 4 300 9 Practice partitioning Compact Number bonds up Column to ten (to avoid addition counting in ones when adding up columns) 110 13 = 423 As the children become more confident in column addition 347 + 122 347 +122 Then 347 Then, with carrying +122 9 469 60 they can gradually start to use the compact method for 159 speed. + 264 423 1 It is vital that they still understand that the small ‘1’ represents tens or hundreds. 400 469 10 ‘Moving digits’ ITP Same number of decimal places As with the compact column addition strategy it is vital that Compact to investigate Column decimals. +54.6 km addition with Practice partitioning 133.1 km decimals Number bonds up to ten (to avoid 78.5 km always taking care with columns keep carried numbers half size 1 1 Then, different number of decimal places counting in ones when 124.9 adding up columns) + 7.25 132.15 11 children understand what each column represents in terms of value.