Natinal Curriculum Prgramme f Study: Cunt in steps f 2, 3, and 5 frm 0, and in tens frm any number, frward and backward. Recall and use multiplicatin and divisin facts fr the 2, 5 and 10 multiplicatin tables, including recgnising dd and even numbers. Shw that multiplicatin f tw numbers can be dne in any rder (cmmutative) and divisin f ne number by anther cannt. Slve prblems invlving multiplicatin and divisin, using materials, arrays, repeated additin, mental methds, and multiplicatin and divisin facts, including prblems in cntexts. Y2 MENTAL CALCULATION Multiplicatin & Divisin FLUENCY By the end f Year 2, children shuld fluently derive and recall: dubles f all numbers t 20, e.g. duble 16, and crrespnding halves dubles f multiples f 10 t 50, e.g. duble 30, and crrespnding halves multiplicatin facts fr the 2, 5 and 10 times-tables, and crrespnding divisin facts dd and even numbers t 100 COUNT IN STEPS OF 2, 3, AND 5 FROM 0, AND IN TENS FROM ANY NUMBER, FORWARD AND BACKWARD Cunting n and back t zer in steps f 2, 3, and 5. Cunting n and back in 10s frm any given number The cunting stick can be cnsidered as part f a cntinuus r empty number line with clearly marked intervals alng the stick t represents specific pints. Tell the children, they are cunting in steps f 3 and practice cunting frwards and backwards frm a starting pint f zer, cunting in steps f 3 as each interval line is tuched. Attach number cards t the interval lines t remind children f the steps. Make links t multiplicatin and divisin. What are 2 steps f 3? Hw many steps f 3 make 30? Hw d yu knw? Hw culd we write that? When cunting n in 10s, make the beginning f the stick any number, fr example 14. Cunt alng the stick in 10s frm 14. What patterns d the children ntice? Ask, if this is 14 and we are cunting n in 10s, what number will this be (pint t an interval further alng the stick.)? Pint t the centre f the stick and say, if this is 77 and we are cunting in 10s, what are the numbers either side? What are the numbers at the beginning and end f the stick? 1
Seat the pupils in a circle and explain that yu will be cunting in 2s. Hlding a beanbag, cunt 0 and then thrw t a pupil wh cntinues the cunt in 2s (by saying 2). They in turn, thrw it t anther pupil wh says 4 and s n. Alter the rules s that when yu say backwards, the next persn wh catches the bean bag has t cunt back in 2s. This cntinues until yu say frwards. Use als fr cunts f 3, 5 and 10. Link cunting n in 5s t the divisin f a clck face. Explain that there are small divisins all the way arund a clck face that measure minutes. Hwever, when we are telling the time it wuld be difficult t cunt each minute n a clck face s we cunt them in grups f 5. Ask the children if they can see where the first grup f 5 minutes wuld be and label that pint. Where wuld be the next grup f 5 minutes? Hw many minutes wuld that be altgether (10)? Label that pint and cntinue arund the clck until all intervals are labelled. Hw many minutes are there all arund the clck? When the big (minute) hand travels all the way arund the clck, hw much time has passed? (60 minutes r 1 hur)? Alngside a practical cunting activity, demnstrate using a number line t cunt n in steps f 2, 3 and 5. Fr example, Hw many glves altgether? 6 steps f 2 wuld lk like: Using write n/wipe ff number lines, ask pupils t cunt n a given amunt f steps, fr example Shw me 7 jumps f 5 n a number line. What number d yu end n? Hw can yu write this as an additin sentence? Hw can yu write this as a multiplicatin sentence? 2
RECALL AND USE MULTIPLICATION AND DIVISION FACTS FOR THE 2, 5 AND 10 MULTIPLICATION TABLES, INCLUDING RECOGNISING ODD AND EVEN NUMBERS Deriving and recalling multiplicatin facts fr the 2, 5 and 10 times-tables and crrespnding divisin facts Recgnising dd and even numbers t 100 Recgnising multiples f 2, 5 and 10 Cnnecting the 10 x table t place value knwledge. Shw pupils hw t use their fingers t keep track f cunting in steps. T calculate, fr example 2 x 6, they culd hld up 6 fingers and mve each in turn as they cunt n in tws (each finger representing a cunt f 2). Encurage pupils t see the link between multiplicatin and divisin by asking, Hw many 2s in 12? 2, 4, 6, 8, 10, 12 T calculate 5 x 7, the pupil wuld hld up 7 fingers and cunt n in fives. Overtime, pupils may be able t visualise this prcess in their head and calculate withut the use f their fingers. Ask pupils what patterns they see in the 10 x table. Hw can these patterns help them t recall the 10 x table facts? Shw them a place value chart. Each rw is 10 x bigger than the rw abve it. Explain that when a number is multiplied by 10, the digits mve ne place t the left and the spare place is filled with a zer because zer is a place hlder. Remve sme f the numbers frm the place value chart, can the pupils wrk ut what the missing numbers are? What is the value f the 2 digit in each f the numbers 2, 20 and 200? Lk at scaling thrugh the language f, fr example, 10 times larger/ bigger than What number is 10 times bigger than 5? Make a twer 5 times bigger than this ne. Hw many cubes will we need? 5 times bigger 4 times bigger 3 times bigger 2 times bigger 1 times bigger 3
Put ut 3 chairs and label them hundreds (H), tens (T) and units r nes (U/O). Seat a child in the units chair and give them the number 5. Explain that when 5 is multiplied by 10, the digits mve ne place t the left. Ask anther pupil t mve the seated pupil ne place t the left. What d we d with the empty chair? Seat anther pupil in the units chair and give them a 0 t hld. What number d we make when we multiply 5 by 10? What was the value f the 5 digit at the start? What is the value f the 5 digit nw? What wuld happen if we multiplied by 10 again? Repeat with ther numbers. Lk at patterns in the 2, 5 and 10 times tables. Wuld the number 32 be in any f these tables if we extended them past x 12? Hw d yu knw? Why wuldn t 32 be in the 5 r 10 times tables? Repeat with ther numbers. Can yu think f any numbers that will be in the 2 and the 5 times tables r the 2, 5 and 10 times tables? Create a set f cards with multiplicatins facts fr the 2, 5 and 10 times tables n ne side and the answers n the ther side. Ask the children t lay the cards with the multiplicatin facts shwing. Playing in grups f tws r threes, the pupils take it in turns t select a card and say what the answer is, turning the card ver t check. If the answer is incrrect they must leave the card with the multiplicatin fact shwing. Play cntinues until all the cards are turned ff. Alternatively, place the cards with the answers shwing and pupils need t determine what the multiplicatin fact is. Lk at a selectin f multiplicatin facts such as 5 x 2, 10 x 3, 2 x 6 etc. Ask the pupils t match the statements with representatins using structural apparatus. Fr example 10 x 3 5 x 2 2 x 6 In year 1, pupils will have explred dd and even numbers and hw t identify them up t 20. Ask pupils t clur in the even numbers n a hundred square in red. What patterns can they see in the red clured numbers and in the nn-clured numbers? Can they use these patterns t determine whether 107 wuld be clured red? What abut 134? Why/ why nt? 4
SHOW THAT MULTIPLICATION OF TWO NUMBERS CAN BE DONE IN ANY ORDER (COMMUTATIVE) AND DIVISION OF ONE NUMBER BY ANOTHER CANNOT Making and anntating arrays See als Written Calculatin Guidance, Year 2 Multiplicatin Making arrays using physical bjects and representing them in drawings and Anntating arrays using multiplicatin Year 2 Divisin Intrducing arrays fr visualisatin f divisin Place a rw f 5 cunters nt a grid (in rder t maintain a well rganised array). Ask the pupils hw many cunters they can see. Place anther rw f 5 cunters belw the first rw. Ask the pupils hw many cunters altgether nw. Encurage the pupils t cunt n in 5s as ppsed t nes. Repeat with anther rw. Mdel writing the crrespnding additin and multiplicatin sentences. Lk at hw many cunters in ne clumn. Hw many cunters in 2 clumns? In 3 clumns? In 4 clumns? In 5 clumns. Again, writing the crrespnding additin and multiplicatin sentences. What d the children ntice? What is the same and what is different abut the number sentences? Ask the pupils, D yu think that this will be the same fr all arrays?. Investigate with ther arrays t see if 2 numbers can be multiplied in any rder. Use this array t shw 15 3 as hw many grups f 3 in 15. Ask pupils, Will we get the same answer if we wrk ut 15 5? Demnstrate finding hw many grups f 5 in 15. Explre the multiplicatin and divisin sentences that can be wrked ut using an array. What patterns can the pupils see? 4 x 5 = 20 5 x 4 = 20 20 5 = 4 20 4 = 5 5
SOLVE PROBLEMS INVOLVING MULTIPLICATION AND DIVISION, USING MATERIALS, ARRAYS, REPEATED ADDITION, MENTAL METHODS, AND MULTIPLICATION AND DIVISION FACTS, INCLUDING PROBLEMS IN CONTEXTS. Wrking with a range f materials and apparatus t represent multiplicatin and divisin prblems. Using gruping and sharing strategies t slve divisin prblems. Presenting prblems in a range f cntexts including fractins and measures. See als Written Calculatin Guidance, Year 2 Divisin Cnsidering remainders when dividing and Using base-ten resurces t supprt divisin Pupils shuld be tld that they are learning abut Divisin and that sharing and gruping are different divisin appraches as ppsed t ver emphasising the vcabulary f sharing in place f divisin. Use the Interactive Teaching Prgramme Gruping t demnstrate divisin by gruping n a number line. Pupils can als use bead strings t cunt n in small grups and t grup fr divisin. What is 3 x 5? Hw many grups f 3 can yu make frm 15 beads? Using a range f structural apparatus and the strategies detailed abve, ask pupils t represent prblems such as Pencils are bught in packs f 10. The teacher has 50 pencils, hw many packs has he bught? Explain hw yu have slved this. Which f these numbers wuld have a remainder f 1 when divided by 5? Which ne (s) wuld nt? Hw d yu knw? 20, 56, 37, 42, 75, 81 Kate needs t make up 5 party bags. She has 30 sweets. Hw many des she need t put int each bag s that they hld the same amunt? One fr this bag, ne fr this bag, ne fr this bag...leading t 6 sweets in each bag. 6
A bubble gum csts 10p, hw much will it cst t buy 4 bubble gums? OR Find half f 24..duble 18 duble 60 Half f 20 = 10 Half f 4 = 2 Half f 24 = 10 + 2 = 12 Duble 10 = 20 Duble 8 = 16 Duble 18 = 36 It takes Tm 2 minutes t read a page f his bk. Hw lng will it take him t read 12 pages? 2 2 2 2 2 2 2 2 2 2 2 2 OR Using Cuisenaire rds/ bars 7