"If you see 5 kiwi and 2 kākāpō in the bush, how many birds will that be altogether?" Te Kahas work shows that he is able to: -solve simple addition problems -use his fingers to count a set of objects. Moniques work shows that she is able to: -solve simple addition problems -mentally form and count sets of objects.Students are able to count a set of objectsor form sets of objects to solve simpleaddition and subtraction problems. They solveproblems by counting all the objects.
Required knowledgeTo move to the next level of the numberstrategy progression, you need to beable to:• count on and back from numbersbetween one and 100;• count from one by imaging the countingprocess;• count on or count back to add orsubtract one from a set of objects. Questions to help students focus on the next learning step could include: • Which is the biggest number? • Can you start counting from there? • How many more do you need to count? • Is it easiest to start from the bigger number or the smaller number?
"If you have 7 books and then you are given 5 more, how many will you have altogether?" Jewel’s work shows that she is able to: -count on to solve a simple addition problem:Students are able to use counting on orcounting back to solve simple addition or “If you had 13 marbles and then you lostsubtraction problems. 5 in a game, how many would you have left?” Jewel’s work shows that she is able to: -also count back.
Required knowledgeTo move to the next level of the numberstrategy progression, you need to be Where to nextable to:• identify tens and ones in two-digit Jewel now needs to move tonumbers; treating numbers as• recall addition-to-ten and subtraction- abstract ideas or units. When shefrom-ten has an abstract ideafacts;• recall doubles up to nine; of a number, she can treat it as a• count on and count back to solve “whole” or canaddition and partition it and then recombine itsubtraction sums; to solve addition or• instantly identify numbers on a tensframe. subtraction problems.
"Billy has $25, and Sam has $9. How much more money than Sam has Billy got?" Roimatas work shows that she is able to: •solve subtraction problems •derive an answer from known basic facts. Martins work shows that he is able to: •solve subtraction problems •derive an answer from known basic facts.Students are able to use a limited range of mental strategies to estimateanswers and solve addition or subtraction problems. These strategiesinvolve deriving the answer from known basic facts (for example, doubles,fives, and making tens).
Required knowledgeTo move to the next level of the numberstrategy progression, Roimata and Martin needto be able to:• recall addition and subtraction facts to 20;• partition numbers into tens and ones;• find how many tens and hundreds there are innumbers to 10 000. WHERE TO NEXT? Roimata and Martin now need to expand the strategies they can use to solve addition and subtraction problems. In particular, they need to understand more about place value and compensation strategies.
"Billy and Sarah each have $12 and Sharon has $18. How much money have they got altogether?" Inekes work shows that she is able to partition and recombine numbers to solve a problem. Marcos work shows that he is able to partition and recombine numbers to solve a problem. Marcos work shows that he is able to partition and recombine numbers to solve a problem.Students are able to choose appropriately from a broad range of advancedmental strategies to estimate answers and solve addition and subtractionproblems involving whole numbers (for example, place value positioning, rounding,compensating, and reversibility). They use a combination of known facts and alimited range of mental strategies to derive answers to multiplication and divisionproblems (for example, doubling, rounding, and reversibility).
Required knowledge To move to the next level of the number strategy progression, Ineke, Marco, and Nick need to be able to recall their multiplication and division facts to 100 and to record the results ofWhere to next? multiplication and divisionIneke, Marco, and Nick need to using equations.increase their range ofmultiplicative strategies for Questions to help Ineke, Marco, andsolving whole-number Nick focus on the next learning stepproblems and problems involving could include:decimals. • Can you think of any multiplication facts that might help you? • Do you know how to multiply a number by 10? By 100? • What numbers are easy to multiply in your head? • What numbers are easy to divide in your head?
Compensation Place value partitioning Inverse Operations
The teacher talk…if you know that 6 + 6 = 12 you mayuse this to derive 6 + 7 = (6 + 6) + Compensation1 = 13. This same strategyunderpins the renaming of 74 – 19as 74 – 20 + 1 to find the answerto 74 – 19. 74-19=And if I’m a student…I know that it’s easier to count intens. The closest ten to 19 is 20. Making a problem easier by changing one part of a multiple ofSo 74 – 20 = (74, 64, 54) 54! ten, then adjusting the other part to make the equation balance.I took away 1 too many (remember,19 + 1 to make 20) so I have tomake the answer go up 1 more. Confused still? Ask the teacher to clarify.So 74 – 20 = 54 + 1 = 55
The teacher talk…Breaking or partitioning numbers Place Valueso that they can be recombined toform “tens” is another additivestrategy. PartitioningFor example, 18 + 6 = (18 + 2) + 4 =20 + 4.And if I’m a student…I know that it’s easier to count in 18 + 6 =tens. The closest ten to 18 is 20.I need two more to get 20. I can Making a problem easier by changing one part of a multiple ofmove 2 from the 6 to the 18, and ten, then adjusting the othermake 20. That means the 6 part to make the equationbecomes 4. balance.I’ve made the question easier forme to work out. Confused still?18 + 6 = Ask the teacher to clarify.18 + 2 = 20 + 4. 20 + 4 = 24.
The teacher talk…This involves using known Inverseaddition/subtraction facts to derivethe opposite subtraction/addition fact. OperationsFor example, 62 – 34 = ?? can bereworked as 34 + ?? = 62 and 34 + (30– 2) = 62.And if I’m a student… 62 – 34 =I know that 34 + something = 62. Making a problem easier byI can use lots of adding strategies changing one part of a multiple ofhere. I could use a number line… ten, then adjusting the other part to make the equation +6 +20 +2 balance.34 40 60 62 Confused still? Ask the teacher to clarify.Now, I add the top number together.6 + 20 + 2 = 28