Easy Street

Students are able to count a set of objects or form sets of objects to solve simple addition and subtraction problems. They solve problems by counting all the objects.

"If you see 5 kiwi and 2 kākāpō in the bush, how many birds will that be altogether?"

Te Kaha's work shows that he is able to:-solve simple addition problems -use his fingers to count a set of objects.

Monique's work shows that she is able to:-solve simple addition problems -mentally form and count sets 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?

Required knowledgeTo move to the next level of the number strategy progression, you need to be able to:• count on and back from numbers between one and 100;• count from one by imaging the counting process;• count on or count back to add or subtract one from a set of objects.

Students are able to use counting on or counting back to solve simple addition or subtraction problems.

"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:

Jewel’s work shows that she is able to:-also count back.

“If you had 13 marbles and then you lost 5 in agame, how many would you have left?”

Required knowledgeTo move to the next level of the number strategy progression, you need to be able to:• identify tens and ones in two-digit numbers;• recall addition-to-ten and subtraction-from-tenfacts;• recall doubles up to nine;• count on and count back to solve addition andsubtraction sums;• instantly identify numbers on a tens frame.

Where to next

Jewel now needs to move to treating numbers as

abstract ideas or units. When she has an abstract idea

of a number, she can treat it as a “whole” or can

partition it and then recombine it to solve addition or

subtraction problems.

Students are able to use a limited range of mental strategies to estimate answers and solve addition or subtraction problems. These strategies involve deriving the answer from known basic facts (for example, doubles, fives, and making tens).

"Billy has $25, and Sam has $9. How much more money than Sam has Billy got?"

Roimata's work shows that she is able to:•solve subtraction problems •derive an answer from known basic facts.

Martin's work shows that he is able to:•solve subtraction problems •derive an answer from known basic facts.

Required knowledgeTo move to the next level of the number strategy progression, Roimata and Martin need to be able to:

• recall addition and subtraction facts to 20;• partition numbers into tens and ones;• find how many tens and hundreds there are in numbers to 10 000.

WHERE TO NEXT?Roimata and Martin now need to expand the strategiesthey can use to solve addition and subtractionproblems. In particular, they need to understand moreabout place value and compensation strategies.

Students are able to choose appropriately from a broad range of advanced mental strategies to estimate answers and solve addition and subtraction problems involving whole numbers (for example, place value positioning, rounding, compensating, and reversibility). They use a combination of known facts and a limited range of mental strategies to derive answers to multiplication and division problems (for example, doubling, rounding, and reversibility).

"Billy and Sarah each have $12 and Sharon has $18. How much money have they got altogether?"

Ineke's work shows that she is able to partition and recombine numbers to solve a problem.

Marco's work shows that he is able to partition and recombine numbers to solve a problem.

Marco's work shows that he is able to partition and recombine numbers to solve a problem.

Required knowledgeTo move to the next level of the number strategyprogression, Ineke, Marco, and Nick need to be able to recall their multiplication and division facts to 100 and to record the results of multiplication and divisionusing equations.

Questions to help Ineke, Marco, and Nick focus on the next learning step could include:• 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?

Where to next?Ineke, Marco, and Nick need to increase their range of multiplicative strategies for solving whole-numberproblems and problems involving decimals.

Place value partitioning

Inverse Operations

Compensation

Compensation

74-19=

The teacher talk…if you know that 6 + 6 = 12 you may use this to derive 6 + 7 = (6 + 6) + 1 = 13. This same strategy underpins the renaming of 74 – 19 as 74 – 20 + 1 to find the answer to 74 – 19.

And if I’m a student…I know that it’s easier to count in tens. The closest ten to 19 is 20.

So 74 – 20 = (74, 64, 54) 54!

I took away 1 too many (remember, 19 + 1 to make 20) so I have to make the answer go up 1 more.

So 74 – 20 = 54 + 1 = 55

Making a problem easier by changing one part of a multiple of ten, then

adjusting the other part to make the equation balance.

Confused still?Ask the teacher to clarify.

Place Value Partitioning

18 + 6 =

The teacher talk…Breaking or partitioning numbers so that they can be recombined to form “tens” is another additive strategy.For example, 18 + 6 = (18 + 2) + 4 = 20 + 4.

And if I’m a student…I know that it’s easier to count in tens. The closest ten to 18 is 20. I need two more to get 20. I can move 2 from the 6 to the 18, and make 20. That means the 6 becomes 4.

I’ve made the question easier for me to work out.18 + 6 =18 + 2 = 20 + 4. 20 + 4 = 24.

Making a problem easier by changing one part of a multiple of ten, then

adjusting the other part to make the equation balance.

Confused still?Ask the teacher to clarify.

Inverse Operations

62 – 34 =

The teacher talk…This involves using known addition/subtraction facts to derive the opposite subtraction/addition fact.For example, 62 – 34 = ?? can be reworked as 34 + ?? = 62 and 34 + (30 – 2) = 62.

And if I’m a student…I know that 34 + something = 62.

I can use lots of adding strategies here. I could use a number line…

+6 +20 +2

34 40 60 62

Now, I add the top number together.6 + 20 + 2 = 28

Making a problem easier by changing one part of a multiple of ten, then

adjusting the other part to make the equation balance.

Confused still?Ask the teacher to clarify.