2. "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.
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.
3. Required knowledge
To 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.
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?
4. "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 or
counting back to solve simple addition or “If you had 13 marbles and then you lost
subtraction problems. 5 in a
game, how many would you have left?”
Jewel’s work shows that she is
able to:
-also count back.
5. Required knowledge
To move to the next level of the number
strategy progression, you need to be Where to next
able to:
• identify tens and ones in two-digit Jewel now needs to move to
numbers; treating numbers as
• recall addition-to-ten and subtraction- abstract ideas or units. When she
from-ten has an abstract idea
facts;
• recall doubles up to nine; of a number, she can treat it as a
• count on and count back to solve “whole” or can
addition and partition it and then recombine it
subtraction sums; to solve addition or
• instantly identify numbers on a tens
frame. subtraction problems.
6. "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.
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).
7. Required knowledge
To 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
strategies
they can use to solve addition and subtraction
problems. In particular, they need to understand
more
about place value and compensation strategies.
8. "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.
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).
9. 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 of
Where to next?
multiplication and division
Ineke, Marco, and Nick need to
using equations.
increase their range of
multiplicative strategies for
Questions to help Ineke, Marco, and
solving whole-number
Nick focus on the next learning step
problems 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?
10. Compensation
Place value
partitioning
Inverse
Operations
11. The teacher talk…
if you know that 6 + 6 = 12 you may
use this to derive 6 + 7 = (6 + 6) +
Compensation
1 = 13. This same strategy
underpins the renaming of 74 – 19
as 74 – 20 + 1 to find the answer
to 74 – 19. 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. Making a problem easier by
changing one part of a multiple of
So 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 to
make the answer go up 1 more. Confused still?
Ask the teacher to clarify.
So 74 – 20 = 54 + 1 = 55
12. The teacher talk…
Breaking or partitioning numbers Place Value
so that they can be recombined to
form “tens” is another additive
strategy.
Partitioning
For 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 of
move 2 from the 6 to the 18, and
ten, then adjusting the other
make 20. That means the 6 part to make the equation
becomes 4. balance.
I’ve made the question easier for
me to work out. Confused still?
18 + 6 = Ask the teacher to clarify.
18 + 2 = 20 + 4. 20 + 4 = 24.
13. The teacher talk…
This involves using known
Inverse
addition/subtraction facts to derive
the opposite subtraction/addition fact. Operations
For example, 62 – 34 = ?? can be
reworked 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 by
I can use lots of adding strategies changing one part of a multiple of
here. 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
