After Two years of School students should be able to:

Strategy

Imagine you have 9 stamps and 12 letters.
How many more stamps would you need to post all the letters?

Nine tui stamps.

Letters requiring stamps.

The student gets the correct answer of 3 stamps by counting on 10, 11, 12 and tracking the count of 3. Alternatively, they may count back 11, 10, 9, tracking the count of 3.
If the student successfully uses a part–whole strategy, they exceed the expectation (for example '9 stamps and 1 more is 10, and that leaves 2 more stamps, which is 12', or '12 is 4 threes, and 9 is only 3 threes, so I need 3 more stamps').

Multiplication/Division

Here is a string of 12 sausages to feed 2 hungry dogs.
Each dog should get the same number of sausages. How many will each dog get?

Two dogs and sausages.

'
The student uses equal sharing to distribute the sausages between the dogs. This might involve skip-counting ('2 sausages makes 1 each, 4 sausages makes 2 each ... 12 sausages makes 6 each') while tracking the count mentally or with fingers, or it might involve halving, that is, dividing 12 into 6 and 6. (Note that 6 and 6 is a symmetrical partitioning of 12.)

Patterns

Show the student a number strip with coloured cubes lined up along it, as in the diagram below. Provide extra coloured cubes.

Number strip and cubes.

What colour cube goes on the number 13 in this pattern?
The student identifies the unit of repeat (yellow, blue, red, white) and continues the pattern one cube at a time until they identify a yellow cube on 13. If the student notices that multiples of 4 have a white cube and therefore 13 has a yellow cube, they exceed the expectation.

Measurement

Pencils and cuisenaire rods.

Place 3 pencils of different lengths end-on-end with gaps between them, as shown. Give the student a collection of white, red, and light green Cuisenaire™ rods.
Place rods underneath each pencil to show how long it is. Without moving the pencils, can you tell me how much longer the orange pencil is than the blue pencil? The student places the same-coloured rods, with no gaps or overlaps, from one end to the other of each pencil. They count on or back to find the difference in length without needing to directly align the pencils. For example, if the orange pencil is 7 red rods long and the blue pencil is 4 red rods long, the student counts 5, 6, 7 or uses 4 + 3 = 7 to work out that the difference is 3 red rods. If the student uses different-coloured rods and shows that they understand that, for example, 2 white rods are the same length as 1 red rod, they exceed the expectation.

Geometry

Student pair cartoon.

The students work in pairs.
One student has a picture of a group of attribute blocks laid out in a certain way. The other student has a set of actual attribute blocks.
Without showing their partner the picture or pointing to the blocks, the first student describes to the second how to arrange the group of blocks so that it matches the picture, and the second student follows their instructions.
The student giving the instructions uses the appropriate positional language and geometric terms for shapes, and they accurately describe colours and turns (half and quarter). The other student is able to assemble the figure correctly with no errors in position or orientation of shapes.

Statistics

Student reading graph.

Provide the student with the graph.
The student is able to say how many books individual students read (for example, 'Kate reads 6 books. Sione reads 7.').
The student finds the difference between the number of books read by Aroha and Leilani by counting on or back (for example, 'Aroha reads 6 more books than Leilani. I just counted the extra ones.').
To compare the total books read by girls and boys, the student needs to recognise which names are girls’ names and which are boys’. (You may need to help.) They count up the total for both and compare them. If the student uses additive thinking rather than counting, they exceed the expectation (for example, 'The boys read 8 books and 7 books. 8 + 7 = 15 because 7 + 7 = 14'). If the student realises that the comparison is not representative (or fair) because there are 3 girls and only 2 boys, they exceed the expectation.
The student should be able to ask their own comparison questions about the data, for example, 'How many more books does Oliver read than Kate?'

Example 2

Five cubes.

Let the student watch as you put 4 blue cubes and 1 yellow cube into a paper bag.
Put your hand in the bag and take out a cube, but don’t look at it.
What colour will it be?
The student identifies the two possible outcomes. If they omit one of them (for example, 'It will be blue because there are more of them') or identify an outcome that is not possible (for example, 'It will be green because that is my favourite colour'), they do not meet the expectation.
If the student states that getting a blue cube is more likely than a yellow cube because there are more blue cubes than yellow cubes in the bag, they exceed the expectation.

After Two years of School students should be able to:

Imagine you have 9 stamps and 12 letters.StrategyHow many more stamps would you need to post all the letters?

The student gets the correct answer of 3 stamps by counting on 10, 11, 12 and tracking the count of 3. Alternatively, they may count back 11, 10, 9, tracking the count of 3.

If the student successfully uses a part–whole strategy, they exceed the expectation (for example '9 stamps and 1 more is 10, and that leaves 2 more stamps, which is 12', or '12 is 4 threes, and 9 is only 3 threes, so I need 3 more stamps').

Here is a string of 12 sausages to feed 2 hungry dogs.Multiplication/DivisionEach dog should get the same number of sausages. How many will each dog get?

The student uses equal sharing to distribute the sausages between the dogs. This might involve skip-counting ('2 sausages makes 1 each, 4 sausages makes 2 each ... 12 sausages makes 6 each') while tracking the count mentally or with fingers, or it might involve halving, that is, dividing 12 into 6 and 6. (Note that 6 and 6 is a symmetrical partitioning of 12.)

Show the student a number strip with coloured cubes lined up along it, as in the diagram below. Provide extra coloured cubes.PatternsWhat colour cube goes on the number 13 in this pattern?

The student identifies the unit of repeat (yellow, blue, red, white) and continues the pattern one cube at a time until they identify a yellow cube on 13. If the student notices that multiples of 4 have a white cube and therefore 13 has a yellow cube, they exceed the expectation.

MeasurementPlace 3 pencils of different lengths end-on-end with gaps between them, as shown. Give the student a collection of white, red, and light green Cuisenaire™ rods.

Place rods underneath each pencil to show how long it is.

Without moving the pencils, can you tell me how much longer the orange pencil is than the blue pencil?

The student places the same-coloured rods, with no gaps or overlaps, from one end to the other of each pencil.

They count on or back to find the difference in length without needing to directly align the pencils. For example, if the orange pencil is 7 red rods long and the blue pencil is 4 red rods long, the student counts 5, 6, 7 or uses 4 + 3 = 7 to work out that the difference is 3 red rods.

If the student uses different-coloured rods and shows that they understand that, for example, 2 white rods are the same length as 1 red rod, they exceed the expectation.

GeometryThe students work in pairs.

One student has a picture of a group of attribute blocks laid out in a certain way. The other student has a set of actual attribute blocks.

Without showing their partner the picture or pointing to the blocks, the first student describes to the second how to arrange the group of blocks so that it matches the picture, and the second student follows their instructions.

The student giving the instructions uses the appropriate positional language and geometric terms for shapes, and they accurately describe colours and turns (half and quarter). The other student is able to assemble the figure correctly with no errors in position or orientation of shapes.

StatisticsProvide the student with the graph.

The student is able to say how many books individual students read (for example, 'Kate reads 6 books. Sione reads 7.').

The student finds the difference between the number of books read by Aroha and Leilani by counting on or back (for example, 'Aroha reads 6 more books than Leilani. I just counted the extra ones.').

To compare the total books read by girls and boys, the student needs to recognise which names are girls’ names and which are boys’. (You may need to help.) They count up the total for both and compare them. If the student uses additive thinking rather than counting, they exceed the expectation (for example, 'The boys read 8 books and 7 books. 8 + 7 = 15 because 7 + 7 = 14'). If the student realises that the comparison is not representative (or fair) because there are 3 girls and only 2 boys, they exceed the expectation.

The student should be able to ask their own comparison questions about the data, for example, 'How many more books does Oliver read than Kate?'

## Example 2

Let the student watch as you put 4 blue cubes and 1 yellow cube into a paper bag.

Put your hand in the bag and take out a cube, but don’t look at it.

What colour will it be?

The student identifies the two possible outcomes. If they omit one of them (for example, 'It will be blue because there are more of them') or identify an outcome that is not possible (for example, 'It will be green because that is my favourite colour'), they do not meet the expectation.

If the student states that getting a blue cube is more likely than a yellow cube because there are more blue cubes than yellow cubes in the bag, they exceed the expectation.