Example 1
There are 6 baskets and 24 muffins in each basket.
How many muffins are there altogether?
The student uses an efficient multiplicative strategy to solve the problem mentally. This might involve drawing on their knowledge of place value (for example, 6 x 20 + 6 x 4), working with tidy numbers (for example, 6 x 25 – 6 x 1), or doubling and halving (for example, 6 x 24 = 12 x 12).
If the student uses repeated addition or doubling (for example, 24 + 24 = 48, 48 + 24 = 72 ...), they do not meet the expectation. If they use a vertical algorithm to solve the problem, they must explain the place value partitioning involved.
Source: Numeracy Development Projects, Book 2: The diagnostic interview, p. 41.
Geometry and Measurement:
Example 5
Provide the students with coins and kitchen scales, as required for 1. below.
The students at Springfield School made a coin trail using 20-cent coins to raise money for Daffodil Day.
- The length of the coin trail was 21 000 millimetres. What was its length in centimetres? What was it in metres?
- Here are 100 twenty-cent coins. Use the kitchen scales to find their combined weight. Using your answer, what would 1000 twenty-cent coins weigh? What would 10 twenty-cent coins weigh?
For 1., the student reads the scales accurately to give the combined weight as 400 grams. They use their knowledge of place value, metric measures, and multiplicative strategies to correctly answer all other questions – for example, for 1., 'There are 10 millimetres in a centimetre, so 21 000 mm = 2100 cm; there are 1000 millimetres in a metre, so 21 000 mm = 21 m'; for 2., '1000 coins must weigh 10 times 400 grams, which is 4000 grams or 4 kilograms; 10 coins must weigh one-tenth of 400 grams, which is 40 grams.'
Source: adapted from 'Coin trail' (MS2161) in the Assessment resource banks
Example 6
Give the student the following collection of shapes.
- What is a common property of all these shapes?
- Identify a property that some of the shapes have and sort all the shapes into groups by that property.
For 1., the student identifies at least one property that is common to all the shapes – for example, they all have 4 sides, 4 corners (vertices), or straight sides (that is, they are all polygons).
For 2., the student identifies an appropriate property and sorts the shapes into classes by that property – for example, whether each shape has:
Statistics:
Example 8
Show the student the illustrations below.
Here are the results from a class opinion poll, recorded on a tally chart and displayed in three different graphs.
Look at the data gathered in the poll. Suggest some different types of questions that could be answered from the data, for example, summary questions like 'How many girls disagree that keeping animals in zoos is wrong?' or comparison questions like 'Do more boys or girls agree that keeping animals in zoos is wrong?'
Now write down some 'I wonder' questions about people’s opinions on topics of interest to you, your friends, or your family. Work with one or two other students to use the statistical enquiry cycle to investigate one or more of your questions.
Source: http://nzcurriculum.tki.org.nz/National-Standards/Mathematics-standards/The-standards/End-of-year-7