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By the end of year 8, students will be achieving at level 4 in the mathematics and statistics learning area of The New Zealand Curriculum.
Examples:
Number and Algebra
Example 1
Example 1
Mani competed in the hop, step, and jump at the athletics sports.
Her jump was 2.65 metres, and her step was 1.96 metres.
The total of her triple jump was 5.5 metres.
How long was her hop?
The student applies their knowledge of decimal place value to correctly calculate the answer. They use a combination of mental and written strategies, which may include equations, vertical algorithms, or empty number lines.
Example 2
Example 2
Andre has ordered 201 tennis balls. They are sold in cans of 3 balls.
How many cans should he receive?
The student gets the correct answer of 67 and, when explaining their strategy, demonstrates understanding of division and place value. Their strategy might involve partitioning numbers into hundreds, tens, and ones, using tidy numbers (for example, 210) and compensating, or using divisibility rules (for example, 'There are 33 threes in 100 with one left over').
Source: adapted from GloSS, Assessment I, task 10.
Geometry and Measurement:
Geometry and Measurement:
Example 4
Example 4
Give the student a ruler, a toy car to measure, and the illustration of boxes shown above.
Use the ruler to measure as accurately as possible how long, how wide, and how high this car is. Give your answer firstly in millimetres and then in centimetres.
Using the ruler, the student accurately measures the length, width, and height of the toy car to the nearest millimetre, and they are able to convert between millimetres and centimetres. They choose the most suitable box – that is, the one with dimensions that exceed the dimensions of the car by the least possible amount.
Source: adapted from NEMP’s 2005 report on mathematics, p. 40.
Statistics:
Example 7
Example 7
Jane’s class was doing a unit on healthy eating. Jane wanted to see if the unit would make any difference to her classmates’ eating habits, so she developed a scale to measure the healthiness of the lunches they were eating.
She applied the scale before and after the unit and created two dot plots to display the results.
Jane concluded that because of the unit, her classmates were now eating healthily. Do you agree? Why or why not?
The student uses data from the graphs to support and/or argue against Jane’s conclusion. For example, they should identify that more students are now eating healthier lunches and that all students are now bringing or buying a lunch. With prompting, they should be able to identify that although the spread of unhealthy to healthy lunches has not changed, the clustering of lunch scores has shifted to more above zero than below, and therefore the 'middle healthiness' has increased.
The student should point out that Jane’s conclusion that 'her classmates were now eating healthily' is not supported by the data, which shows that a small group of students continue to eat unhealthy lunches. They should also recognise that without additional data (such as a larger sample across different days or information from interviews), the improvement in lunch healthiness is not necessarily due to the class unit. For example, the tuck shop may have changed its menu while the class was doing the unit.
Source: Second tier support material for the revised New Zealand Curriculum.
Source: http://nzcurriculum.tki.org.nz/National-Standards/Mathematics-standards/The-standards/End-of-year-8
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