Illustrating the Mathematics Standards

image map. Breakdown of Waste: Illustrating the year 5 standard

The following examples of student work illustrate achievement at the mathematics standard for year 5.

The task used in this illustration was part of a unit on waste, packaging, and recycling, stemming from a school-wide focus on sustainability. The unit was based on the Material World (from the science learning area), but this particular task also had links to achievement objectives for number strategies, number knowledge, and measurement from the mathematics and statistics learning area in The New Zealand Curriculum.

The Task

Breakdown of Waste Timeline

Year 1Year 2Year 3Year 4Year 5Year 6Year 7Year 8
  1. Select some food and packaging items from the table that the class created after last week’s research.
    Time that items found in school lunchboxes take to break down
    Apple core: 2 months
    Banana skin: 4 weeks
    Orange skin: 5 weeks
    Sandwich crust: 2 weeks
    Leftover noodles: 6 weeks
    Bread: 12 days
    Plastic bag: 10 years

    Paper bag: 8 weeks
    Plastic wrap: 25 years
    Greaseproof paper: 8 weeks
    Plastic water bottle: 450 years
    Waste items.
  2. Draw a timeline. Place your selected items on the timeline to show how long each item takes to break down.
  3. Choose one food and one packaging item from your timeline and calculate the difference between the times that they take to break down.
Some features of students’ work used to make judgments in relation to the mathematics standards are described on the pages linked below. There is also an illustration of the year 6 standard and an illustration of the year 7 standard for this task. (Names used for students are fictional.)

New Zealand Curriculum: Level 3 National Standards: By the end of year 5
In solving problems and modelling situations, students will:
Number and Algebra
  • use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages (number strategies)
  • know basic multiplication and division facts (number knowledge)
Number and Algebra
  • apply additive and simple multiplicative strategies and knowledge of symmetry to:
    – combine or partition whole numbers
    – find fractions of
    sets, shapes, and quantities 
Geometry and Measurement
  • use linear scales and whole numbers of metric units for length, area, volume and capacity, weight (mass), angle, temperature, and time (measurement)

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Breakdown of Waste, Year 5

PDF of this task and Illustrations of the year 5, 6 and 7 standards (1.35MB)