Units of Work

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Teaching and learning activities for around five classroom mathematics sessions. Units include links to the NZC, specific learning outcomes, descriptions of sequenced teaching and learning activities, useful questions to use with students, a list of the resource materials required, and any copymasters needed.

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Level Five
Integrated
Units of Work
In this unit students work with ratios in the context of mixing fruit drinks and other situations.
  • Convert between millilitres and litres.
  • Convert ratios to fraction and percentage expressions.
  • Find equivalent ratios.
  • Compare ratios.
  • Reduce ratios to simplest form using common factors.
  • Combine ratios.
  • Solve problems involving rates.
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Level Five
Number and Algebra
Units of Work
The purpose of this unit is to engage students in applying their knowledge and skills about rates to solve problems that involve, distance and time within the context of fuel efficiency, depreciation, and speed. This unit integrates with the technology learning area.
  • Use tables, graphs, double number lines, and equations to solve problems with rates.
  • Develop and execute calculator algorithms to solve rate problems.
  • Solve problems where a measure is missing but the rate is given.
  • Solve problems where two measures are given but the rate is unknown.
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Level Three
Number and Algebra
Units of Work
This unit introduces students to equivalent fractions. Unlike whole numbers that occupy a unique position on the number line, there is an infinite set of fractions that represent the same value. Fraction that are of equal value are said to be equivalent.
  • Put fractions on a number line in their correct position in relation to zero and one.
  • Show that equivalent fractions occupy the same place on a number line.
  • Rename fractions as many equivalent fractions.
  • Know how to find equivalent fractions of a set.
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Level Four
Geometry and Measurement
Units of Work
This unit examines the use of rotation to specify angles as an amount of turn. The context of the unit, irrigating trees, requires the calculation of lengths and measurement of angles based on a four-quadrant number plane.
  • Identify the location of a point on a four-quadrant number plane using coordinates.
  • Average the x and y values of a set of coordinates to locate the centroid of the points.
  • Use scale or Pythagoras’ Theorem to find the distance between points on a number plane.
  • Measure the bearing (angle...
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Level One
Number and Algebra
Units of Work
This unit supports students in using counting to compare and combine collections.
  • Use counting to find the number when two different collections are compared (difference).
  • Use counting to find the number when two or more collections are joined (addition).
  • Use counting to find the number when objects are removed from a collection (subtraction).
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Level Three
Geometry and Measurement
Units of Work
In this unit students interpret 2-dimensional representations of 3-dimensional objects and learn to create their own representations.
  • Construct plan views of solid objects.
  • Create nets that fold to form solid objects.
  • Classify 3-dimensional shapes by their properties.
  • Identify 3-dimensional shapes in the environment.
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Level Three
Number and Algebra
Units of Work
This unit supports students in recognising percentages in everyday contexts, gaining knowledge of simple percentages as proportions, and finding simple percentages of amounts.
  • Know common percentages as proportions of a whole amount.
  • Express common percentages as fractions and vice versa.
  • Express simple ratios as part-whole decimals.
  • Calculate simple percentages of amounts.
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Level Three
Number and Algebra
Units of Work
This unit is an early introduction to decimals. Numbers used are restricted to hundreds, tens, ones, and tenths. Only addition and subtraction operations are used.
  • Read and write decimals to two places.
  • Represent decimals on linear scales, like thermometers.
  • Add and subtract decimals to one decimal place using combining and partitioning strategies.
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Level Two
Number and Algebra
Units of Work
In this unit students explore multiplication by finding totals in ‘sets of equal sets’ contexts. Students also encounter division through forming equal sets.
  • Use multiplication by two, five and ten to solve problems with equal sets.
  • Use multiplication two, five and ten to solve division problems with equal sets.
  • Pose multiplication and division problems.
  • Record working with multiplication and division using diagrams and equations.
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Level Three
Geometry and Measurement
Units of Work
This unit examines the use of reflective and rotational symmetry in the design of plates. Traditionally, designers often used symmetry to make plates aesthetically pleasing, however, more modern designs are often asymmetric.
  • Find all the lines of symmetry on a given shape.
  • Identify the order of rotational symmetry for a given shape (how many times it "maps" onto itself in a full turn).
  • Create designs which demonstrate reflection symmetry and rotational symmetry (orders 2, 3, 4, 6).
  • Identify the invariant properties of a...