# Illustrating the Mathematics Standards

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#### Stained Glass Window: Illustrating the year 6 standard

The following examples of student work illustrate achievement at the mathematics standards for year 6.

The task used in this illustration was part of a visual arts and technology unit in which students were asked to design a stained glass window. The students explored geometric shapes used in stained glass patterns and the technology associated with joining pieces of glass.

For this task, the students were asked to use a “maths lens” and to document aspects of number, geometry, and measurement evident in their designs.

The task relates to achievement objectives for Number and Algebra and for Geometry and  Measurement from the mathematics and statistics learning area in The New Zealand Curriculum.

#### Stained Glass Window

1. Design a stained glass window to fit a 1-square-metre frame.
2. After you have designed your window, divide a piece of paper into three sections, Number, Geometry, and Measurement, and describe your design, using numbers, symbols, and mathematical language. For example:
• under Number, calculate the fraction that each shape is of the whole
• under Geometry, comment on transformations in your design
• under Measurement, calculate the areas of coloured glass needed for your design and the perimeter of the shapes (you can use this later to work out how much lead you will need).

Some features of students’ work used to make judgments in relation to the mathematics standards are described below. There is also an illustration of the year 7 standard and an illustration of the year 8 standard for this task.

 New Zealand Curriculum: Level 3 National Standards: By the end of year 6 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) Number and Algebra apply additive and simple multiplicative strategies flexibly to: - combine or partition whole numbers, including performing mixed operations and using addition and subtraction as inverse operations- 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 find areas of rectangles and volumes of cuboids by applying multiplication (measurement) describe the transformations (reflection, rotation, translation, or enlargement) that have mapped one object onto another (transformation) Geometry and Measurement measure time and the attributes of objects, choosing appropriate standard units represent and describe the results of reflection, [and] rotation, and translation on shapes or patterns

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