# Illustrating the Mathematics Standards

#### Interlocking Photo Frames: Illustrating the year 6 standard

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

The task used in this illustration relates to achievement objectives for Number and Algebra from the mathematics and statistics learning area in The New Zealand Curriculum. It was adapted from an activity in Figure It Out, Algebra: Book One, Link (years 7–8), pages 12–13.

#### Interlocking Photo Frames

Nikki’s mum is on the organising committee for the new community centre. They want to hang photos of local people, community activities, and historical places around the walls.

Nikki’s mum suggests that they use a series of interlocking photo frame pieces. (Each frame has 4 pieces, but two frames “share” a piece when they are joined together.) The committee try this idea with 3 photos and find that they would need 10 frame pieces.

1. If 10 frame pieces are needed for 3 photos, how many pieces are needed for 8 photos?
2. Can you find a rule for the number of frame pieces needed for any number of photos? Apply your rule to different numbers of photos.
3. How many frame pieces are needed for 99 photos?

Some features of students’ work used to make judgments in relation to the year 6 mathematics standard are described below.  There is also an illustration of the year 5 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) know basic multiplication and division facts (number knowledge) connect members of sequential patterns with their ordinal position and use tables, graphs, and diagrams to find relationships between successive elements of number and spatial patterns (patterns and relationships) 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 determine members of sequential patterns, given their ordinal positions describe spatial and number patterns, using: - tables and graphs - rules that involve spatial features, repeated addition or subtraction, and simple multiplication

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