1. NZ Maths
  2. Supporting professional practice
  3. Curriculum elaborations
  4. National Standards Illustrations
  5. Interlocking Photo Frames

Interlocking Photo Frames

The Ministry is migrating nzmaths content to Tāhurangi.           
Relevant and up-to-date teaching resources are being moved to Tāhūrangi (tahurangi.education.govt.nz). 
When all identified resources have been successfully moved, this website will close. We expect this to be in June 2024. 
e-ako maths, e-ako Pāngarau, and e-ako PLD 360 will continue to be available. 

For more information visit https://tahurangi.education.govt.nz/updates-to-nzmaths

image map.

Year 1Year 2Year 3Year 4Year 5Year 6Year 7Year 8

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

The Task

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 mathematics standard are described below. 

Interlocking Photo Frames: Illustrating the year 5 standard
Interlocking Photo Frames: Illustrating the year 6 standard

PDF of this task and Illustrations of the year 5 and 6 standards (1.20MB)