dy/dan: Pixel Pattern

Start of pixel pattern problem

The mathematics GCSE requires students to apply mathematics in unfamiliar contexts. Dan Mayer’s activity ‘Pixel Pattern’ contains some interesting ideas on this topic and draws together work on sequences, rates, dimensions, ratio, coordinates and equations.

A video clip shows the growth of a pattern created from pixels. The pattern is set inside a rectangle. When will the pixel pattern break through the box? After how many seconds? At which point on the perimeter of the rectangle?

The dimensions of the bounding rectangle are 182 units by 98 units. Individual pixels are 1 square unit. One way of solving the problem is to use coordinate axes:

91 units on x and 49 units on y

A focus on the first quadrant gives the following:

Pixels after 0, 1, 2, 3, seconds

Resolving into components and equating with the dimensions of the bounding box gives:

Horizontal        1.5n + 1 = 91               Vertical            n + 0.5 = 49

The equation for vertical motion gives a solution of 48.5 seconds, which would round up to 49 seconds since the pattern changes each second.

In terms of differentiation, a gentle introduction would be to eliminate the blue pixels:

Pixels easier version

An extension would be to vary the up or across components:

Pixels harder version

If you give this activity a go then please let the community know what approaches your students take by leaving a comment to this post.

We have recently added Dan Mayer’s ‘dy/dan Three Act Math’ materials, this example being ‘Pixel Patterns’.

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Encourage active learning in secondary mathematics lessons with the use of manipulatives.

Manipulatives - or “objects to think with - include counters, interlocking cubes, Cuisenaire rods and tiles etc". Research suggests that their use is beneficial to mathematical understanding, and can help students with retention, problem solving and reasoning.

This two day, residential, hands-on, practical experience is suitable for all teachers of mathematics in secondary school.

This is a residential course, fees include meals and accommodation for the duration of the course. 

A full list of CPD is available here.





Age11-14, 14-16
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