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P6 Growing patterns and tables

Today’s problem — free all day, every step. Every day has one.

Patchwork badges — orange and purple triangles, Figure n

A craft club stitches triangular patchwork badges. Each badge, Figure n, is a triangle made up of small orange and purple triangular pieces of felt. The table shows the piece counts for the first four figures. Figure | Orange pieces | Purple pieces | Total pieces 1 | 1 | 0 | 1 2 | 2 | 2 | 4 3 | 3 | 6 | 9 4 | 4 | 12 | 16

  1. (a) Find the number of orange pieces and purple pieces in Figure 5.
  2. (b) Find the total number of pieces in Figure 40.
  3. (c) Find the percentage of pieces in Figure 40 that are purple.
One step of the worked solution to Patchwork badges — orange and purple triangles, Figure n, drawn in pencil.
9 steps, drawn in pencil

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The pattern behind it: Growing patterns and tables

Find the rule, so Figure 250 is no harder than Figure 4.

In this one. Two rules read straight off the table - the total is the figure number squared, and the orange count is the figure number - let you answer for Figure 40 without ever drawing Figure 40.

The first threeeach one adds 3Figure 14Figure 2+3Figure 3+3Any figure3n + 1Figure nFigure 250 = 751

How to spot it

A row of figures or a table of numbers is shown for the first few terms only, and the question asks for a term far further along, such as 'Figure 6' or 'Figure 250'.

Common mistake

Children extend the sequence one term at a time by drawing or counting. Finding the fixed step or relationship lets them jump straight to the term asked for.

Try one like it

Challenging Grey and white triangles — Figure 250 Figure n is a triangle of small white and grey triangles. Given the counts for Figures 1–4, find (a) Figure 5's counts, (b) the to…
All 4 with this pattern →

The 33 problem patterns

All 33 patterns, one to a page — the 19 behind Primary 5 and 6 word problems, and the skills the younger years are built on. The bar model, how to spot it in the question, and the mistake children make. A booklet you can print. Free.

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