P6 Growing patterns and tables
Today’s problem — free all day, every step. Every day has one.
Triangular mosaics — red and blue tiles in Figure n
A tiler is designing a set of triangular mosaic patterns for a lobby floor. Each pattern, Figure n, is a large triangle made up of small red and blue triangular tiles. The table shows the tile counts for the first four figures. Figure | Red tiles | Blue tiles | Total tiles 1 | 1 | 0 | 1 2 | 3 | 1 | 4 3 | 5 | 4 | 9 4 | 7 | 9 | 16
- (a) Find the number of red tiles and blue tiles in Figure 5.
- (b) Find the total number of tiles in Figure 50.
- (c) Find the percentage of tiles in Figure 50 that are blue.
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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. The table already holds the answer — read the rule for the total and the rule for red straight off it, and the third column comes free by subtraction, so Figure 50 costs no more work than Figure 5.
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…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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