Question P6 Growing patterns and tables
Today’s problem — free all day, every step. Every day has one.
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
Answer
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MathBrush is being tested with a few parent groups, and every solution on the site is open to them — one household, all children. If you were given a code, it goes in once and this device remembers it.
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65 worked examples are free without a code, two from every pattern. No account, either way.
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.
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'.
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.
Worked examples of all 33 patterns and skills, in a booklet you can print.