The pattern
Growing patterns and tables
Find the rule, so Figure 250 is no harder than Figure 4.
A sequence is given a few terms at a time, and the job is to find the rule that carries it forward without drawing everything in between. Put the figure number and its count side by side in a table, then look for what changes by a fixed step and what stays the same. The rule answers Figure 250 as easily as Figure 4.
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.
17 worked solutions
Standard
- continue a number sequence Continue this number pattern: 3000, 3500, 4000, __. What is the next number?
- continue a number sequence Continue this number pattern: 2400, 2500, 2600, __. What is the next number?
- continue a number sequence 305, 355, 405, __. What comes next?
- continue a number sequence 240, 260, 280, __. What comes next?
- continue a number sequence 20, 25, 30, __. What comes next?
- continue a number sequence 42, 44, 46, __. What comes next?
- Dot pattern — Figure 6 A pattern is made up of dots. Figure 1 has 4 dots, Figure 2 has 7 dots and Figure 3 has 10 dots. How many dots will there be in Fi…
- Farmer Aziz puts fence posts around square flower beds. Bed 1 uses 5 posts, Bed 2 uses 8 posts, and Bed 3 uses 11 posts. How many posts will Bed 6 need?
- Mrs Tan is setting out chairs in rows for a wedding dinner. Row 1 has 6 chairs, Row 2 has 10 chairs, and Row 3 has 14 chairs. How many chairs will be in Row 5?
- Red beads — a bracelet pattern Ravi is threading red beads onto bracelets. Bracelet 1 has 3 red beads, Bracelet 2 has 7 red beads, and Bracelet 3 has 11 red bead…
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…
- 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 triangul…
- PSLE 2023 — Rods and straws grid A grid is built from rods and straws: the rods run one way and the straws run across them, so a grid m sections long and n section…
- PSLE 2024 — Repeating digits 2041 The digits 2, 0, 4, 1 repeat to form the sequence 2, 0, 4, 1, 2, 0, 4, 1, ... The digits used add up to 230. How many digits are t…
- PSLE 2025 — Two patterns common terms Pattern 1: 3, 7, 11, 15, ... Pattern 2: 7, 12, 17, 22, ... The number 7 is the first common term in both patterns. What is the sum…
- 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…
Very challenging
All the problem patterns → · the revision list
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.
A PDF, and a note when new solutions go up.