KA-0008Continuing a visual pattern
3 points, difficulty 1 of 3Level 3–4about 60sThe first three patterns are made of dots and follow a rule. How many dots will the fifth pattern have?
Text description of the figure
Three dot patterns in a row. The first has one column of 2 dots with a single dot above it, making 3. The second has two columns of 2 dots with a single dot above, making 5. The third has three columns of 2 dots with a single dot above, making 7.
Hints
Take them one at a time. The first gives nothing away.
1A nudge
Write the counts down as numbers first.
2The strategy
Turn the pictures into a list of numbers, then look at the difference between one number and the next. A steady difference means you can count on rather than draw.
3The full solution
The counts are 3, 5, 7, so each stage adds 2. Stage four is 9 and stage five is 11.
Solution
The reliable way
Write the dot counts as a list: 3, 5, 7. Each pattern adds one more column of 2 dots, so the counts go on 9 and then 11. The fifth pattern has 11 dots. The transferable idea: convert a picture pattern into numbers before you look for the rule.
The elegant way
Stage n is n columns of 2 dots plus a single dot on top, so it has 2n + 1 dots, giving 11 at stage five.
Why this is on the test: It checks whether a student reads the picture into numbers, which is the step that makes every later pattern question tractable.