A staircase pattern has 1 block at step 1, 3 blocks at step 2, 6 blocks at step 3, and 10 blocks at step 4. How many blocks are added at each step?
A2 blocks added each step
B3 blocks added each step
CThe amount added increases: 2, then 3, then 4
DThe amount added decreases each step
From step 1 to 2: 3-1=2 blocks added. From step 2 to 3: 6-3=3 blocks added. From step 3 to 4: 10-6=4 blocks added. The amount added is increasing by 1 each time (2, 3, 4, so the next step adds 5). This is a non-constant growth rate, which is different from patterns that add the same amount each step. These are called triangular numbers.
Question 2 Multiple Choice
A growing pattern adds 4 tiles at each step. Step 1 has 4 tiles. How many tiles does step 7 have?
A24 tiles
B28 tiles
C32 tiles
D16 tiles
If step 1 has 4 tiles and each step adds 4 more: step 2 has 8, step 3 has 12, step 4 has 16, step 5 has 20, step 6 has 24, step 7 has 28. Alternatively, step n has 4n tiles, so step 7 = 4 x 7 = 28 tiles. The position rule (4 times the step number) gets you there without listing every step.
Question 3 True / False
A repeating pattern and a growing pattern are the same thing because both follow rules.
TTrue
FFalse
Answer: False
Both follow rules, but they are fundamentally different types. A repeating pattern cycles through the same unit over and over (circle-square-circle-square — no step is bigger than another). A growing pattern gets larger at each step (1 tile, 3 tiles, 5 tiles, 7 tiles — each step has more). The rule for a repeating pattern says 'what to cycle'; the rule for a growing pattern says 'how much to add each step.'
Question 4 Short Answer
Why is it useful to record a growing pattern in a table with step numbers and tile counts?
Think about your answer, then reveal below.
Model answer: A table organizes the data so you can see the numerical relationship clearly. By putting step numbers in one column and tile counts in another, you can spot the rule: is the count increasing by the same amount? Is it doubling? Is it connected to the step number by a formula? The table converts a visual pattern into a numerical one, making it easier to find the rule and predict future steps. It also prepares you for graphing and function tables in later math.
The table is a bridge between the visual and the abstract. When students see 'step 1 → 3, step 2 → 5, step 3 → 7,' they can spot 'add 2 each time' more easily than by counting tiles in increasingly complex figures. This is also the format of input-output tables, which are a stepping stone to understanding functions.