SME
Grade 5 Math · Problem type
Graph two numerical patterns
Use this for “Rule A: start at 0, add 3. Rule B: start at 0, add 6. Graph the pairs.”
Chart
First number (across)
Second number (up)
0
0
3
6
6
12
9
18
12
24
The point is 12 across and 24 up.
This is an example. Type your own values to start a new problem.
Term
example
First rule’s step
example
Second rule’s step
example
First number (across)
calculated
Second number (up)
calculated
Formulas
4 × 3 = 12
Term × first rule’s step = first number
4 × 6 = 24
Term × second rule’s step = second number
Assumptions
•
Two patterns start at 0. Each term adds the same amount to each pattern.
•
Pair the terms: the first pattern’s number goes across, the second’s goes up.
•
The earlier points are drawn too: they make a straight line from 0.
Step-by-step
WE KNOW
Term: 4
First rule’s step: 3
Second rule’s step: 6
FIND
first number (across), second number (up)
Step 1 · Find first number (across)
4 × 3 = ?
Term × first rule’s step = first number
The first pattern adds its step once for each term.
0, 3, 6, 9, 12 → 12
First number (across) = 12
Step 2 · Find second number (up)
4 × 6 = ?
Term × second rule’s step = second number
The second pattern adds its step once for each term.
0, 6, 12, 18, 24 → 24
Second number (up) = 24 (each second number is 2 times the first)
Check
Put the numbers back in. Both sides should match.
4 × 3 = 12 ✓
4 × 6 = 24 ✓
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