Number Pattern Relationships
Generate two numerical patterns using two given rules; identify relationships between corresponding terms; form ordered pairs and graph them on a coordinate plane
What a learner can do afterwards
- Generate sequences starting at 0 with rules 'add 3' and 'add 6'; observe terms in one are twice the other
- Form ordered pairs from corresponding terms and plot them on a coordinate grid
- Explain informally why the relationship between the two sequences holds
1 · Read
You already know how to build a number pattern from a rule, like starting at 0 and adding 3 each time. Now you will build two patterns at once, using two different rules, and compare them term by term.
Line up the terms by position: term 1 is 0 and 0, term 2 is 3 and 6, term 3 is 6 and 12. Every Pattern B term is exactly double the matching Pattern A term, because each Pattern B step (6) is double each Pattern A step (3).
To graph a pair, use the Pattern A term as the x-coordinate and the Pattern B term as the y-coordinate. The pair (3, 6) means 3 right and 6 up from the corner, just like the coordinate grids you already know.
Two patterns from two rules, paired term by term, become points you can plot and explain.
More to read
Generate patterns
Two rules can run side by side. Starting at 0, add 3 gives 0, 3, 6, 9, while add 6 gives 0, 6, 12, 18. Each term in the second list is twice the matching term in the first. The doubling holds because 6 is twice 3. Comparing lists term by term reveals links that one list alone hides.
Interpret relationships
Matching terms form ordered pairs. The two lists above give (0, 0), (3, 6), (6, 12) and (9, 18). In each pair the second number doubles the first. Tables keep the pairs tidy. Reading down the second column shows the same doubling every time.
Graph points review (positive numbers only)
Pairs plot as points on a coordinate grid. (3, 6), (6, 12) and (9, 18) sit on one straight line through (0, 0). The straightness pictures the doubling rule. Curves would mean a wobblier link. Plotting turns number patterns into shapes you can see.
Explore more
2 · Watch
به انگلیسیTake it off screen
Where it sits
Optional connections
This opens up
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
17 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.