Cogito
Grade 5 Math · Chapter 8 · Lesson 4
Patterns as Pairs
Two rules, plotted together.
10 problems · about 16 minutes · 5.OA.B.3, 5.G.A.2
What this lesson teaches
The child generates two patterns from two rules, relates the terms, and plots the pairs.
- Two rules give two patterns.
- Their matching terms can be paired and plotted.
- Steady rules give points in a straight line.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — The Coordinate Plane: In (6, 1), how far across do you go?
Answer 6
Why 6 across, then 1 up.
Review — The Volume Formula: Volume of a 7 by 3 by 2 box?
Answer 42
Why 42 cubic units.
Warm Up
Straightforward practice. Get the method working first.
4 problemsA adds 3, B adds 12, from 0. What is B when A is 9?
Answer 36
Why 36.
What do two patterns become when you pair their terms?
Answer Points that can be plotted.
Why Each pair of terms is a point on the grid.
A adds 2, B adds 6, from 0. What is B when A is 8?
Answer 24
Why B is 3 times A.
A adds 4, B adds 8, from 0. What is B when A is 12?
Answer 24
Why B is double A.
Build It Up
The same ideas with more to keep track of.
2 problemsA adds 1, B adds 5, from 0. What is B when A is 7?
Answer 35
Why B is 5 times A.
Do the plotted pairs fall in a straight line?
Answer Yes.
Why Both rules add a fixed amount each time.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Two Rules: Rule A adds 3, rule B adds 9, both from 0. What is B when A is 6?
Answer 18
Why 18.
The Relationship: Rule A adds 5, rule B adds 10, both from 0. What is B when A is 20?
Answer 40
Why 40.