A focused Grade 5 learning session for Analyzing Relationships Between Patterns using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can compare two patterns and explain their relationship.
Analyzing Relationships Between Patterns is the Grade 5 skill of students identify apparent relationships between corresponding terms of two patterns that start with the same number. They explain these relationships informally using operations and connect them to graphed points on the coordinate plane.
Strong understanding comes from naming what the numbers, shapes, units, or data values represent, then showing the idea with a model or clear steps before solving.
The key to this topic is understanding the structure behind the work, not just following a rule. Students should be able to talk through what is happening, point to a model, and explain why the answer makes sense.
Question: Pattern A starts at 2. Pattern B starts at 2. Pattern A increases by 1 each step, and Pattern B increases by 3 each step. Complete the table.
| Step | Pattern A | Pattern B |
|---|---|---|
| 1 | 2 | 2 |
| 2 | 3 | 5 |
| 3 | 4 | ? |
How the model helps: Pattern B increases by 3 each step: 2, 5, 8. At step 3, Pattern B is 8.
Question: Pattern M: 5, 10, 15, 20. Pattern N: 8, 13, 18, 23. What is the relationship?
| M | N | |
|---|---|---|
| 5 | 8 | |
| 10 | 13 | |
| 15 | 18 | |
| 20 | 23 |
Answer: \(N = M + 3\)
Question: Pattern P: 2, 4, 6, 8, 10. Pattern Q: 6, 12, 18, 24, 30. What is the rule?
| Position | Pattern P | Pattern Q |
|---|---|---|
| 1 | 2 | 6 |
| 2 | 4 | 12 |
| 3 | 6 | 18 |
Answer: \(Q = 3 \times P\)
Question: A video game store counts inventory. Game A: 50, 100, 150, 200. Game B: 10, 20, 30, 40. Write the relationship between A and B.
| Game B | Game A |
|---|---|
| 10 | 50 |
| 20 | 100 |
| 30 | 150 |
| 40 | 200 |
Answer: \(A = 5 \times B\)
Why it works: Game A inventory is always 5 times Game B: 10 × 5 = 50, 20 × 5 = 100, 30 × 5 = 150, 40 × 5 = 200.
Analyzing Relationships Between Patterns gets easier when students read the model, track what each number means, and explain why the answer fits the situation.
Understand the structure first, then solve, check, and explain why the answer makes sense.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
Look at the pattern: \(2, 20, 200, 2{,}000, \ldots\) What is the next number?
Answer D: \(20{,}000\)
Each term is multiplied by 10: \(2{,}000 \times 10 = 20{,}000\).
The pattern \(5, 10, 15, 20, \ldots\) adds the same amount each time. Which choice gives the rule and the 8th term?
Answer A: Add 5; 40
The pattern grows by 5 each time. Counting terms gives \(5,10,15,20,25,30,35,40\), so the 8th term is 40.
Pattern: \(64, 32, 16, 8, \ldots\) What's next?
Answer D: \(4\)
Each term is half the previous: \(8 \div 2 = 4\).
Pattern: \(3, 6, 12, 24, \ldots\) What's next?
Answer D: \(48\)
Each term is twice the term before it: \(3\) becomes \(6\), \(6\) becomes \(12\), and \(12\) becomes \(24\). Keep that same rule, so \(24 \times 2 = 48\).
Pattern: \(100, 90, 80, 70, \ldots\) What is the 8th term?
Answer C: \(30\)
Subtract 10 each time: 100, 90, 80, 70, 60, 50, 40, 30.
Pattern A is \(1, 2, 3, 4, \ldots\) and Pattern B is \(3, 6, 9, 12, \ldots\). If Pattern A gives the \(x\)-value and Pattern B gives the \(y\)-value, what ordered pair comes next?
Answer D: \((5, 15)\)
Pattern A adds 1 each time and Pattern B adds 3 each time. The next matching values are 5 and 15, so the next ordered pair is \((5,15)\).
The table shows a pattern. What is the missing value?
Answer B: \(28\)
Rule: Output \(= 7 \times\) Input; \(7 \times 4 = 28\).
Pattern: \(40, 36, 32, 28, \ldots\) What is the rule and next term?
Answer B: \(-4\); \(24\)
Each term is 4 less than the term before it. After 28, the next term is 24.
Pattern A has dots \(1,4,7,10,\ldots\). Pattern B has dots \(2,8,14,20,\ldots\). Which statement describes the relationship between matching figures?
Answer B: Pattern B has twice as many dots as Pattern A.
Compare matching figures: \(2=2\times1\), \(8=2\times4\), \(14=2\times7\), and \(20=2\times10\). Pattern B has twice as many dots as Pattern A.
Pattern \(5, 10, 20, 40, 80, \ldots\) What is the 7th term?
Answer B: \(320\)
Keep doubling after 80: the 6th term is 160, and the 7th term is 320.
Pattern: \(2, 5, 11, 23, \ldots\) Next?
Answer D: \(47\)
Rule: double and add 1. \(23 \times 2 + 1 = 47\).
