5th Grade Patterns and Ordered Pairs Worksheet Solutions (PDF)

5th Grade math worksheet solutions: Patterns and Ordered Pairs – Maths PDF

This answer key lists the terms, ordered pairs and relationships for all 20 pattern problems. Write the term from the first pattern first in every ordered pair. Check that your graphs show points that line up, which happens when each pattern adds the same amount every time.

Grade 5 · Common Core State Standards: 5.OA.B.3

Exercise 1 – Add 5 pattern

Start at 0 and keep adding 5: $0, 5, 10, 15, 20, 25$.

Terms: 0, 5, 10, 15, 20, 25

Exercise 2 – Add 4 pattern

$0+4=4$, $4+4=8$, $8+4=12$, $12+4=16$, $16+4=20$.

Terms: 0, 4, 8, 12, 16, 20

Exercise 3 – Two rules

A: $0, 2, 4, 6, 8$. B: $0, 6, 12, 18, 24$.

Both patterns completed.

Answer: A: 0, 2, 4, 6, 8; B: 0, 6, 12, 18, 24

Exercise 4 – Write ordered pairs

Pair the terms in the same position. Put the A term first.

$(0, 0), (3, 9), (6, 18), (9, 27)$

Answer: $(0, 0), (3, 9), (6, 18), (9, 27)$

Exercise 5 – Fill in the table

A adds 5: $5+5=10$, so the missing A term is 10.

B adds 10: $20+10=30$, so the missing B term is 30.

Answer: 10 and 30

Exercise 6 – Compare terms

$12\div3=4$, $24\div6=4$, $36\div9=4$.

Each B term is 4 times the corresponding A term.

Exercise 7 – Plot four points

For each pair, go right the first number and up the second number.

The four points.

Answer: the four points lie on a straight line

Exercise 8 – Pairs from two rules

A: $0, 7, 14, 21$. B: $0, 3, 6, 9$.

Pairs: $(0, 0), (7, 3), (14, 6), (21, 9)$

The first coordinate (pattern A) grows faster, because it adds 7 each time and B adds only 3.

Exercise 9 – Find the missing pair

The second numbers go up by 6 each time: 0, 6, 12, ?, 24. So $12+6=18$.

Check: $18+6=24$.

Answer: $(6, 18)$

Exercise 10 – Find the rules

The first numbers go up by 5. The second numbers go up by 10.

Rule for A: start at 0, add 5. Rule for B: start at 0, add 10.

Each B term is 2 times its A term.

Exercise 11 – Smaller second pattern

A: $0, 6, 12, 18$. B: $0, 3, 6, 9$.

Pairs: $(0, 0), (6, 3), (12, 6), (18, 9)$.

Each B term is half of its A term, or each A term is 2 times its B term.

Exercise 12 – Read the graph

Pairs: $(0, 0), (2, 5), (4, 10), (6, 15)$.

First numbers: start at 0, add 2. Second numbers: start at 0, add 5.

When the first number is 8: $15+5=20$.

Answer: 20

Exercise 13 – Which pairs belong?

A: 0, 3, 6, 9, 12. B: 0, 6, 12, 18, 24.

$(6, 12)$: 6 is the third A term and 12 is the third B term. Yes.

$(9, 15)$: 9 is the fourth A term, but the fourth B term is 18. No.

$(12, 24)$: fifth A term 12, fifth B term 24. Yes.

Answer: $(6, 12)$ and $(12, 24)$

Exercise 14 – Liam's pair

A: 0, 4, 8, … B: 0, 8, 16, …

When A is 4 (second term), B is 8 (second term), not 12. Liam added 8 and 4 instead of using the B pattern.

Correct pair: $(4, 8)$

Exercise 15 – Farmers market apples

Bags: $0, 1, 2, 3, 4$. Cost: $0, 3, 6, 9, 12$.

Pairs: $(0, 0), (1, 3), (2, 6), (3, 9), (4, 12)$.

4 bags cost $\$12$.

Exercise 16 – Road trip

Hours: 0, 1, 2, 3, 4. Miles: 0, 50, 100, 150, 200.

Pairs: $(0, 0), (1, 50), (2, 100), (3, 150), (4, 200)$.

Miles after 5 hours: 250. After 6 hours: 300 (or $6\times50=300$).

Answer: 300 miles

Exercise 17 – Water bottles

Games: 0, 2, 4, 6, 8, 10. Bottles: 0, 10, 20, 30, 40, 50.

Pair for 10 games: $(10, 50)$.

Answer: 50 bottles

Exercise 18 – Cookie boxes

Cookies: 0, 6, 12, 18. Dollars: 0, 4, 8, 12.

Pairs: $(0, 0), (6, 4), (12, 8), (18, 12)$.

For 18 cookies she earns $\$12$.

Exercise 19 – Saving money

Priya: 0, 5, 10, 15, 20, 25. Diego: 0, 10, 20, 30, 40, 50.

Pairs: $(0, 0), (5, 10), (10, 20), (15, 30), (20, 40), (25, 50)$.

Diego’s total is always 2 times Priya’s total.

Diego’s total is 2 times Priya’s.

Exercise 20 – Bike ride

(a) Minutes: 0, 15, 30, 45, 60. Miles: 0, 3, 6, 9, 12. Pairs: $(0, 0), (15, 3), (30, 6), (45, 9), (60, 12)$.

(b) Continue: 75 min is 15 miles, 90 min is 18 miles. 18 miles

All Grade 5 chapters: Grade 5 math.

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