5th Grade Patterns and Ordered Pairs Worksheets with Answers (Free PDF)

5th grade numerical patterns worksheet – Maths PDF

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This 5th grade numerical patterns worksheet covers patterns and ordered pairs (Common Core 5.OA.B.3), with a free PDF to print.

Key takeaway: This worksheet helps fifth grade students practice writing patterns from rules, forming ordered pairs, and describing relationships between two patterns.

Topic: Patterns and Ordered Pairs (5th grade)
Content: 20 worksheet problems, from easy to challenging
Standards: 5.OA.B.3
Answers: On a separate page, so you can try every worksheet problem first
Format: Free printable PDF, US Letter, black and white

This worksheet helps fifth grade students practice writing patterns from rules, forming ordered pairs, and describing relationships between two patterns. Also, tables, graphs, and real situations such as costs, miles, and savings show why the patterns match.

There are 20 problems. The first six write terms and ordered pairs from two rules and compare corresponding terms. The next six plot pairs, find a missing pair, find rules from pairs, and read a graph. Then, the last eight are word problems about apples, a road trip, water bottles, cookie boxes, savings, and a bike ride. Also, allow about 35 minutes.

These 20 problems practice numerical patterns and ordered pairs (Common Core 5.OA.B.3). You will extend patterns made by two rules, write corresponding terms as ordered pairs, find how the terms are related, and plot points on a coordinate plane.

The first problems are short pattern checks. The last six are word problems about money, miles and games. Write every term you find before you answer.

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

5th grade numerical patterns worksheet: worksheet problems 1 to 10

1 – Add 5 pattern

First, write the first six terms of this pattern. Start at 0 and add 5.

2 – Add 4 pattern

Next, write the first six terms of this pattern. Start at 0 and add 4.

3 – Two rules

Pattern A: start at 0 and add 2. Pattern B: start at 0 and add 6. Write the first five terms of each pattern.

Fill in the boxes.

4 – Write ordered pairs

Pattern A: 0, 3, 6, 9. Pattern B: 0, 9, 18, 27. Write the four ordered pairs of corresponding terms.

5 – Fill in the table

Pattern A starts at 0 and adds 5. Pattern B starts at 0 and adds 10. Copy and complete the table.

Find the two missing numbers.

6 – Compare terms

Pattern A: 0, 3, 6, 9. Pattern B: 0, 12, 24, 36. How do the terms in B compare with the corresponding terms in A?

7 – Plot four points

Next, plot the ordered pairs $(0, 0), (1, 3), (2, 6), (3, 9)$ on a coordinate plane like the one shown.

Plot the points.

Worksheet problem 8 and after

8 – Pairs from two rules

Pattern A starts at 0 and adds 7. Pattern B starts at 0 and adds 3. Write the first four ordered pairs. Which coordinate grows faster?

9 – Find the missing pair

Now, these ordered pairs come from two patterns: $(0, 0), (2, 6), (4, 12), (6, ?), (8, 24)$. Find the missing number.

10 – Find the rules

Also, the ordered pairs $(0, 0), (5, 10), (10, 20), (15, 30)$ come from two patterns. Write the rule for each pattern and tell how the terms are related.

Worksheet problems 11 and up

11 – Smaller second pattern

Pattern A: start at 0, add 6. Pattern B: start at 0, add 3. Write the first four ordered pairs and describe how the terms are related.

12 – Read the graph

Next, the graph shows ordered pairs from two patterns that start at 0. Write the ordered pairs, write the rule for each pattern, and tell the second number when the first number is 8.

Four points on a graph.

13 – Which pairs belong?

Pattern A starts at 0 and adds 3. Pattern B starts at 0 and adds 6. Which of these ordered pairs come from the patterns? $(6, 12), (9, 15), (12, 24)$

14 – Liam's pair

Pattern A starts at 0 and adds 4. Pattern B starts at 0 and adds 8. Liam says that $(4, 12)$ is a pair of corresponding terms. Explain his mistake and give the correct pair.

15 – Farmers market apples

Also, at the farmers market, Maya buys bags of apples. Each bag costs $\$3$. Number of bags: start at 0, add 1. Total cost: start at 0, add 3. Write the ordered pairs for 0 to 4 bags and tell the cost of 4 bags.

Each bag costs $3.

Worksheet problem 16 and after

16 – Road trip

Jamal’s family drives 50 miles each hour. Hours: start at 0, add 1. Miles: start at 0, add 50. Write the ordered pairs for 0 to 4 hours. How many miles do they drive in 6 hours?

17 – Water bottles

Next, a Little League team plays games. Games: start at 0, add 2. Water bottles used: start at 0, add 10. How many water bottles are used in 10 games?

18 – Cookie boxes

Sofia packs cookies at a bake sale. Cookies: start at 0, add 6. Dollars earned: start at 0, add 4. Write the first four ordered pairs. How many dollars does she earn for 18 cookies?

19 – Saving money

Priya saves $\$5$ each week. Diego saves $\$10$ each week. Both start with $\$0$. Write ordered pairs (Priya’s total, Diego’s total) for weeks 0 to 5. How does Diego’s total compare with Priya’s?

Plot the pairs here if you like.

20 – Bike ride

Mei rides her bike 3 miles every 15 minutes. Minutes: start at 0, add 15. Miles: start at 0, add 3. (a) Write the ordered pairs for 0 to 60 minutes. (b) How many miles does she ride in 90 minutes? (c) How many minutes does it take to ride 21 miles?

Key facts behind this 5th grade numerical patterns worksheet

Key facts

Each number in a pattern is called a term.
Corresponding terms are the terms in the same position in two patterns.
In an ordered pair (x, y), x tells how far right and y tells how far up.
Then, if one pattern adds twice as much as the other, its terms are twice as large.
Points from patterns that add the same amount each time lie on a straight line.

Common mistakes with this 5th grade numerical patterns worksheet

Students pair the first term of one pattern with the second term of the other. Also, pair terms in the same position.
Students describe a relationship as add when it is multiply. Instead, test whether the ratio of the terms is the same for every pair.
Students write ordered pairs as (y, x). The first number comes from the first pattern. Slow down at that step and check it twice.
Students stop at a table without answering the story question. Also, use the pattern to find the value asked.

Tips before you start the worksheet problems

Write the position number above each pair of terms. Also, it makes sure that you match the right terms.
Check your rule on every pair. Then, if one pair breaks the rule, rethink it. Repeat this habit on every problem for the best results.
Teachers can ask students to explain one graph by describing how the points line up. Repeat this habit on every problem for the best results.

Download the 5th grade numerical patterns worksheet as a PDF with the button below and keep it with your notes.

5th grade numerical patterns worksheet: frequently asked questions

How do you write the rule for a pattern from a list?

Find what is added or multiplied each time and state the start. For 0, 8, 16, 24, the rule is start at 0 and add 8. Check the rule on every neighboring pair. A quick check like this takes only a few seconds and prevents most errors.

How do you use a pattern to answer a question about a later term?

Continue the pattern or use the relationship. If pages go up by 4 every 2 minutes, then 10 minutes is 5 steps of 4, so 20 pages. Use a table to keep track. A quick check like this takes only a few seconds and prevents most errors.

How do you decide whether an ordered pair belongs to two patterns?

Find the terms in the same position in both patterns and compare. If the pair’s first number is the third term of the first pattern, its second number must be the third term of the second.

All Grade 5 chapters: Grade 5 math.

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