5th Grade Patterns and Ordered Pairs Test with Answer Key (Free PDF)

5th grade numerical patterns test – Maths PDF

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

Key takeaway: This test helps fifth grade students show that they can write patterns from rules, form ordered pairs, graph them, and describe how two patterns are related.

Topic: Patterns and Ordered Pairs (5th grade)
Content: 9 questions with point values, about 45 minutes
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 test helps fifth grade students show that they can write patterns from rules, form ordered pairs, graph them, and describe how two patterns are related. Also, it is worth 20 points and takes 45 minutes.

The nine questions begin with two rules and ordered pairs of corresponding terms, then describe the relationship between two patterns. Then, later questions graph a pair of patterns, complete a table, read a graph, solve lemonade and reading stories, and check a classmate’s ordered pair. Also, show your work and label your graph.

This test covers numerical patterns, ordered pairs and graphing for Grade 5 (5.OA.B.3). It has 9 questions worth 20 points. You have 45 minutes. Show your terms and your ordered pairs. Use a ruler and a sharp pencil when you plot points. Calculators are not allowed.

Time and points

About this test

Grade: Grade 5
Chapter: Patterns and Ordered Pairs
Standards: 5.OA.B.3
Time: 45 minutes
Total: 20 points

5th grade numerical patterns test: questions

1 – Two rules [2 pts]

Pattern A: start at 0 and add 4. Pattern B: start at 0 and add 8. Write the first five terms of each pattern.

Pattern A (1 point)
Also, Pattern B (1 point)

2 – Ordered pairs [2 pts]

Pattern A: 0, 6, 12, 18, 24. Pattern B: 0, 2, 4, 6, 8. Write the five ordered pairs of corresponding terms.

3 – Relationship [2 pts]

Pattern A starts at 0 and adds 2. Pattern B starts at 0 and adds 10. Describe how the terms of B are related to the corresponding terms of A.

4 – Graph the pattern [3 pts]

Pattern A: start at 0, add 2. Pattern B: start at 0, add 3. Use the first four terms of each pattern.

Write the four ordered pairs. (1 point)
Plot the four points on the plane. (2 points)

Coordinate plane.

5 – Missing terms [2 pts]

Pattern A starts at 0 and adds 5. Pattern B starts at 0 and adds 15. Find the missing numbers in the table.

Find the two ? values.

6 – Read the graph [2 pts]

First, the graph shows corresponding terms of two patterns that start at 0. Write the rule for the first numbers and the rule for the second numbers. What is the second number when the first number is 12?

Points from two patterns.

Question 7 and after

7 – Lemonade stand [3 pts]

Noah makes lemonade. Pitchers: start at 0, add 1. Cups of lemonade: start at 0, add 8.

Write the ordered pairs for 0 to 4 pitchers. (2 points)
How many cups does Noah make with 7 pitchers? (1 point)

8 – Reading pages [3 pts]

Aisha reads at a steady pace. The table shows the first terms of the two patterns.

Aisha’s reading.

How many pages does Aisha read in 60 minutes? (1 point)
How many minutes does she need to read 20 pages? (2 points)

9 – Is the pair correct? [1 pt]

Pattern A starts at 0 and adds 6. Pattern B starts at 0 and adds 10. Ethan says that \((12, 18)\) is a pair of corresponding terms. Is he correct? Explain.

Key facts behind this 5th grade numerical patterns test

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 test

Students pair terms from different positions. Also, pair terms in the same position. Slow down at that step and check it twice.
Students describe a relationship with add when it is multiply. Divide the second term by the first to test.
Students plot (y, x) instead of (x, y). Move right by the first number, then up. Slow down at that step and check it twice.
Students accept a classmate’s pair without checking positions. Instead, find both terms in the same position. Slow down at that step and check it twice.

Test-taking strategy

Write the position of each term above your lists. Finally, this keeps your pairs correct. Repeat this habit on every problem for the best results.
Label both axes on your graph. Labels are part of a complete answer. Repeat this habit on every problem for the best results.
Parents can review the night before by asking the child to make two patterns and write their ordered pairs.

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

5th grade numerical patterns test: frequently asked questions

How do I graph two patterns?

Write ordered pairs from corresponding terms, then plot each pair. Label the axes and use equal spacing. Points from patterns with fixed steps line up on a straight line. A quick check like this takes only a few seconds and prevents most errors.

How do I explain the relationship between two patterns?

State how the second terms compare with the first terms, such as five times as large, and show one or two pairs as evidence. Use the pairs to check your rule. A quick check like this takes only a few seconds and prevents most errors.

How do I check whether a classmate’s pair is correct?

Find the terms in the same position in both patterns. If the classmate’s numbers do not match those terms, the pair is wrong. Then write the correct pair. A quick check like this takes only a few seconds and prevents most errors.

All Grade 5 chapters: Grade 5 math.

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