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Patterns and Relationships - Worksheet 8 - 5th Grade

Hard

Apply and compare explicit arithmetic rules to inputs and sequences.

hard: Use another set to practice explaining and checking your answers.

18 problems · 15-20 minutes · Skills: algebraic thinking, patterns

About This Worksheet

This hard-level worksheet contains 18 problems designed for 5th Grade students practicing patterns and relationships. Hard worksheets feature challenging problems including multi-step questions, missing values, and real-world applications to push students further.

Use signed arithmetic, substitute values and read expressions with variables.

  • Apply and compare explicit arithmetic rules to inputs and sequences.
  • Check your result using the method in the example before moving to the next question.

How to Solve: Worked Example

Example Problem: Sequence A starts at 0 and adds 5 each step. Sequence B starts at 0 and adds 35 each step. What is the value of B after 5 steps?
Solution Steps:
  1. Sequence B adds 35 per step.
  2. Multiply by 5 steps.
Answer: 175
Tip: Check your result using the method in the example before moving to the next question.
1
Sequence A starts at 0 and adds 3 each step. Sequence B starts at 0 and adds 3 each step. What is the value of B after 5 steps?
2
Sequence A starts at 0 and adds 9 each step. Sequence B starts at 0 and adds 63 each step. What is the value of B after 8 steps?
3
Sequence A starts at 0 and adds 8 each step. Sequence B starts at 0 and adds 72 each step. What is the value of B after 8 steps?
4
Sequence A starts at 0 and adds 2 each step. Sequence B starts at 0 and adds 8 each step. What is the value of B after 4 steps?
5
Sequence A starts at 0 and adds 5 each step. Sequence B starts at 0 and adds 25 each step. What is the value of B after 11 steps?
6
Sequence A starts at 0 and adds 3 each step. Sequence B starts at 0 and adds 27 each step. What is the value of B after 6 steps?
7
Sequence A starts at 0 and adds 8 each step. Sequence B starts at 0 and adds 56 each step. What is the value of B after 2 steps?
8
Sequence A starts at 0 and adds 2 each step. Sequence B starts at 0 and adds 14 each step. What is the value of B after 11 steps?
9
Sequence A starts at 0 and adds 9 each step. Sequence B starts at 0 and adds 72 each step. What is the value of B after 10 steps?
10
Sequence A starts at 0 and adds 7 each step. Sequence B starts at 0 and adds 63 each step. What is the value of B after 2 steps?
11
Sequence A starts at 0 and adds 2 each step. Sequence B starts at 0 and adds 6 each step. What is the value of B after 2 steps?
12
Sequence A starts at 0 and adds 3 each step. Sequence B starts at 0 and adds 6 each step. What is the value of B after 2 steps?
13
Sequence A starts at 0 and adds 5 each step. Sequence B starts at 0 and adds 35 each step. What is the value of B after 3 steps?
14
Sequence A starts at 0 and adds 7 each step. Sequence B starts at 0 and adds 7 each step. What is the value of B after 4 steps?
15
Sequence A starts at 0 and adds 2 each step. Sequence B starts at 0 and adds 6 each step. What is the value of B after 12 steps?
16
Sequence A starts at 0 and adds 3 each step. Sequence B starts at 0 and adds 9 each step. What is the value of B after 6 steps?
17
Sequence A starts at 0 and adds 7 each step. Sequence B starts at 0 and adds 28 each step. What is the value of B after 9 steps?
18
Sequence A starts at 0 and adds 2 each step. Sequence B starts at 0 and adds 6 each step. What is the value of B after 9 steps?

Answer Key

1. 152. 5043. 5764. 325. 2756. 1627. 1128. 1549. 72010. 12611. 1212. 1213. 10514. 2815. 7216. 5417. 25218. 54

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Frequently Asked Questions

How do I download this patterns and relationships - worksheet 8 worksheet?

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How do I find worksheets at different difficulty levels?

Each subtopic has 10 worksheets: Worksheets 1-3 are Easy, 4-7 are Medium, and 8-10 are Hard. Start with Easy worksheets to build confidence, then progress to harder ones.

What skills does this algebraic thinking worksheet cover?

This worksheet focuses on algebraic thinking, patterns. It is designed for 5th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.

Can I use this worksheet in my classroom?

Yes. All worksheets on K12Worksheets are free for classroom use. You can print copies for your entire class. With 10 worksheets per subtopic at three difficulty levels, you have plenty of options for differentiated instruction and individualized practice.

How many problems are on this worksheet?

This worksheet contains 18 problems. It typically takes 15-20 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.