Free Printable WorksheetMathGrade 5Math CurriculumVA 5.15

5.174 Use Tree Diagrams and the Fundamental Counting Principle Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Grade 5 Math worksheet provides structured practice on 5.174 Use Tree Diagrams and the Fundamental Counting Principle. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Skill description: Select the correct answer for identify a tree diagram or the Fundamental Counting Principle to count the number of possible outcomes for a two-stage event and identify probabilities. Select the interpretation or measure (mean, median, mode, range) that correctly answers the question about the data. Corresponding standards: VA 5.15.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Grade 5

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related 5.174 Use Tree Diagrams and the Fundamental Counting Principle skill assessments:

Problem 1Difficulty: Mastery
A color spinner has 6 colors, including blue. A number card is chosen from 1 through 5. What is the probability of not spinning blue and choosing an odd number?
A1/6
B1/3
C1/2
D5/6
Solution & Explanation:There are 6 × 5 = 30 outcomes. Not blue gives 5 color choices, and odd numbers are 1, 3, and 5, giving 3 number choices. 5 × 3 = 15 favorable outcomes, and 15/30 = 1/2.
Problem 2Difficulty: Mastery
Use the tree diagram shown. It has 24 endpoints, and each first-stage choice has 6 second-stage branches. Half of the first-stage choices are labeled indoor. How many endpoints are indoor outcomes?
Solution & Explanation:There are 24 / 6 = 4 first-stage choices. Half of 4 is 2 indoor choices. Each has 6 endpoints, so 2 × 6 = 12 indoor endpoints.
Problem 3Difficulty: Mastery
Which pair of stages would create exactly 32 equally likely outcomes?
A4 first-stage choices and 8 second-stage choices
B5 first-stage choices and 6 second-stage choices
C7 first-stage choices and 4 second-stage choices
D3 first-stage choices and 9 second-stage choices
Solution & Explanation:Multiply the two stages. 4 × 8 = 32, while the other choices give 30, 28, and 27.

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Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

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QIs this 5.174 Use Tree Diagrams and the Fundamental Counting Principle worksheet free for teachers and homeschoolers?

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Grade 5 Math students. It aligns with educational standard VA 5.15 (Primary standard selected for prompt fields in this prompt cell: VA 5.15. Skill statement in this prompt cell: Select the correct answer for identify a tree diagram or the Fundamental Counting Principle to count the number of possible outcomes for a two-stage event and identify probabilities. Select the interpretation or measure (mean, median, mode, range) that correctly answers the question about the data. Associated standards listed with this skill in this prompt cell: VA 5.15. Use this prompt-provided wording as the supporting standard description for this workflow.).

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