Math Competition Problems Vol. 1: Number Theory 15 Problems (Grades 6-8)

Description

Challenge students with competition-style math problems designed to develop deep reasoning, strategic thinking, and persistence. This set of 15 non-routine number theory problems reflects the style and rigor of middle school math competitions such as AMC 8 and MathCounts, moving beyond basic practice to focus on structure, patterns, and mathematical insight.

Problems are intentionally sequenced by difficulty and require students to think flexibly, justify their reasoning, and apply multiple strategies—key skills for success in math competitions and advanced problem solving.

This resource is ideal for:

Math club and competition preparation
Gifted and advanced learners
Enrichment lessons and challenge days
Early finishers who need rigorous, meaningful work
Small-group or whole-class problem-solving sessions

Each problem is designed to feel purposeful and challenging rather than procedural, helping students build confidence and independence as mathematical thinkers.

⭐ Difficulty Levels

Problems are labeled to support differentiation and scaffolding:

★ Warm-Up: Accessible competition-style problems that introduce key ideas
★★ Core: Standard competition-level problems requiring multi-step reasoning
★★★ Challenge: Advanced problems designed to stretch students and reflect upper-level AMC 8 / MathCounts difficulty

What’s Included:

Student Version (PDF): A clean, print-ready worksheet containing all 15 competition-style problems, formatted for classroom or math club use.
Teacher Answer Key (PDF): A complete answer key with clear, competition-appropriate solutions and one-line hints for instructional support.
Slides Presentation (.pptx): A digital presentation with problems and solutions, ideal for projecting, whole-class discussion, or uploading to Google Slides for digital use.

Grade Level:

Grades 6–8 (appropriate for advanced 5th grade or early high school enrichment)

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Math Competition Problems Vol. 1: Number Theory 15 Problems (Grades 6-8)

Name: Math Competition Problems Vol. 1: Number Theory 15 Problems (Grades 6-8)
Brand: Chalkboard Puzzles
SKU: 15118403
Price: 4.00 USD
Availability: InStock

Chalkboard Puzzles

$4.00

Highlights

Digital downloads

Microsoft PowerPoint, PDF

Grades

6th - 8th

Subjects

Math Test Prep, Numbers, Other (Math)

Standards

CCSS6.NS.B.4

CCSSMP1

CCSSMP2

Description

This resource is ideal for:

Math club and competition preparation
Gifted and advanced learners
Enrichment lessons and challenge days
Early finishers who need rigorous, meaningful work
Small-group or whole-class problem-solving sessions

Each problem is designed to feel purposeful and challenging rather than procedural, helping students build confidence and independence as mathematical thinkers.

⭐ Difficulty Levels

Problems are labeled to support differentiation and scaffolding:

★ Warm-Up: Accessible competition-style problems that introduce key ideas
★★ Core: Standard competition-level problems requiring multi-step reasoning
★★★ Challenge: Advanced problems designed to stretch students and reflect upper-level AMC 8 / MathCounts difficulty

What’s Included:

Student Version (PDF): A clean, print-ready worksheet containing all 15 competition-style problems, formatted for classroom or math club use.
Teacher Answer Key (PDF): A complete answer key with clear, competition-appropriate solutions and one-line hints for instructional support.
Slides Presentation (.pptx): A digital presentation with problems and solutions, ideal for projecting, whole-class discussion, or uploading to Google Slides for digital use.

Grade Level:

Grades 6–8 (appropriate for advanced 5th grade or early high school enrichment)

Report this resource to TPT

Reported resources will be reviewed by our team. Report this resource to let us know if this resource violates TPT's content guidelines.

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Questions & Answers

Standards

to see state-specific standards (only available in the US).

CCSS6.NS.B.4

Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).

CCSSMP1

Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

CCSSMP2

Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize-to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.