Number Evidence
About This Worksheet
This worksheet helps sixth-grade students analyze statements about factors, multiples, prime numbers, and greatest common factors. Each “mystery file” includes a mathematical claim that contains an error, and students must find the mistake and correct the statement. The activity asks students to use number theory ideas as evidence instead of simply completing a calculation. That makes it especially useful for checking whether students truly understand the meaning of terms like factor, multiple, prime, and GCF. It also gives them practice explaining why a claim is right or wrong.
What Students Practice
Students inspect number statements involving factor lists, multiples, prime numbers, least common multiples, and greatest common factors. They decide which part of each statement is incorrect and rewrite the idea so it becomes mathematically accurate. Some problems require students to list missing factors or multiples, while others ask them to reconsider whether a number is prime or whether a GCF or LCM has been identified correctly. This gives students a broad review of several number theory concepts in one activity. The explanation piece also pushes them to think beyond simply producing a corrected number.
Why This Matters
Students often memorize definitions without fully understanding how the ideas are connected. Error analysis helps reveal whether they can actually recognize a valid factor list, a correct multiple pattern, or a reasonable GCF or LCM. It also teaches them to question mathematical statements and support corrections with evidence. That kind of reasoning is important in later algebra, where students must check whether expressions, equations, and solutions are valid. Building this habit now can make students more careful and confident problem solvers.
Teaching Tips
Ask students to underline the exact part of each statement that seems suspicious before they make a correction. Encourage them to prove their thinking with multiplication, division, or a short factor or multiple list. If they are unsure, have them return to the definition of the term being used rather than guessing. You can also let students compare corrections with a partner and explain why their version is more accurate. This makes the worksheet especially useful for discussion-based review.
Curriculum Standards
This worksheet supports CCSS.MATH.CONTENT.6.NS.B.4 by reinforcing greatest common factors, least common multiples, and the factor relationships that support those skills. It also reviews prime and composite number reasoning as an important number theory foundation. Because students must critique and correct mathematical statements, the activity also supports mathematical communication and reasoning. It works well for review, formative assessment, partner work, or intervention near the end of a number theory unit.