Seventh Grade · Math · week 25

Consecutive-number puzzles

Translate consecutive-integer word problems into linear equations and solve for the unknown integers.

Consecutive integers are integers in a row, like 5, 6, 7 -- each one is one more than the last. If the first is called n, the next is n + 1, then n + 2, and so on. Consecutive EVEN or ODD integers instead skip by 2 each time: n, n + 2, n + 4.

Turn the puzzle into an equation by adding up all the expressions and setting the sum equal to the total given. Solve for n first, then use n to state every number the puzzle asked for.

📋 For the teacher
Teach it (10–15 min):
  • Write out the expressions for each integer BEFORE building the equation -- n, n+1, n+2 for regular integers, or n, n+2, n+4 for even or odd.
  • Remind them that "consecutive even" and "consecutive odd" both skip by 2, since every other integer is the same type (even or odd).
  • Always finish by stating every number the puzzle asked for, and check that they truly sum to the given total.
  • Try building one of these puzzles backwards -- pick three numbers first, then write the sum as the puzzle.
Talk about it:
  • How do consecutive integers differ from consecutive even or odd integers when writing expressions?
  • Why does checking your final numbers by adding them back up matter?
  • Could a "three consecutive integers" puzzle ever have a solution that is not a whole number? What would that tell you?

Mastery looks like: They correctly set up and solve a consecutive-integer equation, and state every number the puzzle asked for.

Common stumbles: Using n, n+1, n+2 for a consecutive EVEN or ODD puzzle instead of n, n+2, n+4; forgetting to state all the requested numbers at the end.

Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
Records attendance + 15 min of Math for this learner.
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