Comparing Possible Solutions · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Comparing Possible Solutions

Science · Scientific Inquiry · ages 8-11
Name ______________________   Date ____________

  1. A puzzle asks you to make the number 64 by multiplying the same number again and again. Which of these really makes 64?

    • 7 times 7 times 7
    • 8 times 8
    • 9 times 9
    • 6 times 6 times 6

  2. Before comparing solutions, what should you do first?

    • Think of several possible solutions
    • Pick the first idea
    • Build the solution right away

  3. It is a good idea to think of only one solution and go with it.

    Circle one:   True   False

  4. What do you compare your solutions against?

    • Which one looks the prettiest
    • The criteria and constraints of the problem
    • Which one you thought of first

  5. Three answers all solve the make-64 puzzle and follow the digit rule: 2 to the power 6, 4 to the power 3, and 8 to the power 2. The puzzle maker adds a wish: please use the smallest bottom number you can. Which answer should you pick, and why?

    • 8 to the power 2, because it is the shortest to write
    • 2 to the power 6, because its bottom number 2 is the smallest
    • 4 to the power 3, because it is in the middle

  6. The puzzle has a rule: you may use each digit from 1 to 9 only one time. Three kids wrote answers: 2 to the power 6, 4 to the power 4, and 8 to the power 2. Which answer breaks the rule?

    • 2 to the power 6
    • 4 to the power 4
    • 8 to the power 2

  7. Three boat designs were tested for how many coins they held before sinking. Which design held the most coins? Type the number.

    Boat A4Boat B9Boat C6

    Answer: ______________

  8. This bar chart shows how many blocks each bridge design held before breaking. The goal is to hold the most weight. Which design meets the goal best?

    Design A3Design B6Design C4
    • Design A
    • Design C
    • Design B

  9. Mia is building an equation puzzle. She wants it to have exactly one answer. She knows a trick: if the x part is the same on both sides, the puzzle breaks. Which of her tries has exactly one answer?

    • 3x + 2 = 3x + 5
    • 2x + 1 = 3x + 4
    • 4x + 1 = 4x + 1

  10. Maya has three paper parachute plans. The goal is to fall slowly, and the constraint is to use only one sheet of paper. Plan A falls slowly but uses two sheets. Plan B falls fast and uses one sheet. Plan C falls slowly and uses one sheet. Which plan should Maya choose?

    • Plan A
    • Plan B
    • Plan C
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Comparing Possible Solutions W1-mt_HveO1bOXpJ-s1

  1. 8 times 8 · 8 times 8 equals 64, so that is a correct solution to the puzzle.
  2. Think of several possible solutions · You need more than one idea to compare, so start by coming up with several possible solutions.
  3. False · Thinking of several solutions gives you more to compare, so you have a better chance of finding the best fit.
  4. The criteria and constraints of the problem · The criteria and constraints tell you what the solution needs to do and what rules it must follow.
  5. 2 to the power 6, because its bottom number 2 is the smallest · All three answers work, so you compare them against the new wish. The bottom numbers are 2, 4, and 8, and 2 is the smallest.
  6. 4 to the power 4 · 4 to the power 4 uses the digit 4 two times, and the rule says each digit can be used only once.
  7. 9 · Comparing the three numbers, 9 is the largest, so that design held the most coins.
  8. Design B · Design B's bar is tallest, so it held the most weight and best meets the goal.
  9. 2x + 1 = 3x + 4 · Only the middle equation has a different x part on each side, so exactly one number makes it true.
  10. Plan C · Plan C is the only one that meets both the goal of falling slowly and the constraint of one sheet of paper.
Worksheet · LightMySky