Adding Ones

Goals

• • Number Sense

  • Problem Solving

  • Factorization

What To Do

• 1. Explain the game

     1. Pick a number, start with a low 2 digit number, e.g. 18

     2. The challenge is to make a sum adding up to your number using only 1's, and using as few as possible.

     3. for the example of 18 here are some possible solutions

        1. (1+1+1+1+1+1+1+1+1) * (1+1) Total ones: 11

        2. (1+1+1+1+1+1)*(1+1+1) Total ones: 9

        3. (1+1)*(1+1+1)*(1+1+1) Total ones: 8 - this is the winner

  2. Work in pairs and get each pair of kids to pick a 2-digit number. They must find the lowest number of ones that can be used to make the number.

  3. After a few minutes record each of the numbers chosen and the least number of ones found for each number, but not any of the solutions.

  4. Now rotate the numbers used between groups and see if another group can find the best solution and even improve on it

  5. At the end get the the kids to show their best solutions for each number

  6. Repeat the game again

  7. Discuss strategies for finding the least number of ones

Homework

• • Workout the 'least ones' for the following numbers

    • Beginner

      • 36

      • 27

      • 40

    • Intermediate

      • 72

      • 63

    • Hard

      • 49

Adding Complexity

• • For a more advanced version of the game (5/6th grade):

    • allow the use of powers, as well as addition, subtraction and multiplication

    • use a 3 digit number to find a solution for

Background Information