This problem solving activity has a number focus.
Maddie has a dart board on which the outer ring scores 3 points and the inner ring scores 7 points. Maddie has three darts.
What scores can Maddie get?
Maddie decides to change the rules. She can now add and subtract the 3s and 7s.
What possible positive scores can she get?
What whole positive numbers can Maddie get if she uses any of the four operations of addition, subtraction, multiplication and division?
This problem gives students the opportunity to be systematic in the way they combine numbers, and to be alert to number patterns.
Note that this is not a probability problem. The challenge is to see what scores can be made.
Maddie has a dart board on which the outer ring scores 3 points and the inner ring scores 7 points. Maddie has three darts.
Students could be given more darts; there might be different points for the two rings of the board; more rings could be used.
They might also be asked how many ways there are of getting each number, or of getting negative whole numbers.
Maddie can get three 3s; two 3s and a 7; one 3 and two 7s; or three 7s.
2 = 3x3 – 7 | 2 = (7 + 7) ÷ 7 | 2 = (3 + 3) ÷ 3 | 3 = 3 + 7 - 7 | 3 = 3 x 3 ÷ 3 |
3 = 3 x 7 ÷ 7 | 3 = 7 x 3 ÷ 7 | 3 = 3 ÷ 3 x 3 | 3 = 7 x 3 | 4 = 3 + 3/3 |
4 = 3 + 3/3 | 4 = 3 ÷3 + 3 | 4 = 3 + 7 ÷ 7 | 4 = 7 ÷7 + 3 | 6 = 3x3 – 3 |
7 = 3 ÷ 3 + 7 | 7 =7 x 7 ÷ 7 | 7 = 7 x 3 ÷ 3 | 7 = 3 x 7 ÷ 3 | 7 = 3 ÷3 x 7 |
7 = 7 ÷7 x 7 | 8 = 7 + 7/7 | 8 = 7 ÷ 7 + 7 | 10 = 7 + (3 ÷ 3) | 12 = 3 x 3 + 3 |
12 = (7 - 3) x 3 | 14 = 3 x7 – 7; | 16 = 3 x3 + 7; | 18 = 3x 7– 3 | 18 = (3 + 3) x 3 |
24 = 3 x 7+ 3 | 27 = 3 x 3 x 3 | 28 = (7 – 3)x7 | 28 = 3 x 7 + 7 | 30 = (7 + 3)x3 |
42 = (7 + 7)x3 | 42 = 7 x 7 + 7 | 42 = (3 + 3) x 7 | 46 = 7x7– 3 | 46 = 7x7– 3 |
52 = 7 x 7 + 3 | 56 = 7 x 7+ 7 | 63 = 3 x 3 x 7 | 70 = (7 + 3) x7 | 98 = (7 + 7)x 7 |
147 = 3 x7x7 | 343 = 7 x 7 x7 |
Note the systematic approach to finding these solutions.
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/darts at 8:56pm on the 26th February 2024