1. Starter Problem Solving – Leap Frog Investigation
Learning Objective: Develop our problem solving skills Spot the Pattern Look for the pattern in the sequence of numbers and write the next 3 numbers in the pattern. Extension: Write the nth term. 1) 5, 8, 11, 14, ) 2, 10, 18, 26, 34, ) 19, 13, 7, 1, ) 34, 25, 16, ) 1, 4, 9, 16 ……

2. Where is Problem Solving useful?

4. The Riemann Hypothesis

5. What kind of student can solve problems?

6. Frogs
Investigation

7. Frogs Instructions: Frogs can JUMP over ONE frog to a free lily pad
Frogs can SLIDE to the NEXT free lily pad
Shortest number of moves needed to swap the yellow frogs with red frogs
Frogs not allowed to go back in their original direction

8. Slide

9. Jump

10. 1 frog on both sides

11. 1 frog on both sides
You need to find a way of recording your results

12. Can you move the red frogs to the right, and the green to left?
Number of Frogs
on each side (n)
Jumps
Slides
Total Moves 1 2 3 4 5
How many jumps did it take?
How many slides did it take?

13. What if we had two frogs on either side?

16. Leap Frogs
You need to use the following website to move the frogs to look for patterns with the frogs:
x.html#/student
(or just google “Nrich frogs student”)
In pairs, one person move the frogs and the other person count the number of jumps and slides.

17. What did you find?
What is the relationship between the number of frogs and the number of hops?
What is the relationship between the numbers of frogs and the number of slides?

18. Number of Frogs
(on each side) (n)
Jumps
Slides
Moves 1 2 3 4 5 1 2 3 4 4 8 9 6 15 16 8 24 25 10 35

19. n x 2 2n Slides = 2n S = 2n x 2 Slides Number of Frogs
(on each side) (n)
Slides 1 2 4 3 6 8 5 10
x 2
n x 2 2n
Slides = 2n
S = 2n

20. n² Hops = n² H = n² Squared Hops Number of Frogs (on each side) (n) 12 4 3 9 16 5 25
Squared n²
Hops = n²
H = n²

21. S = 2n H = n² Moves = n² + 2n M = n² + 2n + = Hops Slides Moves
Number of Frogs
(on each side) (n)
Hops
Slides
Moves 1 2 3 4 8 9 6 15 16 24 5 25 10 35 + =
H = n²
S = 2n
Moves = n² + 2n
M = n² + 2n

22. How can we extend the frogs problem?
What if we had different number frogs on each side?