Problem Solving Leap Frog Investigation Starter Learning Objective

Problem Solving – Leap Frog Investigation Starter 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, 17. . . . 2) 2, 10, 18, 26, 34, 42. . . . 3) 19, 13, 7, 1, -5. . . . 4) 34, 25, 16, 7. . . . 5) 1, 4, 9, 16 ……

Where is Problem Solving useful?

The Riemann Hypothesis

What kind of student can solve problems?

Frogs

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

Slide

Jump

1 frog on both sides

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

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

What if we had two frogs on either side?

Leap Frogs • You need to use the following website to move the frogs to look for patterns with the frogs: https: //nrich. maths. org/content/00/12/game 1/frogs/inde 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.

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?

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

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

Number of Frogs (on each side) (n) Hops 1 1 2 4 3 9 4 16 5 25 n² Hops = n² H = n² Squared

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

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