Problems
Jumping Cricket
Stage:1 Challenge Level:
El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?
Chocs, Mints, Jellies
Stage:1 Challenge Level:
In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do it?
The Big Cheese
Stage:2 Challenge Level:
Investigate the area of 'slices' cut off this cube of cheese. What would happen if you had different sized blocks of cheese to start with?
Pasta Timing
Stage:2 Challenge Level:
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
Pizza Cut
Stage:2 Challenge Level:
Using only 6 straight cuts, find a way to make as many pieces of pizza as possible. (The pieces can be different sizes and shapes).
Wonky Watches
Stage:2 Challenge Level:
Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.
World of Tan - Sports Car
Stage:2 Challenge Level:
Can you fit the tangram pieces into the outline of this sports car?
Differs
Stage:3 Challenge Level:
Choose any 4 whole numbers and take the difference between consecutive numbers, ending with the difference between the first and the last numbers. What happens when you repeat this process over and. . . .
Quick Times
Stage:3 Challenge Level:
32 x 38 = 30 x 40 + 2 x 8; 34 x 36 = 30 x 40 + 4 x 6; 56 x 54 = 50 x 60 + 6 x 4; 73 x 77 = 70 x 80 + 3 x 7 Verify and generalise if possible.
F'arc'tion
Stage:3 Challenge Level:
At the corner of the cube circular arcs are drawn and the area enclosed shaded. What fraction of the surface area of the cube is shaded? Try working out the answer without recourse to pencil and. . . .
Ratty
Stage:3 Challenge Level:
If you know the sizes of the angles marked with coloured dots in this diagram which angles can you find by calculation?
Mathematical Swimmer
Stage:3 Challenge Level:
Twice a week I go swimming and swim the same number of lengths of the pool each time. As I swim, I count the lengths I've done so far, and make it into a fraction of the whole number of lengths. . . .
Area I'n It
Stage:4 Challenge Level:
Triangle ABC has altitudes h1, h2 and h3. The radius of the inscribed circle is r, while the radii of the escribed circles are r1, r2 and r3 respectively. Prove: 1/r = 1/h1 + 1/h2 + 1/h3 = 1/r1 +. . . .
Rollerball
Stage:4 Challenge Level:
Last weekend Mrs Shoe won a prize and she gave her winnings to her children in order. After sharing out her winnings in this way she found that she had divided the money equally amongst all. . . .
Arc Invariant
Stage:4 Challenge Level:
Two perpendicular chords of a circle meet at a point P inside the circle and cut off arcs a, b, c and d on the circumference of the circle. What is the relationship between the arcs a, b, c and d?
Bendy Quad
Stage:4 Challenge Level:
Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.
LOGO Challenge - Sequences and Pentagrams
Stage:3, 4 and 5 Challenge Level:
Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?
Summats Clear
Stage:5 Challenge Level:
Find the sum, f(n), of the first n terms of the sequence: 0, 1, 1, 2, 2, 3, 3........p, p, p +1, p + 1,..... Prove that f(a + b) - f(a - b) = ab.
Rain or Shine
Stage:5 Challenge Level:
Predict future weather using the probability that tomorrow is wet given today is wet and the probability that tomorrow is wet given that today is dry.
