Posing Questions and Making Conjectures
Magic Letters
Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
Summing Consecutive Numbers
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
Spaces for Exploration
Alf Coles writes about how he tries to create 'spaces for exploration' for the students in his classrooms.
How Much Can We Spend?
A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?
Interactive Spinners
This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.
Tilted Squares
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
What Numbers Can We Make?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Can They Be Equal?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
Where Can We Visit?
Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?
Consecutive Negative Numbers
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Posing Questions and Making Conjectures - Short Problems
A collection of short Stage 3 and 4 problems on Posing Questions and Making Conjectures.
Charlie's Delightful Machine
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Arithmagons
Can you find the values at the vertices when you know the values on the edges?
Cuboid Challenge
What's the largest volume of box you can make from a square of paper?
Searching for Mean(ing)
If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?
A Little Light Thinking
Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?
Pair Products
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
Pick's Theorem
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
Multiplication Arithmagons
Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?
Impossible Triangles?
Which of these triangular jigsaws are impossible to finish?