Posing Questions and Making Conjectures - Lower Secondary

Posing Questions and Making Conjectures is part of our Thinking Mathematically collection.

Summing Consecutive Numbers

Stage: 3 Challenge Level:

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

Pick's Theorem

Stage: 3 Challenge Level:

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.

Producing an Integer

Stage: 3 and 4 Short Challenge Level:

Weekly Problem 46 - 2011
Multiply a sequence of n terms together. Can you work out when this product is equal to an integer?

Pair Products

Stage: 4 Challenge Level:

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

Tilted Squares

Stage: 3 Challenge Level:

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

Squarely in the Middle

Stage: 3 Short Challenge Level:

Weekly Problem 20 - 2013
Can you calculate the answer to a large sum?

Odds and Evens

Stage: 3 and 4 Challenge Level:

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

Interactive Spinners

Stage: 3 and 4 Challenge Level:

This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.

White Box

Stage: 2, 3, 4 and 5 Challenge Level:

This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.

Difference Dynamics

Stage: 4 and 5 Challenge Level:

Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?

What Numbers Can We Make?

Stage: 3 Challenge Level:

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

Magic Letters

Stage: 3 Challenge Level:

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

Supercomputer

Stage: 4 Short Challenge Level:

Weekly Problem 28 - 2014
What is the units digit of the given expression?

Little Difference

Stage: 3 and 4 Short Challenge Level:

Weekly Problem 30 - 2014
What is the value of $2006 \times 2008 - 2007 \times 2007$?

Eulerian

Stage: 3 and 4 Short Challenge Level:

Weekly Problem 37 - 2014
Which of the five diagrams below could be drawn without taking the pen off the page and without drawing along a line already drawn?

Last-but-one

Stage: 3 Short Challenge Level:

Weekly Problem 1 - 2016
What is the last-but-one digit of 99! ?

Ones, Twos and Threes

Stage: 3 Short Challenge Level:

Weekly Problem 5 - 2017
Each digit of a positive integer is 1, 2 or 3, and each of these occurs at least twice. What is the smallest such integer that is not divisible by 2 or 3?

Leaning Over

Stage: 3 and 4 Short Challenge Level:

Weekly Problem 31 - 2017
The triangle HIJ has the same area as the square FGHI. What is the distance from J to the line extended through F and G?