Year 7 Exploring and noticing

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

The Number Jumbler can always work out your chosen symbol. Can you work out how?

Can you select the missing digit(s) to find the largest multiple?

Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?

Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

Can you work as a team to make doughnuts by matching these fractions, decimals and percentages?

The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the ten numbered shapes?

How many different number families can you find?

Choose some fractions and add them together. Can you get close to 1?

Can you explain the strategy for winning this game with any target?

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?

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a parallelogram.

In the 2020 Olympic Games, sport climbing was introduced for the first time, and something very interesting happened with the scoring system. Can you find out what was interesting about it?

How many different symmetrical shapes can you make by shading triangles or squares?

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Are these games fair? How can you tell?

Find the frequency distribution for ordinary English, and use it to help you crack the code.

Explore the effect of reflecting in two parallel mirror lines.

Here is a chance to play a fractions version of the classic Countdown Game.

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?

Can you find a way to identify times tables after they have been shifted up or down?

Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...

Create some shapes by combining two or more rectangles. What can you say about the areas and perimeters of the shapes you can make?

Follow this recipe for sieving numbers and see what interesting patterns emerge.

Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...

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

Imagine a very strange bank account where you are only allowed to do two things...

Can you find sets of numbers which satisfy each of our mean, median, mode and range conditions?

Can you figure out how sequences of beach huts are generated?

By selecting digits for an addition grid, what targets can you make?

How many ways can you find to put in operation signs (+, −, ×, ÷) to make 100?

Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?

If you move the tiles around, can you make squares with different coloured edges?

In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?

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?

Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...