Functions and Graphs - Stage 3

KS 4 Challenge Level:

In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

Walk and Ride

KS 2 & 3 Challenge Level:

How far have these students walked by the time the teacher's car reaches them after their bus broke down?

How Far Does it Move?

KS 3 Challenge Level:

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.

Speeding Up, Slowing Down

KS 3 Challenge Level:

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.

Up and Across

KS 3 Challenge Level:

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its vertical and horizontal movement at each stage.

Parallel Lines

KS 3 Challenge Level:

How does the position of the line affect the equation of the line? What can you say about the equations of parallel lines?

Perpendicular Lines

KS 3 Challenge Level:

Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?

Diamond Collector

KS 3 Challenge Level:

Collect as many diamonds as you can by drawing three straight lines.

Negatively Triangular

KS 4 Challenge Level:

How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?

Maths Filler

KS 4 Challenge Level:

Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?

At Right Angles

KS 3 Challenge Level:

Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?

Reflecting Lines

KS 3 Challenge Level:

Investigate what happens to the equations of different lines when you reflect them in one of the axes. Try to predict what will happen. Explain your findings.

Translating Lines

KS 3 Challenge Level:

Investigate what happens to the equation of different lines when you translate them. Try to predict what will happen. Explain your findings.

Surprising Transformations

KS 3 Challenge Level:

I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?

How Steep Is the Slope?

KS 3 Challenge Level:

On the grid provided, we can draw lines with different gradients. How many different gradients can you find? Can you arrange them in order of steepness?

Exploring Simple Mappings

KS 3 Challenge Level:

Explore the relationship between simple linear functions and their graphs.

Fill Me Up

KS 3 Challenge Level:

Can you sketch graphs to show how the height of water changes in different containers as they are filled?

Functions and Graphs Stage 3 - Short Problems

KS 3 & 4

A collection of short Stage 3 and 4 problems on straight line graphs.

Lattice Points on a Line

KS 3 Short Challenge Level:

How many lattice points are there in the first quadrant that lie on the line 3x + 4y = 59 ?