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Broad Topics > Sequences, Functions and Graphs > Graphs

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Mathsjam Jars

Stage: 4 Challenge Level: Challenge Level:1

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

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Exploring Quadratic Mappings

Stage: 4 Challenge Level: Challenge Level:1

Explore the relationship between quadratic functions and their graphs.

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Exploring Simple Mappings

Stage: 3 Challenge Level: Challenge Level:1

Explore the relationship between simple linear functions and their graphs.

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Surprising Transformations

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Translating Lines

Stage: 3 Challenge Level: Challenge Level:1

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

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Reflecting Lines

Stage: 3 Challenge Level: Challenge Level:1

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.

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Immersion

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Various solids are lowered into a beaker of water. How does the water level rise in each case?

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Maths Filler

Stage: 4 Challenge Level: Challenge Level:1

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

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Equation Matcher

Stage: 5 Challenge Level: Challenge Level:1

Can you match these equations to these graphs?

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Real-life Equations

Stage: 5 Challenge Level: Challenge Level:1

Here are several equations from real life. Can you work out which measurements are possible from each equation?

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Diamond Collector

Stage: 3 Challenge Level: Challenge Level:1

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

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Matchless

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

There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?

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Perpendicular Lines

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Parallel Lines

Stage: 3 Challenge Level: Challenge Level:1

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

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Spaces for Exploration

Stage: 3 and 4

Alf Coles writes about how he tries to create 'spaces for exploration' for the students in his classrooms.

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Steady Free Fall

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Can you adjust the curve so the bead drops with near constant vertical velocity?

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Up and Across

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

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Speeding Up, Slowing Down

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

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How Far Does it Move?

Stage: 3 Challenge Level: Challenge Level:1

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.

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Exponential Trend

Stage: 5 Challenge Level: Challenge Level:1

Find all the turning points of y=x^{1/x} for x>0 and decide whether each is a maximum or minimum. Give a sketch of the graph.

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Fence It

Stage: 3 Challenge Level: Challenge Level:1

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

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Walk and Ride

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Cubics

Stage: 4 and 5 Challenge Level: Challenge Level:1

Knowing two of the equations find the equations of the 12 graphs of cubic functions making this pattern.

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Parabolas Again

Stage: 4 and 5 Challenge Level: Challenge Level:1

Here is a pattern composed of the graphs of 14 parabolas. Can you find their equations?

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Parabella

Stage: 5 Challenge Level: Challenge Level:1

This is a beautiful result involving a parabola and parallels.

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Parabolic Patterns

Stage: 4 and 5 Challenge Level: Challenge Level:1

The illustration shows the graphs of fifteen functions. Two of them have equations y=x^2 and y=-(x-4)^2. Find the equations of all the other graphs.

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How Many Solutions?

Stage: 5 Challenge Level: Challenge Level:1

Find all the solutions to the this equation.

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More Realistic Electric Kettle

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

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Interpolating Polynomials

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.

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What's That Graph?

Stage: 4 Challenge Level: Challenge Level:1

Can you work out which processes are represented by the graphs?

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Electric Kettle

Stage: 4 Challenge Level: Challenge Level:1

Explore the relationship between resistance and temperature

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Which Is Bigger?

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?

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Which Is Cheaper?

Stage: 4 Challenge Level: Challenge Level:1

When I park my car in Mathstown, there are two car parks to choose from. Which car park should I use?

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Quadratic Transformations

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Explore the two quadratic functions and find out how their graphs are related.

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More Quadratic Transformations

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Here are some more quadratic functions to explore. How are their graphs related?

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Guess the Function

Stage: 5 Challenge Level: Challenge Level:1

This task depends on learners sharing reasoning, listening to opinions, reflecting and pulling ideas together.

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Steve's Mapping

Stage: 5 Challenge Level: Challenge Level:1

Steve has created two mappings. Can you figure out what they do? What questions do they prompt you to ask?

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Alison's Mapping

Stage: 4 Challenge Level: Challenge Level:1

Alison has created two mappings. Can you figure out what they do? What questions do they prompt you to ask?

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Charlie's Mapping

Stage: 3 Challenge Level: Challenge Level:1

Charlie has created a mapping. Can you figure out what it does? What questions does it prompt you to ask?

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Graphic Biology

Stage: 5 Challenge Level: Challenge Level:1

Several graphs of the sort occurring commonly in biology are given. How many processes can you map to each graph?

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Four on the Road

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Four vehicles travel along a road one afternoon. Can you make sense of the graphs showing their motion?

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Curve Match

Stage: 5 Challenge Level: Challenge Level:1

Which curve is which, and how would you plan a route to pass between them?

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Curve Fitter

Stage: 5 Challenge Level: Challenge Level:1

Can you fit a cubic equation to this graph?

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Maths Filler 2

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Can you draw the height-time chart as this complicated vessel fills with water?

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Bio Graphs

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

What biological growth processes can you fit to these graphs?

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Graphical Interpretation

Stage: 4 Challenge Level: Challenge Level:1

This set of resources for teachers offers interactive environments to support work on graphical interpretation at Key Stage 4.

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Motion Sensor

Stage: 4 Challenge Level: Challenge Level:1

Looking at the graph - when was the person moving fastest? Slowest?

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Take Your Dog for a Walk

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Use the interactivity to move Mr Pearson and his dog. Can you move him so that the graph shows a curve?

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You Tell the Story

Stage: 2 Challenge Level: Challenge Level:1

Can you create a story that would describe the movement of the man shown on these graphs? Use the interactivity to try out our ideas.

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Golden Construction

Stage: 5 Challenge Level: Challenge Level:1

Draw a square and an arc of a circle and construct the Golden rectangle. Find the value of the Golden Ratio.