There are **90** NRICH Mathematical resources connected to **GeoGebra**, you may find related items under Physical and Digital Manipulatives.

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Some of the numbers have fallen off Becky's number line. Can you figure out what they were?

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Join pentagons together edge to edge. Will they form a ring?

Use the applet to explore the area of a parallelogram and how it relates to vectors.

Use the applet to make some squares. What patterns do you notice in the coordinates?

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How much of the square is coloured blue? How will the pattern continue?

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Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

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Can you make sense of these three proofs of Pythagoras' Theorem?

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

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Can you work out which spinners were used to generate the frequency charts?

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

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It would be nice to have a strategy for disentangling any tangled ropes...

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The sine of an angle is equal to the cosine of its complement. Can you explain why and does this rule extend beyond angles of 90 degrees?

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Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 ÷ 360. How did this help?

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A dot starts at the point (1,0) and turns anticlockwise. Can you estimate the height of the dot after it has turned through 45 degrees? Can you calculate its height?

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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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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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The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

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

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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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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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Can you find an efficent way to mix paints in any ratio?

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Can you work out how to produce different shades of pink paint?

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Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

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What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?

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Can you find triangles on a 9-point circle? Can you work out their angles?

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We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

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A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

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Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

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Using a ruler, pencil and compasses only, it is possible to construct a square inside any triangle so that all four vertices touch the sides of the triangle.

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Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

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Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.

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Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?

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A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

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There are lots of ideas to explore in these sequences of ordered fractions.

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In how many ways can you fit all three pieces together to make shapes with line symmetry?

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Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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Quadratic graphs are very familiar, but what patterns can you explore with cubics?

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Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

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Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

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Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?

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Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?

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Use these four dominoes to make a square that has the same number of dots on each side.

Week 2

How well can you estimate angles? Playing this game could improve your skills.