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 Different types of paper Q22: Paper generator Static shape resources: different types of graph paper, 2-D and 3-D shapes, nets and a football pitch. Write on top of the backgrounds. Use this button to hide the buttons panel. Click on the eyes to show it. Q1: 3 x 3 pinboards Q2: 4 x 4 pinboards Q3: Lots of dots (sq cm)

 Angle and rotation, length Show/hide protractor Rotate buttons Rotate the angle Zoom button Measure length Estimate, draw and measure angles Q5: Place in order of size a set of angles each less than 180 degrees. Q6: Say whether an angle is acute or obtuse and estimate the size to the nearest 5 degrees.   Measuring an angle Q7: Measure an angle. An angle is randomly generated; keep clicking until you are happy with the angle. The angle can be estimated or measured. Move the angle by dragging its 'corner'. Reveal the protractor and move it into position then rotate it to fit over the angle. The angle can also be rotated.     Measuring length with a ruler Q8: Measure the length of each of three lines. Drag the ruler into position. Q9: Measure the length of each side of a quadrilateral. A quadrilateral is randomly generated; keep clicking until you are happy with the quadrilateral. Drag the ruler to measure one side of the quadrilateral. Use the rotate buttons to line up the ruler and the side. Use the zoom button to zoom in or out. The quadrilateral can be moved by dragging the top left corner.   Angles on a straight line

Position and direction: coordinates

The coordinates of three of the vertices of a square or rectangle are given:

. . what are the coordinates of the fourth vertex? . . what is the area of the rectangle? ..what is the perimeter of the rectangle?
Q11:
Positive coordinates

Identify the coordinates

The coordinates of some of the vertices of a shape are given, the numbers on the axes and the grid are hidden. What are the coordinates?
Drag the shapes or click on the 'change' button.

See the example on the left.

Coordinates and reflections

 Q15: Interactive coordinates and reflections resource: drag the shape with the black outline. The coordinates can be worked out without showing the numbers on the axes or the grid. Click next to the letters to reveal the coordinates. Show or hide the grid, the numbers on the axes, the mirror line or the reflections of the shapes. The mirror line can be dragged to the left and right.

Reflective symmetry, reflection, rotation and translation

The rectangle's outline is can be shown or hidden.

Reflect shapes

Q16: Interactive reflections resource: drag the yellow shape with the black outline and watch the reflections change. Select the shape using the buttons. Turn the labels and coordinates on or off.

Q17: Reflect shapes in a vertical or horizontal mirror line.

Q18: Reflect shapes in a diagonal mirror line.

Rotate a triangle about a point

Q19: Interactive rotation resource: drag the yellow triangle and watch the transformations. Move the centre of rotation (the red point). Use the buttons to show or hide the rotations. Turn the labels and coordinates on or off.

The transparent triangles can be used as 'answers'. Select the triangle and drag it to where you think the rotation is going to be.

Reflect, rotate and translate a triangle

Q20: Interactive transformations resource: drag the yellow triangle and watch the transformations. Use the buttons to show or hide the translation, reflections or rotations. Turn the labels and coordinates on or off.

The transparent triangles can be used as 'answers'. Select the triangle and drag it to where you think the reflection or rotation is going to be.

Rotational symmetry and rotations about a point

Q24: Rotational symmetry and rotating shapes

Use the slider to determine the angle and select the shape using the shape buttons.
The shape's outline can be shown so that rotational symmetry can be investigated. Click on a shape button to reset the shape.
The shapes can be dragged about so that they can be rotated about a different corner, for example.

Hide or show the outline of the shape, its shadow, its eyes and the grid. Showing the eyes is useful to see which way up the shape is. The shadow shows from where the shape has been moved.

Click in the top right quadrant. The tiles will be reflected in the other three quadrants.

Keep clicking on a tile to rotate it.

Q21: Make reflection patterns with Truchet tiles.
In 1704, Sebastien Truchet created all the possible patterns formed by tiles like this:

 First select select the tile. Use the white tile to delete a tile. Use the sliders to change the colour. Click in the top right quadrant of the grid. The tiles will be reflected in the other three quadrants. Keep clicking on a tile to rotate it. The pattern can be cleared by clicking on the eraser button. Click on the printer button to print a pattern.

 Christmas maths A Christmas tree drawn using Logo. Q23: Angles in Christmas trees Two Christmas maths activities: Use the computer programming language Logo to draw a Christmas tree. First decide on the internal angle of the pointy bits on the tree and an angle in the tub. Then work out all the other angles. Write Logo procedures to draw the tree. It will soon show whether you've worked out all the angles. Instead of using Logo, draw the Christmas tree accurately using a ruler and protractor. If you don't get back to the start it's not accurate! If you've subscribed to Active Worksheets there are a couple of worksheets you could use.