Mult-e-Maths



Measuring angles and drawing polygons 6GEO1

National curriculum objective

Pupils should be taught to:

• draw 2-D shapes using given dimensions and angles.

Prior knowledge and skills

• Use a protractor to measure angles.

• Understand and using angle measure in degrees.

• Add several 2- and/or 3-digit numbers.

Vocabulary

protractor, angle, measure, unit, degrees, triangle, polygon, sum, total

Resources

• small whiteboards and pens

• protractors and rulers

• plain paper

• large sheet of paper (big enough to draw a rectangle whose sides can be walked around)

Oral and mental starter

Set questions testing students knowledge of number bonds to 90 and 180, (e.g. 120 + ? = 180; 47 + ? = 90) for pupils to solve mentally. Ask:

Q What is the missing number?

How did you work it out?

Pupils could show their answers on small whiteboards. Discuss their methods of calculation.

Main teaching activity

Whole class

(Screen 1, Activity 1, Question 1)

Q Is the angle marked with a red arrow acute or obtuse? Why?

Q What unit do you use to measure angles? (degrees)

What do you estimate the size of this angle to be? How did you make your estimate?

Pupils show their estimates on small whiteboards. Click inside the red arc and then on the ‘Angle checker’ [pic] button in the bottom toolbar to open a pop-up menu. Invite a pupil to use the scroll arrows to enter their estimate in the number boxes revealed. Click on the ‘Check’ button to reveal a comment about their estimate. Repeat with other pupil’s estimates that satisfy the requirements until the exact angle size is identified. Alternatively, you can press the ‘Show answer’ button at any time to reveal the size of the angle.

Repeat the activity for estimating the size of other angles, including reflex angles, and to explain their reasoning. To change the orientation and/or size of the angle each time, click on it and drag the end of one or both of its arms.

Q How can you measure the size of an angle?

Establish that you can use a protractor. Drag the yellow panel to the bin to reveal an on-screen semi-circular protractor. Note: To resize the protractor, click on it and then drag one of its resizing handles. To rotate the protractor, click on it and then on the ‘Rotate’ button [pic] that appears in the bottom toolbar; you rotate by dragging. To stop the rotation, you need to click on the ‘Select’ tool [pic] in the top toolbar.

Q What do you need to remember when using a protractor?

Discuss suggestions. Model measuring the angle on the board to reinforce key points:

• Drag the protractor until its centre is on the point where the arms of the angle join.

• Click on the ‘Rotate’ button and rotate it until its baseline is along one arm of the angle. Check that the centre of the protractor hasn’t moved.

• Use understanding of the approximate size of the angle to decide whether you must use the inner or outer scale of the protractor.

• Count on from 0( until you reach the point on the scale that is directly over the second ‘arm’ of the angle.

Move to question 2 (screen 2). Explain that you want to draw an angle measuring 35°, using the red line on the board as one of the arms of the angle.

Ask pupils to use a ruler to draw a straight line on plain paper in a similar orientation to the one on the whiteboard.

Q What do you need to do to draw an angle of 35°?

As pupils identify each step in the process, model it on the board. Pupils then carry out the same step on their paper.

The example on the board has three steps (as indicated by yellow panels from left to right), remove a panel to reveal the next step:

• Decide where you want to put the 35° angle and line up your protractor accordingly. The read off 35° from the scale and mark a point.

• Use a ruler to join the point marked at 35° to the end of the line that makes the vertex of 35°.

When each pupil has drawn their angle, ask them to join the ends of the angle’s arms to create a triangle; to show this on the board, remove the final yellow panel.

Ask pupils to measure and record the sizes of each of their triangle’s angles. They then calculate and record the sum of the three angles. If desired, you can use screen 3 to demonstrate measuring the angles using the on-screen protractor, which can be found in the ‘Shape and space toolbox’ [pic] in the vertical toolbar. The angles in the triangle on the board are approximately 35°, 86° and 59°; remove the yellow panel to reveal the sum of angles as 180°.

Pairs

Pupils discuss their results for the activity just carried out.

Q What do you notice about the angles of a triangle? Is this always true?

Pupils repeat the activity to test their hypotheses, and then discuss their findings.

Whole class

Use pupil’s findings to establish that the angles of a triangle always add up to 180°.

(Screen 4, Activity 2, Question 1)

Q How could you give instructions for drawing this triangle?

Discuss suggestions. Establish that you could give a series of instructions involving moving and turning, just like you might enter a route into a programmable robot.

Explain that you want to start your instructions from the red dot, moving in the direction shown by the red arrow.

Q What movement instruction shall you give first?

Establish that one clear way to express it is ‘Forwards 4 cm’. Use the ‘Pen’ tool to record this on the peach-coloured panel as F 4 cm.

Establish that this instruction takes you to the top corner of the triangle, and that you now need an instruction of turn.

Q Where must you position the protractor to find the angle of turn?

(Resize the on-screen protractor as appropriate.) Establish that the protractor needs to be in the position shown on the right, with its centre point on the top corner of the triangle and its baseline aligned along the vertical side of the triangle. Rotate the protractor and drag it into position. Measure the angle you must turn through to get from the vertical side of the triangle to its right-hand side.

Q What turning instruction are you going to record?

Establish that you need to turn right. Use the ‘Pen’ tool [pic] to record the appropriate instruction, using R to stand for ‘turn right’ (i.e. R 110°).

Continue in this way until you have a complete set of instructions for the triangle (F 4 cm, R 110°, F 6 cm, R 140°, F 6 cm, R 110°). Note: Clicking on the ‘Select’ button will turn off the ‘Pen’ tool.

Q What is the total of the angles turned through? (360°)

Why is this different from the sum of the triangle angles that you found earlier?

Use the ‘Pen’ tool to draw the angles you have just turned through on the diagram on the board. Establish that they are not the angles inside the triangle.

Ask pupils to measure the angles they would have to turn through to draw one of the triangles they created earlier. Explain that they will need to extend the sides of the shape, as on the board.

Q What is the total of the angles? (360°) Why? (To make the shape closed, you must end up facing the same direction as at the start, so you must make a whole turn altogether.)

Individuals

Pupils use a protractor and a ruler to write instructions for drawing hexagons on plain paper. They begin by drawing an irregular hexagon. They then try a regular hexagon.

Q What can you tell me about the total amount of turn?

Are all the angles the same?

Support: Work with pupils. They write instructions for drawing a rectangle on a large sheet of paper. Pupils then take turns to ‘walk’ the rectangle as the instructions are read aloud.

Extension: Ask pupils to investigate other regular polygons in the same way.

Other tasks

You could ask pupils to:

• use a programmable robot to draw a given polygon or arrangement of polygons, such as that shown here on the right.

Review

Discuss instructions for drawing polygons from the independent activity.

Q What do you notice about the total angle turned through when you draw a polygon? (It is always 360(.)

Key idea and assessment

You can use angles and lengths to give instructions for drawing a polygon.

Can pupils:

• use a protractor to measure and draw angles?

• say that the sum of a triangle’s angles is 180(?

• use angles and lengths to give instructions for drawing a polygon and explain why the sum of the angles in these instructions is 360(?

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