Mult-e-Maths



Drawing and measuring angles 5GEO3

National curriculum objective

Pupils should be taught to:

• draw given angles, and measure them in degrees(°).

Prior knowledge and skills

• Know angles are measured in degrees.

• Estimate and compare acute, obtuse and reflex angles.

Vocabulary

angle, vertex, acute, right, obtuse, straight, reflex, protractor, degree

Resources

• plain paper

• rulers

• protractors

Oral and mental starter

(Screen 1: Activity 1, Question 1)

Have pupils review knowledge of angles.

Q What is an angle? (Answers may vary: a measure of turning; when two straight lines meet at a point, etc.)

What is the term for the point where the two lines meet? (Vertex)

How can we measure how far open an angle is? (Using degrees; using a protractor.)

Ask pupils to read and define the words on the right-hand side of the screen: acute (less than 90°); right (90°), obtuse (greater than 90° but less than 180°); straight (180°); reflex (greater than 180° but less than 360°).

Ask pupils to drag each word to the correct angle on the left. For each angle, you might also ask:

Q What is your estimate of the measure of this angle?

Clicking on an angle will bring up a bottom toolbar with an ‘Angle Checker’ button [pic] that allows pupils to input their estimation for checking. Yellow text will appear within the pop up to indicate if the estimate is too small or too large, or correct. You can also press ‘Show answer’ to provide the correct answer.

You can also create a new angle by opening the ‘Shape and Space Toolbox’ [pic] in the vertical toolbar and clicking on the angle tool [pic]. By dragging one of the ends of the angle, you can change the measure of the angle. You might say a specific angle measure and ask a pupil to approximate that measure.

Main teaching activity

Whole class

(Screen 2: Activity 2, Question 1)

In the starter, pupils may have mentioned that protractors are used for measuring angles. If so, refer to this when talking about screen 2.

Have pupils examine the protractor on the screen. You might also hand out protractors to each pupil so they can examine a protractor individually.

Q What do you notice about the protractor? (Answers may vary: it is a half-circle; the numbers go from 0 to 180; there are two sets of numbers; the two sets of numbers go in opposite directions around the arc; there are different sized marks on the curved edge, the long lines meet at a point, etc.)

If pupils do not name all of these things, point them out to the class. Discuss that the numbers are degree measurements and that the marks on the curved edge indicate degrees. The longer marks indicate every 10 degrees, the medium marks indicate 5s, and the small marks indicate 1s.

Use the angle on the board to demonstrate how to measure angles. Drag the protractor so that the point where the lines meet on the protractor is aligned with the vertex of the angle. Make sure that one of the lines of the angle aligns with the centre point on the baseline of the protractor (so that the line of the angle is aligned with one of the 0/180 measurements). Then start at the zero aligned with one edge of the angle and follow that set of measurements until you reach the other line of the angle and read the angle measurement.

If you use the zero on the left edge of the protractor, use the outer set of measurements. If you use the zero on the right edge, use the inner set of measurements.

Pupils may ask which side of the protractor to start with. Explain you can use either side as zero – but be sure that whichever side you use as zero, that you use that scale for the measurement. You can demonstrate to pupils how to use both zeroes.

If necessary, drag the protractor off the angle and change the angle to a different size by dragging one/both of the arms, and repeat the demonstration using the new angle measurement. You can rotate the protractor as required by clicking on it and then on the ‘Rotate’ button [pic] in the bottom toolbar, and then dragging to rotate. You will need to click on the ‘Select’ tool [pic] in order to turn off the rotation tool so that you can move the protractor as required.

Reflex angles can be measured using the full-circle protractor found in the ‘Shape and Space Toolbox’. The full-circle protractor can also be used to measure the other types of angles as well. If you only have full-circle protractors for pupils to use, simply replace the half-circle protractor with the full-circle protractor in your demonstration.

Individually or Pairs

Have pupils use plain paper, pens and rulers to draw angles. You might suggest they draw two different acute angles and two different obtuse angles, though you can adapt this number to your individual pupils.

After carefully drawing the angles, have pupils use the protractors to measure their angles and write the degree measurement next to the angle.

Have individuals or pairs exchange papers with another individual or pair to check.

Pupils may find that their angle measurements differ by several degrees. You might discuss why this might be (such as the protractor might not be aligned exactly, or the lines of the angle are drawn using thick pen) and decide on a reasonable margin of error. For example, measurements within 3 degrees of one another can count as correct.

Whole Class

When pupils are confident measuring angles, discuss with pupils how to draw angles to specific measurements.

Move to screen 3. Choose an angle measure to start with, for example 45°. Drag the protractor so that the angle’s vertex aligns with the centre point of the protractor and one of the arms is aligned with zero on the protractor. Then, drag the other angle arms to the correct 45° measurement on the protractor. Pupils can check they have used the correct set of numbers by remembering that 45° is an acute angle. If the resulting angle is obtuse, they have likely used the incorrect set of numbers and created a 135° angle instead.

To create a specific angle, such as 45°, on paper, pupils first start with a single straight line. Place the protractor over the line and align the protractor centre point with the end of the line that is to be the angle’s vertex. Make sure the protractor is then aligned so that the other end of the line is aligned with zero on the protractor. Find the place on the protractor for 45° and use a pen to make a small mark on the paper at that point. Remove the protractor and use a ruler to connect the vertex to that point. Again, pupils can check they have used the correct set of numbers by remembering that 45° is an acute angle. If the resulting angle is obtuse, they have likely used the incorrect set of numbers and created a 135° angle instead.

Individually or Pairs

Have pupils use plain paper, pens, rulers and protractors to draw angles. Drag the yellow panel at the bottom of the screen to reveal five angle measures for pupils to create.

After carefully drawing the angles, have pupils use the protractors verify their angles are the correct measurement.

Have individuals or pairs exchange papers with another individual or pair to check.

Other tasks

You could ask pupils to:

• demonstrate how to use a half-circle protractor to measure a reflex angle.

• demonstrate how to use a full-circle protractor to measure a reflex angle.

Review

Use the randomisers (blue panels) to generate angles by clicking on one of the randomisers and then clicking the ‘Roll’ button [pic] that appears in the bottom toolbar. Use the number on the top randomiser as the tens digit and the number on the bottom randomiser to indicate if the ones digit is 0 or 5. For example, a 6 on the top randomiser and a 2 on the bottom randomiser will represent 60 degrees.

You might ask pupils to use the measurement to approximate the size of the angle and then use the protractor to check. You might also use the measurement to have pupils use the protractor on the board and adjust the angle to the exact measurement.

Pupils might also create this angle on paper and check each other’s work. Repeat as necessary.

Key idea and assessment

Drawing given angles and measuring them in degrees.

Can pupils …

• measure angles in degrees?

• draw angles to specified degree measures?

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