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Fraction Classroom · 2.6.0 · Student pages

Choose a protractor scale from the baseline zero

Read labelled dual-scale protractor records by locating the vertex and baseline zero, then check the reading against the angle's opening.

Anonymous group code: __________   Date: __________

Centre at O; OA is the right-pointing baseline and OB points up-left in the upper semicircle. L starts at the left zero; R starts at the right zero. Both numbers at OB are exact labels at the same tick.RayL scaleR scaleOA: right180°0°OB: up-left60°120°Read from OAOther zeroUse 120°
Centre at O; OA is the right-pointing baseline and OB points up-left in the upper semicircle. L starts at the left zero; R starts at the right zero. Both numbers at OB are exact labels at the same tick.

Start with a diagnostic

diagnostic. The protractor centre is on the vertex and the baseline ray points left. At that baseline, L reads 0° and R reads 180°. The second ray points up and right and crosses a tick labelled L 130° / R 50°. What is the angle measure, and which starting zero justifies it?

Build the idea

model. The protractor centre is on vertex O. Baseline ray OA points right and lies on R 0° / L 180°. Ray OB points up and left, crossing a tick labelled L 60° / R 120°. What is angle AOB?

  1. Draw a labelled sketch with O as the vertex, OA pointing right and OB pointing up and left. Mark that the instrument centre is at O and its baseline is aligned with OA. The supplied tick labels, rather than the sketch's apparent size, determine the exact reading.
  2. Read both numbers at the baseline first: R is 0° and L is 180°. Circle R 0° and choose R for this angle. The correct scale is the one whose zero lies on the starting ray.
  3. Follow R from OA through the upper opening to OB. Its label at OB is 120°, while the other scale reads 60°. Record angle AOB = 120° and name R as the scale used.
  4. Check the direction: OA points right and OB points up-left, so the chosen opening is greater than 90° and less than 180°. A 60° reading would describe the opening from a left-pointing baseline to OB, a different angle.

Worked example: 120°. OA starts at R 0°, so follow R through the upper semicircle to OB and read R 120°. The opening from a right-pointing ray to an up-left ray is obtuse, matching 120°.

Practise and explain

Try p1–p3 with a partner. Use a drawing and label your units. Try e1 independently before comparing responses.

p1. Support: the centre is on the vertex. The baseline points right at L 180° / R 0°. The second ray points up-right and meets L 145° / R 35°. Enter the angle in degrees and circle the scale's starting zero on your record.

p2. Core: the centre is on the vertex. The baseline points left at L 0° / R 180°. The second ray points up-left and meets L 55° / R 125°. Enter the angle in degrees and explain why the 125° label is not the reading from this baseline.

p3. Challenge: a paper protractor is rotated so its aligned baseline ray points upward. Its centre is on the vertex. At the baseline, Blue reads 0° and Red reads 180°. The second ray is reached through the instrument's semicircle and reads Blue 125° / Red 55°; the selected opening is obtuse. Enter its measure in degrees and explain why a page-left/page-right rule is insufficient.

e1. Independent check: the centre is on the vertex and the baseline points left at L 0° / R 180°. The second ray points up-right and reads L 140° / R 40°. Enter the angle in degrees. Draw a labelled direction sketch, name the scale and state whether the opening is acute or obtuse.

Transfer the idea

transfer. In the worked record, leave OB pointing up-left but replace the right-pointing baseline OA with a left-pointing ray OC. What is angle COB in the upper semicircle? Explain whether the target angle changed, then explain what happens if the whole page is simply rotated without changing either ray relative to the other.