Support
Answer and teaching response
35 · The right-pointing baseline starts at R 0°, so read R 35°. The up-right second ray gives an acute opening, consistent with 35°. The two labels at this tick sum to 180°.
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.
Get student and teacher materialsPrepare the lesson
Learning goal: Select the scale that starts at zero on the baseline ray, follow that scale to the second ray and justify the reading with the ray directions and an acute or obtuse check.
You will need: Paper and pencil; a classroom protractor for the optional paper construction. Every required reading is supplied as exact labelled data. Use labelled sketches to show directions; no precision measurement from a screen or printed image is required. For the L/R records, L starts at 0° on the left and ends at 180° on the right; R starts at 0° on the right and ends at 180° on the left, over the same upper semicircle.
Start with a 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?
Check the reasoning and choose a starting point
130°, using L because L is 0° on the left-pointing baseline. The angle opens more than a right angle. · The two printed numbers belong to different starting rays. Choosing 50° because it is smaller or always choosing one scale misses the baseline condition.
Start with support: If the learner selects 50° or names no baseline zero, draw O with a left-pointing baseline and mark L 0° there. Trace the upper opening to the up-right ray while following L. Use p1, then recheck a left-baseline record whose second ray reads L 100° / R 80°: the answer is 100°.
Ready for core: If the learner selects 130°, cites L's starting zero and identifies an obtuse opening, give the right-baseline worked record. Require the learner to choose its starting zero afresh before reading the second ray.
Work through an example
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?
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°.
- 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.
- 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.
- 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.
- 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.
Run the 40-minute lesson
- 5 minutes. Give the diagnostic and collect the angle, scale and starting-zero explanation. Route learners using the diagnostic. Have everyone mark vertex O and the baseline direction on a labelled sketch.
- 10 minutes. Read the worked table together. One partner points to the baseline zero while the other traces the selected scale to OB; switch roles. Compare the exact 120° reading with an obtuse estimate. If using a classroom protractor, align its centre and zero on paper and sketch a 120° angle; otherwise annotate the supplied reading record.
- 15 minutes. Support learners use p1 and then the left-baseline 100° recheck. Ready learners solve p2 and explain why the scale changes with the baseline. Pairs use p3 to test the same rule on a rotated instrument with different scale names. Record the starting label, chosen scale and final reading for each item.
- 10 minutes. Give e1 independently for four minutes, requiring a baseline-zero reason as well as the angle. Use three minutes to compare the acute/obtuse check, then three minutes to discuss the transfer's changed starting ray. Learners who choose the other reading return to marking zero; learners who choose correctly explain why turning the page preserves the angle.
A useful error to discuss
A learner might say: Always read the smaller number, or always use the inner scale regardless of which way the baseline points.
Cover the second-ray labels and ask the learner to find zero on the baseline ray first. Uncover the labels and follow only that scale. Then compare the result with a right-angle opening; the scale's location inside or outside is not the deciding condition.
Practise at your level, then check independently
Use the diagnostic to choose support or core practice, then try the challenge. Complete the independent check without help. Enter a number, fraction or mixed number. The number check does not assess your drawing or explanation.
Core
Answer and teaching response
55 · Follow L because its zero is on the left-pointing baseline. L 55° matches the acute opening from left to up-left. R 125° starts from the opposite horizontal ray.
Challenge
Answer and teaching response
125 · Blue starts at zero on the actual baseline, so Blue 125° is the reading. Rotating the instrument changes its direction on the page, while its starting zero still identifies the correct scale. The obtuse opening agrees with 125°.
Independent check
Answer and teaching response
140 · The baseline starts at L 0°, so L 140° is the reading. From a left-pointing baseline to an up-right ray the upper opening is obtuse. R 40° belongs to the opposite starting ray.
Transfer the idea
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.
Discuss a possible response
Angle COB is 60°, read from L 0° at the left-pointing ray to L 60° at OB. Replacing the baseline selects a different opening. Rotating the whole page keeps the two rays' relative directions and their starting-zero relationship, so it preserves whichever angle was selected.
Choose the next teaching step
- Identifies the vertex and states that the protractor centre and baseline are aligned before reading.
- Chooses a scale by its zero on the starting ray and follows that same scale to the second ray.
- Uses the supplied exact labels and justifies the reading with the stated ray directions.
- Checks acute or obtuse size without using the sketch as a precision measuring tool.
Support: Hide the target tick labels until the learner has circled zero on the baseline. Use a finger to trace that one scale, then uncover the labels and check the reading against a right angle. Recheck a left-baseline L 100° / R 80° record before removing this routine.
Extend: Write two reading records for a 70° angle: one with the baseline at a left zero and one at a right zero. At the target tick the paired labels are 70° and 110°, with the chosen scale determined by its baseline zero. If a classroom protractor is available, sketch each angle on paper and label the chosen scale.
Materials for your group
Student pages and teacher answers are separate. Keep the HTML files or print them in your browser.
Revisit a prerequisite
Number Line Launch is a prerequisite for reading from an identified zero and counting equal intervals on a scale. Its full lesson locates fractions on a straight number line; this investigation adds an angular vertex, baseline alignment and dual protractor scales.