AC9M4M04 • Homework
Estimating and Comparing Angles worksheet
Use this printable homework sheet for written working, application and reflection alongside the online learning activities.
Open practiceEight written homework tasks
Use separate paper for large drawings. Keep physical constructions and observations for an adult to check. You will need paper for folding or tracing, pencil, a straightedge, a set square and an adult-supervised spirit level. Every task stands alone and the PDF may present them in a different order.
Six descriptions, six names
Write the angle name for each turn: (a) less than one right angle but more than no turn; (b) exactly one right angle; (c) greater than one but less than two right angles; (d) exactly two right angles; (e) greater than two but less than four right angles; (f) exactly four right angles. Then explain the difference between a straight angle and a revolution.
Draw a comparison gallery
On separate paper, draw one acute, one obtuse and one reflex angle. Mark the intended opening of each with an arc and label it. Draw or trace a right-angle benchmark beside the gallery. Write how each angle compares with one, two or four right angles, using both limits where needed.
Construct and use a template
Make a paper right-angle template: fold once, then fold so the first folded edge lies exactly on itself. Mark the corner where the folds meet. Keep the template for an adult to inspect. On separate paper, sketch how you made it. Choose two safe flat angles in your surroundings. For each, name the object, draw and mark the angle, write an estimate before checking, show the template corner and one edge aligned, then record smaller than, equal to or greater than a right angle after checking.
Interior angles in two shapes
On separate paper, draw a rectangle in a tilted position and mark one interior angle. Draw a different closed straight-sided shape with an inward corner, shade its inside and mark one interior reflex angle with a long arc. Label both marked angles and explain each using right angles.
Record two pointer turns
Draw two separate pointer diagrams on paper, each with an upward starting arm. In the first, turn anticlockwise through two right angles. In the second, turn anticlockwise through three right angles. Mark the entire turn of each with an arrow, draw its finishing arm, name each angle and explain which turn is larger.
Same opening, different arms
Draw an acute angle on separate paper and mark its opening. Trace it onto another piece of paper, rotate the trace, and extend its arms to make them longer than in the original. Label the drawings A and B. Compare them by matching their vertices and one arm, and write what happens to the other arms. Explain whether the angle size changed.
Use a set square and a straightedge
On separate paper, draw a line using a straightedge. Place the straightedge back along the line and record whether the drawn part matches it without a bend. Use a set square to draw a second line perpendicular to the first. Sketch the tool placement so both edges at its square corner fit, mark the right angle and explain why the lines are perpendicular.
Use a spirit level and explain its limit
With an adult, use a spirit level on a safe reachable shelf or tabletop. Place its measuring face on the surface and read the horizontal vial. On separate paper, sketch the setup and bubble position, then record level or not level in the direction checked. Explain why this reading alone does not prove a side support meets the surface at a right angle, and describe a tool check for that join. Arrange access with a teacher if no spirit level is available.
Answer guide and evidence to check
Six descriptions, six names
(a) acute; (b) right; (c) obtuse; (d) straight; (e) reflex; (f) revolution. A straight angle is a half turn, equal to two right angles, and its arms point in opposite directions. A revolution is a complete turn, equal to four right angles, finishing in the starting direction. Require all six names and the half/full-turn explanation.
Draw a comparison gallery
Inspect three actual diagrams with clear intended arcs, correct labels and a right-angle benchmark. Acute is greater than no turn and less than one right angle. Obtuse is greater than one and less than two. Reflex is greater than two and less than four; the long opening must be marked. Accept any valid orientations, arm lengths and examples. No degree measurements are required.
Construct and use a template
Require the actual double-folded template with its right-angle corner, a construction sketch and two separate real-angle records. Each record needs the chosen object, marked intended angle, before-check estimate, vertex-and-edge placement evidence and a correct checked comparison. Estimates may be corrected after checking. For example, a rectangular cover corner may be equal and a partly opened card may be smaller. Accept any safe examples and correct observations; angle names are optional.
Interior angles in two shapes
The tilted rectangle must have square corners; its marked interior angle is right, equal to one right angle. The second shape must be a closed non-self-crossing polygon with an inward corner. Its long marked arc must lie inside the shaded shape and be reflex: greater than two and less than four right angles. Accept an L-shaped outline or other valid concave construction; a reflex angle need not equal exactly three right angles.
Record two pointer turns
First: the pointer finishes down after a half turn; the angle is straight, equal to two right angles. Second: it finishes right after three quarters of a turn; the angle is reflex, equal to three right angles. The second turn is larger by one right angle. Require both start and finish arms, accurate anticlockwise arrows showing the entire turn, angle names and a comparison. The three-quarter turn must not be replaced by a short clockwise arrow.
Same opening, different arms
Require the original acute drawing, an actual traced and rotated copy with longer arms, labels and marked openings, and comparison evidence. When the vertices and one arm align, the other arms align too. The openings are equal: turning and lengthening arms do not change the angle. Accept any clear acute opening and rotation; a claim without a matching trace does not show the requested construction.
Use a set square and a straightedge
Require an actual straightedge check with an observation about the drawn line, an actual set-square construction, a placement sketch at the meeting point with both adjacent edges aligned, a right-angle mark and an explanation that perpendicular lines meet at a right angle. Accept any orientation and line lengths. One aligned edge is insufficient. If the first line bends, accept redrawing and checking a straight line before the perpendicular construction.
Use a spirit level and explain its limit
Require actual supervised use, correct measuring-face contact and the horizontal vial, a setup sketch showing bubble position, and a conclusion matching the observation. Centred between the marks means level in the checked direction; off-centre means not level. The support direction is untested, so the bubble alone cannot establish the join angle. A set square must be placed at the join with both square-corner edges fitted to the two directions. Accept either observed outcome; do not mark tool use complete from a prediction alone.