Measuring Angles: a week of ready-to-teach maths

Five days of lessons for Year 5 Measurement. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus sixteen angle cards, twelve clock cards, a mini-check and every answer.

Start here: five minutes to Monday

1. Skim the week at a glance on the next page.
2. Print the five days. Each day is two A4 sheets: a plan and a worksheet.
3. Cut out the angle cards and the clock cards once, and keep each set in an envelope.
4. Open the free interactive unit on your board. Every plan tells you which picture to show and which buttons to press.
5. Teach straight from the plan. Timings, talk prompts, misconceptions and answers are all on the one page.

No maths background needed

This pack is written for the busy generalist teacher. Each plan explains the idea in plain words, lists the misconceptions children bring, and gives the answers. The big idea of the week: an angle is an amount of turn, measured in degrees, with 360° in a full turn. Two benchmarks, 90° for a right angle and 180° for a straight angle, give every name and every estimate, and a protractor measures exactly when its centre sits on the vertex and the scale that starts at 0 lies along one arm. Angles keep their size however a page is printed, so the drawn angles in this pack can be measured.

One day, one lesson

The five lessons fill a week of maths, one lesson of about 50 minutes a day. Run them in order: each day stands on the one before. Every plan marks a split point if your timetable runs two shorter sessions.

The week at a glance

One lesson a day for a week. Each day stands on the day before, so run them in order.

How the week builds

Day 1 names angles by comparing them with a right angle; Day 2 brings in degrees; Days 3 and 4 estimate, measure and construct with a protractor; and Day 5 reaches reflex angles and ties every name to a size. It builds on Year 4’s estimating and comparing angles by name against a right angle (AC9M4M04), and it leads to Year 6, where angles on a straight line and at a point are used to find unknown angles (AC9M6M04).

Materials for the week (one trip)

• From the classroom: a protractor per child (or per pair), rulers, sharp pencils, scrap paper for right-angle checkers, scissors, envelopes, this pack printed.
• Cut out once: the sixteen angle cards (Days 1 and 3) and the twelve clock cards (Day 2). A geared teaching clock helps on Day 2.

Words for the word wall

angle, arm, vertex, degree, acute, right, obtuse, straight, reflex, revolution, protractor, estimate

Dear families

This week in maths, Year 5 measures angles in degrees. A right angle, like the corner of a book, is 90°; a straight line is 180°; a full turn is 360°. Angles smaller than a right angle are acute, between a right angle and a straight line obtuse, and bigger than a straight line reflex.

Try this at home

• Hunt for right angles at home: doors, tiles, windows. Find one acute and one obtuse angle too.
• Open a door or a laptop a little at a time. Is it acute, right or obtuse now?
• Look at a clock at 3 o’clock and 4 o’clock. How many degrees between the hands?
• Ask: how many right angles make a full turn?

Angles I found this week

Fill one row a day. Write where you found an angle, its name and your estimate in degrees.

Printed from the free seegongsik Measuring Angles teaching pack · seegongsik.com/au/y5/measurement/AC9M5M04/pack

Names for angles

An angle is the amount of turn between two arms that meet at a vertex. Its name comes from comparing it with a right angle (a square corner) and a straight angle (a straight line): acute is smaller than a right angle, obtuse is between a right angle and a straight line, and reflex is more than a straight line. A paper right-angle checker settles any doubt.

We are learning to

• name acute, right, obtuse, straight and reflex angles,
• check an angle against a right angle,
• see that turning an angle does not change it.

Success criteria

• I can sort angles by name and say how I decided.
• I can draw an acute, an obtuse and a reflex angle.

You need

The angle cards (cut-out sheet 1), one set per group. A scrap of paper per child for a right-angle checker. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the sort; start Session B with Part B.

Watch for these ideas

• Judging by the length of the arms. Longer arms do not make a bigger angle.
• Thinking a turned angle has changed. Its size and name stay the same however it faces.
• Mixing up acute and obtuse. Acute is the sharp one, smaller than a right angle.

Answers

• Part A: acute: A, E, J, L, O; right: B, H, P; obtuse: C, G, K, M; straight: F; reflex: D, I, N.
• Part B: drawings vary; check each with a right-angle checker. Part C: two right angles make a straight angle; four make a full turn.

Names for angles

A. Sort the angle cards. Write the card letters.

B. Draw one of each. Mark the angle with an arc.

C. Right angles together

How many right angles make a straight angle? How many make a full turn? Explain with words or a drawing.

Degrees and turns

Angles are measured in degrees, with 360° in a full turn, so a quarter turn (a right angle) is 90° and a half turn (a straight angle) is 180°. A clock face splits the full turn into twelve equal steps of 360 ÷ 12 = 30°. At 2 o’clock the hands are 2 steps apart, so the angle between them is 2 × 30 = 60°.

We are learning to

• use 360° for a full turn, 180° for a half turn and 90° for a quarter turn,
• find the angle between clock hands in steps of 30°,
• link fractions of a turn to degrees.

Success criteria

• I can find the angle between the hands of a clock at any o’clock.
• I can say how many degrees are in a quarter, a half and a full turn.

You need

The clock cards (cut-out sheet 2), one set per pair. A teaching clock if you have one. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the clock cards; start Session B with Part B.

Watch for these ideas

• Counting the numbers instead of the steps: from 12 to 2 is two steps, though three numbers are touched.
• Thinking each step is 5 degrees, like 5 minutes. A step is 360 ÷ 12 = 30°.
• Finding the inside angle when the arc marks the outside one.

Answers

• Part A: A 60° acute, B 90° right, C 150° obtuse, D 240° reflex, E 30° acute, F 180° straight, G 60° acute, H 270° reflex, I 150° obtuse, J 30° acute, K 120° obtuse, L 90° right.
• Part B: a quarter turn 90°, a half turn 180°, three quarters of a turn 270°, a full turn 360°, an eighth of a turn 45°, a third of a turn 120°. Part C: 15 minutes 90°, 20 minutes 120°, 5 minutes 30°, 45 minutes 270°.

Degrees and turns

A. The clock cards: the marked angle and its name

B. Turns in degrees

C. The minute hand

The minute hand makes a full turn every hour. How many degrees does it turn in:

Estimate, then measure

An estimate comes first: is the angle less than 90°, between 90° and 180°, or more? Then closer: about halfway to 90° is 45°, a little past 90° is about 100°. The protractor then measures exactly, and the estimate catches a misread scale: an angle of 105° estimated as ‘a bit more than a right angle’ cannot be 75°.

We are learning to

• estimate an angle from 90° and 180°,
• measure an angle with a protractor,
• use the estimate to check the measure.

Success criteria

• My estimates are within about 20° of the measures.
• I can measure an angle to within 2°.

You need

A protractor per child or per pair. The angle cards from Day 1. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the angle cards.

Watch for these ideas

• Reading the wrong scale: 65° measured as 115°. Check against the estimate.
• Placing the edge of the protractor, not its centre mark, on the vertex.
• Stopping the arm short of the scale. Extend the arm with a ruler until it crosses the numbers.

Answers

• Part A (allow 2° either way): 40°, 75°, 110°, 135°, 160°, 25°; estimates vary.
• Part B: C 150°, G 115°, K 135°, M 100°. Part C: the reading of 140° is wrong; the angle is smaller than a right angle, as Lee’s estimate says, so it is 40°, read on the other scale.

Estimate, then measure

A. Estimate each angle first, then measure it

Extend the arms with a ruler if they are too short to reach the protractor’s scale.

B. Measure four angle cards

C. Check the reading

Lee estimated an angle as about 40°, then measured it as 140°. Which is more likely to be wrong? What should Lee do?

Read and construct

A protractor has two scales running opposite ways. The one to read is the scale whose 0 lies on the base arm; the other gives 180° minus the angle. To construct an angle of 65°, draw a base arm, centre the protractor on its end, mark 65 on the scale that starts at 0 on the arm, and join the mark to the vertex with a ruler.

We are learning to

• choose the protractor scale that starts at 0 on the base arm,
• read an angle with its base arm on the right or on the left,
• construct an angle of a given size.

Success criteria

• I can read the right scale on a protractor every time.
• I can draw an angle to within 2° of the size asked for.

You need

A protractor and a ruler per child. Sharp pencils. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the 65° construction again.

Watch for these ideas

• Reading the scale that starts at the other side, so 35° is read as 145°.
• Lining up the edge of the protractor with the arm instead of its base line through the centre.
• Joining the mark to the wrong end of the base arm. The second arm starts at the vertex.

Answers

• Part A: 50° (outer scale, 130° on the other); 125° (outer scale, 55° on the other); 30° (inner scale, 150° on the other); 110° (inner scale, 70° on the other).
• Part B: check each with a protractor; 55°, 140°, 25°, allowing 2° either way. Part C: answers vary; fold paper twice, or trace a book corner.

Read and construct

A. Read each protractor: use the scale that starts at 0 on the base arm

B. Construct each angle on its base arm

C. Without a protractor

Draw a right angle without a protractor. Explain how you know it is 90°.

Reflex angles and names

A protractor reaches only 180°, so a reflex angle is measured through the angle inside it: the two together make a full turn of 360°. If the inside angle is 70°, the reflex angle is 360 − 70 = 290°. Every size has a name: acute below 90°, right at 90°, obtuse to 180°, straight at 180°, reflex beyond, and a revolution at 360°.

We are learning to

• measure a reflex angle by measuring the angle inside it,
• name any angle from its size in degrees,
• find, estimate and name angles around us.

Success criteria

• I can measure a reflex angle and explain how.
• I can name an angle from its size, even close to 90° or 180°.

You need

A protractor per child or per pair. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the reflex model again.

Watch for these ideas

• Measuring the inside angle and stopping there. The reflex angle is the one round the outside.
• Taking the inside angle from 180° instead of 360°.
• Calling 178° straight or 182° obtuse. Only exactly 180° is straight.

Answers

• Part A: 15° acute, 90° right, 179° obtuse, 181° reflex, 270° reflex, 89° acute, 120° obtuse, 360° revolution.
• Part B (allow 2° either way): inside 60°, reflex 300°; inside 135°, reflex 225°; inside 40°, reflex 320°. Part C: answers vary.

Reflex angles and names

A. Name each angle from its size

B. Measure each reflex angle: measure the inside angle, then take it from 360°

Extend the arms with a ruler if they are too short to reach the scale.

C. Angle hunt

Angle cards

Cut out the sixteen cards (Days 1 and 3), one set per group. The arc marks the angle on each card. Turn a card any way you like: an angle’s size does not change when it turns.

Teacher note: the sort is on the Day 1 plan, and the measures for Day 3 are on its plan.

Clock cards

Cut out the twelve cards (Day 2), one set per pair. The arc marks the angle between the hands. The twelve numbers split a full turn of 360° into twelve equal steps.

Teacher note: two cards mark the outside angle, a reflex angle. The sizes are on the Day 2 plan.

What we know: Measuring Angles

Work on your own. Use a protractor where you need one, and extend short arms with a ruler.

1. Name this angle.   __________
2. What is the name of an angle of 205°?   __________
3. Circle the best estimate for this angle:  30° 60° 120°
4. Read the protractor.   ______°
5. Measure this angle.   ______°
6. Construct an angle of 70° on this base arm.
7. Measure this reflex angle.   ______°
8. What is the angle between the hands at 4 o’clock, and its name?   ______°   __________

Answers and marking guide

Answers

1. obtuse (150°)
2. reflex
3. 60°
4. 115° (not 65°, the other scale)
5. 35°, allowing 2° either way
6. Check with a protractor: 70°, allowing 2° either way
7. 260°: the inside angle is 100°, and 360 − 100 = 260
8. 120°, obtuse

A quick three-level guide

Eight questions, four ideas. A child at standard answers most questions and can say why, by comparing each angle with 90° and 180° before and after measuring.

Weekly class record

Jot a tick as you move around the room; the mini-check fills any gaps. A tick a day is plenty.

The five columns are the five days: naming angles, using degrees, estimating then measuring, reading and constructing, and reflex angles.