Angles and Turns: a week of ready-to-teach maths

Five days of lessons for Year 3 Measurement. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus angle cards, turn cards, a right-angle tester, 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 turn cards once; they are reused all week.
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. An angle is an amount of turn. A quarter turn makes a right angle, the square corner of a book or a window, and it is the benchmark for the week: angles are smaller than, the same as, or bigger than a right angle. The length of the arms does not change an angle; only the turn between them does. No degrees yet; that comes later.

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 starts with the body: turning to face a new way. Day 2 names the quarter turn as a right angle and gives every child a tester, which Day 3 uses to compare other angles. Day 4 compares turns and links them to a clock, and Day 5 orders them. It leans on Reading Clocks to the Minute (AC9M3M04) and Sorting Objects by Their Features (AC9M3SP01).

Materials for the week (one trip)

• From the classroom: scissors, pencils, scrap paper for right-angle testers, this pack printed.
• Card strips and paper fasteners, two strips and one fastener per pair, to make angle makers.
• A teaching clock, a pair of scissors and a book to show angles.
• Cut out once, use all week: the angle cards and the turn cards in this pack.

Words for the word wall

angle, turn, arm, corner, quarter turn, half turn, three-quarter turn, full turn, right angle, smaller than, bigger than, clockwise, compare, order

Dear families

This week in maths, Year 3 is learning that an angle is an amount of turn, and comparing angles with a right angle (a square corner).

Try this at home

• Hunt for right angles together: the corners of a book, a door, a tile, a screen.
• Open a door a little, then wide: is the angle smaller or bigger than a right angle?
• Play turns: face the fridge, make a quarter turn. What are you facing now?
• Look at the clock: from 12 to 3, the minute hand makes a quarter turn.

Our angles this week

Fill one row a day: an angle you found, and whether it is smaller than, the same as, or bigger than a right angle.

Printed from the free seegongsik Angles and Turns teaching pack · seegongsik.com/au/y3/measurement/AC9M3M05/pack

An angle is a turn

An angle is an amount of turn. Stand facing the board and turn to face the window: that is a quarter turn. Two quarter turns make a half turn, three make a three-quarter turn, and four bring you back to where you started: a full turn.

We are learning to

• make and name quarter, half, three-quarter and full turns,
• see an angle as the amount of turn between two arms,
• say that a bigger turn makes a bigger angle.

Success criteria

• I can make and name quarter, half, three-quarter and full turns.
• I can say that an angle is an amount of turn.

You need

Space to stand and turn. Two card strips and a paper fastener per pair. The turn cards (cut-out sheet 2). The worksheet.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the angle makers; start Session B with the worksheet and the cards.

Watch for these ideas

• Thinking longer arms make a bigger angle. The turn makes the angle, not the arms.
• Calling a half turn a quarter. Count the quarters: two quarters make a half.
• Thinking a full turn is no turn. It goes all the way round, back to the start.

Answers

• Turns: 1. quarter turn; 2. three-quarter turn; 3. half turn; 4. full turn.
• Quarter turns: a half turn is 2, a three-quarter turn is 3, a full turn is 4.
• Facing: from the board, a quarter turn faces the window; from the board, a half turn faces the door; from the window, a three-quarter turn faces the board; from the door, a full turn faces the door.

An angle is a turn

Name the turn

Each turn starts at the top arm and sweeps round like a clock hand.

How many quarter turns?

A half turn is ______ quarter turns. A three-quarter turn is ______ quarter turns. A full turn is ______ quarter turns.

Which way are you facing?

The right angle

A quarter turn makes a right angle: the square corner you see on a book, a window or a tile. Fold a scrap of paper in half and in half again, lining up the fold, and the folded corner is a right-angle tester that fits a square corner exactly.

We are learning to

• know that a quarter turn makes a right angle,
• make a right-angle tester and use it to check corners,
• find right angles in shapes and in the classroom, facing any way.

Success criteria

• I can make a right-angle tester.
• I can find right angles around me.

You need

Scrap paper for testers (one each), or the tester on cut-out sheet 2. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the hunt; start Session B with the shapes and Show me.

Watch for these ideas

• Thinking a right angle must look like an L. A right angle can face any way.
• Calling any corner a right angle. Test it: the tester must fit exactly, with no gap.
• Mixing up a right angle with the right-hand side. Here, right means square.

Answers

• Shapes, right angles: A 4, B 4, C 1, D 0, E 2, F 0.
• Hunt: any square corners, such as a book, a desk, a door, a window pane, a tile or a sheet of paper.

The right angle

Right-angle hunt

Use your tester. Write where you found six right angles.

Mark the right angles

Draw a small square in each right-angle corner. Then write how many right angles the shape has.

Bigger or smaller than a right angle

The right angle is a benchmark. Hold the tester in the corner of an angle: if the angle is narrower, it is smaller than a right angle; if it opens wider, it is bigger. Scissors opening a little, a slice of pizza and a door opened wide all make angles to compare.

We are learning to

• compare an angle with a right angle, using a tester,
• sort angles into smaller than, the same as, and bigger than a right angle,
• find each kind of angle in everyday things.

Success criteria

• I can say if an angle is smaller than, the same as, or bigger than a right angle.
• I can check with my tester.

You need

Right-angle testers from Day 2. A pair of scissors and a book. The angle cards (cut-out sheet 1). The worksheet.

Lesson flow (about 50 minutes)

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

Watch for these ideas

• Judging by the length of the arms. Compare the turn, not the arm length.
• Thinking an angle facing down is smaller. Turning the page does not change the angle.
• Calling a nearly-right angle a right angle. The tester must fit exactly.

Answers

• Angles: A smaller, B right angle, C bigger, D smaller, E right angle, F bigger, G smaller, H bigger.
• Drawn: any angle narrower than the tester, one that fits it exactly, and one wider.
• Angle cards: the sort is in the cut-out teacher note.

Bigger or smaller than a right angle

Check each angle with your tester. Write smaller, right angle or bigger.

Draw one of each

Which turn is bigger?

To compare two angles, see which is the bigger turn: a half turn is bigger than a quarter turn. A clock hand shows it: from 12 to 3 is a quarter turn, 12 to 6 a half turn, 12 to 9 a three-quarter turn, and all the way back to 12 a full turn.

We are learning to

• compare two turns and say which is bigger,
• describe the turns a clock hand makes as quarter, half, three-quarter and full,
• see that a half turn is two right angles and a full turn is four.

Success criteria

• I can say which of two turns is bigger.
• I can describe a clock-hand turn.

You need

A teaching clock. The angle makers from Day 1. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Which turn is bigger?; start Session B with Turns on a clock.

Watch for these ideas

• Thinking the turn from 3 to 9 is bigger than from 12 to 6. Both are half turns.
• Counting the numbers instead of the quarters (12 to 3 is “3 turns”). It is one quarter turn.
• Comparing the arm lengths. Look at how far it turned.

Answers

• Bigger turn: 1. the three-quarter turn; 2. the quarter turn (a right angle); 3. the full turn.
• Clock: 3 to 9 is a half turn; 9 to 12 is a quarter turn; 12 to 9 is a three-quarter turn; 6 to 6 is a full turn; 3 to 6 is a quarter turn.
• Right angles: a half turn is 2, a three-quarter turn is 3, a full turn is 4.

Which turn is bigger?

Circle the bigger turn

Turns on a clock

How many right angles?

A half turn is ______ right angles. A three-quarter turn is ______. A full turn is ______.

Order the turns

Ordering angles is ordering turns: quarter, half, three-quarter and full, from smallest to largest. The right angle is the benchmark: angles smaller than it come first, then the right angle, then the angles that open wider.

We are learning to

• order turns and angles from smallest to largest,
• use the right angle as a benchmark when ordering,
• describe angles in everyday things as smaller than, the same as, or bigger than a right angle.

Success criteria

• I can order turns from smallest to largest.
• I can describe angles in everyday things.

You need

Right-angle testers. The angle cards (cut-out sheet 1). The worksheet. The unit’s self-check quiz.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the ordering; start Session B with the everyday angles and the quiz.

Watch for these ideas

• Ordering by where the angle sits on the page. Order by the amount of turn.
• Putting a full turn first because the arms line up. A full turn is the biggest turn.
• Ordering two big angles by arm length. Compare how far each one turns.

Answers

• Order, smallest first: Q, R, P, T, S (R is a right angle).
• Everyday: a door opened a little smaller; the corner of a book right angle; a laptop opened wide bigger; the hands of a clock at 3 o’clock right angle; the hands of a clock at 4 o’clock bigger; the hands of a clock at 1 o’clock smaller.
• Board: quarter, half, three-quarter.

Order the turns

Order the angles

Use your tester. Write the letters from the smallest angle to the biggest.

Smallest ______   ______   ______   ______   ______ Biggest

Everyday angles

Is each angle smaller than, the same as, or bigger than a right angle?

Angle cards

Cut out the twelve cards. On Day 3, pairs sort them into smaller than, the same as, and bigger than a right angle, checking with a tester. On Day 5, they order a handful from smallest to biggest.

Teacher note: card 1 smaller, card 2 right angle, card 3 bigger, card 4 smaller, card 5 bigger, card 6 right angle, card 7 smaller, card 8 bigger, card 9 smaller, card 10 bigger, card 11 right angle, card 12 smaller.

Turn cards and a right-angle tester

Cut out the twelve turn cards for the Day 1 game: draw a card, do the turn, and a partner checks. Cut out the tester too, for any child who needs one on Day 2.

What we know: Angles and Turns

Work on your own. You may use a right-angle tester.

1. Name the turn in question 1: ______________________
2. A three-quarter turn is ______ quarter turns.
3. A right angle is a ______________ turn.
4. Is the angle in question 4 smaller than, the same as, or bigger than a right angle? ______________
5. Is the angle in question 5 smaller than, the same as, or bigger than a right angle? ______________
6. The minute hand turns from 12 to 9. That is ______________ turn.
7. Which is bigger, a half turn or a quarter turn? ______________
8. Name something in the classroom that has a right angle: ______________________

Answers and marking guide

Answers

1. A half turn.
2. 3.
3. Quarter.
4. Smaller.
5. Bigger.
6. A three-quarter turn.
7. A half turn.
8. Any square corner: a book, a desk, a door, a window, a tile, a sheet of paper.

A quick three-level guide

Eight questions, three ideas. A child at standard compares an angle with a right angle whichever way it faces, and names the common turns.

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 turns, right angles, comparing with a right angle, clock turns, and ordering turns.