Class 5 Mathematics Chapter 3: Angles as Turns

Statue!

The Class 5 children are playing Statue in the school ground. They spin on one spot. Then the teacher shouts, Statue! Everybody freezes. Ashutosh has come right back to where he started. Sahana is facing the other way. Who turned more? To answer that, we need a way to measure a turn.

A full turn

Ashutosh keeps one foot fixed and spins all the way around. He stops facing the same way as before. That is a full turn. A giant wheel does the same thing. Each seat comes back to the spot it started from.

A half turn

Sahana spins only part of the way. She stops facing straight backwards. That is a half turn. Her nose now points the opposite way. Half a turn takes you across the circle, not around it.

A quarter turn

Now turn just enough to face sideways. Your left shoulder becomes your front. That is a quarter turn. It is the turn you make when you step off a path and walk along a wall instead.

Turns add up

Turns can be joined together. Two quarter turns in the same direction make a half turn. Four quarter turns bring you back to the start, so they make a full turn. Two half turns also make a full turn. Reema tried all three on the giant wheel.

Where a turn begins

A turn only makes sense when you know where it started. So mark the starting point first. On a giant wheel the seat has its own mark. In the Statue game, notice which wall you were facing before you spun.

Turning things at home

Turns are everywhere at home. A tap turns. A door on hinges swings open. A pair of scissors opens and closes. So do tongs and a clothes clip. The cover of a file swings back on its spine.

How far can it turn?

Every turning thing has its own limit. A clothes clip opens only a little, far less than a quarter turn. A door can swing much more than a quarter turn. A file cover can open flat, which is a half turn. A tap can keep going, turn after turn.

Your body knows turns

Stand still and face the door. Make a quarter turn to your right. Now make one more. You are facing away from the door. Two quarter turns have added up to a half turn, and your body felt it happen.

Remember

• A full turn brings you back to the start.
• A half turn leaves you facing the opposite way.
• A quarter turn leaves you facing sideways.
• Four quarter turns make one full turn.

Scenario:

A class plays a turning game in the yard. Each child faces the gate, then follows an instruction. Ravi makes a half turn and ends facing the wall behind him. Then he makes another half turn and faces the gate again. He says the second turn undid the first. His teacher asks the class what two half turns add up to. One full turn. The children check by walking it. Nita then makes four quarter turns and also ends facing the gate. The class writes both findings down. Two halves and four quarters each bring you back where you began.

Analysis:

Two different sets of turns and the same ending. A full turn is what returns you to the start, however it is split up.

Activity:

Stand facing a door. Make two half turns, then four quarter turns. Write where you end up each time.

Title:

Play Statue with turns

Safety:

Clear the floor of stools and wires before you spin.

What You Notice:

Two quarter turns always leave you facing the wall behind you. Four bring you back to the first wall.

The minute hand of a clock makes one full turn every hour.

A potter keeps the wheel spinning through full turn after full turn.

Adding quarter turns — Two to the side, four to the start. — Two quarter turns take you to the opposite side. Four bring you home.

Pragya's two straws

Pragya joins a green straw and a yellow straw with a paper clip. She holds the green one still. Then she turns the yellow one, a little at a time. The gap between the straws opens up. That gap is an angle. Every turn she makes gives the angle a new size and a new name.

The right angle

Pragya turns the yellow straw a quarter of a full turn. The two straws now make a neat corner, like the corner of a book. We call this a right angle. A quarter turn and a right angle are the same thing.

The acute angle

Now she turns less than a quarter turn. The gap is narrow and sharp. That is an acute angle. The corner of a slice of cake is acute. So is the angle between the blades of a pair of scissors barely opened.

The obtuse angle

Next she turns past a quarter but stops short of a half. The gap is wide and open. That is an obtuse angle. A book opened almost flat shows an obtuse angle between its covers.

The straight angle

Pragya keeps going until she has made a half turn. Now the two straws lie in one straight line. That is a straight angle. It looks like a single stick, but it is really two arms opened right out.

Can two acute turns stay acute?

Try it with the fan. Two small acute turns can still be acute. Two one-twelfth turns make a one-sixth turn, which is still acute. But two one-sixth turns make a one-third turn, and that is obtuse. So it depends on how big each one is.

Make your own angle tool

Cut a circle from tracing paper. Fold it in half, then in half again, then once more. Open it out and you have 8 equal parts. Fix a straw at the centre and mark a starting point. Your angle tool is ready.

Turns in eighths

Turn the straw by one part and you have made a one-eighth turn. One eighth is half of a quarter, so it is acute. Two eighths make a quarter turn, a right angle. Three eighths is obtuse. Four eighths is a half turn, a straight angle.

Sixths and twelfths

Fold a fresh circle in half, then into 3 equal parts. Now you have 6 parts. A one-sixth turn is acute. Fold one of those parts in half again. That smaller piece is a one-twelfth turn, the smallest tool in your set.

The minute hand measures turns

A clock face does the same job. The minute hand makes a full turn in 60 minutes. So 15 minutes is a quarter turn and 30 minutes is a half turn. 45 minutes is a three-quarter turn. A one-twelfth turn is just 5 minutes.

Remember

• A quarter turn is a right angle.
• Less than a quarter turn is acute.
• Between a quarter and a half turn is obtuse.
• A half turn is a straight angle.

Scenario:

A class compares three corners: a book corner, a slightly open door, and a wide open door. Imran says they are all angles so they are all the same. His teacher gives each child a book corner to hold against the others. The book corner fits the first exactly. The slightly open door is smaller than it. The wide door is bigger. The class names them. A quarter turn is a right angle, smaller than that is acute, and bigger is obtuse. Imran sees that the book corner worked as a measure, because it is a right angle he can carry about.

Analysis:

Imran treated all angles as one thing. A book corner is a right angle, so holding it against another angle sorts it at once.

Activity:

Use a book corner to test six corners in your room. Sort them into right, acute and obtuse.

Title:

Fold your own angle tool

Safety:

Ask an adult to help with the scissors and the pin.

What You Notice:

Two parts always make a neat corner, and four parts always make one straight line.

The corner of any page in your notebook is a right angle.

A paper fan opens through acute, right and obtuse angles as you spread it.

Naming angles by turn — Under a quarter is cute, over a quarter is obtuse. — Compare every angle with a quarter turn first, then give it its name.

Minutes and turns — Sixty minutes, one whole turn. — Share 60 minutes the way you share the circle, so 15 minutes is a quarter turn.

Two ways round

The clock on the classroom wall never stops. Its hands always travel the same way, past 1, then 2, then 3. Ravi spins his pencil the other way on the desk. Both are turns of the same size, but they are not the same turn. So we need two words, one for each way round.

Clockwise

The way the hands of a clock move is called clockwise. From the top they go to the right, then down, then to the left, then back to the top. Trace it with your finger on a clock face until the path feels easy.

Anti-clockwise

The opposite way round is called anti-clockwise. From the top it goes to the left first, then down, then to the right. A quarter turn clockwise and a quarter turn anti-clockwise are the same size. They simply land you in different places.

Four directions

Stand outside and face North. East is on your right, South is behind you and West is on your left. Going clockwise the order is North, East, South, West. Going anti-clockwise it is North, West, South, East.

One right angle on the compass

A right angle is a quarter turn, so it moves you to the next direction along. From North, one right angle clockwise takes you to East. The same right angle taken anti-clockwise takes you to West instead.

Two right angles

Two right angles make a half turn. From North you land on South. Turn the other way and you still land on South. A half turn is the one case where both directions agree.

Three and four right angles

Three right angles from North take you to West if you go clockwise. Four right angles make a full turn, so you finish exactly where you began. Facing East and turning four right angles leaves you facing East.

More than a full turn

What about five right angles clockwise? The first four bring you home. The fifth is one extra quarter turn. So from West you finish facing North. Count the whole turns first, then use whatever is left over.

Taps, lids and nuts

Turn a tap clockwise and the water shuts off. Turn it anti-clockwise and the water runs. A bottle lid closes clockwise too. Watch which way your hand goes the next time you open a jar.

Padma at the market

Padma stands facing the toy shop. She makes a half turn clockwise and now faces the sweet shop behind her. Could she have reached the sweet shop another way? Yes. A half turn anti-clockwise would have taken her there too.

Remember

• Clockwise follows the hands of a clock.
• Anti-clockwise goes the opposite way.
• One right angle moves you to the next direction.
• Four right angles bring you back to the start.

Scenario:

The tap by the playground in a school near Nashik drips all through the afternoon. The children notice a puddle growing under it. Their teacher asks them to watch how the tap is used. Most children push the handle but never turn it far enough. A tap only shuts when the handle is turned clockwise until it stops. The class measures the drip and finds that a slow leak can waste many buckets in a week. They paint a bright arrow on the wall above the tap. The arrow shows the clockwise way, and the puddle soon dries up.

Analysis:

A turn has a direction as well as a size. Knowing the clockwise way to close a tap saves water every single day.

Activity:

Check the taps at home. Note which way each one closes and whether any of them drips.

Title:

The compass floor game

Safety:

Move chairs out of the way before you start turning.

What You Notice:

Two right angles always land you on the opposite wall, whichever way you go round.

Most screws and bottle lids tighten clockwise and loosen anti-clockwise.

A merry-go-round usually turns anti-clockwise, the opposite way to a clock.

The clockwise order of directions — Never Eat Slimy Worms. — The first letters give North, East, South and West in clockwise order.