Properties of Shape · 2020-04-03 · 5 –Properties of Shape • If I turn from North East to...

5Fluency & Reasoning Teaching Slides

Properties of Shape

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Fluency & Reasoning Teaching Slides

Measuring Angles in Degrees

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Activity 1 Measuring Angles in Degrees

5 – Properties of Shape

Use the sentence stems to describe the turns made by the minute hand. Compare the turns to a right angle.

The turn from ____ to ____ is ________ than a right angle. It is an _______ angle.





The turn from ____ to ____ is ________ than a right angle. It is an _______ angle.

12 4 largerobtuse



The turn from ____ to ____ is ________ than a

right angle. It is an ______ angle.





The turn from ____ to ____ is ________ than

a right angle. It is a ______ angle.







122 smaller

acute



38 larger

obtuse

The turn from ____ to ____ is ________ than

a right angle. It is a ______ angle.

312 larger

reflex



Use the compass to complete the table.

Turn Degrees Type ofangle

Fraction of a turn

North East to South East clockwise

90⁰ Right angle ¼ of a turn

North West to North West clockwise

South West to South East anti-

clockwise

South West to ________ clockwise

180⁰

North East to East clockwise

1/8 of a turn




Use the compass to complete the table.

Turn Degrees Type ofangle

Fraction of a turn

North East to South East clockwise


North West to North West clockwise

360⁰ Full angle 1 of a turn

South West to South East anti-

clockwise


South West to ________ clockwise

180⁰ Straight angle ½ of a turn

North East to East clockwise

45⁰ Acute angle 1/8 of a turn


North East


Reasoning 1 Measuring Angles in Degrees


Which angle is the one odd out?



53⁰ is the odd one because the others are

multiples of 45⁰


Could another angle be the odd one out for a different reason??

Which angle is the one odd out?




• If I turn from North East to North West, I have turned 90⁰.

• If I turn from East to North West, I will have turned through an obtuse angle.

• If I turn from South West to South, my turn will be larger than 350⁰.

Always, Sometimes or Never True?




• If I turn from North East to North West, I have turned 90⁰.

• If I turn from East to North West, I will have turned through an obtuse angle.

• If I turn from South West to South, my turn will be larger than 350⁰.

Always, Sometimes or Never True?

All are sometimes true, depending on whether you turn clockwise or anti-clockwise or even

more than one turn.

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Discuss

What unit do we use to measure angles?

How can we tell whether an angle is acute?

How do we know which scale to use on a protractor?

Where will you place your protractor when measuring an angle?

Does moving the paper help you to measure an angle?

13

Measuring Angles in Degrees




Measuring with Protractor


Activity 1 Measuring with Protractor

Put these angles in order of size. Explain how you know.


a b c d




a bcd

Put these angles in order of size. Explain how you know.



Read the angles shown on the protractor.




Read the angles shown on the protractor.


What’s the same? What’s different?

40⁰ 65⁰

70⁰

?



Estimate the size of the angles and then use a protractor to measure them to the nearest degree.

How close were your estimates?





How close were your estimates?


30⁰ 65⁰ 30⁰


Reasoning 1 Measuring with Protractor


Who do you agree with?

Explain why.?

I have measured the angle correctly because my protractor

is on the line accurately.

I have measured the angle correctly because my

protractor is the right way round.




Who do you agree with?

They are both correct. It doesn’t matter which way the protractor is as long as it is placed on the angle correctly.

I have measured the angle correctly because my protractor

is on the line accurately.

I have measured the angle correctly because my

protractor is the right way round.





110⁰ 145⁰

167⁰





138⁰ 130⁰ 148⁰



Identify obtuse angles in the image. Estimate the size of the angles, and then measure them.




Identify obtuse angles in the image. Estimate the size of the angles, and then measure them.


45⁰ (Acute)

25⁰ (Acute)110⁰ (Obtuse)

140⁰ (Obtuse)




Leanna is measuring an obtuse angle. What’s her mistake?




Leanna has not placed the 0 line of the protractor on one of the arms of

the angle.

Leanna is measuring an obtuse angle. What’s her mistake?




How many ways can you find the value of the angle?




You may:

• Subtract 140-17=123⁰

• Add up on the protractor as a number line e.g. 3 + 100 + 20 = 123⁰

• Place the protractor correctly

How many ways can you find the value of the angle?


Discuss

How do you know an angle is obtuse?

Can you see where obtuse angles would be measured on the protractor?

Can you estimate the size of this angle?

What is the size of the angle? What mistake might someone make?

Where will you place your protractor first?

33

Measuring with Protractor




Drawing Accurately


Activity 1 Drawing Accurately

Draw lines that measure:




Draw lines that measure:


What’s the same? What’s different??



Draw:




Draw:


What do you notice about your pair of angles??



Draw:




Draw:


Compare your angle with a partner.?


Reasoning 1 Drawing Accurately


Always, Sometimes, or Never True?

• Two acute angles next to each other make an obtuse angle.

• Half an obtuse angle is an acute angle.

• 180⁰ is an obtuse angle.


Reasoning 1 Drawing Accurately



• Two acute angles next to each other make an obtuse angle.

• Half an obtuse angle is an acute angle.

• 180⁰ is an obtuse angle.


Discuss

How many millimetres are in a centimetre?

How do we draw a line that measures _____?

Explain how to draw an angle.

What’s the same and what’s different about drawing angles of 80⁰ and 100⁰?

How can I make this angle measure ___ but one of the lines have a length of ___ ?

43

Drawing Accurately




Angles on a Straight Line


Activity 1 Angles on a Straight Line

Fill in the blanks.


There are ___ degrees in a right angle.

There are ___ right angles on a

straight line.

There are ___ degrees on a straight

line.



Fill in the blanks.


There are ___ degrees in a right angle.

There are ___ right angles on a

straight line.

There are ___ degrees on a straight

line.

90

2

180



Calculate the missing angles.


33⁰127⁰

94⁰a bc





147⁰ 53⁰ 86⁰

33⁰127⁰

94⁰a bc





127⁰

64⁰

33⁰x

yz

64⁰37⁰





16⁰ 52⁰ 57⁰

Is there more than one way to calculate the missing angles??

127⁰

64⁰

33⁰x

yz

64⁰37⁰


Reasoning 1 Angles on a Straight Line


Tia is measuring two angles on a straight line.

Explain why at least one of Tia’s angles must be wrong.

My angles measured 63⁰and 129⁰.

?




Tia is measuring two angles on a straight line.

Her angles total more than 180⁰

My angles measured 63⁰and 129⁰.




Calculate the size of the angles.

40⁰

e

f

g

• The total of angle f and g are the same as angle e.

• Angle e is 30⁰ more than the size of given angle.

• Angle f is 10⁰ more than angle g.


Discuss

How many degrees are there in a right angle?

How many will there be in two right angles?

If we place two right angles together, what do we notice?

How can we calculate the missing angles?

How can we mentally subtract a number from 180⁰?

55

Angles on a Straight Line




Angles around a Point


Activity 1 Angles around a Point

Complete the sentences.


¼ of a turn

= 1 right

angle

= 90⁰

½ of a turn

= __ right

angles

= _____⁰

of a turn

= 3 right angles

= _____⁰

A full turn

= __ right angles

= _____⁰



Complete the sentences.


¼ of a turn

= 1 right

angle

= 90⁰

½ of a turn

= __right

angles

= _____⁰

of a turn

= 3 right angles

= _____⁰

A full turn

= __ right angles

= _____⁰

2

180270

4

360

34





67⁰a

65⁰b 67⁰

34⁰51⁰

ab

a =

b =

a =

b =





a

ba

b

79⁰a =

b = 113⁰

25⁰a =

b = 129⁰

67⁰ 65⁰67⁰

34⁰51⁰


137⁰

157⁰

61




238⁰aaa

a

aaa

a a

a





238⁰ 137⁰

157⁰

aaa

a

aaa

a a

a

45⁰ 122⁰ 66⁰


Reasoning 1 Angles around a Point


a

b

de

c

Write other sentences about this picture.




a

b

de

c

Write other sentences about this picture.




66⁰

a

c

b

Two sticks are on a table. Without measuring, find the three missing angles.


Discuss

How many right angles are there in 14 , 12 , 34 of a full turn?

If you know a half turn/full turn is 180/360 degrees respectively, how can this help you calculate the missing

angle?

What is the most efficient way to calculate a missing angle? Would you use a mental or written method?

When you have several angles, is it better to add them first or to subtract them one by one?

67

Angles around a Point




Lengths and Angles in Shapes


Activity 1 Lengths and Angles in Shapes

Look at the square and the rectangle.





Calculate the size of the angles in each shape.


a a

bb

c

d

e c e

d



Calculate the size of the angles in each shape.


What’s the same? What’s different?

a

b d90⁰

90⁰

45⁰

c

45⁰

135⁰

90⁰ 90⁰

e

90⁰

?



Here is a square cut into two triangles.


Use the square to calculate the size of the angle.?



Here is a square cut into two triangles.


90⁰

45⁰90⁰+ 90⁰+ 45⁰= 225⁰


Reasoning 1 Lengths and Angles in Shapes


Do you agree? Explain why.

The missing angles are 60⁰because 180⁰ / 3 = 60⁰

?

Rosie is calculating the missing angles in the shape.




Rosie is calculating the missing angles in the shape.

She is wrong. The angles are not equal.

The angles will be worth 45⁰, 90⁰, and 45⁰ because the line shows a square being split in half diagonally. This

means 90⁰ has been divided by 2.

The missing angles are 60⁰because 180⁰ / 3 = 60⁰




Esin has this triangle on the left side. She makes the composite shape on the right using triangles identical to

the one on the left.

60⁰

60⁰60⁰

47 mm

47 mm

47 mm

a

b

c

Calculate the perimeter of the shape and the missing angles.?




Esin has this triangle on the left side. She makes the composite shape on the right using triangles identical to

the one on the left.

60⁰

60⁰60⁰

a

b

c

Perimeter= 47mm x 9 = 423mm

a = 60⁰ x 4 = 240⁰

b = 60⁰ x 2 = 120⁰

c = 60⁰ x 3 = 180⁰

Use your own triangle, square or rectangle to make a similar problem.

47 mm

47 mm

47 mm

?


Discuss

Look at the rectangle and square. Where can you see parallel lines? How many right angles do they have?

What can you say about the lengths of the sides in a rectangle or in a ___?

If I fold a square in half diagonally to make a triangle, what will be the size of each of the angles in the triangle?

Using what you know about squares and rectangles, how can you calculate the sizes of the angles?

78

Lengths and Angles in Shapes




Regular and Irregular Polygons


Activity 1 Regular and Irregular Polygons

Sort the shapes into irregular and regular polygons.




Sort the shapes into irregular and regular polygons.





Draw a regular polygon and an irregular polygon on the grids.


. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .



Look at the 2D shapes. Decide whether the shape is a regular or irregular polygon.


Measure the angles to check.?



Look at the 2D shapes. Decide whether the shape is a regular or irregular polygon.



Reasoning 1 Regular and Irregular Polygons



• A regular polygon has equal sides but not equal angles.

• A triangle is a regular polygon.

• A rhombus is a regular polygon.

• The number of angles is the same as the number of sides in any polygon.





• A regular polygon has equal sides but not equal angles.

• A triangle is a regular polygon.

• A rhombus is a regular polygon.

• The number of angles is the same as the number of sides in any polygon.

• Never true – equal sides have equal angles.

• Sometimes true – equilateral triangles are but scalene are not.

• Sometimes true – if the rhombus has right angles and is a square.

• Always true.




How many regular and irregular polygons can you find in this picture?


Discuss

What is a polygon?

Can a polygon have a curved line?

Name a shape which isn’t a polygon.

What makes a polygon irregular or regular?

Is a square regular?

Are all hexagons regular?

89

Regular and Irregular Polygons




Reasoning about 3D Shapes


Activity 1 Reasoning about 3D Shapes

Look at the different nets. Describe the 2D shapes used to make them and identify the 3D shape.




Look at the different nets. Describe the 2D shapes used to make them and identify the 3D shape.




Use equipment, such as Polydron or 2D shapes, to build the 3D solids being described.






Can the descriptions make more than one shape??



Draw another dot on the nets so the dots are on opposite faces when the 3D shape is constructed.



Reasoning 1 Reasoning about 3D Shapes


Do you agree? Explain why.

Malachi says:

If two 3D shapes have the same number of vertices,

then they also have the same number of edges.

?




Malachi says:

No, e.g. a square-based pyramid and a triangular prism.

If two 3D shapes have the same number of vertices,

then they also have the same number of edges.




Example is shown above.

Using different 3D solids, how can you represent them from different views? Work out which representation goes

with which solid.

Front view

Plan view

Side view

?


Discuss

What’s the difference between a face and a curved surface?

Name some 3D solids which have curved surfaces and some which don’t.

What faces can we see in the net? What shape will this make?

Which face will be opposite this face? Why?

Can we spot a pattern between the number of faces and the number of vertices a prism or pyramid has?

102

Reasoning about 3D Shapes


Properties of Shape · 2020-04-03 · 5 –Properties of Shape • If I turn from North East to...

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