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L.O.1 To be able to recall the 9 times table and use it to derive associated number facts

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9

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Q. Can we use our knowledge of the 9 times table to say the 90 times table?

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. 1

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. 9 x9 clock

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**Q. How can we use our x9 clock to work out 40 x 9?**

x9 clock

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**The outer number divided by the inner one is always 9.**

x9 clock

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**Q. How can we use our x9 clock to work out 540 ÷ 9?**

x9 clock

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L.O.2 To understand and use angle measure in degrees, To be able to identify and estimate acute and obtuse angles To be able to calculate angles in a straight line.

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**Q. What unit do we measure angles in?**

REMEMBER… An ANGLE is an amount of TURN. Q. What unit do we measure angles in?

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**We use the symbol ° to show degrees.**

Q. How many degrees are there in a right angle? We use the symbol ° to show degrees. like this 36° or 178° or 317°.

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**What is the size of this angle?**

What is it called?

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**Q. What is the name of an angle smaller than 90°?**

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**An angle less than 90° is called an acute angle.**

Copy into your book: Angles < 90° are called acute angles

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. START FINISH The horizontal line on the right has been turned through 1 right angle or 90°.

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**Estimate the size of these angles.**

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**Estimate the size of these angles.**

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**What do we know about A + B?**

A + B are called COMPLEMENTARY angles.

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**Q. What size are these angles?**

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**Q. What size is this angle now?**

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**The angle is 180° and is made up of 2 right angles.**

Copy into your books: Straight line = 2 right angles = 180°

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**90° < Angles < 180° are called obtuse angles.**

Complementary angles on a straight line are called : obtuse acute Copy into your book: 90° < Angles < 180° are called obtuse angles.

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Oral work with 2D shapes.

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**By the end of the lesson children should be able to:**

Know that an angle less than 90° is acute; an angle between 90° and 180° is obtuse. Begin to identify and estimate acute, obtuse and right angles. Identify acute, obtuse and right angles in 2D shapes. Calculate angles in a straight line.

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**To be able to say whether angles are acute, obtuse or right angles. **

L.O.1 To be able to say whether angles are acute, obtuse or right angles. To be able to estimate and order angles.

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**Look at each of these angles.**

Decide if each is A acute, O obtuse or R right-angled. 1 2 3 5 4 6 7 8

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**Q. What could we use in the classroom to**

Q. What could we use in the classroom to check that an angle is a right angle?

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**Q. How many angles has this triangle?**

Q. What is the name of this angle? Q. What size is this angle?

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**We are going to identify each angle and write in its letter.**

A B C D E F G H I

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**Now we shall estimate to put the letters in order of size.**

A B C D E F G H I How can we be sure?

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**L.O.2 To be able to calculate angles in a straight line**

To be able to use a protractor to measure and draw acute and obtuse angles to 5°

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**We have four strips of card.**

They are at right angles. We are going to move the red one !

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. Q. How many degrees has the red strip turned?

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. Q. How many degrees has the strip turned now ?

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. Q. How many degrees has the strip turned?

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. The strip has moved all the way round to where it started. How many degrees has it turned?

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**A whole turn = 4 right angles = 360°**

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REMEMBER…. It is possible to turn through more than 360°

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LOOK… Q. How many degrees has the red strip turned now ?

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**What is the angle of turn?**

The circle has 10 equally spaced points on its circumference. Q. If the arrow moves around all ten points and ends back where it started how many degrees has it turned through? Q. If the arrow moves to the next point on the circumference how many degrees has it turned through? What is the angle of turn?

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**The circle has 10 equally spaced points on its circumference.**

Q. If the arrow moves around all ten points and ends back where it started how many degrees has it turned through? ° Q. If the arrow moves to the next point on the circumference how many degrees has it turned through? 36° The angle of turn if the arrow moves to the next point is 360° ÷ 10 = 36°

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The line is a RADIUS. It connects the centre of the circle in a straight line to a point on the circumference. Where should I draw another radius to make an angle of 72° ?

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**36° x 2 = 72° Either of the dotted lines will give an angle of 72°.**

One is clockwise from our original radius and the other is anti-clockwise. 72° 72°

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**Where should I draw another radius to make an angle of 108° ?**

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**36° x 3 = 108° Either of the dotted lines will give an angle of 108° .**

One is clockwise from our original radius and the other is anti-clockwise. 108° 108°

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**Where should I draw another radius to make an angle of 144° ?**

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**36° x 4 = 144° Either of the dotted lines will give an angle of 144° .**

One is clockwise from our original radius and the other is anti-clockwise. 144° 144°

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**This circle has 9 equally spaced points on its circumference.**

Q. If the arrow moves to the next point on the circumference how many degrees has it moved through? Q. What is the angle of turn?

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**This circle has 9 equally spaced points on its circumference.**

Q. If the arrow moves to the next point on the circumference how many degrees has it moved through? 40° Q. The angle of turn if the arrow moves to the next point is 360° ÷ 9 = 40 °

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**Calculate and write down the following angles of turn moving clockwise:**

from A to C from C to F from B to G from D to G from C to I from A to G from H to E A B H G I C D F E

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**The points are joined in order. How many sides has the shape?**

1 9 2 3 4 8 7 6 5

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**The shape has 9 sides so is called a NONAGON.**

1 9 2 3 4 8 7 6 5 The sides are the same length, the angles are the same so it is REGULAR.

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**There are 9 internal angles. They are all the same.**

1 9 2 3 4 8 7 6 5 Each internal angle is 140°.

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**The points are joined differently. What is this shape called?**

1 9 2 3 4 8 7 6 5

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**It has 18 straight edges so it must be a polygon.**

9 2 3 4 8 7 6 5 Some of the edges turn inwards so it is a CONCAVE POLYGON

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**There is a regular nonagon inside the shape!**

1 9 2 3 4 8 7 6 5 What size are the angles on the circumference of the circle?

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**Using a corner of paper we see the angles are about 100°.**

9 2 3 4 8 7 6 5 Estimate then measure the size of some other angles.

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**The circles are in pairs. **

Number the points round each circle. Start at the top with 1. Go clockwise. Be accurate. Use a sharp pencil. For column A join each point to THE NEXT ONE. For column B join each point to THE NEXT BUT ONE i.e. 1→3, 3→5 and so on. A B

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**You should have something like this.**

B You should have something like this. What can we say about the shapes we have made?

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**Copy and complete this table**

Number of points and name of shape Angle at centre of circle 3 4 5 6 7 8 nonagon 360° ÷ 9 = 40° decagon 360° ÷ 10 = 36°

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**triangle 360° ÷ 3 = 120° 4 square 360° ÷ 4 = 90° 5 pentagon**

Number of points and name of shape Angle at centre of circle triangle 360° ÷ 3 = 120° square 360° ÷ 4 = 90° pentagon 360° ÷ 5 = 72° hexagon 360° ÷ 6 = 60° heptagon 360° ÷ 7 = 51° octagon 360° ÷ 8 = 45° nonagon 360° ÷ 9 = 40° decagon 360° ÷ 10 = 36°

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**By the end of the lesson children should be able to:**

Begin to identify, estimate and calculate acute, obtuse and right angles. Identify acute, obtuse and right angles in 2-D shapes Estimate the size of angles and begin to use a protractor to measure angles.

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L.O.1 To be able to recall the 7 times table and use it to derive associated number facts.

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7

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. 7 x7 clock

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**Answer these in your books:**

1.Q. What is 40 x 7? 2.Q. What is 6 x 70? 3.Q. What is 3 x 0.7? 4.Q. What is 90 x 7? 5.Q. What is 5 x 70? 6.Q. What is 8 x 0.7? 7.Q. What is 7 x 0.07?

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**Q. What is the outer number divided by the inner number?**

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L.O.2 To be able to calculate angles in a straight line To be able to use a protractor to measure and draw acute and obtuse angles to 5°

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**triangle 360° ÷ 3 = 120° 4 square 360° ÷ 4 = 90° 5 pentagon**

The angle for the heptagon is really ° but we’ll call it 51°! Number of points and name of shape Angle at centre of circle triangle 360° ÷ 3 = 120° square 360° ÷ 4 = 90° pentagon 360° ÷ 5 = 72° hexagon 360° ÷ 6 = 60° heptagon 360° ÷ 7 = 51° octagon 360° ÷ 8 = 45° nonagon 360° ÷ 9 = 40° decagon 360° ÷ 10 = 36° NOTICE how the angle reduces as the number of points grows

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**We are going to look at the pentagon**

B We are going to look at the pentagon Draw lines between two adjacent points on the circumference to the centre of the circle to make an angle. Q. What did we calculate this angle to be?

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**You should have something like this. **

Measure the angle to check it is 72°. Q. What type of angle is this? Now draw in the angle at the centre for each of the other shapes in column A. Measure each of the angles and compare them with those in the table. What do you notice? 72°

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**There are 5 interior angles in the regular pentagon. **

Q. What type of angles are these? Measure and record these angles. Q. What size is each angle? Measure and record the interior angles of the other regular polygons. Q. Are all their interior angles obtuse? What do you notice about them? X X X X X

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**The second shape looks like a regular pentagon at the centre with triangles on the outside.**

The outside edge makes a concave polygon. Q. How many sides has this concave polygon? Measure and record the angles on the circle. Do the same for the other concave polygons in column B. What do you notice? What shapes do you recognise?

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**- Q. What size do you think these two angles are?**

B Q. What must be the sum of the two angles?

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**In your book draw two diagrams with angles**

In your book draw two diagrams with angles like the ones on the previous slide. Measure and record your angles. Check the angles on your partner’s diagrams.

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REMEMBER… When you are measuring angles with a protractor it is helpful if you first ESTIMATE the size of the angle then have a way of checking.

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**By the end of the lesson children should be able to:**

Begin to identify, estimate, order, measure and calculate acute, obtuse and right angles; Calculate angles on a straight line.

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KS3 Mathematics S1 Lines and Angles

KS3 Mathematics S1 Lines and Angles

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