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**To be able to count on or back in equal steps including beyond zero.**

L.O.1 To be able to count on or back in equal steps including beyond zero.

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**We are going to count up in 25’s.**

Q. Will we meet the number 450 if we go up in 25’s? How do you know?

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**We shall start at 1000 and count back in 25’s**

We shall start at 1000 and count back in 25’s. You will need to say the next number before it is written down. We shall go round the class taking it in turns. Q. What will happen when we get to zero?

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**We shall count on and back in steps of 0.5.**

We’ll start at 0 go up to 10 then back to -5.

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**We shall count on and back in steps of 0.1.**

We’ll start at 0 go up to 4 then back to -2.

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**i In your book write the numbers we reach if we follow these rules:**

Start Steps Size Direction Finish number Forward 825 Back Back Forward Back Back Forward Forward Make up some more to test your partner.

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L.O 2 To be able to recognise reflective symmetry in regular polygons. To make and investigate a general statement about familiar shapes by finding examples that satisfy it.

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This square is folded. Q. What do we call the line created by this fold?

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**It is called a “line of symmetry”**

Q. Are there any other lines of symmetry in the square?

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**Q. In what other way can we find lines of symmetry?**

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**a line of reflective symmetry A line of symmetry is sometimes called**

a mirror line and sometimes called a line of reflective symmetry

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**Using mirrors find and draw in the reflective symmetry of the other polygons on Activity sheet 5a1.**

Copy into your book and investigate this statement: “The number of lines of symmetry of a regular polygon is always the same as the number of edges.”

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**“Irregular polygons have no lines of symmetry.”**

Do the same with this: “Irregular polygons have no lines of symmetry.” Are the two statements true or false? How do you know?

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We know that the first statement is true but the second is false as there are irregular polygons which have lines of symmetry. LOOK! Both these shapes are irregular but have lines of symmetry. Where are the lines of symmetry?

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**Q. Are the number of lines of symmetry on a**

Q. Are the number of lines of symmetry on a regular polygon always the same as the number of sides or edges? Q. Is there a rule we can make? Q. Is there a shape which does not fit this rule?

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**The vertical line is a line of symmetry.**

Draw the completed shape neatly in your book. Q. How many edges will the completed shape have?

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**Q. Is the shape a regular hexagon? Why?**

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**The shape is irregular and has ONE line of symmetry.**

Q. Will all irregular hexagons have one line of symmetry?

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**This irregular hexagon has no lines of symmetry.**

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**Q. Can we write down two statements that we think are true?**

Regular polygons have the same numbers of lines of symmetry as they have sides or edges. 2. Irregular polygons can have lines of symmetry.

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

Recognise that the number of axes of reflective symmetry in regular polygons is equal to the number of sides. Find examples that match a general statement, for example, a regular hexagon has 6 sides and 6 lines of symmetry.

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**To be able to visualise 2-D shapes and to recognise lines of symmetry.**

L.O.1 To be able to visualise 2-D shapes and to recognise lines of symmetry.

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**Close your eyes and visualise a square.**

Imagine there is a line joining the mid-point of two sides which are next to each other. Cut along this line. You now have two shapes. Q. What are the names of these shapes?

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**You might have thought of this.**

You have an isosceles right-angled triangle and an irregular pentagon.

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**Q. Do the two shapes have any lines of symmetry?**

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**This is the line which gives both shapes symmetry.**

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**This is the line which gives both shapes symmetry.**

You might be able to understand better if the square is rotated like this.

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Close your eyes again and imagine that the mid-points of the other two sides of the original square were also joined. Cut along this line so that you now have three shapes. Q. What are the three shapes? Q. Do they have lines of symmetry?

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**` You might have thought of this.**

You have TWO isosceles right-angled triangles and an irregular hexagon.

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**` These are the lines of symmetry.**

The triangles have ONE line of symmetry but the hexagon has TWO!

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L.O.2 To be able to complete symmetrical patterns with two lines of symmetry at right angles.

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**Complete the shape on the sheet OHT 5a. 1 you have been given**

Complete the shape on the sheet OHT 5a.1 you have been given. Measure accurately and carefully. There are TWO lines of symmetry. Before you begin try to think what the final shape will look like.

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**This is the shape you were given**

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**You should have drawn something like this.**

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**We’ll use another shape**

We’ll use another shape. I need a volunteer to complete this on the board. Q. Does it matter if we use a horizontal or vertical line of symmetry first?

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**Complete the shapes on Activity sheet 5a.2**

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**Q. How many sides has each of the finished shapes?**

Notice: The number of sides on each finished shape is an even number. Why is this? Has “doubling” anything to do with it? The shapes are all polygons because they have straight sides and are all irregular.

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Write the area of the shape on grid1 then complete the shape using the line of symmetry and record the area of the drawn shape. Predict its area mentally first! Write the prediction rule then finish the other shapes. Does your rule work?

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

Complete patterns squared paper with two lines of symmetry at right angles.

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**To be able to visualise 2-D shapes and to recognise lines of symmetry.**

L.O.1 To be able to visualise 2-D shapes and to recognise lines of symmetry.

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**Q. What are these two new shapes?**

You are going to close your eyes and visualise a shape as you did yesterday. This time you have a rectangle. Join the mid point of the longer side to the mid point of the shorter side and cut along that line so the rectangle is in two shapes. Q. What are these two new shapes?

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**You should see something like this.**

One shape is a scalene right-angled triangle. The other is an irregular pentagon.

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**Q. Do the two shapes have any lines of symmetry?**

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**Neither shape has a line of symmetry.**

Now imagine a rectangle as before. Imagine a line from the mid-point of a longer side to the mid-point of a shorter side and a line from this mid point to the mid-point of the other long side. Q. How many new shapes are made? What are their names?

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**You should see something like this.**

There are two scalene right-angled triangles and a pentagon. Only the pentagon has a line of symmetry.

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**This shows the ONE line of symmetry.**

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L.O.2 To be able to recognise parallel and perpendicular lines.

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**Here are a pair of parallel lines. **

We know they are parallel because the perpendicular distance between them is constant. Q. Write in your books any pairs of parallel lines you can see in the classroom. Check them carefully.

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**Q. Are there any parallel lines on shape 1?**

The use of arrows shows the parallel lines. What about the other shapes? Which ones do not have pairs of parallel sides?

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**We’ll concentrate on the properties of the rectangle.**

Q. What can you tell me about the sides and angles of this rectangle? Q. What symbol do we use to show an angle is a right angle? Q. Do you know any other way of describing two lines at right- angles?

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**Are there any perpendicular lines in the classroom? Where?**

Lines which are at right angles are said to be PERPENDICULAR to each other. Are there any perpendicular lines in the classroom? Where? Let’s look back to the 8 shapes. Are there any perpendicular edges on any of the other shapes on the board? Trap. Kite

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**Q. What is the name of this shape?.**

Q. Can you see any parallel and perpendicular lines? How many pairs of parallel? How many pairs of perpendicular? Q. Which other shape have we seen which has the same number of parallel and perpendicular lines?

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**The rectangle has the same number of parallel and perpendicular lines as the square.**

Q. With a partner draw a shape with one pair of parallel lines and two pairs of perpendicular lines.

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

Know that perpendicular lines are at right-angles to each other and parallel lines are the same distance apart. Recognise and identify parallel and perpendicular lines in the environment and in regular polygons such as the square, hexagon and octagon.

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L.O.1 To be able to recall facts in 5 and 6 times tables and begin to derive division facts.

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Q. What shape is this?

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**Q. If I have 6 irregular pentagons how many sides can I see altogether?**

Q. If I have 20 internal angles how many irregular pentagons do I have? Q. How many vertices are there with 8 irregular pentagons? Q. If I can see 30 sides how many irregular pentagons do I have?

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Q. What shape is this?

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**Q. If I have 5 irregular hexagons how many sides can I see?**

Q. How many vertices do 7 irregular hexagons have? Q. If I can see 24 sides how many irregular hexagons are there? Q. How many sides do 9 irregular hexagons have?

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L.O.2 To be able to recognise positions and use co-ordinates. To be able to recognise perpendicular and parallel lines.

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**REMEMBER….. E R T I C A L axis**

We are going to plot some co-ordinates on the grid. The first one is 7,2. Q. Where is this point on the grid? Q. Where is your name on the grid? Plot 7.2 with a small cross on your grid. Use a colour. REMEMBER….. The first number tells you the HORIZONTAL axis The second tells you the V E R T I C A L axis

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**5,4 ; 3,6 ; 1,8 Now we shall plot some more points. Plot these:**

5,4 ; 3,6 ; 1,8 What can you say about these points? Join 7,2 to 1,8 with a straight line. Are the points 2,7 ; 4,5 and 6,3 on this line? Which other points would fit on the line if we extended it?

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Find 3,4 I want to draw a new line through 3,4 that is parallel to the first line. Q. Which points would be on this new line? Write them in your book. When we are all agreed you may mark them on your grid.

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**This shows our parallel lines so far.**

I want to draw more parallel lines – the next one will pass through point 1,2. Write in your book the other points it will pass through. Do the same for a line going through 6,6 . When you’ve done that draw in the lines.

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**Our parallel lines should look like this.**

I now want to draw a line perpendicular to the others that passes through 7,9. Q. Which points will go on that line? Write in your book the points it will pass through. When we are all agreed you may mark them on your grid.

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**The perpendicular should look like this.**

Write in your books ALL the points the following perpendicular lines will pass through: A line through 5,10 A line through 0,1 When you have written all the points draw the lines on your grid.

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**Your completed grid should look like this.**

If it does you may have a HOUSEPOINT ! WOW!

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**On your new grid plot the points 0,8 and 2,8 then join them with a pencil and ruler.**

Q. How long is this line? The line is one side of a square. Complete the square. Plot the points 4,8 and 6,6. These points are the vertices of a square. How many squares can you draw with these two points as vertices?

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**Yours may look like this.**

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**On your new, new grid identify these points with a small cross:**

0, ,0 Q. If we join these points with a straight line what points will the line pass through? Let’s do it. Q. If we draw a parallel line through 0,2 which other points will our new line pass through? If I draw a perpendicular to this last line from 4,0 which points will it pass through? Q. If our last two lines are two sides of a square can you tell me some points on the other sides?

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**Yours may look like this !**

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

Read and plot points using co-ordinates in the first quadrant Know that perpendicular lines are at right angles to each other Know that parallel lines are the same distance apart.

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L.O.1 To be able to recall facts in 7,8 and 9 tables and begin to derive division facts.

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LOOK Q. What is a seven-sided shape called?

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**Q. If I have four heptagons how many sides do I have?**

Q. If I can see 70 sides how many heptagons do I have? Q. How many internal angles do 6 heptagons have?

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LOOK CAREFULLY Q. What is this shape called?

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**Q. I have a set of octagons and the total. number of sides is 48**

Q. I have a set of octagons and the total number of sides is 48. How many octagons are in my set? Q. If I have seven octagons how many internal angles are there? Q. How many sides are there in nine octagons?

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**LOOK EVEN MORE CAREFULLY**

Q. What is this shape called?

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**Q. If I have six nonagons how many sides can I see?**

Q. How many nonagons are there if I have thirty six internal angles? Q. How many nonagons are there if I can see forty five sides?

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L.O.2 To be able to visualise 3-D shapes from 2-D drawings.

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**Q. How many cubes do you think made up this solid shape?**

Q. How could we check?

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**Q. How many more cubes do we need to make this 3-D shape?**

Q. How many extra cubes are needed to make this shape into a cube? Q. What size would the cube be?

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**Q. How many squares would you see if you looked down on the first shape?**

On your squared paper draw what you would see if you looked down on the first 3-D shape. Q. How many squares would you see if you looked at the first shape from the end where one cube projects. Draw this view on your paper.

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**Q. How many squares would you see if you looked down on the second shape?**

Draw that view. Q. How many squares would you see if you looked at the second shape from the “staircase” end. …from the end which has three projecting blocks? Draw both views.

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**These are three views of a shape made from seven interlocking cubes.**

Work with a partner to make the shape. Be prepared to talk about how you decided what to do.

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**Q. Is this shape the same as the one you were asked to make?**

Q. Which of the 3-D representations make it easier for you to visualise the 3-D shape?

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

Visualise 3-D shapes from 2-D drawings

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