Introduction

Teachers notes KS1 KS3 KS4 Printable page KS2 Shape These units are designed to make it easy for a pupil to find their way to some mathematics - but not so easy for them to find this page! The teacher may be sitting one-to-one with the pupil, or allowing groups of pupils to work alone. If the teacher has the appropriate equipment - a large projected computer screen - they could use these materials with the whole class. This page contains suggested tasks and further questions you could ask the pupils on each topic. Try to introduce and use words from the listed vocabulary - which are highlighted here in bold the first time they are mentioned. There is a long list of words for Years 4, 5 and 6 to learn! Interactive exercises will use interactive buttons. See the page on buttons. The circle is not included in the KS2 resources but in KS3 instead. These notes - and the units themselves - are still in an early stage of development. Any comments would be appreciated - particularly from KS2 teachers. Overall there are 17 topics arranged in four sections: KS1 1. Recognising 2. Describing 3. Creating KS2 4. Lines 5. Angles 6. Measures 7. Classifying KS3 & KS4 Foundation 8. Angles & lines 9. Polygons 10. Circles 11. Constructing KS4 Higher 12. Angles and lines 13. Circle theorems 14. Circles and angles 15. Congruence 16. Locus 17. Think!	4. Lines >> a1 Introduce the words parallel, perpendicular and diagram. Level 3 a2 Which lines are parallel and perpendicular? Level 3 a3 Describe each group. Level 3 a4 Move the parallel lines into groups. Level 3 b1 What is the connection between the red and blue lines? Level 3 b2 What is the connection between the red and blue lines? Level 3 b3 Introduce the word equilateral. Some lines cross over others. The point where this occurs is called the point of intersection. Level 3 b4 What is meant by exactly the same? Introduce the word congruent? Level 3 c1 These shapes are called parallelogram and rhombus. What are their properties? Level 3 c2 What is special about this hexagonal shape? What does regular mean? The other quadrilateral is a rhombus. What are its properties? Level 3 c3 What does isosceles or equilateral mean? The seond quadrilateral is a kite. What are its properties? Level 3 c4 What does quadrilateral mean? Level 3
	5. Angles >> a1 How many sides does this shape have? It is called a heptagon. Level 3 a2 Name the shapes - right angled triangle, square, quadrilateral. Level 3 a3 6. The lines are perpendicular. Level 3 a4 How many degrees in a right angle? What do the two angles always add up to? Level 3 b1 Introduce the terms acute and obtuse. Level 3 b2 Use the terms acute, obtuse and right angle. Level 3 b3 Explain the difference between convex and concave. Level 3 b4 It cannot be done! Why not? How many vertices does this polygon have? What is it called? Level 3 c1 What do the angles add up to? Level 5 c2 What do the angles round a point add up to? Angles bigger than 180 degrees are called reflex. Level 5 c3 The sum of the angles in a triangle equals the "angle in a straight line", i.e., 180 degrees. Level 5 c4 Try to make a rectangle. What do the angles add up to? Level 5
	6. Measures >> a1 Count the squares. This is called the area of the rectangle. Introduce perimeter too. Could also use oblong instead of rectangle.   a2 Use the blue square to count. Check the perimeter too.   a3 Two halves make a whole.   a4 Look for areas to combine into one who square unit.   b1 Pupils must understand they should use all 12 squares to make shapes, and then find the perimeter.   b2 This is a maximising problem. The largest area will be when the rectangle is a square, 64 square units. Note the word construct instead of make.   b3 Interactive exercise. The first page to use interactive buttons. Make sure the pupils understand what each one does. Do all the shapes have the same perimeter? How about areas of 3 square units?   b4 Interactive exercise. Make sure the pupils understand the buttons.   c1 The blue rectange should be compared with the yellow ones. What are the dimensions of the yellow rectangles?   c2 Estimate the areas using the grid.   c3 The parallelogram is being "sheared" and so its area does not change.   c4 Open ended. Why does the perimeter change when the top red point is moved? When is the perimeter minimum for any given area?
	7. Classifying >> a1 Name each shape. Describe symmetries, any properties of lines or angles.   a2 Name each polygon. What are the green lines called? How many in each polygon? How do they show you what the angles in the polygon add up to? How many of these diagonals would an octagon have?   a3 Identify correctly the parallelogram, rhombus, trapezium, rectangle and square. What properties do they have involving parallel lines, perpendicular lines, angles?   a4 Identify correctly the parallelogram, rhombus, trapezium, rectange, square, kite, quadrilateral with no properties, quadrilateral with one right angle.   b1 Each polygon must be moved to the correct region. Check correct terms: equilateral, isosceles, square, quadrilateral, regular, irregular   b2 Give accurate descriptions for each type of shape.   b3 Give accurate descriptions for each type of shape.   b4 Give accurate descriptions for each type of shape. Is it possible for an equilateral shape not to be regular? (Yes - a rhombus.)   c1 Can you make a square or hexagon? What other shapes can you make? What are the areas of each piece? There are 5 tangram pieces; note that only one of the two red parallelograms should be used in any particular construction.   c2 Interactive exercise. Can you construct scalene, isosceles, equilateral (not possible!) and right-angled triangles? Find ones with the largest possible area, or smallest possible area. Compare with c3.   c3 Interactive exercise. Can you construct scalene, isosceles, equilateral and right-angled triangles? Find ones with the largest possible area, or smallest possible area. Compare with c2.   c4 Interactive exercise. Can you construct scalene and equilateral quadrilaterals? How about a square, rectangle, parallelogram, rhombus (not obvious but possible), kite, trapezium? Find ones with the largest possible area, or smallest possible area.