Introduction

Teachers notes KS1 KS2 KS4 Printable page KS3 & KS4 Foundation 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. The topics are suitable for both KS3 and KS4 Foundation. There is one remaining unit targetted at KS4 Higher. Interactive exercise will use interactive buttons. See the page on buttons. All the Constructing tasks are of this type. These notes - and the units themselves - are still in an early stage of development. Any comments would be appreciated - particularly from KS3 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!	8. Angles & lines >> a1 These angles are called adjacent angles. They always add up to 180°. Use the letters to describe the angles, ie., Ð ACD and ÐBCD. a2 What do you notice? The angles round a point always add up to 360°. Use the letters to describe the angles too. For example, angle 1=ÐABD. a3 Opposite angles are equal. Notice the connection with the diagonals of a rectangle. a4 Make sure students understand the difference between acute, obtuse, right angle and reflex. b1 What does parallel and perpendicular mean? b2 The yellow angles are called alternate angles and are always equal. What do you call the points where the lines cross? b3 The green angles are called corresponding angles and are always equal. b4 Students should point out the 3 angles equal to the green one, and 3 angles equal to the yellow one. c1 What happens when you turn the pointer more than 360°? What happens when it is moved clockwise? c2 Blue=45°, yellow=30°, brown=135°, red=120°, purple=60°, green=80°. Which angles are acute, which are obtuse? c3 What do you notice about the 3 angles in the blue triangle? They always add up to 180°. What is special about the red triangle? What are the angles in an equilateral triangle? c4 What do you notice about the 4 angles? They always add up to 360. d1 Use the properties of alternate angles. d2 Use the properties of alternate and corresponding angles. d3 Use the properties of alternate and corresponding angles. d4 The three angles at C must each be 120°. Then use the properties of alternate and corresponding angles. What is each of the three polygons called?
	9. Polygons>> a1 Equilateral, scalene, isosceles, right angled. a2 Square, parallelogram, trapezium, rhombus, quadrilateral, rectangle, kite, right-angled. Can you make the kite into an arrowhead? a3 What is each shape called? a4 What is each shape called? b1 Can you make a square, rectangle or isosceles triangle? Is a kite, pentagon, hexagon or octagon possible? b2 Squares and octagons can make a semi-regular tesselation. b3 Total of the angles inside an n-sided polygon is 180(n-2)°. b4 Exterior angles add up to 360°. c1 The area of a triangle=half the base x height c2 The area is unchanged by "shearing". c3 The area of a prallelogram=base x height c4 Why does the area not change when you move the red point? d1 Interactive exercise. Can you construct equilateral, isosceles, right-angled or scalene triangles? (Equilateral is not possible!) d2 Interactive exercise. How many isosceles triangele can be constructed in total? (28?) d3 Interactive exercise. Can you construct a square, rectangle, parallelogram, general quadrilateral or kite? (A rhombus is not possible!) d4 Interactive exercise. How many squares can be constructed in total? (6?)
	10. Circles >> a1 How do you change each circle? a2 Can you make them the same size and just touching? a3 What does concentric mean? a4 What other patterns can you make? b1 Make sure the differences between radius, diameter, chord, circumference and tangent are understood. b2 When do a sector and a segment look the same? b3 What is each polygon called? Plot the values of the areas on a graph. b4 The area is approximately 3 times the square of the radius. c1 The radius and tangent will be perpendicular. c2 The radius bisects the chord. c3 Interactive exercise. Explain first what each of the buttons do. c4 Interactive exercise. Explain first what each of the buttons do.
	11. Constructing >> a1 Construct a scalene triangle by using the 'construct a line' button. a2 Construct a scalene quadrilateral by using the 'construct a line' button. a3 Construct a right-angled triangle by using the 'construct a line' button. a4 Construct a parallelogram triangle by using the 'construct a parallel line' button. b1 b1-b4 give the student four stages in constructing an equilateral triangle. First add a side. b2 This time the student has to construct a point and two sides. b3 First a circle must be constructed to allow point C to be identified. b4 The student has to construct the triangle starting with only one side AB. c1 c1-c4 give the student four stages in constructing a square. c2 The 'construct a parallel line' button is needed. c3 Two points and two lines have to be constructed. c4 The student has to construct the square starting with only one side AB. d1 Use the perpendicular line button. d2 Use the perpendicular line button. d3 Difficult! First you have to construct a circle centred on C. d4 More difficult. First construct a point and then a circle centred at C that passes through the point. e1 Use the compass to construct a point on one line which is the same distance from A as the given point on the other line is. e2 Use the midpoint button. e3 First construct two circles of radius AB. e4 Repeat the solution to b3 then add the midpoint. f1 First construct two circles of radius AB. f2 First construct one circle of radius AB and chose a point on it. f3 Use the compass to construct the lines. f4 Use the compass to construct the lines.