Year 7 Unit Plan Angle Connections For Scribd

Unit Plan for Year 7 Angle Connections Unit: Angle connections Delivered: Time to deliver: MPA map for this unit:

From Year 7 use correctly the vocabulary, notation and labelling conventions for lines, angles and shapes

use a ruler and protractor to:

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measure and draw lines to the nearest millimetre and angles, including reflex angles, to the nearest degree construct a triangle, given two sides and the included angle (SAS) or two angles and the included side (ASA)

distinguish between and estimate the size of acute, obtuse and reflex angles identify parallel and perpendicular lines; know the sum of angles at a point, on a straight line and in a triangle; recognise vertically opposite angles

From Year 8 solve geometrical problems using side and angle properties of equilateral, isosceles and right-angled triangles and special quadrilaterals, explaining reasoning with diagrams and text; classify quadrilaterals by their geometrical properties use straight edge and compasses to construct:

• • • • •

use bearings to specify direction identify alternate angles and corresponding angles; understand a proof that:

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Live content and examples click here!

the midpoint and perpendicular bisector of a line segment the bisector of an angle the perpendicular from a point to a line the perpendicular from a point on a line a triangle, given three sides (SSS)

the angle sum of a triangle is 180° and of a quadrilateral is 360° the exterior angle of a triangle is equal to the sum of the two interior opposite angles

Audit of Personal Learning and Thinking Skills in this unit: Process and evaluate information, applying mathematics to familiar and unfamiliar contexts. Pupils plan what to do, selecting the most appropriate methods, tools and models when representing situations or problems.

Work collaboratively as well as independently.

Combine understanding, experiences, imagination and reasoning to construct new knowledge. Develop their own lines of enquiry and convincing arguments to support their decisions and conclusions. Think creatively, drawing on their knowledge and understanding of mathematics and identifying the mathematical features that are important. Showing initiative, confidence, commitment and perseverance.

Evaluate their own and others' work and respond constructively. Work logically towards results and solutions, and to value feedback and learn from mistakes.

Develop convincing arguments to influence others and take part in discussions.

Where does all this fit in terms of attainment? Click here to see level by level descriptions for this work. Description of content: Content At any stage it may be appropriate to give “traditional” reinforcement activities for students to complete in their books, on paper etc. Support: Some standard teaching needed to demonstrate how to use a protractor to measure acute and obtuse angles to the nearest degree. Don’t see why you should stop with obtuse angles really so try to include reflex too. Highlight and refer to correct vocabulary for these angles. Students now need to be given a set of cards either the SmartBoard Straight lines, Triangles or Stars (or as Word docs Straight lines, triangles or stars.) Students could work in small teams to measure each of the angles on their cards and total them up. As you wander around you check their accuracy by seeing if their totals match what they should. Try to get them to tell you how you are doing this without measuring i.e. can they start to identify that every straight line has the same total and also what that total is. Sum up findings from this investigation and perhaps put a diagram on the board from one of these sets of cards with two angles filled in – can they tell you the missing angle and how did they calculate it?

Further points

Opportunity to estimate angle sizes using resource such as the following, the first few are restricted to angles up to obtuse: http://www.innovationslearning.co.uk/subjects/maths/activities/year6/angles/game.asp http://www.mathplayground.com/alienangles.html http://www.interactivestuff.org/sums4fun/estimatea.html (good for reinforcing where the angle is rather than the size of it) http://nrich.maths.org/public/viewer.php?obj_id=1235 bog standard estimate angles in up to all four quadrants dependent on the level you choose. http://www.xpmath.com/forums/arcade.php?do=play&gameid=75 http://www.bbc.co.uk/schools/ks3bitesize/maths/shape_and_space/angles_1_2.shtml good for matching vocab and pictures http://www.bbc.co.uk/keyskills/flash/kfa/kfa.shtml includes reflex angles and changes the starting point. Involves Ninja fighting – cool! Core: Any of the Support ideas that may be needed, especially knowing angle sum for triangle, straight line and at a point. Students could work in groups to generate a set of instructions for another class (e.g. a year 6 class) so that they can follow the instructions to be able to (a) measure any given angle and then to (b) draw any given angle (nearest degree and nearest millimetre.) Check they can estimate and name angles using possible links above. Show students a picture of a triangle with the crucial SAS information only marked. Check they understand that the other angles and sides are irrelevant but that it is important that they recognise the angle as being sandwiched between the two known sides. Get class comments about how they would start to draw this themselves i.e. what would they do first, second etc. Get to the point where you are happy that they will be ok to start to draw one of these from a picture. With students in groups give out the triangle cards (next pages of SmartBoard file) or here as Word doc, with the first task being to sort them into piles recognising which are SAS and which are ASA and making sure class has got this. Each group is to then generate a set of instructions which would allow another student over the phone to draw the same triangle. When completed select a few groups to read out their instructions for the rest to follow to check the validity of their descriptions. Ensure good angle specific vocabulary rather than general vocabulary. Students need to have their shapes previously made in the “Symmetry and position” unit – i.e. the origami

shapes. Alternatively, a sheet with all the relevant shapes drawn on or in Word here – maybe better as there are more than the shapes they could make. Do a bit of standard teaching about labelling vertices with a single letter, lines by using a letter for each end, an angle by using the three letters of the sides making the angle and a shape by using all the letters of the vertices. Students are now to label each corner of their shapes and then to complete the maths shorthand sheet for their shapes. Ensure that students are clear that they are looking for features which are true rather than specific cases e.g in a parallelogram they may complete the following: Maths short hand ∠ABC is the same as ∠BCD AB is the same as CD Core and extension:

What is important Shape ABCD is a parallelogram Opposite angles are the same Opposite sides are the same

Having used the pictures or the folded shapes to generate such information try now to get students to work entirely algebraically on shapes - no need to stress the algebra side though. Students should try to use as few letters as possible to label all the angles given on the shapes. Extend your levels of expectation dependent on the progress and ability of your class. For example, an isosceles triangle could be: 180 – 2a

b

a

a

a

a

a (180 – a) / 2

(180 – a) / 2

Once these properties are practised some basic finding the missing angle questions would do no harm! Core but mainly extension:

Given parallel lines investigation sheet or in Word, students can measure angles labelled and start to make connections about which are the same and which total to 180 degrees. For core groups the term “opposite angle” is important along with its fact, and for extension groups you need to include “corresponding” and “alternate” and their facts too. Move on to the extended investigation or here in Word, where from the given pictures students are to try to work out what is the fewest number of angles they need to be told for each picture in order to be able to fill in all other angles on the picture. Challenge each group to do this at the board and reward the lowest successful bidders. Extension: Talk a little about the difference between evidence and proof, could take the example of asking them all to draw a triangle, measure each angle, add them up, what would happen? How many should they do before they were convinced that the total was always 180? Clarify this as evidence but not proof. Clarify that proofs need some starting fact, in this case ours is that a straight line is 180 (this is an agreed convention, not needing a proof!) Explain that they are only allowed to use this fact, plus those they now know about angles on parallel lines to prove that all triangles will add up to 180o. Give groups the triangle proof sheet or (here in Word) and some starting prompts and ask them to try to develop a convincing explanation of why the triangle must add up to 180 degrees. Go on to see if they can then explain why a quadrilateral will always total 360o (prompt with splitting into triangles but insist they convince you why there will only be two triangles in a quadrilateral and showing you where the two sets of 180 are that total to 360) Give investigating triangle angles or here in Word, sheet for students to use to measure the marked angles and investigate the connections that exist by adding together two angles. Trying to get them to discover or state that the two angles at the corner total 180 (straight line) and that the other two add up to the external one marked. Then they need now to try to reason an argument about why this is true given the starting fact that straight lines total 180 degrees. Extension: Using their folded shapes as prompts, or the sheet with all the shapes on, get students sitting back to back in pairs. One student chooses a shape from the sheet and the other has to ask only yes/no questions in order to identify the shape. Stick to quadrilaterals. Make sure that they know that they cannot name any shapes in their questions – e.g. they cannot ask “is it a parallelogram?” When done for a while challenge one who thinks they did well to identify your shape – choose something like a non-isosceles trapezium with two right angles as they are often not aware that a trapezium could have a right angle. Use this activity to now establish that they are to devise a flow chart or sorting diagram that separates all of the quadrilaterals – expect them to do a rough draft and thoroughly check it before they turn this into a well

presented document. They do find this hard so the checking stage is vital to stress and to allow time for. Extension: Before working on the next task you could try the following activity to help students start to visualise some of what they will be doing: http://woodgears.ca/eyeball/index.html as it includes bisectors, midpoints etc. Teach how to use compasses to find the perpendicular bisector and therefore midpoint of a line segment. Demonstrate how to use compasses to construct and SSS triangle and then give them a list of some to draw including some equilateral and some which are impossible (such as 10, 6, 3) and get them to explain/generalise how they could tell if one was impossible. Check they know that equilateral means equal sides and angles and therefore that each is 60o. Demonstrate how to construct an angle bisector. Now being able to draw a 60o angle as part of an equilateral and being able to bisect an angle should mean that they can now start to construct part of a protractor: Draw 60, bisect to 30, bisect both halves to get 15 and 45 Draw another 60 on top of the first to get 120, bisect the second 60 to get 90, bisect both halves to get 75 and 105. Alternatively, draw axes and bisect to construct and label an 8 or 16 pointed compass NESW, then NE, SE, SW, NW etc.