There are 366 different Starters of The Day, many to choose from. You will find in the left column below some starters on the topic of Angles. In the right column below are links to related online activities, videos and teacher resources.

A lesson starter does not have to be on the same topic as the main part of the lesson or the topic of the previous lesson. It is often very useful to revise or explore other concepts by using a starter based on a totally different area of Mathematics.

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### Angles Starters:

Air Traffic Control: Work out which aircraft are in danger of colliding from their positions and direction of travel. An exercise in understanding bearings.

Angle Estimates: Estimate the sizes of each of the angles then add your estimates together.

Pie Chart: An exercise in estimating what the sectors of a pie chart represent.

Sectors: Work out which sectors fit together to make complete circles. Knowledge of the sum of the angles at a point will help find more than one correct solution to this puzzle.

Square Angles: Find a trapezium, a triangle and a quadrilateral where all of the angles are square numbers.

Angle Thinking: Find the range of possible angles, x, for which tan x > cos x > sin x

Geometry Snack: Find the value of the marked angle in this diagram from the book Geometry Snacks

Hands Together: The hands of a clock are together at midnight. At what time are they next together?

#### Snooker Angles

An online game for one or two players requiring an ability to estimate angles.

Transum.org/go/?to=snookerangles

### Curriculum for Angles:

#### Year 5

Pupils should be taught to know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles more...

Pupils should be taught to draw given angles, and measure them in degrees (°) more...

Pupils should be taught to identify:
- angles at a point and one whole turn (total 360°)
- angles at a point on a straight line and a turn (total 180°)
- other multiples of 90° more...

Pupils should be taught to use the properties of rectangles to deduce related facts and find missing lengths and angles more...

#### Year 6

Pupils should be taught to draw 2-D shapes using given dimensions and angles more...

Pupils should be taught to compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons more...

Pupils should be taught to recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles. more...

#### Years 7 to 9

Pupils should be taught to draw and measure line segments and angles in geometric figures, including interpreting scale drawings more...

Pupils should be taught to describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, and other polygons that are reflectively and rotationally symmetric more...

Pupils should be taught to derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies more...

Pupils should be taught to apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles more...

Pupils should be taught to understand and use the relationship between parallel lines and alternate and corresponding angles more...

Pupils should be taught to derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon, and to derive properties of regular polygons more...

Pupils should be taught to apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides, including Pythagorasâ€™ Theorem, and use known results to obtain simple proofs more...

#### Years 10 and 11

Pupils should be taught to {apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results} more...

### Feedback:

Comment recorded on the 3 October 'Starter of the Day' page by S Mirza, Park High School, Colne:

"Very good starters, help pupils settle very well in maths classroom."

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"My year 8's absolutely loved the "Separated Twins" starter. I set it as an optional piece of work for my year 11's over a weekend and one girl came up with 3 independant solutions."

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"A really useful set of resources - thanks. Is the collection available on CD? Are solutions available?"

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Keep it up and thank you!"

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"Thanks very much for this one. We developed it into a whole lesson and I borrowed some hats from the drama department to add to the fun!"

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"Thank you so much for your wonderful site. I have so much material to use in class and inspire me to try something a little different more often. I am going to show my maths department your website and encourage them to use it too. How lovely that you have compiled such a great resource to help teachers and pupils.
Thanks again"

Comment recorded on the 21 October 'Starter of the Day' page by Mr Trainor And His P7 Class(All Girls), Mercy Primary School, Belfast:

"My Primary 7 class in Mercy Primary school, Belfast, look forward to your mental maths starters every morning. The variety of material is interesting and exciting and always engages the teacher and pupils. Keep them coming please."

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Thanks for such a great resource!"

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"This triangle starter is excellent. I have used it with all of my ks3 and ks4 classes and they are all totally focused when counting the triangles."

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"Really good site. Lots of good ideas for starters. Use it most of the time in KS3."

Comment recorded on the 19 October 'Starter of the Day' page by E Pollard, Huddersfield:

"I used this with my bottom set in year 9. To engage them I used their name and favorite football team (or pop group) instead of the school name. For homework, I asked each student to find a definition for the key words they had been given (once they had fun trying to guess the answer) and they presented their findings to the rest of the class the following day. They felt really special because the key words came from their own personal information."

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"This is a great memory aid which could be used for formulae or key facts etc - in any subject area. The PICTURE is such an aid to remembering where each number or group of numbers is - my pupils love it!
Thanks"

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Comment recorded on the 2 May 'Starter of the Day' page by Angela Lowry, :

"I think these are great! So useful and handy, the children love them.
Could we have some on angles too please?"

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### Notes:

Pupils should understand that angles represent an amount of turning and be able to estimate the size of angle. When constructing models and drawing pupils should be able to measure and draw angles to the nearest degree and use appropriate language associated with angles.

Pupils should know the angle sums of polygons and that of angles at a point and on a straight line. They will learn about angles made in circles by chords, radii and tangents and recognise the relationships between them.

Pupils will work with angles using trigonometry, transformations and bearings. In exams pupils are often instructed that while non-exact answers should be given to three significant figures, angle answers should be given to one decimal place.

### Angles Teacher Resources:

Angle Theorem Kim's Game: A memory game to be projected to help the whole class revise the circle angle theorems.

Angle Theorems: Diagrams of the angle theorems with interactive examples.

Circle Theorems: Diagrams of the circle theorems to be projected onto a white board as an effective visual aid.

Geometry Toolbox: Create your own dynamic geometrical diagrams using this truly amazing tool from GeoGebra.

Kite Maths: Can you make a kite shape from a single A4 size sheet of paper using only three folds?

Plane Bearings: A visual aid designed to help pupils estimate three figure bearings.

### Angles Activities:

Angle Chase: Find all of the angles on the geometrical diagrams.

Angle Parallels: Understand and use the relationship between parallel lines and alternate and corresponding angles.

Angle Points: Apply the properties of angles at a point, angles on a straight line and vertically opposite angles.

Angles in a Triangle: A self marking exercise involving calculating the unknown angle in a triangle.

Circle Theorem Pairs: A pairs game based around ten theorems about the angles made with chords, radii and tangents of circles.

Circle Theorems Exercise: Show that you understand and can apply the circle theorems with this self marking exercise.

Estimating Angles: Estimate the size of the given acute angles in degrees.

Geometry Toolbox: Create your own dynamic geometrical diagrams using this truly amazing tool from GeoGebra.

Measuring Angles: Measure the size of the given angles to within two degrees of their actual value.

Online Logo: An online version of the Logo programming language with 30 mathematical challenges.

Pie Charts: Develop the skills to construct and interpret pie charts in this self-marking set of exercises.

Polygon Angles: A mixture of problems related to calculating the interior and exterior angles of polygons.

Proof of Circle Theorems: Arrange the stages of the proofs for the standard circle theorems in the correct order.

Scale Drawings: Measure line segments and angles in geometric figures, including interpreting scale drawings.

Snooker Angles: An online game for one or two players requiring an ability to estimate angles.

Finally there is Topic Test, a set of 10 randomly chosen, multiple choice questions suggested by people from around the world.

Alternatively, for the more advanced student, there is an ever-growing collection of Exam-Style Questions with worked solutions on the topic of Angles.

### Angles Investigations:

Tessellations: Drag the shapes onto the canvas to create tessellating patterns and investigate the laws of tessellations.

### Angles Videos:

Angle Properties Song: A song about the angles made with parallel lines.

Ruler and Compass Construction: A demonstration of standard ruler and compass constructions

The 50 Cent Riddle: A 50 cent coin has 12 equal sides. If you place two coins next to each other on a table, what is the angle formed between the two coins?

### Angles Worksheets/Printables:

Angle Chase Worksheets: A set of printable Angle Chase sheets on which pupils fill in the missing angles.

Mearsuring Lines and Angles: Practice using a ruler and protractor on this worksheet with answers provided.

Polybragging Cards: Printable cards for the Polybragging game. Use the properties of polygons to win.

Links to other websites containing resources for Angles are provided for those logged into 'Transum Mathematics'. Subscribing also opens up the opportunity for you to add your own links to this panel. You can sign up using one of the buttons below:

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#### Angle Chase

Find all of the angles on the geometrical diagrams.

Transum.org/go/?to=chase

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Roger Kidney, Dulwich Prep School, Cranbrook

Tuesday, January 21, 2014

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