The KING’S Medium Term Plan [Mathematics …...life. During the five first weeks, students will link the mathematical knowledge acquired to the world that surrounds them, resulting

The KING’S Medium Term Plan – [Mathematics Department]

Y7 Learning Cycle 2 Programme

Module Number (fractions, percentages, BIDMAS) and Algebra (substitution, simplification…)

Challenging

question

‘Why and how have the places we live in changed over the years?’

Subject

Challenging

Question

‘How has Geometry influenced our buildings nowadays? ’ In the present learning cycle, students will evaluate how

Geometry and Algebra are used in architecture and engineering, and will analyse the importance of Mathematics in real

life. During the five first weeks, students will link the mathematical knowledge acquired to the world that surrounds them,

resulting in a better understanding of each of the concepts studied such as algebra and shapes.

Lines of

Enquiry Week 1: ‘How were codes like Enigma cracked?’ Simple concepts of algebra will be studied this week such as

simplification and substitution with both positive and negative numbers. The knowledge acquired this week, will be applied during the rest of the learning cycle. Week 2: ‘Why is it important to know the properties of shapes very well in architecture?’ This second week, students will learn about regular and irregular 2D shapes as well as their properties and how to apply these in real life situations. Week 3: ‘Why would engineers need to know how angles on a straight line work?’ Over this week, pupils will learn about different types of angles and how to calculate the missing angle on a straight line and around a point. To make the task more complicated, some angles will be given as algebraic expressions and pupils will be required to apply what they learned in Week 1 to solve those questions. Week 4: ‘Why did the witches in previous centuries decided to use triangles as their symbols?’ This week´s learning builds on the previous week´s studies of shapes and angles as pupils are broadening their knowledge and calculating angles inside different shapes and in particularly, triangles. Students will have to apply the properties they learned before to determine the missing angles. Week 5: ‘Where is the knowledge of circles used in architecture? At this point we will look at properties of circles and the relationship between the different parts of the circle. Pupils will also investigate where the number Pi comes from by measuring the diameter and the circumference of several circles. Week 6-7: Assessment followed by gap teaching – from assessment analysis.

LC2 Mastery Overview

Progress

Objectives

Underlined

the extension

work for

certain GP

can be seen.

By the end of Learning Cycle 2 in Mathematics SWBAT: A) Understand the differences between formulae, equation and expression. B) Collect like terms in algebraic expressions with more than one unknown. C) Substitute positive and negative values in simple algebraic expressions. D) Substitute decimal values on expressions and integers in more complicated expressions (including squares) E) Recognise and describe different 2D shapes as well as their properties.

F) Identify different types of angles. G) Determine how to measure an angle using a protractor. H) Measure reflex angles using a protractor and/or doing calculations. I) Calculate angle on a straight line and around a point. J) Apply their knowledge about algebra to calculate missing angles using algebraic expressions. K) Calculate interior and exterior angles of polygons. L) Calculate the number of sides in a polygon given the exterior angle. M) Determine the parts of the circle and use the relationship between radius and diameter. N) Investigate where Pi comes from. Assessment in week 6 will be against the above objectives.

Gap teaching from analysis of assessments in week 7 after the half term.

Week 1

4 hours of

lessons plus

1 hour of

homework

given out on

Tuesday each

week.

Lesson 1: Hypothesis – ‘2x – 7 is called equation’.

Progress Outcomes:

Herodotus, Hippocrates and Aristotle

Understand why letters are used in algebra.

Analyse how to write a statement using symbols.

Evaluate the difference between formulae, equations and expressions.

Archimedes and Euclid

Analyse how to translate worded questions into algebraic language.

If you worked for the secret police, why would it be useful for you to be good in algebra?

Today´s work will be peer assessed in lesson.

Additional

intervention

on Tuesday

evening each

week.

Learning Activities:

Do Now – Numeracy thinking task

Activity to discuss why it is better to use symbols in certain occasions.

Questions to write different statements in algebra language.

Table colouring the different equations, formulae and expressions.

Create your own formulae, expressions and equations using a variety of letters and symbols.

Assessment of hypothesis – write an evaluation of the hypothesis using examples of today’s work

Lesson 2: Hypothesis – ‘ Only the letters x and y are used in algebra’. Progress Outcomes:


Understand how to use mathematical symbols to make statements correct.

Understand how to use letters for unknown numbers and the rules of algebra.

Apply understanding of algebraic rules in order to simplify expressions by collecting like terms.


Recall algebraic rules in order to simplify expressions by collecting like terms.

Understand how to expand single brackets.

Analyse how to simplify questions with two pairs of single brackets.

Pupils to mark their own work in green during lesson against the lesson´s objectives. Learning Activities:

Do Now – collect the fruits! Count different types of fruit and use symbols to write answers.

Enter a mathematical symbol such as + to make a calculation or situation correct such as 5? If 4 = 20, 4a? 2a = 6a etc.

Pupils will do a small activity where they create sentences with a letter to replace a number such as ‘in a football team there are E players’; ‘I am A years old’ etc. Discuss if the letter used matters.

Main part of the lesson, pupils will do a card sort activity where they are to match up an expression with a simplified version and write into their books. These vary in difficulty.

Simplify expressions questions with powers, fractions and lone integers Lesson 3: Hypothesis – ‘The Enigma code was developed by a mathematician’.

Progress Outcomes:


Recall what expressions are.

Evaluate how to substitute positive integers into expressions with more than one unknown.

Apply knowledge to code cracking.


Evaluate how to substitute positive integers into expressions with more than one unknown.

Analyse how to substitute negative numbers in expressions that may include powers.

Evaluate how to substitute fractions into expressions. Discuss if using decimals may be more useful than using fractions.

If you were to conquer a country, why would a mathematical code be useful?

Knowledge check using a quiz, which will be peer assessed during the lesson.


Do Now – critical thinking task to write out simple expressions in full (un-simplify)

Activity where pupils will invent their own codes in order to understand how substitution in algebra works.

Recall what is meant by an expression. Discuss other words for substitution and where it is used in real life. Pupils will be given a range of positive values for letters and they will work together to calculate the answers to the substitution.

REACH: Pupils will try substitution with decimal numbers. Lesson 4: Hypothesis – Problem Solving: ‘Egyptian hieroglyphs can be cracked easily’. Progress Outcomes:


Recall what expressions are.

Research what the most used codes are.

Apply your knowledge of substitution to solve real life formulae questions.


Analyse how to use substitution with real life formulas.

Evaluate how to write a formula from a worded question.

Solve worded questions to find real life formulas and their value.

Books will be marked so pupils can act on the feedback written on their books following the colour dot system.


Do Now – critical thinking task to write out simple expressions in full (un-simplify)

Activity where pupils will invent their own codes in order to understand how substitution in algebra works.

Recall what is meant by an expression. Discuss other words for substitution and where it is used in real life. Pupils will be given a range of negative values for letters and they will work together to calculate the answers to the substitution.

REACH: Pupils will try substitution with negative decimal numbers and squared unknowns

Home learning: Given on Tuesday each week and due in the following Tuesday.

This week, pupils will have to solve different questions based on substitution and simplification.

REACH: More challenging activities will be given to those pupils making extraordinary progress in lessons.

SUPPORT: Consolidation activities will be given to those pupils struggling with the topic. Extra support will be offered after school.

Week 2

4 hours of

lessons plus

1 hour of

homework

given out on

Tuesday each

week.

Additional

intervention

on Tuesday

evening each

week.

REACH (Review & Recap, Evaluate & Endeavour, Attainment & Achievement, Challenge yourself, Hone your skills) Improvement time to be allocated in one lesson every week from week 2 so pupil´s can learn from the

mistakes they have made the previous week. Individual feedback will be provided as well as personalised improvement questions depending on what each pupil has done wrong. Lesson 1: Hypothesis – ‘ There are only two four-sided shapes: square and rectangle’. Progress Outcomes:


Recall all the names of the shapes that you know so far.

Analyse what the differences between them are.

Evaluate what the most important properties of each shape are including properties of triangles.


Recall the different properties of all 2D shapes, including different types of triangles.

Analyse what congruent shapes look like in order to find a definition for “congruent”.

Understand what similar shapes are and what is the different between similar and congruent.

Evaluate how to calculate missing sides of similar shapes.

Today´s work will be peer assessed in lesson. Learning Activities:

Do Now – are the names of shapes correct?

Activity to match the properties with the correct shape(s).

Questions to identify more properties of shapes.

REACH: Identify which angles and sides should be the same in more difficult shapes such as trapeziums.

Reflect on the hypothesis.

Lesson 2: Hypothesis – ‘There is only on kind of shape with five sides: a regular pentagon.’ Progress Outcomes:


Recall the properties of basic shapes.

Understand the differences between regular and irregular shapes.

Analyse what symmetry is and where we can find it around us.


Understand the differences between regular and irregular shapes.

Recall what symmetry is.

Analyse what rotational symmetry is and where to find it in nature,

If you were a biologist, where would you find symmetry?

Pupils to mark their own work in green during lesson against the lesson´s objectives. Learning Activities:

Do Now – Identify the basic properties of the shapes on the board.

Activity to distinguish between regular and irregular shapes.

Questions so as to find out the lines of symmetry of different shapes.

REACH 1: Activity to find the planes of symmetry of 3D solids.

REACH 2: Questions to find the rotational symmetry of different shapes.

Reflection of learning and hypothesis. Lesson 3: Hypothesis – Problem Solving: ‘All triangles are the same’.

Progress Outcomes:

Recall the different types of triangles.

Understand the different symbols used to indicate that two sides are the same, that there is a right angle…

Analyse the properties of each type of triangle.

REACH: Evaluate how to find hidden information about shapes in worded questions.


Books will be marked so pupils can act on the feedback written on their books following the colour dot system. Learning Activities:

Do Now – Identify the correct triangle.

Activity drawing symbols on the given triangles to show different properties.

Questions to identify the different properties in each triangle.

REACH: Which types of triangles do you have in the given compound shapes? How do you know it?

Reflection of learning and hypothesis.

Home learning: Given on Tuesday each week and due in the following Tuesday.

This week, pupils will be given a written homework to find different shapes around them. Then take a picture of them and

analyse the properties studied this week.



Week 3

4 hours of

lessons plus

1 hour of

homework

given out on

REACH (Review & Recap, Evaluate & Endeavour, Attainment & Achievement, Challenge yourself, Hone your skills) Improvement time to be allocated in one lesson every week from week 2 so pupil´s can learn from the mistakes they have made the previous week. Individual feedback will be provided as well as personalised improvement questions depending on what each pupil has done wrong. Lesson 1: Hypothesis – ‘There is no angle bigger than 180º’.

Progress Outcomes:

Recall different types of angles.

Analyse how to measure an angle with a protractor.

Tuesday each

week.

Additional

intervention

on Tuesday

evening each

week.

Evaluate the level of accuracy given by a protractor.

REACH: Create a step by step guide of how to measure reflex angles using a protractor and calculations

Pupils to mark their own work in green during lesson against the lesson´s objectives.


Do Now – Match the angles with their names.

Activity to explain how angles can be classified.

Questions to measure angles with a protractor.

Lesson 2: Hypothesis – ‘Angles on a straight line add up to 360º.

Progress Outcomes:

Recall different types of angles.

Understand why angles on a straight line add up to 180º.

Analyse how much angles around a point add up to.

REACH: Evaluate how to calculate missing angles using algebraic expressions.



Do Now – Research what angles on a straight line and angles at a point are.

Activity to calculate missing angles on straight lines.

Questions to calculate missing angles at a point.

Lesson 3: Hypothesis – Problem Solving: ‘Knowing that angles in a triangle add up to 180º, helps to calculate angles in a quadrilateral’. Progress Outcomes:

Recall different types of triangles and quadrilaterals.

Understand that angles in a triangle add up to 180º.

Evaluate why angles in quadrilaterals add up to 360º.

REACH: Calculate missing angles using algebraic expressions.

Books will be marked so pupils can act on the feedback written on their books following the colour dot system.


Do Now – Are the names of the shapes correct?

Activity calculating missing angles in triangles and quadrilaterals.

More difficult questions where properties of triangles and quadrilaterals need to be applied in order to calculate

missing angles.

Reflection of learning and hypothesis.

Mid term assessment will de done at the end of week 3.

Home learning: Given on Tuesday each week, and due in the following Tuesday.

This week pupils will be given homework to consolidate their knowledge 2D shapes and calculating missing angles.



Week 4

4 hours of

lessons plus

1 hour of

homework

given out on

Tuesday each

week.

Additional

intervention

on Tuesday

evening each

week.


mistakes they have made the previous week. Individual feedback will be provided as well as personalised improvement questions depending on what each pupil has done wrong. This week the improvements will be based on the Midterm assessment done the previous week.

Lesson 2: Hypothesis – ‘ Triangles do not help when calculating missing angles in shapes with more than four

sides’.

Progress Outcomes:

Herodotus, Hippocrates and Aristotle.

Recall the names of all polygons studied in Week 2.

Understand how to much angles add up to inside a polygon.

Understand how to calculate the interior angles in any irregular shape using triangles.

Archimides and Euclid.

Understand how to calculate the interior angles in any irregular shape using triangles.

Evaluate how to calculate missing interior angles in regular polygons.

Create a formula to remember how to calculate a missing interior angle in a regular polygon.

Today´s work will be peer assessed in lesson.


Do Now – quick activity to recall the names of different shapes such as hexagon, pentagon…

Calculate how much angles add up to in the shapes seen previously in the do now.

Questions to calculate missing angles using the properties of the shapes.

REACH: Calculate missing angles that include algebraic expressions.

Reflect on learning and discuss the challenge question.

Lesson 3: Hypothesis – ‘A pentagon has not got an exterior angle’. Progress Outcomes:


Understand how to draw the exterior angle of a polygon.

Recall that angles on a straight line add up to 180º.

Analyse how to calculate a missing exterior angle.

Archimides and Euclid.

Analyse how to calculate an exterior angle knowing the interior one.

Evaluate how to calculate the interior angle in a regular polygon, given the exterior one.

Analyse how the exterior angle theorem works.

Knowledge check using a quiz, which will be peer assessed during the lesson. Learning Activities:

Do Now - discuss if the interior angles have been correctly worked out.

Activity to calculate missing exterior angles in different polygons.

Why would an architect need to know about angles?

Questions working out the interior angle backwards.

Lesson 4: Hypothesis – Problem Solving: ‘The exterior angle theorem can only be applied to scalene triangles’. Progress Outcomes:


Recall what the exterior and interior angles in a polygon are.

Understand how to determine from a worded question which angle we need to calculate.

Analyse how to calculate the interior angle of irregular polygons.


Recall how to calculate the interior angle in any polygon.

Understand how to apply the exterior angle theorem.

Evaluate how to calculate missing angles using algebra.


Do Now - discuss if the exterior angles have been properly calculated.

Apply the “Exterior Angle Theorem” to different triangles.

REACH: Calculate the number of sides of a polygon given the exterior angle.

Investigation: Would the Exterior Angle Theorem work for any polygon?

Home learning: Given on Tuesday each week, and due in the following Tuesday.

This week pupils will be given homework about calculating exterior and interior angles in different polygons.


SUPPORT: Consolidation activities will be given to those pupils struggling with the topic. Extra support will be offered after school. From the mid term assessments extra intervention will be planned accordingly.

Week 5

. 4 hours of

lessons plus

1 hour of

homework

given out on

Tuesday each

week.

Additional

intervention

on Tuesday

evening each

week.


mistakes they have made the previous week. Individual feedback will be provided as well as personalised improvement questions depending on what each pupil has done wrong. COGNITIVE ACCELERATION TASK: The art gallery Pupils will also take part today in a CA task to develop their deep thinking skills.

Background: There is a mathematical problem known as the “Art Gallery Problem”, which explores how many security

guards would be needed to watch over the exhibits of an art gallery with straight sides. This lesson begins by allowing the

pupils to explore different types of polygons, using the Art Gallery as a hook and then moves into looking at the sum of the

interior angles in a polygon.

Episode 1:

Draw or display the first two shapes from NS1 on the board.

Ask what is the same and what is different about the two shapes.

Explain that the shapes are birds-eye views [“plan views”] of two art galleries. So that no one is tempted to steal any of the

exhibits there are security guards who stand in the galleries and watch the visitors and the exhibits. Where would be a bad

place for the security guard to stand in the first gallery? The guard stands somewhere around the edge of the gallery and

moves his head to see what is going on. Where can he stand in each gallery to ensure he can see every part of the gallery?

Take feedback from the pairs. An extra question: “If the guard walks around near the edge of the gallery he can go

anywhere in the first gallery and still see everything. Where mustn’t he go in the concave gallery?”

Share the ideas for a gallery that needs two guards.

Are the heptagons all different, or can they be categorised? Collect the ideas on the board and

discuss them.

Episode 2:

Explain that in some Art Galleries they use electronic sensors to detect intruders at night. This is cheaper than having the

guards there when the gallery is closed.

A sensor is placed at each corner of the room and rotates from side-to-side, sweeping out the angle at that corner. If it

detects something moving then it sounds an alarm.

We are going to try to find out how many degrees the sensors need to turn through altogether … without doing any

measuring!

The pupils should work in pairs to divide the polygons on NS3 into triangles. They can do this however they like and

should use two different methods for the two different diagrams of each polygon. Stress that the lines they draw should not

cross.

After a few minutes they could pool their ideas with another pair.

Take feedback as a whole class.

It is likely to crop up that there are millions of different ways of dividing the polygons up. Some of these will involve

dividing up one of the sides of the polygon. Push the pupils towards versions that only join vertices (corners) of the

polygons.

Discover as a whole class that however you do this you always get three triangles in a pentagon and 4 triangles making a

hexagon. Pupils can then predict what will happen for other polygons.

Focusing on one of the polygons (up on the board), colour in the angles in the first triangle. Ask the

pupils how many degrees that makes so far? Then colour the angles of the next triangle and not

down 180. Repeat for the other triangles and show the pupils that the angles you have coloured

(from the triangles) are the same as the angles in the hexagon! How could they work out the sum of

the angles in a hexagon? Repeat this process for other polygons. Some pupils may have a rule.

Episode 3: Ask the pupils: “What is a regular hexagon?”

How can we use the fact that the angles add up to 720 to work out the size of each angle in a regular hexagon? Work out

the interior angle of each of the regular polygons.

What do they notice? The difference between the angles gets smaller as the number of sides goes up.

Lesson 2: Hypothesis – ‘The only parts of the circle are radius and diameter’. Progress Outcomes:

Recall what a circle is.

Analyse the different parts of the circle.

Evaluate what the relationship between diameter and circumference.

REACH: Analyse how to calculate Pi.

Pupils to mark their own work in green during lesson against the lesson´s objectives.


Do Now – Research the different parts of the circle.

Activity drawing circles and their different parts.

Investigation measuring the circumference of different circles with a tape measure and the diameter to find Pi.

Assessment of the hypothesis.

Lesson 3: Hypothesis – Problem Solving: ‘Two diameters make a radius’. Progress Outcomes:

Recall the parts of the circle.

Analyse how to calculate the circumference of a circle.

REACH: Apply your knowledge to calculate perimeters of shapes with curved edges.

Knowledge check using a quiz, which will be peer assessed during the lesson. Learning Activities:

Do Now – Is the circle labelled correctly?

Activity to investigate the link between the radius and the diameter.

GCSE exam questions to calculate the radius and diameter of different circles.

REACH: calculating the radius and diameter with expressions involving algebra.

Reflection of learning and discuss the hypothesis of the lesson.

Lesson 4: Hypothesis – Problem Solving: ‘Circular shapes are not used in real life’.

Progress Outcomes:

Recall how to calculate the circumference of a circle.

Analyse how to calculate the area of the circle.

REACH: Evaluate how to solve worded questions.


Do Now – what is wrong about these diameters?

Activity using real life shapes to calculate the radius and the diameter.

REACH: design a piece of jewellery that includes a circular shape and determine its radius and diameter.

What do circles have to do with sports?

Assessment of the hypothesis.

Home learning: Given each Tuesday and due in the following Tuesday.

This week pupils will be given homework to consolidate their knowledge on this LC for REVISION.


SUPPORT: Consolidation activities will be given to those pupils struggling with the topic. Extra support will be offered after school. From the mid term assessments extra intervention will be planned accordingly.

Week 6 Revision using levelled booklets followed by assessments.

Gap Analysis Reinforcement

Week 7

Gap

Reinforcemen

t

As seen in the lesson activities each week, gap teaching will not just be at the end of the Learning Cycle after exam

analysis has taken place. Gap teaching is an integral part to each unit of work and will consist of summary sheets, mini-

tests and tasks where gaps can be filled and REACH activities can be delivered.

Extended Learning

(This is not

part of the

‘timed’

schedule but is

seen as

additional

support)

Extended learning will in a variety of forms. During home learning pupils may be asked to use the following sites where

they complete quick quizzes, CIMT tasks, GCSE style questions and more open ended tasks.

1) Levelled quizzes

http://www.educationquizzes.com/ks3/maths/

2) Lots of maths online help and activities – as well as mini tests http://www.bbc.co.uk/schools/websites/11_16/site/maths.shtml

3) http://uk.ixl.com/math/year-7

This link is useful for additional revision and practice on all areas of maths. For semester 4 pupils should click on

the Geometry areas for practice questions.

4) http://www.bbc.co.uk/bitesize/ks3/maths/handling_data/

this link will provide good revision and extended learning opportunities on the semester 5 project

5) http://sport.maths.org/content/KS3

in depth links to maths and sport

Extended learning will also be in lesson plans where links are made to the history theme of historical changes.

During Tuesday and Thursday enrichment pupils will have the chance to strengthen skills and develop them further. We will

look at UKMT challenges, levelled tasks, GCSE questions and build a Kings Maths Team ready to enter competitions in

year 8.

http://www.educationquizzes.com/ks3/maths/

http://www.bbc.co.uk/schools/websites/11_16/site/maths.shtml

http://uk.ixl.com/math/year-7

http://www.bbc.co.uk/bitesize/ks3/maths/handling_data/

http://sport.maths.org/content/KS3

Documents

The KING’S Medium Term Plan [Mathematics …...life. During the five first weeks, students will link the mathematical knowledge acquired to the world that surrounds them, resulting