Developing A Purposeful Approach To Delivering Level 6 Mathematics Within Primary Schools Aiming High – Achieving Level 6 In Mathematics Course Presenter – Dave Rowe

Course Objectives To discuss the Level 6 teaching programme in mathematics and explore links to the current Year 6 objectives To practise and embed key Level 5 & 6 number skills, especially the links between fractions, decimals and percentages, and the emphasis on algebraic thinking To explore the ‘new’ topic areas in mathematics that are introduced at Level 6, and how these can be developed with pupils To begin planning a programme of support to challenge and inspire pupils working towards Level 6 in mathematics

Overview Of The Day (i) Overview of L6 – extensions of L5 and new topics Session 1 – Algebraic Thinking: - –Nth terms –Linear equations –Graphs and statements Session 2 – Number: - –Fractions, Decimals, Percentages Session 3 – Shape, Space, Measure & Data –Angles –Volume –Data Handling

For mental arithmetic fluency… These books cover all four rules of number, working approximately at Levels 4 (Beginner), 5 (Intermediate) and 6 (Advanced). There are also many opportunities to rehearse key fraction, decimal and percentage calculations and equivalences

Level 6 – New or Extension? What needs to be taught separately What can be taught as an extension of Level 5 content Number  Use of trial and improvement to solve equations like x 3 + 5x = 38  Add and subtract fractions with common denominators  Solve linear equations with integer coefficients like 2x - 7 = 8 – 3x  Plot the graph of y = mx + c  Find and describe in words the rule for the nth term in a sequence  Work out one number as a fraction or percentage of another  Understand that fractions, decimals and percentages can be equivalent to each other (eg 0.5=50%)  Calculate using ratio  Find and describe in words the rule for the next term in a sequence (linear)

What needs to be taught separately What can be taught as an extension of Level 5 content Shape, Space and Measures  Recognise 2D representations of 3D objects (Using isometric grids)  Find the area and circumference of a circle  Find the volume of cuboids  Enlarge a shape by a positive scale factor  Write instructions to make a computer draw a shape  Classify quadrilaterals by knowing their properties  Find the missing angles when two parallel lines are intersected  Solve angle problems in polygons Handling Data  Interpret what a scatter diagram tells us  Understand correlation  Work with continuous data  Construct pie charts  Find all the possible outcomes of two experiments  Use the fact that the probability of mutually exclusive events add up to 1 Level 6 – New or Extension?

Algebra – Should it be: - ‘Y’ the xxx do we teach it?

Algebra – Should it be: - ‘Y’ the xxx do we teach it? OR

Algebra – Should it be: - ‘Y’ the xxx do we teach it? OR Algebra - The Joy Of ‘x’!

Guardian of The Rule How does this game prepare children for the skills of algebra? x 2 + 1

Guardian of The Rule How does this game prepare children for the skills of algebra? ?

Guardian of The Rule How does this game prepare children for the skills of algebra? x 5 - 2

Guardian of The Rule How does this game prepare children for the skills of algebra? ?

Algebra – linking co-ordinates to equations Moving towardsy = mx + c Use dowelling rods. ( 1, 1) ( 2, 2) ( 3, 3) ( 4, 4) Key Changes – Upper Key Stage 2

Algebra – linking co-ordinates to equations Moving towardsy = mx + c x y ( 1, 1) ( 2, 2) ( 3, 3) ( 4, 4) Key Changes – Upper Key Stage 2

Algebra – linking co-ordinates to equations Moving towardsy = mx + c x y ( 1, 1) ( 2, 2) ( 3, 3) ( 4, 4) Key Changes – Upper Key Stage 2 y = x

Algebra – linking co-ordinates to equations Moving towardsy = mx + c Key Changes – Upper Key Stage 2 y = 2x

Algebra – linking co-ordinates to equations Moving towardsy = mx + c x y ( 1, 2) ( 2, 4) ( 3, 6) ( 4, 8) Key Changes – Upper Key Stage 2 y = 2x

Algebra – linking co-ordinates to equations Try a few more examples yourself: - y = ½ x y = 4x y = 6x y = x 4 Key Changes – Upper Key Stage 2

Algebra – linking co-ordinates to equations Moving towardsy = mx + c x y ( 1, 2) ( 2, 3) ( 3, 4) ( 4, 5) Key Changes – Upper Key Stage 2

Algebra – linking co-ordinates to equations Moving towardsy = mx + c x y ( 1, 2) ( 2, 3) ( 3, 4) ( 4, 5) Key Changes – Upper Key Stage 2 y = x + 1

Algebra – linking co-ordinates to equations Moving towardsy = mx + c Key Changes – Upper Key Stage 2 y = 2x + 2

Algebra – linking co-ordinates to equations Moving towardsy = mx + c x y ( 1, 4) ( 2, 6) ( 3, 8) ( 4, 10) Key Changes – Upper Key Stage 2 y = 2x + 2

Algebra – linking co-ordinates to equations Try a few more examples yourself: - y = ½ x + 2 y = 2x - 1 y = 5x - 2 y = -x+6 Key Changes – Upper Key Stage 2

Algebra – Graphs & Linear Equations Matching Up! Which equation matches which line? y= x _____ y= 2x – 4 _____ x = 4_____ y= -2x +12 _____

Algebra – Graphs & Linear Equations Matching Up! Which equation matches which line? y= x D y= 2x – 4 C x = 4 B y= -2x +12 A

Linear Equations 5m + 4 = 3m m =-3m 2m + 4 = = -4 2m = 18 ÷ 2 = ÷ 2 m = 9

6 - 4y = 2y – = – 4y = 2y + 4y =+4y 18 = 6y 6 3 = y y = 3

Algebra - Trial & Improvement One of the key skills in algebra that children need to practice is ‘trial and improvement’, when trying to find a given value. Try m + 4m = 42, If m was 2, m + 4m = 12 If m was 6, m + 4m = 60 If m was 4, If m was 5, 2 2 2

Algebra - Trial & Improvement One of the key skills in algebra that children need to practice is ‘trial and improvement’, when trying to find a given value. Try m + 4m = 42, If m was 2, m + 4m = 12 If m was 6, m + 4m = 60 If m was 4, m + 4m = 32 If m was 5, m + 4m =

Algebra - Trial & Improvement Look at the Testbase question for trial and improvement, and discuss the methods that you used.

Developing Key Teaching Skills In FDPRP at Levels 5 & 6

FDPRP – Mental Maths ‘Test’ Complete the following questions, jotting down your answers and strategies. –62.5% of 120 –1/9 of 4 litres –0.6 x £35 –1/12 of 9ml –87.5% of 56kg –0.166 x 240 –83.33% of 120m –0.375 x 72 –80% of 55cm –0.125 x 80

Loopy Fractions Play the FDP loop game and discuss how the pieces could be used to support Levels 5 and 6 in maths Could it be differentiated for all learners in Year 6?

The ‘Dashing Dapper Des’ Debate When renowned lethario Des O’Connor was 60, his wife-to-be was only 24 years old! What ages were they, when their ages were in a ratio of 1:2 When Des celebrated his 40 th birthday, what was the ratio of their ages then?

Multiplying Decimals If 0.3 is the answer, what is the question? If 0.2 is the answer what is the question?

Multiplying Decimals Multiplication & Division Facts – Mixed

Divisive Decimals Work out the following calculations, using your knowledge of the rules of division / equivalent fractions = 0.1

Addition & Subtraction Of Fractions Dice Games –Use different dice to create numerators and denominators, initially 10 / 12 sided dice, but try 20 sided and multiple of 10/100 dice as well –Create 2/3/4 fractions using the dice and ask the children to either add or subtract the fractions created. –E.g. Roll 2 x 12 sided dice twice (3 & 8, 4 & 5). Each time use the larger number for the denominator and either add or subtract them. 3/8 + 4/5 or 4/5 – 3/8

Programme of Work - Content Discuss the weekly content of the programme for supporting Level 6 attainment

Using Testbase Effectively To Support New Knowledge Alternate and corresponding angles Enlargements Area & Perimeter of trapezia & circles Volume

Alternate & Corresponding Angles – ‘Z’ Angles Understanding alternate and corresponding angles is relatively simple but is mainly new content at Level 6

Enlargements Give children practice in drawing enlargements of shapes, by scaling up each of the dimensions by a given scale factor, starting at the origin

Crop Circles

Isometric Grids Give children plenty of practice in using isometric grids to draw shapes – even as an adult it can be a tricky skill to develop.

From ‘Maxi-Box’ To ‘Maxi-Cuboid’ Using isometric paper, draw several cuboids in which the length + width + height = 12cm Which of these has the largest / smallest volume? Can you make a generalisation for any cuboid?

Scatter Diagrams - Correlation Look at the three scatter diagrams on the handout. One has positive correlation, one has negative correlation and one has no correlation. Decide which of them fit the following criteria: - –Time spent watching football / number of DIY jobs completed –Cups of coffee drunk in a week / annual wages –Time spent cooking / time spent washing up

Scatter diagram A Scatter diagram B Scatter diagram C

The Shape, Space, Area, Perimeter & Angles 100 to 1 Quiz

Question 1 Find the volume of a cuboid that is 6cm x 9cm x 4cm

Question 1 Find the volume of a cuboid that is 6cm x 9cm x 4cm 216 cm cubed

Question 2 What is the formula to work out the area of a circle?

Question 2 What is the formula to work out the area of a circle? Pi multiplied by radius squared

Question 3 Taking ‘Pi’ as 3, what is the circumference of a circle with a radius of 8?

Question 3 Taking ‘Pi’ as 3, what is the circumference of a circle with a radius of 8? 48cm

Question 4 A)What is angle A worth? B) What is angle B worth?

Question 4 A)What is angle A worth? B) What is angle B worth? Angle A =

Question 5 What is the name of a 9 sided polygon?

Question 5 What is the name of a 9 sided polygon? A nonagon

Question 6 What are the internal angles of a regular hexagon worth?

Question 6 What are the internal angles of a regular hexagon worth? 120 degrees

Internal Angles Of Any Regular Polygon The external angles of any polygon will always add up to 360 degrees. Divide 360 by the number of sides to get the external angles of any regular polygon. Subtract this from 180 to get the internal angles

Question 7 What is the area of a trapezium with parallel sides of 3 and 5 cm, and height of 4 cm?

Question 7 What is the area of a trapezium with parallel sides of 3 and 5 cm, and height of 4 cm? 16cm squared

Question 8 A rectangle has a perimeter of 48cm. What is the largest area that it could be?

Question 8 A rectangle has a perimeter of 48cm. What is the largest area that it could be? 144 cm squared

Question 9 A rectangle is 12 cm by 5cm – how long is the diagonal?

Question 9 A rectangle is 12cm by 5cm – how long is the diagonal? 13cm

Question 10 What are the internal angles of a regular decagon worth?

Question 10 What are the internal angles of a regular decagon worth? 144 degrees

Question 11 What is the name of a 20 faced polyhedron?

Question 11 What is the name of a 20 faced polyhedron? Icosahedron

Question 12 Taking Pi as 3, what is the area of a quadrant of a circle with a diameter of 28cm?

Question 12 Taking Pi as 3, what is the area of a quadrant of a circle with a diameter of 28cm? 192 cm squared

Question 13 What is the name of a 100 faced polyhedron?

Question13 What is the name of a 100 faced polyhedron? Hectahedron

Tiebreaker Estimate the length of each edge of a cube with volume 40cm cubed

Tiebreaker Estimate the length of each edge of a cube with volume 40cm cubed 3.42cm

Conclusion Plan your additional teaching programme to:- – Emphasise the key content (Algebra & FDPRP) – Introduce and give as much detail as possible into the new content (Algebra, areas and circumferences, angles, volume, scatter diagrams, correlation etc) Plan your current teaching programme to include:- Extended content from Levels 4 & 5 (FDPRP, Ratio, Number properties, volume, probability etc)