developing a purposeful approach to delivering level 6 mathematics within primary schools aiming...

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…

• www.30secondchallenge.com

• 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

http://www.30secondchallenge.com/

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 x3 + 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 –Algebra –Should it be: -

‘Y’ the xxx do we teach it?


‘Y’ the xxx do we teach it?OR


‘Y’ the xxx do we teach it?OR

Algebra - The Joy Of ‘x’!Algebra - The Joy Of ‘x’!

Guardian of The Rule

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

2 7

3 10

5 16

8 17

x 2 + 1



2 8

3 13

5 23

8 ?



2 12

3 20

5 36

8 60

x 5 - 2



2 7

3 12

5 28

8 ?

Algebra – linking co-ordinates to equations

Moving towards y = mx + cUse dowelling rods. ( 1 , 1) ( 2 , 2) ( 3 , 3) ( 4 , 4)

Key Changes – Upper Key Stage 2


Moving towards y = mx + c

x y ( 1 , 1) ( 2 , 2) ( 3 , 3) ( 4 , 4)




x y ( 1 , 1) ( 2 , 2) ( 3 , 3) ( 4 , 4)


y = x




y = 2x



x y ( 1 , 2) ( 2 , 4) ( 3 , 6) ( 4 , 8)


y = 2x


Try a few more examples yourself: -

y = ½ xy = 4xy = 6xy = x

4




x y ( 1 , 2) ( 2 , 3) ( 3 , 4) ( 4 , 5)




x y ( 1 , 2) ( 2 , 3) ( 3 , 4) ( 4 , 5)


y = x + 1




y = 2x + 2



x y ( 1 , 4) ( 2 , 6) ( 3 , 8) ( 4 , 10)


y = 2x + 2


Try a few more examples yourself: -

y = ½ x + 2y = 2x - 1y = 5x - 2y = -x+6


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 +22 -3m =-3m

2m + 4 = 22 -4 = -4 2m = 18

÷ 2 = ÷ 2 m = 9

6 - 4y = 2y – 12 +12 = + 12 18 – 4y = 2y

+ 4y =+4y 18 = 6y

6 63 = 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


• 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 = 45

2

2

2

2

2


• Look at the Testbase question for trial and improvement, and discuss the methods that you used.

Developing Key Developing Key Teaching Skills In Teaching Skills In

FDPRP at Levels 5 & 6FDPRP 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 40th 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

1.10 2. 5 3.

0.2 0.025 160= 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


• 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


Question13


• 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)

developing a purposeful approach to delivering level 6 mathematics within primary schools aiming...

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