listening to you, working for you teaching fractions, decimals and percentages at levels 5/6 elaine...

Listening to you, working for you www.bexley.gov.uk

Teaching Fractions, Decimals and Percentagesat Levels 5/6

Elaine LambertSecondary Mathematics Consultant

Bexley LA

www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.uk

Objectives Improve participants knowledge of resources and

pedagogies that will enhance student understanding of FDP at levels 5 and 6

Participants will build a better understanding of the role of FDP in making progress through the mathematics curriculum

Participants will identify individual next steps to improve learning of FDP in their classrooms


The Big Picture

In small groups:

Highlight all the criteria on the APP grids that are related to FDP

Come up with two or three sentences that describe the big picture of FDP in levels 5 and 6


The Big Picture

Fluency in calculation

Equivalence

Understanding proportionality

Measurement

MPA


The Big Picture “ Proportionality underlies key aspects of number, algebra,

shape, space, measures and handling data”

“ In many problems, making the appropriate choice between fractions, decimals, percentages or ratio will be crucial. Students can only make such a choice if they have a sound understanding of equivalence”

SNS, Teaching Mental Maths from Level 5

“ Research shows that making links between interconnected

ideas helps pupils to make sense of the subject, avoid misconceptions, and retain what they learn”

SNS, Interacting with mathematics


The Big Picture “Teachers usually introduce rules to help pupils remember

particular results or steps in methods. However, few are always true and many are never convincingly developed with pupils so that they understand the particular context within which a rule might be used”

Eg To multiply by 10 you add a nought

“Where it is considered that rules might be useful, they should be unambiguous and developed with the pupils. The unthinking use of rules should be discouraged”

Understanding the score 2008 Ofsted


The Big Picture “Pupils’ learning is based too much on their

acquisition of methods, rules and facts as part of the strong focus on tests and exams, and too little on their understanding of the underpinning concepts, on connections with earlier learning and other topics in mathematics, and on helping them to make sense of mathematics so that they can use it independently”

Understanding the score, 2008, Ofsted


Decimals

Fluency in calculation– Rounding– Use known facts to derive unknown facts– Addition, subtraction, multiplication and division– Multiply and divide by 0.1, 0.01, 10, 100 etc– Ordering– Recurring decimals– Problem solving

Equivalence– With fractions and percentages

Measurement– Reading scales– Converting between units of length


Web Diagrams


Place value http://nationalstrategies.standards.dcsf.gov.u

k/node/96385?uc=force_uj


Place value chart


Calculate this

0.024 x 0.04

How would you teach it?


0.024 x 0.04 24 x 4 = 96 24 x 0.4 = 9.6 24 x 0.04 = 0.96 2.4 x 0.04 = 0.096 0.24 x 0.04 = 0.0096 0.024 x 0.04 = 0.00096


0.024 0.04


0.024 0.04

0.024 = 0.024 x 100

0.04 0.04 x 100

= 2.4

4

24 4 = 6

2.4 4 = 0.6


0.024 0.04 24 4

1000 100

= 24 x 100

1000 4

= 24 = 24 = 3

4 x 10 40 5


Problem Solving34918 = 19.38888….

18349 = 0.0515759…


Two way tables


Fractions (and percentages)

Fluency in calculation– Addition, subtraction, multiplication and

division– Ordering

Equivalence– With decimals, percentages and ratio

Understanding proportionality– Calculate fractions of quantities


Equivalence with ratio The scale on a map

Parts of a whole


http://www.fi.uu.nl/wisweb/applets/mainframe_en.html

Fraction Bar and Percent Bar


Web Diagrams


Web diagrams


Number lines


Aligning Diagrams Aaron earns £42 a week. He spends 23% of

his earnings on CDs. How much money does he spend on CDs each week?


Two way tables Aaron earns £42 a week. He spends 23% of

his earnings on CDs. How much money does he spend on CDs each week?


Mathematics ITP http://nationalstrategies.standards.dcsf.gov.u

k/search/secondary/results/nav:50236

Fractions Decimal Number Line Moving Digits Number Dials Ratio and Proportion


Gap Task – next session 10th Feb

Identify one or two personal targets to improve learning of FDP at levels 5/6 in your classrooms.

Identify one or two different resources/techniques that you will trial that might help you meet those targets

Report back next time


Next session – 10th Feb here in the Moorland Suite

Feedback from Gap Tasks

The use of Rich Tasks for learning and assessing FDP

Next steps

listening to you, working for you teaching fractions, decimals and percentages at levels 5/6 elaine...

Documents

big picture of fdp

mathematics slide

big picture pupils learning

big picture proportionality

big picture fluency

big picture teachers

student understanding

ofsted slide