Teaching Fractions, Decimals and Percentages at Levels 5/6

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Teaching Fractions, Decimals and Percentagesat
Levels 5/6

• Elaine Lambert
• Secondary Mathematics Consultant
• Bexley LA

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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

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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

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The Big Picture

• Fluency in calculation
• Equivalence
• Understanding proportionality
• Measurement
• MPA

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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

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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

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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

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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

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Web Diagrams
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Place value

• http//nationalstrategies.standards.dcsf.gov.uk/no
  de/96385?ucforce_uj

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Place value chart
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0.024 x 0.04

• Calculate this

• How would you teach it?

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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

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0.024 ? 0.04
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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

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0.024 ? 0.04

• 24 ? 4
• 1000 100
• 24 x 100
• 1000 4
• 24 24 3
• 4 x 10 40 5

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(No Transcript)
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Problem Solving
349?18 19.38888. 18?349 0.0515759
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Two way tables
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Fractions (and percentages)

• Fluency in calculation
• Addition, subtraction, multiplication and
  division
• Ordering
• Equivalence
• With decimals, percentages and ratio
• Understanding proportionality
• Calculate fractions of quantities

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Equivalence with ratio

• The scale on a map

• Parts of a whole

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http//www.fi.uu.nl/wisweb/applets/mainframe_en.ht
ml

• Fraction Bar and Percent Bar

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Web Diagrams
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Web Diagrams
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Web Diagrams
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Web diagrams
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Number lines
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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?

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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?

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Mathematics ITP

• http//nationalstrategies.standards.dcsf.gov.uk/se
  arch/secondary/results/nav50236
• Fractions
• Decimal Number Line
• Moving Digits
• Number Dials
• Ratio and Proportion

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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

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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