Fractions Content

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Fractions Content

• Sharing the issues
• Anna Miller 027 2269751
• anna.miller_at_canterbury.ac.nz

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Whakatauki

• Nau te rourou, naku te rourou,
• ka ora te manuhiri
• With your food basket and
• my food basket the guests will be fed.

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Session Outcomes

• Expand upon our personal understanding of
  fractions and the discover a range of teaching
  strategies.
• Challenge and critique our own knowledge of
  fractions.
• Explore a variety of activities.
• To discuss good teaching of fractions and the
  importance of it.
• Critique activities to how these may be used
  within your own class.
• View useful resources to support planning
  teaching.

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Junior School Starters

• Draw my family half of us are girls.
• What language do you use?
• What language do the children use?
• What language do you not use?
• What are the essential learning outcomes that are
  intended in this lesson?
• How would you use this activity?
• Tell us about your family!

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Difficulties Confusions associated with
teaching understanding of fractions?

• Whole number concepts are transferred to
  fractions

• 1/6 is bigger than ½
• because the ones are the same, but the six is
  bigger than the two
• 1 ½ 11/10
• both are one more than the whole
• ¾ 9/10
• because they both just need one more to make a
  whole
• ½ 1/3 2/5
• Because they add the nominator and denominator
  whole number thinking,

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Lets Get Nasty

• 
  
• 4 2 8 4
• Aim to add fractions together to make largest
  total.
• Teams throw dice
• How many Fourths? Eighths? Halves (Twoths)? You
  may keep and decide where it goes OR give away
  and the opposing team decides which fraction it
  will make.
• Find your fraction pieces?
• Yes you can rename allow the children to
  discover this.

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Loopy

• Fraction Loopy

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When the Door Bell Rang
Learning Motivation x Value
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Students must make connections between
Representations
Symbols
Words
half
1_2
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Remember Use a range of models
length representation
region representation
set representation
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Discrete Models
Discrete Made up of individual objects. For
example collections of counters, cubes, lollies
or biscuits in a packet, e.g. ¾ of this set is
blue
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Continuous Models

• Continuous models are those where a shape,
  length, region or object can be split into parts.
  For example squares, circles, 2D shapes, pizza,
  glass of water, play dough.
• e.g. ¾ of this line is blue and ¾ of this square
  is blue .

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What if?

• This is a part
• It has a value of 2
• This is the whole
• What is the part?
• What is its value?
• This is the part and value is 1.5
• What is the fraction?
• What is the value for 5 parts?
• Call this by its fraction name

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Class Quilt

• Make a class quilt
• Valuing Maths
• Wall displays
• Discovering for selves
• Colour half your quilt
• Colour quarter of your quilt
• Colour third of your quilt
• Be creative -

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Smartie Fractions

• Yum!
• Who for? Stage?
• Reinforce
• New Learning
• Extension

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Ordering fractions, decimals percentages.
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Whole to Part

• Most fraction problems are about giving students
  the whole and asking them to find parts.
• Show me ¼ of
• this circle

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Part to Whole

• We also need to give students part to whole
  problems, like
• ¼ of a number is 5.
• What is the number?

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Part to Whole

• What if this is two thirds? What does the whole
  look like?
• Show this in 3 different ways
• If 4 counters are one-half of a set how big is
  the set?
• If 10 counters are five-halves of a set, how many
  counters are in one set?

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Advice to teachers learners

• When something hard comes along, go back to what
  it means!!!
• ie. Generalise with easier numbers
• We are aiming for children to understand the
  concepts (ie. The how and why).procedural maths
  created too many sets of rules even the bright
  children run out of the ability to make sense.
• The why how give the power.
• i.e. knowing the secret!

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Game Time
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What the experts say

• Peter Hughes
• Issues in Understanding Fractions
• Van de Walle
• Grades 5- 8 Chapter 3
• Grades 3-5 Chapter 5
• What are their key points
• How does this effect your practice?
• What are you celebrating? Wanting to adapt /
  change?

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Time to play

• Roll your dough out
• and
• Think about what the following means,
• and
• What does it look like?
• Halve your dough
• Halve it again what have you got?

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I wonder

• ½ ¼
• ½ - ¼
• Now
• Show one third
• Then
• ¼ x 1/3
• Then using that information what is -
• ¾ x 2/3

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Benchmarks

• Amongst most important reference points for
  fractions are 0, ½, 1.
• Have a conversation about why this is so?
• 9/8 2/10, 9/11, 7/19
• 5/12 5/9, 2/11, 9/18,
• 7/11, 2/8, 3/7, 4/7,
• Order these accordingly

How would you use this in your classroom?
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Why do we bother to teach fractions?

• Experience the dense number line
• (preparation for decimals)
• Experience comparing with a unit
• (preparation for proportions and ratios)
• Extending basic operations
• (fractions are used in probability, trig and
  algebra in Level 4)

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Mixing Fractions Decimals

• How does this effect our practice with
  proportions ratios?
• Linking to the framework range of strategies.

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Now What

• Where are we at now?
• Needs
• Expectations
• Teacher needs
• Students needs
• Challenges ahead
• Areas of development

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Key Messages

• Whos doing the thinking?
• Promoting students strategies
• Multiplicative Thinking
• Sharing Best Practice
• Valuing Mathematics

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Reflective

• Make a commitment

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Reflect

• Deepen understanding of fractions/decimals.
• Further understanding of how and when students
  develop fractional / decimal knowledge.
• Uncover/discover some meaningful activities.
• Critique activities. How these can fit your class
  needs and where these fit within the framework.