Fractions 3-6 - PowerPoint PPT Presentation

Loading...

PPT – Fractions 3-6 PowerPoint presentation | free to download - id: 3c4335-NzUwY



Loading


The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
About This Presentation
Title:

Fractions 3-6

Description:

Fractions 3-6 Central Maine Inclusive Schools October 18, 2007 Jim Cook Workshop Goals What should students know and be able to do? What common difficulties do ... – PowerPoint PPT presentation

Number of Views:38
Avg rating:3.0/5.0
Slides: 34
Provided by: cmisforme
Learn more at: http://www.cmisforme.org
Category:

less

Write a Comment
User Comments (0)
Transcript and Presenter's Notes

Title: Fractions 3-6


1
Fractions 3-6
  • Central Maine Inclusive Schools
  • October 18, 2007
  • Jim Cook

2
Workshop Goals
  • What should students know and be able to do?
  • What common difficulties do students have with
    fractions?
  • What instructional practices can help students
    understand fractions?

3
Understanding the meaning of fractions
  • Too much school instruction on fractions is with
    computation. When instruction focuses on the
    meaning of fractions, it is often too brief and
    superficial. As a result, students are forced to
    learn rules and procedures for computations
    without a sound understanding of what theyre
    operating on.

4
What are appropriate goals for fraction
instruction?
  • Name fractional parts of regions and sets
  • Find fractions on a number line
  • Represent fractional parts using standard
    notation (proper and improper fractions, mixed
    numbers) and also with concrete and pictorial
    representations
  • Understand equivalence
  • Compare and order fractions
  • Make reasonable estimates with fractions
  • Compute with fractions
  • Solve problems with fractions

5
MLR goals for students
  • 1997 MLR Grade 3
  • Read, write model, and compare simple fractions
    with denominators of 2, 3, 4
  • 2007 MLR Grade 3
  • Students recognize, name, illustrate, and use
    simple fractions
  • Recognize, name, and illustrate fractions with
    denominators from two to ten
  • Recognize, name, and illustrate parts of a whole
  • Compare and order fractions with like numerators
    or with like denominators

6
MLR goals for students
  • 1997 MLR Grade 4
  • Read, compare, order, classify, and explain
    simple fractions through tenths
  • Solve real-life problems involving addition and
    subtraction of simple fractions
  • 2007 MLR Grade 4
  • Students understand, name, illustrate, combine,
    and use fractions
  • Add and subtract fractions with like denominators
    and use repeated addition to multiply a unit
    fraction by a whole number
  • List equivalent fractions
  • Represent fractions greater than one as mixed
    numbers and mixed numbers as fractions
  • Connect equivalent decimals and fractions for
    tenths, fourths, and halves in meaningful
    contexts

7
MLR goals for students
  • 1997 MLR Grade 5
  • Read, compare, order, use, and represent simple
    fractions (halves, thirds, fourths, fifths, and
    tenths with all numerators)
  • Compute and model addition and subtraction with
    simple fractions with common denominators
  • Create, solve, and justify the solution for
    multi-step, real-life problems involving addition
    and subtraction with simple fractions with common
    denominators

8
MLR goals for students
  • 2007 MLR Grade 5
  • Students understand, name, compare, illustrate,
    compute with, and use fractions
  • Add and subtract fractions with like and unlike
    denominators
  • Multiply a fraction by a whole number
  • Develop the concept of a fraction as division
    through expressing fractions with denominators of
    two, four, five, and 10 as decimals and decimals
    as fractions

9
MLR goals for students
  • 1997 MLR Grade 6
  • Read, compare, order, use and represent fractions
    (halves, thirds, fourths, fifths, sixths, eighths
    and tenths with all numerators)
  • Compute and model all four operations with common
    fractions
  • Create, solve, and justify the solution for
    multi-step, real-life problems with common
    fractions

10
MLR goals for students
  • 2007 MLR Grade 6
  • Students add, subtract, multiply, and divide
    numbers expressed as fractions, including mixed
    numbers
  • Students understand how to express relative
    quantities as percentages and as decimals and
    fractions
  • Use ratios to describe relationships between
    quantities
  • Use decimals, fractions, and percentages to
    express relative quantities
  • Interpret relative quantities expressed as
    decimals, fractions, and percentages

11
Developing the meaning of fractions
  • Fractions have four basic interpretations
  • Measure
  • Part of a region
  • Part of a set
  • Location on a number line
  • Quotient
  • 1/3 is what you get when you divide 1 pizza
    between three people
  • Ratio
  • The ration of pizzas to people is 1 to 3, 13,
    1/3
  • Operator
  • There are 1/3 as many pizzas as people

12
Developing the meaning of fractions
  • Students should understand all 4 interpretations
    and how they are interrelated. Present fractions
    using all four interpretations.
  • Using manipulatives is important
  • Understanding fractions as parts of regions may
    be easiest

13
Fractions as parts of regions
  • NCTM lesson Fun with Fractions
  • http//illuminations.nctm.org/LessonDetail.aspx?id
    U113

14
Wipe-Out
  • Version I
  • Version II

15
Set modelfractions as parts of sets
  • Get six green triangles
  • Put them into two equal groups
  • Put them into three equal groups
  • Fraction Line-Up

16
Number Line modelfractions as locations on a
number line
  • Find the number line master in your packet

17
Fraction Representations
  • Using a variety of representations and asking
    students to switch between them enhances
    understanding.
  • Real objects
  • Manipulatives
  • Fraction circles
  • Fraction rectangles
  • Pattern blocks
  • Drawings
  • Words
  • Symbols

18
Fraction Representations
  • Ask students to make connections
  • How are these different representations alike?

19
Fraction Representations
  • Ask students to consider negative examples.
  • Why is this not 1/3?
  • Why is this not ¼?

20
Fraction Representations
  • Have students generate their own fractional parts
  • Make a fraction kit.

21
Fraction Kit Activities
  • Cover Up
  • Uncover
  • Version I
  • Version II
  • Whats missing
  • Comparing pairs

22
Fraction Equivalence
  • Students should have strong conceptual
    understanding of equivalent fractions based on
    lots of experience. They can then relate that
    understanding to numerical methods for generating
    equivalent fractions.
  • Simplifying fractions
  • Generating fractions with common denominators

23
Comparing and Ordering Fractions
  • Strong concepts of the relative size of
    fractions, based on experience with physical
    objects and drawings, supports students number
    sense.
  • Estimating with fractions depends on ideas about
    the relative size of fractions.
  • Without sufficient experience with physical
    objects, students make errors, often using
    whole-number thinking when working with fractions.

24
Comparing and Ordering Fractions
  • Students should consider these cases
  • Same denominator
  • Same numerator
  • Fractions with different numerators and
    denominators
  • Students might relate fractions to a benchmark
    like ½.

25
Fractions as Quotients
  • Try sharing 12 cookies between 4 people.
  • Try sharing 3 cookies between 4 people.
  • Use the cookie masters in your materials.
  • Students have more success making thirds, fifths,
    etc. if they use toothpics.
  • Try sharing 7 cookies between 3 people.
  • Help students connect mixed numbers and improper
    fractions.

26
Lesson Ideas for mixed numbers
  • Ask students to share cookies between different
    numbers of people.
  • Use cookie cutouts and glue.
  • Dont use a numbers that are multiples.
  • Do several examples.
  • Share between three, four, and six people.

27
Operating on Fractions
  • NCTM recommends using simple denominators that
    can be visualized concretely or pictorially and
    are apt to occur in real-world settings.
  • Emphasis in instruction must shift from learning
    rules for operations to understanding fraction
    concepts.
  • Begin by asking students to use fraction pieces
    to add fractions.

28
Adding Fractions
  • Pick 2
  • Make a train with two pieces on your whole strip
    that are not the same color.
  • Build another train the same length using pieces
    that are all the same color.
  • Record.
  • Try to build other one-color trains the same
    length. For each, record.

29
Adding Fractions
  • Help students make the connection between the
    procedures for adding fractions and their
    experience with manipulatives. They might even
    invent rules for adding fractions!

30
Multiplying Fractions
  • Use physical objects and drawings to develop
    meaning.
  • Use whole number meaning for multiplication.
  • Repeated addition
  • Use the commutative property and of
  • Use rectangles
  • Help students develop the rules for themselves

31
Dividing Fractions
  • Relate dividing fractions to dividing whole
    numbers
  • 6 2 3
  • How many times can I subtract 2 from 6?
  • How many 2s are in 6?
  • Check by multiplying
  • means into groups of.
  • 6 ½

32
Dividing Fractions
  • Use fraction pieces
  • ¾ ½
  • how many ½s are in ¾?

33
Dividing Fractions
  • True or False?
  • You can multiply the dividend and divisor both
    by the same number, and the answer stays the
    same.
  • If you divide a number by one, you get the same
    number.
About PowerShow.com