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D Hyde L Barratt Summer Targets 09 Parent and Teacher Workshop Fractions difficult to teach

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Link fractions to multiplication and division (eg 6 2 = of 6 = 6 x ... percentages to describe and compare them, for example when looking at pie charts. ... – PowerPoint PPT presentation

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Title: D Hyde L Barratt Summer Targets 09 Parent and Teacher Workshop Fractions difficult to teach


1
D Hyde L Barratt Summer Targets 09 Parent and
Teacher Workshop Fractions difficult to teach
difficult to learn?
2
WARM UP
  • Choose any 5 of these fractions.
  • Work out what fraction is shaded red.
  • If you have that fraction on your bingo card,
    cross it off.

3
Aims
  • To identify some of the difficulties
    misconceptions that children have in this aspect
    of mathematics.
  • To understand the progression in fractions from
    Rec to Y6.
  • To have a range of ideas and activities to help
    support the learning of fractions.

4
What are some of the difficulties around
fractions?
¾
¼
½
5
Feedback from Parents
  • We dont always refer to parts of objects/numbers
    as fractions.
  • When fractions are visually different eg- ½ and
    2/4 are the same.
  • Trying to add fractions with different
    denominators eg- 3/7 2/9.
  • As the denominator gets bigger the fractional
    amount gets smaller.

6
This is how we can use fractions in context.
7
This is how we can use Fractions in Real life
contexts.
8
The variety of ways fractions can be used
A fraction is part of something split into equal
parts
  • a part of a whole ( half an apple, a quarter
    of a pizza)
  • a part of a set ( ¼ of the 12 beads)
  • part of a number ( a quarter of 20)
  • a point on a number line lying between two
    numbers( 1 ½ is halfway between 1 and 2)
  • a result of division ( 3 4 ¾ 0.75)
  • quantities( half an hour, quarter of a mile)

9
Common misconceptions and confusions about
fractions
  • Fractions are always parts of 1, never bigger
    than 1.( misconception)
  • A set of fractional numbers are infinite- between
    any two fractions you can always put another one.
  • Fractions are parts of shapes and not numbers in
    their own right. (misconception)
  • The size of a fraction does not depend on the
    size of either the numerator or denominator, but
    the size of one in relation to the other
  • A fractional area can be shown in several ways,(
    ½ a square) but a fraction of a number can only
    be represented in one way ( ½ of 8 is always 4)
  • The absolute size of a fraction depends on the
    whole of which it is a part( ½ a large cake is
    bigger than ½ of a small one or even ¾ of a
    small one !)

10
If we look at fractions as part of a set ie- in
this example, ½ is worth 16 children.
11
Worms problem
Be careful look for how many is in each set.
12
Vocabulary of fractions may be another area of
confusion
  • Y1 - halve, half
  • Y2 - part, equal parts, fraction, one whole, one
    half, two halves,
  • one quarter, twothreefour quarters
  • Y3 - one third, two thirds, one tenth
  • Y4 - eighth, sixth, fifth, twentieth
  • Y5 - ninth, twelfth, hundredth
  • proper, improper fraction, mixed number,
    numerator, denominator, equivalent,
    reduced to, cancel
  • Y6 thousandth
  • 1999 Framework

13
Vocabulary numerator, denominator introduced in
Y3 Three quarters of shapes sets introduced in
Y2
14
Definitions
  • A fraction is part of something split into equal
    parts.
  • The denominator (bottom part of the fraction )is
    the naming part
  • of the fraction and tells you the size of the
    equal parts it is split into.
  • The numerator (top part of the fraction ) tells
    you the number of
  • these equal parts you have

15
Strands that include fraction
7 Strands 1.Using Applying mathematics 2.Counti
ng Understanding No 3.Knowing Using No
facts 4.Calculating 5.Understanding shape
6.Measuring 7.Handling data
(Y4)
16
Y1 Counting Use the vocabulary of halves
quarters in context
17
Pitch Expectations - Y1
18
Y2 CountingFind one half, one quarter and three
quarters of shapes and sets of objects
19
Pitch Expectations Y2
20
Y3 Counting Read write proper fractions
interpreting the denominator as the parts of a
whole the numerator as the number of parts
identify estimate fractions of shapes use
diagrams to compare fractions establish
equivalents


21
Pitch Expectations Y3
Can you think of a similar type of question?
Jack went to the shops and spent 2/3 of his
money, he had 30p left. How much money did he
have to start with?
22
Y4 CountingRecognise the equivalence between
decimal fraction forms of one half, quarters,
tenths hundredths
23
Y5 Counting Express a smaller whole number as a
fraction of a larger one (e.g. recognise that 5
out of 8 is 5/8 ) find equivalent fractions
(e.g. 7/10 or 4/20) relate fractions to their
decimal representations
24
Year 6 Countingexpress one quantity as a
percentage of another, find equivalent
percentages, decimals and fractions
This game of Boxes gets children thinking about
the size of the fraction as the aim of the game
is to score the most points by winning the boxes.
25
Equivalence Fractions.
How many quarters is the same as one half? (The
equivalent fraction).
26
ITP-fractions this again helps find equivalent
fractions.
27
Gordon's some of the software we have available
for the children to use to support our Target
work.
28
Areas of confusion about fractions
29
When we multiply two whole numbers the product is
usually a larger number- when a multiplication
involves a fraction it is usually smaller
  • a) 2 x ½
  • b) 2 ½

30
Different interpretations of ¾
3 x ¼
¼ of 3

3 4
31
The ¼ times table
32
Different interpretations of ¾
  • Position on a number line

0 ¼ 2/4 ¾ 4/4
5/4
½ 1
1 ¼
33
Thirds SATs question
34
  • Implications for teaching fractions
  • Use an enlarged number line to show children how
    to locate fractions and to understand that larger
    numerators and denominators do not necessarily
    change the value of the fraction.
  • Plans should include making fraction families
    for the common fractions.
  • The relationships between fractions, decimals
    and percentages should be a regular feature of
    oral/mental starters, for example, using a
    counting stick to establish equivalents.

35
Layered Targets for Fractions
Yr 1 Group Target
Must Share objects into equal groups and count how many in each group. Understand the meaning of half in activities.
Should Use the words halves and quarters in activities. Know halves and that two halves make a whole one.
Could Know fraction symbols e.g. ½ and ¼ and find fractions of shapes. E.g. Halves, quarters.
36
Layered Targets for Fractions
Yr 2 Group Target
Must Use the words halves and quarters in activities. Know halves and that two halves make a whole.
Should Know one half, one quarter and three quarters of shapes and sets of objects. Begin to know fraction symbols e.g. ½ and ¼ and find fractions of shapes.
Could To know fraction symbols e.g. ½ and ¼. Find fractions of shapes and the equivalence between them e.g. 2/4 is the same as ½ and 5/10 is the same a s ½.
37
Layered Targets for Fractions
Yr 3 Group Target
Must Know one half, one quarter and three quarters of shapes and sets of objects. Know fraction symbols and find fractions of shapes and the equivalence between them. E.g. Halves, quarters.
Should Read and write proper fractions. Find fractions of numbers and quantities when the numerator is 1. (eg ½ 1/3 and ¼ of 12 litres). Find and estimate fractions of shapes.
Could Find the equivalence between decimal and fraction forms of one half, quarters, tenths and hundredths. Using pictures, find equivalent fractions e.g 6/8 ¾ or 70/1007/10 Understand mixed numbers and place them on a number line (eg 3 ½ ).
38
Layered Targets for Fractions
Yr 4 Group Target
Must Know fractions of shapes and the equivalence between them. E.g. Halves, quarters and tenths. Read and write proper fractions. Find and estimate fractions of shapes. Find fractions of numbers and quantities when the numerator is 1. e.g. ½, ¼ 1/3, and 1/6.
Should Know the equivalence between decimal and fraction forms of one half, quarters, tenths and hundredths. Using pictures find equivalent fractions (eg. 6/8 and ¾, or 70/100 and 7/10), Understand mixed numbers and place them on a number line (eg 3 ½ ).
Could Find equivalent fractions e.g. 7/10 14/20 etc. Explain patterns for equivalent fractions e.g. 1/3 2/6 3/9 4/12 Find fractions using division e.g. 1/100 of 5kg.
39
Layered Targets for Fractions
Yr 5 Group Target
Must Know the equivalence between decimal and fraction for one half, quarters, tenths and hundredths. Use pictures to identify equivalent fractions (eg. 6/8 and ¾, or 70/100 and 7/10). Understand mixed numbers and place them on a number line (eg 3 ½ ).
Should Find equivalent fractions e.g. 7/10 14/20 etc. Explain patterns for equivalent fractions e.g. 1/3 2/6 3/9 4/12 Find fractions using division e.g. 1/100 of 5kg.
Could Simplify fractions by cancelling common factors 5/20 to ¼. Order a set of fractions by changing them to fractions with a same denominator. Understand the link between improper fractions and mixed number fractions and change one to the other. Link fractions to multiplication and division (eg 6 2 ½ of 6 6 x ½ ) express a quotient as a fraction or decimal (eg 67 5 13.4 or 13 and 2/5)
40
Layered Targets for Fractions
Yr 6 Group Target
Must Find equivalent fractions e.g. 7/10 14/20 etc. Explain patterns in equivalent fractions e.g. 1/3 2/4 3/9 4/12 Find fractions using division e.g. 1/100 of 5kg.
Should Simplify fractions by cancelling common factors 5/20 to ¼. Order a set of fractions by changing them to fractions with a same denominator. Understand the link between improper fractions and mixed number fractions and change one to the other. Link fractions to multiplication and division (eg 6 2 ½ of 6 6 x ½ ) express a quotient as a fraction or decimal (eg 67 5 13.4 or 13 and 2/5)
Could Order a set of fraction by changing them to decimals. Know about how big fractions of a whole one are. e.g. 1/3, 1/5. 4/6. Then use fractions and percentages to describe and compare them, for example when looking at pie charts.
41
What can you do to help?
  • Use some of the activities from the pack.
  • Play the Boxes Game, bingo, posting letters
    etc....
  • Count up in different size fractions ( 1/ 4 2/4
    3/4 4/4 5/4 6/4 . ).
  • Talk to your children using vocabulary related to
    fractions.
  • Talk to the teacher about any questions you have.
  • Make Maths fun and enjoyable for you and your
    child.
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