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PPT – D Hyde L Barratt Summer Targets 09 Parent and Teacher Workshop Fractions difficult to teach PowerPoint presentation | free to download - id: 15d669-ZDc1Z

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D Hyde L Barratt Summer Targets 09 Parent and

Teacher Workshop Fractions difficult to teach

difficult to learn?

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.

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.

What are some of the difficulties around

fractions?

¾

¼

½

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.

This is how we can use fractions in context.

This is how we can use Fractions in Real life

contexts.

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)

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 !)

If we look at fractions as part of a set ie- in

this example, ½ is worth 16 children.

Worms problem

Be careful look for how many is in each set.

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

Vocabulary numerator, denominator introduced in

Y3 Three quarters of shapes sets introduced in

Y2

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

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)

Y1 Counting Use the vocabulary of halves

quarters in context

Pitch Expectations - Y1

Y2 CountingFind one half, one quarter and three

quarters of shapes and sets of objects

Pitch Expectations Y2

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

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?

Y4 CountingRecognise the equivalence between

decimal fraction forms of one half, quarters,

tenths hundredths

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

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.

Equivalence Fractions.

How many quarters is the same as one half? (The

equivalent fraction).

ITP-fractions this again helps find equivalent

fractions.

Gordon's some of the software we have available

for the children to use to support our Target

work.

Areas of confusion about fractions

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

Different interpretations of ¾

3 x ¼

¼ of 3

3 4

The ¼ times table

Different interpretations of ¾

- Position on a number line

0 ¼ 2/4 ¾ 4/4

5/4

½ 1

1 ¼

Thirds SATs question

- 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.

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.

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.

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 ).

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.

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)

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.

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.