Transcript Fractional Framework

Fractions …all the parts!
Presented by
D&A
Learning Outcomes
 To link fractions with addition/subtraction
and multiplication/division strategies.
 To make sense of fractions and decimals
using equipment
 To look at BSM and FIO activities related to
fractions.
Fractions
 Draw one half on a piece of paper.
 The trapezium is one quarter of a shape
what does the shape look like?
Regions and Sets
Part to whole
Whole to part
Continuous
(length/region)
This Cuisenaire
rod is two thirds
of a length. How
long is the length?
Discrete (sets)
Here are two
lollies. They are
one-quarter of a
bag. How many
lollies are in the
bag?
Cut this circle into Here are 12
quarters
lollies. If you eat
one-quarter of
them how many do
you get?
Fractional Misconceptions
 No acceptance of the existence of numbers
between numbers
Share 5 biscuits between 4 children …. You
can’t do it!
Fractional Misconceptions
 The numerator relates to the whole
½ is 1 shared between 2
¼ is 1 shared between 4
Fractional Misconceptions


The symbol can be either way up
You can’t have fractions greater than 1
4 = 6
6
4
never been challenged
if fractions greater than 1
haven’t been explored
Fractional Framework
Regions
Knowing how
many parts
make a whole
Number
Sets
Recognising the Using half as an
symbol
operator on
Knowing where other numbers
half lives on a
number line
Stage 2/3
Regions
Know half is 2
equal parts.
Know quarter is
4 equal parts.
Number
Recognise
symbol ½
Recognise
symbol ¼
Sets
Doubles and
halves
Stage 4
Regions
Number
Sets
1 half, 2 halves,
3 halves
1 quarter,
2 quarters,
3 quarters
4 quarters
5 quarters
Place of ½ on a
number line.
Place of 2
halves 3 halves
etc.
Find half and
quarter of a set
by equal
sharing.
Using the Teaching Model
Materials
 Give half of these Smarties to Courtney and the other half
to Kieran
Imaging
 Half of the cake has 4 Smarties.
How many on the whole cake?
Number Properties
 I had 8 Smarties and I ate half of them.
How many did I have left?
Stage 5
Regions
Number
Sets
Comparison and
ordering of unit
fractions by region.
½>¼>⅛
Extend knowledge to
other fractions: Thirds,
fifths, tenths etc.
Meaning of – ths
Identify symbols for
fractions including
those greater than 1
Place of ½ on a
number line
2x½=1
4x½=2
Link to repeated
addition for
multiplication.
Comparison and
ordering of unit
fractions by sets of
½ of 12 = 6
¼ of 12 = 3
Link to repeated
addition and
commutativity of
multiplication.
½ x 12 = 12 x ½ = 6
Stage 6
Regions
Number
Sets
Order unit
fraction
Recognising
equivalence
using materials
Building
decimals, using
pipe numbers
Place of all unit
fractions on the
number line
Particular attention to
tenths
Decimal notation for
tenths
Position of hundredths
on number line.
Decimal notation for
hundredths
Extend to
thousandths.
Solving
fractional
problems using
division.
¼ of 28 from
28 ÷ 4 = 7
Stage 7
Regions
Order non unit
fractions
Number
Order decimals
to 3 decimal
places
Fractions out of Conversion
between
100
fractions,
Percentages
decimals and
percentages.
Sets
Solving fractional
problems using
knowledge of
equivalence
¼ of 64 by ½ 64 = 32
½ 32 = 16
Solve fractional
problems using
multiplication and
division.
⅜ of 64 = 64 ÷ 8 = 8 8
x 3 = 24
Stage 8
Regions
Number
Sets
Solve
percentages,
comparing ratios
and proportions
Visit 4
 Observation of a lesson which includes
warm up, one strategy group and a warm
down.
 Numpa – retesting of children. Data on line
by 15th November.