Year 6 Fractions Programme.

1. Mathematics
in
Middle
and
Upper
Primary
EDUC8505
MATHEMATICS:
YEAR
6
PROGRAMME
STRAND:
NUMBER
–
Understanding
Fractions
NUMBER
Outcomes:
K-­10
Scope
and
Sequence
(DET,
2007)
Compare
and
find
equivalences
for
simple
fractions
and
key
percentages
using
a
range
of
models,
including
number
lines
(DET,
2007).
-­‐ Compare
fractions
using
models,
drawings
and
number
lines.
-­‐ Recognise
simple
equivalences
of
fractions
including
mixed
numerals
and
improper
fractions
through
diagrams
and
models.
-­‐ Order
easily
visualised
fractions,
with
like
and
unlike
denominators,
by
placing
them
on
a
number
line,
using
reference
points
such
as
0,
½
and
1.
Australian
Curriculum
(ACARA,
2010)
–
Number
and
Algebra
Compare
fractions
with
related
denominators
and
locate
and
represent
them
on
a
number
line
(ACMNA125).
Solve
problems
involving
addition
(and
subtraction)
of
fractions
with
the
same
or
related
denominators
(ACMNA126).
Find
a
simple
fraction
of
a
quantity
where
the
result
is
a
whole
number,
with
and
without
digital
technologies
(ACMNA127).
Make
connections
between
equivalent
fractions,
decimals
and
percentages
(ACMNA131).
1

2. Mathematics
in
Middle
and
Upper
Primary
EDUC8505
Lesson
1:
Objectives:
Students
will
develop
percentage
number
sense
by:
-­‐ Assigning
numerical
values
from
0-­‐100
(using
segments
of
10)
to
describe
partial
amounts.
-­‐ Using
repeated
splitting
to
develop
benchmarks
of
0%,
25%,
50%,
75%
and
100%.
-­‐ Using
composition
(i.e.
75+25=100)
to
state
the
remaining
percentage
of
the
whole.
Main
Activities
Resources
Assessment
Ongoing:
Whole
Class
(Discussion),
Pairs
Number
Sense
(McIntosh,
Reys,
&
Hope,
1997,
pg57)
Completed
worksheets,
How
Full
Is
It?
Observations,
See
Appendix
1
Glass
beakers,
masking
tape,
paper,
pens,
water.
Questioning/explanations.
Lesson
2:
Objectives:
Students
will
be
able
to:
-­‐ Say
how
many
lots
of
10%,
25%,
50%
and
100%
fit
into
100%,
re-­‐partition
the
scale
and
link
these
to
fractional
notation
(i.e.
1/10,
¼,1/2,
1).
-­‐ Use
a
calculator
and
understanding
of
fractions
as
quotients
to
work
out
decimals.
-­‐ Apply
benchmark
fractions
and
percentages
to
the
100’s
Grid.
Main
Activities
Resources
Assessment
Pairs,
Individual
(Worksheets)
Bits
&
Pieces
I
(Lappan
et
al,
2002):
100’s
Grid
problems,
blank
100’s
grids.
MAB
Blocks
100’s
Shaded
Hundreds
Grid
Problems.
See
Appendix
2
Lesson
3:
Objectives:
2

3. Mathematics
in
Middle
and
Upper
Primary
EDUC8505
Students
will
be
able
to:
-­‐ Partition
the
100’s
Grid
into
half
in
various
ways.
-­‐ State
that
halves
do
not
need
to
be
congruent,
but
must
be
equal
in
area.
Main
Activities
Resources
Assessment
Individual,
Whole
Class
(Discussion)
Show
Me
A
Half
(McClure,
2005)
Show
me
a
Half
sheet.
See
Appendix
3
Lesson
4:
Objectives:
Students
will
be
able
to:
-­‐ Find
a
simple
fraction
of
a
group
of
objects.
-­‐ State
the
percentage
equivalent
of
the
fraction.
-­‐ State
the
ratios
for
part-­‐to-­‐part
and
part-­‐to-­‐whole
comparisons
of
two
quantities.
Main
Activities
Resources
Assessment
Individual,
Whole
Class
(Discussion)
Fractions
of
a
Group
Worksheets
(modified)
Coloured
counters/blocks
-­‐ superteacher.worksheets.com
See
Appendix
4
Lesson
5:
Objectives:
Students
will
be
able
to:
-­‐ Use
fractions
as
operators
for
groups
of
objects.
-­‐ Understand
the
reversibility
of
fractions
as
operators
for
½
and
double.
Main
Activities
Resources
Assessment
3

4. Mathematics
in
Middle
and
Upper
Primary
EDUC8505
A
Dog’s
Life
Counters,
Unifix
cubes.
Put
on
a
Happy
Face!
(Moseley,
2005)
The
Birthday
Cake
Problem
Extension:
Change
the
fraction:
1/3,
¼
etc
See
Appendix
5
Lesson
6:
Objectives:
Students
will
be
able
to:
-­‐ Use
pattern
blocks
to
generate
symbolic
representations
of
halves,
thirds
and
sixths.
-­‐ Use
pattern
blocks
to
establish
the
relationship
between
these
fractions,
including
equivalences.
-­‐ Use
pattern
blocks
to
place
these
fractions
on
a
number
line.
Main
Activities
Resources
Assessment
Pairs
Exploring
Pattern
Blocks
(modified)
Everything
About
My
Fraction
–
1/2
Pattern
Blocks
Pattern
Block
Line
Up
See
Appendix
6
(Give
students
the
option
of
choosing
(www.curriculumsupport.education.nsw.gov.au).
their
favourite
fraction.)
Lesson
7:
Objectives:
Students
will
be
able
to:
-­‐ Use
pattern
blocks
to
build
a
whole,
given
a
fractional
quantity.
-­‐ Convert
the
fractions
to
percentages
(including
>100%).
Main
Activities
Resources
Assessment
Pairs
Pattern
Blocks
PB
Build
1
Whole
–
How
many
lots
of?
4

5. Mathematics
in
Middle
and
Upper
Primary
EDUC8505
Build
A
Pattern
(www.curriculumsupport.education.nsw.gov.au)
Lesson
8:
Objectives:
Students
will
be
able
to:
-­‐ Use
benchmarking
and
number
sense
strategies
to
compare
the
relative
size
of
fractions.
-­‐ Order
a
set
of
fractions
on
a
number
line.
Main
Activities
Resources
Assessment
Fractions
and
Decimals
Online
Interview
Benchmark
Fractions/Sorting
Fractions
Lesson
9:
Objectives:
Students
will
be
able
to:
-­‐ Use
benchmarking
and
number
sense
strategies
to
compare
the
relative
size
of
fractions.
-­‐ Use
ICT
to
create
visual
and
symbolic
representations
(measurement
model)
of
fractions.
-­‐ Use
ICT
models
to
determine
which
fraction
is
larger/smaller.
Main
Activities
Resources
Assessment
Individual/Pairs
Fraction
Fiddle
–
comparing
non-­‐unit
fractions
Computers
http://junior.stjohns.sa.edu.au/subjects/lob/Mathe
matics_and_Numeracy/los/l2803/index.html
Lesson
10:
Objectives:
Students
will
be
able
to:
-­‐ Estimate
approximate
distances
for
given
fractions
-­‐ Use
the
measurement
model
to
exactly
mark
the
fraction
-­‐ Order
the
fractions
on
a
number
line.
5

6. Mathematics
in
Middle
and
Upper
Primary
EDUC8505
Fractions
and
Decimals
Online
Estimating
Fractions
Interview
Classroom
Activities
Lesson
11:
Objectives:
Students
will
be
able
to:
-­‐ Estimate
the
value
of
an
unknown
fraction
on
a
number
line.
-­‐ Relate
fractions
and
decimals
Mathematics
Teaching
in
the
Small
Group/Pairs,
Whole
Class
(Discussion)
Middle
School
0-­‐1/10th
number
line
multiple
choice
question
Question
Lesson
12:
Objectives:
Students
will
be
able
to:
-­‐ Explain
fractions
as
division
using
equal
sharing
problems
and
models.
Rich
Learning
Tasks
Small
Group,
Whole
Class
(Discussion)
Understanding
Fractions
in
Number
for
Sharing
Chocolate
Bars
Assessment
Primary
Students
How
Much
Do
I
Get?
6