AIL Approach to Numeracy

AIL Approach to
Numeracy
David Folland & Jess Galvin
Year 9 AIL - Birdwood High School

Ken Robinson 2010
http://www.ted.com/talks/ken_robinson_changing_education_paradigms.html

One Size Fits All
We have inherited an education system that was designed for another era

The Compelling Case for Change
Why AIL?

How can (maths)
learning be
personalized for 120
students?

What is Khan Academy? – www.khanacademy.org

Term Goals
Term 2 Khan Academy
As mentioned earlier this term there are 6
key units for this term. Completion of
each of these gives a Challenge Patch
(Shown on the Khan achievements page)
They are:
Addition and Subtraction
Multiplication and Division
Basic Geometry
Angles
Triangles
Rates and Ratios
Do you have any Questions? Please See
Mr Folland

Term 2 Khan Academy Grades
The requirements to achieve each grade
are listed below. The dead line is End of
Week 9
D grade you must achieve 1 challenge
patch from the term 2 list and a minimum
of 50 modules
C grade 3 challenge patches from the list
and 70 Modules
B grade 5 challenge patches (including 3
from the list) and 100 modules
A grade 7 challenge patches (including 5
from the list) and 130 modules

So what
was the
problem
with
Kahn?

 Students did not engage with
the videos.
 Students became frustrated
by the mastery demands.
 Students did not manage
their learning well.
 We didn’t set up effective
coaching structures.
 Students did not complete
goals.
 Students fell behind with their
learning and some didn’t
achieve standards.

 Consultation with parents and
students led to dividing
students into groups where
they could be better
supported.
 Teams of teachers helped
students get back on track
with their maths.

A Change
in Plan –
Streaming

 Learning was not effectively
individualized.

A Better
Model –
Targeted
Teaching
2)
(T

 Steve heard of a model for
individualized maths teaching
used by Rosslyn Shepherd
former principal of
Bridgewater Primary.
 The system revolved around
short Targeted Teaching
sessions to help students
develop their understanding.

Whichallow
comes Curriculum to be
first?
Project to
application

covered

Year 9 AIL Maths and Geography

Year 9 Maths Targeted Teaching Term 3

The Geometry of World War One (The Great War)

Focus Unit - World War One

Geometry is important in military situations. There are many important factors in fields of
battle including: having a large area to base troops; having higher points to attack from
and controlling strategic positions for example bridges, ports, waterways and regions with
sought after resources. The geometry of these areas can have a significant influence on a
battle. This leads to a question:

Does having more area under control lead to victory?

o Select a historical WW1 battlefield (eg Battle of the Somme, Battle of Ypres and
The Gallipoli Campaign)

o Select a date during the conflict
o Capture a map of the field of conflict from the internet (using Google Maps or other
map source) and using digital technologies add the following to the map:
Areas of control of each army (including ‘no man’s land’)
All BOLTSS components
o Border
o Orientation
o Legend
o Title
o Scale
o Source

o Create a Cartesian grid on your map with your origin in the middle of the field
o Determine (x,y) coordinates for both armies’ headquarters/command posts
o Find the distance between these two points. Convert it to metres using your map
scale

o Calculate (showing all working) the area that each army controlled (the methods
required to do this will depend on the shape of the area)

o Compare the amount of area held by each army.
o Determine the victor of the battle. Make a conclusion about area under control and
victory

o Present all of this information in a maths report
o You must reference all information sources

9 AIL Geometry of WW1

Folland 2013

The key task will be a mapping and measurement task based on historic battle field data. The skills that students will
require will vary depending on which battle field they choose.

Maths Concepts
T2 sessions will be needed for all of these, some topics may require two sessions.

For this task you will be examining the geometry of historical battlefields World War One

o
o

Assessment Task

Page 1 of 1

Curriculum Area
1. Number and Algebra
a.
Linear and nonlinear relationships
i.
Review of Cartesian plane and plotting points
ii.
Plot linear relationships on the Cartesian plane with and without the
use of digital technologies (ACMNA193)
iii.
Find the distance between two points located on a Cartesian plane
using a range of strategies, including graphing software
(ACMNA214)
2. Measurement and Geometry
a.
Using units of measurement
i.
Choose appropriate units of measurement for area and volume and
convert from one unit to another (ACMMG195)
ii.
Review of areas of triangles and simple quadrilaterals
iii.
Find perimeters and areas of parallelograms, trapeziums,
rhombuses and kites (ACMMG196)
iv.
Investigate the relationship between features of circles such as
circumference, area, radius and diameter. Use formulas to solve
problems involving circumference and area (ACMMG197)
v.
Calculate the areas of composite shapes (ACMMG216)
b.
Geometric reasoning
i.
Define congruence of plane shapes using transformations
(ACMMG200)
ii.
Develop the conditions for congruence of triangles (ACMMG201)
iii.
Establish properties of quadrilaterals using congruent triangles and
angle properties, and solve related numerical problems using
reasoning (ACMMG202)
iv.
Use the enlargement transformation to explain similarity and
develop the conditions for triangles to be similar (ACMMG220)
v.
Solve problems using ratio and scale factors in similar figures
(ACMMG221)
c.
Pythagoras and trigonometry
i.
Investigate Pythagoras’ Theorem and its application to solving
simple problems involving right angled triangles(ACMMG222)
ii.
Use similarity to investigate the constancy of the sine, cosine and
tangent ratios for a given angle in right-angled triangles
(ACMMG223)
iii.
Apply trigonometry to solve right-angled triangle problems
(ACMMG224)

9 AIL Term 3 Maths Outline

Folland 2013

T2 to be prepared/presented by

Page 1 of 1

Criteria for
Success

Birdwood AIL2013
Maths Information Report Rubric
5
Ideas

4
Ideas

3
Ideas

2
Ideas

1
Ideas

Clearly responds to the meaning and Responds to the meaning and
Attempts to respond to the intention of Does not respond to the intention
intention of the question.
intention of the set question. Discusses the set question. Relies too heavily on of the set question. Relies on the
Demonstrates a thorough
topic beyond a simple recall of facts. the recall of facts.
recount of facts.
understanding of the topic.

Does not address the topic and
discusses aspects of the topic
briefly.
No evidence=No score

Text Structure

Text Structure

Text Structure

Text Structure

Text Structure

Introduction clearly outlines topic in
opening statement. Excellent details.
Diagrams, photos, illustrations, tables
and maps enhance text. Body
discusses key issues in detail and
with clarity. Conclusion summarises
main ideas and includes a valid
judgement on question.

Introduction clearly outlines topic in
opening statement. Very good details
for. Diagrams, photos, illustrations,
tables and maps enhance text. Body
discusses key issues. Conclusion
summarises main ideas and attempts
a valid judgement on question.

Introduction provides a sound outline
in opening statement. Good details.
Diagrams, photos, illustrations, tables
and maps used. Body discusses
points raised in introduction.
Conclusion summarises main ideas
briefly and attempts to make a basic
judgement or comment.

A basic outline in introduction. Bare
detail. Diagrams, photos,
illustrations, tables and maps not
used. Conclusion does not
summarise all arguments and final
judgement/comment is absent.

Introduction does not introduce
topic effectively, body is not
coherent or well constructed and
conclusion does not summarise the
points raised or absent.

Language

Language

Language

Language

Language

Language choice is sophisticated and
well matched to the genre. Precise
and effective words/phrases used in a
natural and articulate manner.
All sentences are consistently
effective, fluent and correct and
express precise meaning
Correct spelling of common words.
Mostly correct spelling of difficult and
challenging words

Language choice is well matched to
the genre. Phrases are expressed in
an articulate manner but limited in
range.
Sentences are mostly correct and
Correct spelling of simple words and
most common and difficult words.
Errors are minimal.

Language choice occasionally
matches the scientific genre but range
is limited. Errors in vocabulary choice
are also evident
Sentences are mostly correct and
Correct spelling of all simple and most
common words. Difficult words contain
errors.

Language choice is limited and
mostly simple. Key scientific words
and phrases are not used
effectively or consistently.
Sentences structure and
effectiveness are inconsistent.
Errors are evident in simple and
common words.

Language choice is consistently
incorrect.
Few correct sentences.
Minimal correct spelling.

Evidence

Evidence

Evidence

Evidence

Evidence

Uses detailed and appropriate
evidence from sources. References
correctly.

Uses evidence and quotes to enhance Evidence lacks detail/relevance/
discussion/argument. Sources are
substance. Sources are limited.
referenced correctly.

Evidence is limited. Sourcing of
information is incorrect.

Evidence is extremely limited and
used incorrectly. Sourcing is
absent.

BOLTSS

BOLTSS

BOLTSS

BOLTSS

BOLTSS

All BOLTSS are present and
All BOLTSS are present and displayed All BOLTSS are present but displayed BOLTSS are present but displayed BOLTSS not evident in any
displayed in an outstanding manner - in a clear and neat manner.
in poor manner OR Missing 1-2
in completely unsatisfactory
capacity.
enhanced presentation.
BOLTSS.
manner OR Missing 3 + BOLTSS.
Coordinates

Coordinates

A Cartesian grid is placed on the map
with highly appropriate scaling and
origin in the centre. All grid references
are calculated correctly.

A Cartesian grid is placed on the map A Cartesian grid is placed on the map
with appropriate scaling and origin in with origin in the centre. Most grid
the centre. All grid references are
references are calculated correctly.
calculated correctly.

Coordinates

Coordinates

A Cartesian grid is placed on the No Cartesian grid or grid references
map; origin is not at the centre.
are presented.
Grid references are not calculated
correctly.

Coordinates

Areas

Areas

Areas

Areas

Areas

The geometric areas selected for the
composite shapes are highly
appropriate approximations of the
area under control.

composite shapes are appropriate
approximations of the area under
control.

composite shapes are somewhat
appropriate approximations of the
area under control.

The geometric areas selected are
simple shapes that do not
approximate of the area under
control.

Geometric areas are not selected.

Formula and Substitutions





Appropriate formula chosen for
solving areas are presented, all
substitutions are shown and correct.

Appropriate formula chosen for solving Most formula chosen are correct; all
areas are presented, all substitutions substitutions are shown however
are shown but some may be in error
some may be in error.

Most formula chosen are correct,
substitutions are not shown

Few correct formulas are used.

Calculations

Calculations

Calculations

Calculations

Calculations

All calculations are performed
All calculations are performed
accurately, showing all worked steps. accurately, showing most worked
steps

Most calculations are performed
accurately, showing some worked
steps

A few errors are found in the
calculations

Calculations contain many errors.

Solution

Solution

Solution

Solution

Solution

All solutions contain highly
appropriate units and are correct
based on information presented

Most solutions contain appropriate
units and are correct based on
information presented

Some solutions contain appropriate
units and are correct based on
information presented

Few solutions contain units or are
correct

No units are given for solutions.

Mathematical Presentation

Constructing data display




All mathematical objects and
equations are presented neatly,
following general presentation
conventions.

Most mathematical objects and
conventions.

Some mathematical objects and
conventions.

Mathematical objects and
Mathematical objects and equations
equations are presented but do not are not neat and do not follow
follow mathematical conventions or conventions.
are not neat.

Analysis

Analysis

Analysis

Analysis

Includes a detailed analysis of
context/themes/issues.
Conclusions/analyses are explained in
detail and are clearly relevant.

Attempts a detailed analysis of text of
context/themes/issues.
Conclusions/analyses are not
explained in enough detail.

Analysis is lacking and does not assist Analysis is limited. Conclusions are
reader to navigate the text.
not relevant to the topic or
Conclusions/analyses are simple or
expressed in any detail.
not relevant to the topic.


Analysis
Analysis is irrelevant or lacking
basic detail. An adequate
conclusion has not been attempted.
No score = No evidence

Feedback

/60

Quilt Sheet- World War One Geometry

Quilt Sheets

Name_______________________

Advisory______

What patches do you already know? Circle your evaluation of your current
knowledge for each of the boxes based on the codes below.
N- Novice (This is new to me)
B-Beginning learner (I am only familiar with this)
L- Learner (I have a solid knowledge of this)
A- Advanced (I can apply this knowledge to a mathematical problem)
I can find slopes of
lines on the Cartesian
Plane

I can Find the distance
between points on the
Cartesian Plane

N B L A

N B L A

I can find the area of
squares and rectangles

kites and rhombuses

N B L A

N B L A

triangles

I can find the
circumference of circles

circles

N B L A

N B L A

N B L A

N B L A

I can use my
knowledge of other
types of area to find
areas of composite
shapes

I can identify similar
triangles

I can identify
congruent triangles

I can solve scale
problems involving
similar triangles

N B L A

N B L A

I know what
Pythagoras’ Theorem
is

I know how to make
use of Pythagoras’
Theorem

I know how to find
sine, cosine and
tangent ratios.

N B L A

N B L A

N B L A

I know about the
Cartesian Plane

I can plot points on the
Cartesian Plane

N B L A

N B L A

I can convert between
units of area

I can convert between
units of volume

N B L A

N B L A

trapeziums

N B L A

N B L A
I know how to use sine,
cosine and tangent
ratios to solve
problems

N B L A

Sign up
Sheets

2

T Sign Up Sheet
Topic __Lines on the Cartesian Plane___________
Day __Tuesday___ Date _20/8__ Slot _3_ Time __9:35__

Room __Booth_________

Name

Teacher ___Mr Folland___

Advisory Attended Take away finished

2
T

Takeaway

Teaching Focus

Teaching Example
& Touch Base Task
T2 Teaching Example
Pythagoras’ formula is used for finding the
length of the third side of a right angled
triangle
1. Identify which side is the unknown
(hypotenuse or shorter side)

2. Place the known values into the
appropriate formula

6cm

3. Solve for the unknown side length

ℎ=

�+�

ℎ=

6 +4

ℎ = 36 + 16
ℎ = 52
ℎ = 7.21�
�

4cm
In this case it is the hypotenuse
Touch Base Tasks:
1.
Find the lengths of the unknown
sides on each of the following
triangles. (You may use a
calculator to solve the square
roots)
a. Find h

c. Find h

8cm

h cm

h cm

h cm

8cm

8cm

6cm

d. Find a
14cm
8cm

b. Find a
a cm

8cm
6cm

a cm

e. Find h
h cm
3.5cm

c.
3.5cm

These tasks will be reviewed in the
Tutorial Session in the next Maths T2
9 AIL Maths – Pythagoras and Right Angled Triangles Folland 2013

Page 1 of 1

Testing
3.

Create values tables for the following equations

13.

Which pairs of triangles are congruent, explain giving reason (not all diagrams to scale)

a. y=2x-3
x

-3

-2

-1

0

1

2

3

4cm
4cm
2cm

y

A

2cm

B

1cm

80
C

1cm
60

Ordered pair

20

b. y=-3x +4
x

-3

-2

-1

0

1

2

3

G
5cm

5cm

y

4cm

6cm

D

5cm

Ordered pair

F
4cm

E

80

/8
4.

60

Plot the lines from 3 on the Cartesian plane, label them a and b
4cm

5

4

1cm

H
3

60

4cm
80
I

J

1cm

5cm

60

2

5cm
5cm

1
-5

-4

-3

-2

-1

3cm

5cm
1

2

3

4

80

5

3cm

K

5cm

5cm

M

L

-1

4cm
4cm

-2

Pair

Reason

-3

-4

-5

/4
/8
9 AIL Maths – Geometry Test

Folland and Verma 2013

Page 2 of 7

9 AIL Maths – Geometry Test

Folland and Verma 2013

Page 7 of 7

Year 9 AIL Targeted Teaching Mathematics - Takeaway

A

2
T

Session

Probability
Name:____________________ Advisory:________ T2 Teacher:_______________

T2 Teaching Focus:
Probability is a measure of how likely something is to happen.
Many events can't be predicted with total certainty. The best we can say is how
likely they are to happen, using the idea of probability.
Tossing a coin
When a coin is tossed, there are two possible outcomes:
Heads (H) or Tails (T)
We say the probability of the coin landing H is ½
And the probability of the coin landing T is ½
Throwing a dice
When a single die is thrown, there are six possible outcomes:
1,2,3,4,5,6
And the probability of any one of them is 1/6
In general
Probability (P) of an event happening =

Number of ways it can happen
Total number of outcomes

T2 Example 1: The chances of rolling a "4" with a die
Number of ways it can happen: 1 (there is only 1 face with a "4" on it)
Total number of outcomes: 6 (there are 6 faces altogether)
So the probability P(4) =

1
6










Task
Targeted Teaching
Takeaway
Touch Base
Tutorial
Tracking
Testing
Feedback and Improvement

Questions?
http://www.slideshare.net/lordfolland/AIL_Numeracy

AIL Approach to Numeracy

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