Grade 8 - International School of Poznan

Transcription

INTERNATIONAL MATHEMATICS BOOK NO. 2-G8
Chapter 4
Main Ideas
Guiding
Questions

Section
Page
Ratio can be of aesthetic as well as quantitative value.
Where do percentages and ratios come from – were they invented or discovered?
Why or how?
How do they help us make sense of our environment?
What are the relationships between these and the other types of rational numbers?
Knowledge and
Skills
Assessment
Tasks
Project Idea
Students should be able to:
Work with equivalent ratios.
4:01 – 4:02
63
Divide a quantity in a given ratio.
4:04
74
Apply ratio knowledge to both rates and scale drawing problems.
4:05 – 4:06
77
Using ratio
4:03
72
Scale my room
4:06
85

End of unit assessment task (eg Diagnostic Tests)

Investigations:
As the new material that students will encounter in this unit deals with ratio, a
project applying ratio would be suitable.
Mona Lisa Smile
Students are to collect pictures of famous people (say 20).
Apply the golden ratio to the faces and see which faces are the closest to Da
Vinci’s golden ratio.
Copyright © Pearson Australia 2009 (a division of Pearson Australia Group Pty Ltd)
Conduct a survey of a given number of people – students at school, parents, people
in the street – to arrange the famous faces in order from most to least attractive.
Compare the results with the golden ratio results and see if they match.
Give reasons why they might not.
This could be a possible inter-disciplinary project with Art and Humanities.
Areas of
Interaction
Approaches to
learning:
Thinking mathematically through challenges and investigative
problem solving
Working Mathematically 91
4
Challenge 4:02
69
Investigation 5:02
97
Environment:
Using investigations to examine the aesthetics of students’
environment
Investigation 4:06
85
Health & Social
The make up of foods and drinks using percentages and ratio.
Practical Activities 4:04
76
Chapter 9
Main Ideas

Section
Page
Equations between variables and relationships can be represented
visually.
Guiding
Questions
What kind of relationship can be represented visually?
Knowledge and
Skills
Graph and interpret linear relationships on the number plane.
9:01 – 9:07
203
9:01
208
Construct and interpret graphs tables and charts of information.
Assessment
Tasks


Investigations:
Collecting graphs
Project Idea
The main big idea in this unit is relationships: recognising them, defining them
and representing them visually.
A suitable project might be:
Stop/Start
Students work in pairs and perform the following exercise:
One has a stop watch and the other six counters.
At the start the second student drops a counter,
1. Walks normally for 10 seconds then drops a counter.
2. Jogs for five seconds and drops a counter.
3. Stands still for five seconds and drops a counter.
4. Runs as fast as possible for five seconds and drops a counter.
5. Walks normally for five seconds and drops a counter.
Students measure the distance between the counters.
Students are to identify the variables involved and to work out the relationship
between them.
Students then construct a visual representation of the relationship (graph).
They are to discuss patterns they see what the graph does at particular times
and parts that are the same.
Some conclusions should be drawn.
This could be a possible inter-disciplinary project with Science.
Alternatively
Students could do a similar project timing how long it takes them to get home
and how far they get in each 5, 18 or 15 minute interval – they could use a
street directory to measure distance, thus incorporating ratio.
Areas of
Interaction
Studying and constructing graphs of data of
populations and the world around them.
9:02 – 9:04, 9:06
208, 234
Investigation 9:01
208
Health & Social
Education:
Some of the graphs used could examine health
statistics and social trends.
Community:
Students could apply knowledge learned in the unit to
their community and look for similar patterns.
These would form part of
a project or assignment
208
and would involve
students collecting data as
in Investigation 9:01
Environment:
Chapter 11
Main Ideas

How can we recognise and describe the same shape given in a different
orientation?
Knowledge and
Skills
Project Idea
Page
1, 2 and 3 dimensional arrangements are quantifiable.
Guiding
Questions
Assessment
Tasks
Section
Use formulae to calculate perimeter and area.
11:01 – 11:03
Calculate the surface area and volume of right prisms.
11:04 – 11:05


Investigations:
283
298
Area in a house
11:01
287
Car parking areas
11:02
293
Estimating volume
11:04
303
Categorising Polygons
This could be done throughout the unit, allowing students to complete the
sections as the progress through the unit.
Have students make up a table with the following polygons drawn alongside
the rows: equilateral triangle, square, regular polygon, regular hexagon,
regular octagon, parallelogram, isometric trapezium, rhombus, circle.
The columns could be headed:
Name? No of axes of symmetry? Degree of rotational symmetry? Diagonals
bisect one another? Opposite angles equal? Diagonals equal? Will tessellate
with? Is it regular? Properties of this shape? Where have I seen this shape in
nature?
By completing the table students will uncover the properties of the shape and
also learn about new ideas of symmetry, geometry in building and in nature
This could be a possible inter-disciplinary project with Art.
Areas of
Interaction
Approaches to
learning:
Looking at shapes around them and interpreting their
use mathematically
11
Fun Spot 11:05
308
Environment:
How shapes occur in the environment, both natural
and man-made
Investigation 11:02
293
Homo Faber:
How geometry helps us interpret nature and in
construction and aesthetics. The establishment of
geometric facts
Investigation 11:01
287
Chapter 14
Main Ideas

There is a difference between measurable and countable data.

Trends in exact relationships may be quantified.

Outcomes can be predictable.
Guiding
Questions
How can we make sense of data once it is collected and how can it be used?
Knowledge and
Skills
Assessment
Tasks
Project Idea
Section
Page
How does organising data lead to predicting outcomes of events?
Construct, read and interpret data in all its forms.
14:02, 14:04 – 14:06
364, 378
Collect and analyse data.
14:01, 14:03
360, 371
Sorting it out
14:02
369
Mean, mode and median
14:03
376
Using computer software
14:05
387

End of unit assessment task (eg: Diagnostic Tests)

Investigations:
Out of Air
Students go and gather a number of people from different age groups and ask
them to hold their breath. For example, 20 people between 10 and 15; 20
people between 15 and 20; 20 between 20 and 25 etc.
They should record their results in different tables for each age group and
calculate the mean and median of each.
Note: students need to use continuous data for this project so a new concept
needs to be introduced which they could discuss as part of the project.
Students are to make conclusions about the ability of different age groups to
hold their breath.
They could try to give reasons for their results and discuss why they think their
experiment may be flawed.
There are many alternatives to this experiment and extensions that could be
explored.
This could be a possible inter-disciplinary project with Science, PE and
Humanities.
Areas of
Interaction
Approaches to
learning:
Approaching a question or problem from an
experimental perspective
14
Environment:
Categorising elements of their immediate
environment
Practical Activity 14:01
363
Investigation 14:02
369
Homo Faber:
Where have statistics been used and why –
advertising and marketing or politics?
Throughout the chapter
discussing different
types of statistics and
where they occur
Health & Social
Education:
How are conclusions drawn about society as a
whole? What is normal or average?
Investigation 14:03
376
Community:
Using statistics to find out about the society in which
we live, or our home country
363
Challenge 14:06
393
INTERNATIONAL MATHEMATICS BOOK NO. 3- G8
Main Ideas
Unit Questions
Knowledge &
Skills
Assessment
Tasks
Project Idea
Unit Plan – Number (Chapter 1)
 Approximation and estimation have their place in calculation
 Proportions and fractions can represent the same thing and can be used to
solve problems
Does the size of a fraction/proportion matter in calculation?
How can factors and multiples be used to simplify problem solving?
Are all the gaps in the number line filled by rational numbers/
ATL Focus
Problem Solving
Logical Thinking
Communication
Section
Page
Operate with integers, fractions, decimals, percentages, ratios and rates
1:01 – 1:07
2
Round to a specified number of significant figures
1:08
17
Convert between fractions and decimals and between rates
1:04, 1:05
8
Approximate and Estimate
 End of unit assessment task (eg: Diagnostic Tests)
 Investigations: Ratios and rational numbers
1:09 – 1:10
19
The new material in this unit deals with proportional change so the project should
involve this somehow.
1. Recipes could be used to calculate the amount of ingredients required for a meal
to feed different numbers of people.
Alternatively, students could use materials required for a school dance for
differing numbers of students attending.
A possible inter-disciplinary project with Humanities (Geography).
Areas of
Interaction
Approaches to
learning:
Thinking mathematically through challenges and
investigative problem solving.
Working Mathematically
1
30,
Challenge 1:05
12
Reading Mathematics
1:09
23
Human Ingenuity:
Health & Social
Education:
Applications of ratios, rates and proportion
How ratios are used everyday in medicine
Main Ideas
Unit Questions
Knowledge &
Skills
Assessment
Tasks
Unit Plan – Algebra (Chapters 4, 5, 6 and 7)
 Symbols can be used to represent unknown quantities.
 Word problems can be represented as equations/inequations/formulae
containing symbols
 Algebra can be applied to problem solving techniques such as Pythagoras’
Theorem and the number plane.
How can a problem be translated into a simple calculation?
How can calculations be represented visually?
How has algebra helped the application of Pythagoras’ Theorem?
ATL Focus
Logical Thinking
Communication
Problem Solving
Collaborative Learning (Investigations)
Section
Page
Perform simple algebraic operations
4:01 – 4:04
75
Expand and simplify simple algebraic expressions.
4:05 – 4:07
80
Use Pythagoras’ Theorem in right triangles and to solve problems.
5:01 – 5:04
92
Apply index laws to simplify numeric and algebraic expressions.
6:01 – 6:03
118
Extend the index laws to negative indices.
6:03
126
Use algebraic techniques to solve linear equations.
7:01 – 7:06
136
Use algebraic techniques to solve simple inequations.
.
 End of unit assessment task (eg: Diagnostic Tests)
 Investigations: Checking Algebraic Simplification by Substitution
Right Angled Triangles
Pythagoras’ Theorem
Pythagorean Triads
Pythagoras and Speed
Exploring Index Notation
Zero and Negative Indices
Solving Equations Using a Spreadsheet
7:07 – 7:08
154
4:05
5:01
5:01
5:02
5:04
6:02
6:03
7:03
81
92
96
103
112
124
129
145
Project Idea
The main big ideas in this unit are

relationships: recognizing them, graphing them and interpreting
them.

Pythagoras’ Theorem: its development and application.
Suitable projects might be:
1. Pythagoras Rules: Investigate:

when, where and how Pythagoras learned about and developed his
theorem on right triangles.

If the theorem was used or developed elsewhere before Pythagoras
developed his theorem (eg: Egypt and China).

An alternative proof for the theorem (eg: President Garfield’s proof
using areas).
Students could do an Internet search to complete the above.
A possible inter-disciplinary project with Humanities (History).
Areas of
Interaction
Approaches to
learning:
Thinking mathematically through challenges and
investigative problem solving.
4, 5, 6 and 7.
Investigation 5:01A
Investigation 5:01B
Challenge 6:01
Fun Spot 7:08 (logic)
90, 116, 134,
163.
92
96
120
159
Environments:
Every day applications of Pythagoras’ Theorem in our
environment.
Ex 5:04
Investigation 5:04
109
112
Development of Pythagoras’ Theorem
Exploring Pythagoras’ Theorem
Zero and negative indices and our number system
Investigation 5:01A
Investigation 5:01B
Investigation 6:03
92
96
129
Human Ingenuity:
:
Main Ideas



Unit Plan – Geometry (Chapter 10)
Angles tell us a lot about shapes and lines and the relationships
between them.
Instruments can be used to construct many of the basic angles and
hence the shapes defined by them.
Shapes can be described as a locus of points following a particular rule.
ATL Focus
Logical Thinking
Communication
Unit Questions
What are the special relationships between angles, angles associated with
intersecting or non-intersecting lines and the consequences that result?
Is there a basic assumption in Geometry on which most results are based (ie:
180 in a triangle or straight line or alternate angles are equal)?
Section
Page
Knowledge &
Skills
Identify and name angles that formed by the intersection of lines and pairs of
lines crossed by a transversal and make use of the relationships between them.
10:01 – 10:05
238
Determine the properties of triangles and quadrilaterals
10:06 – 10:08
253
Apply results related to the angle sum of interior and exterior angles of
polygons.
10:09
265
Assessment
Tasks
Project Idea


End of unit assessment task (eg: Diagnostic Tests)
10:09A
Investigations: The Angle Sum of a Polygon
10:09B
The Exterior Angle Sum of a Convex Polygon
The main new idea in Geometry is Locus so a project with this as a focus may
be suitable:
A Special Curve: On 5mm graph paper draw an interval AB and plot a point F
4 units from the line as shown. The aim is to now plot the locus of points
equidistant from the line and the point. Compasses can be used to mark a point
3 units from F on the 2nd line from AB
3 units from F on the 3rd line from AB
4 units from F on the 4th line from AB and so on
266
268
•
F
•
•
•
•
•
A
B
Students could research the resulting curve (a Parabola) and its special
attributes. To what uses has this curve been put? What is the equation of the
curve you have drawn? Draw this curve using some software (eg Autograph).
A reflector could be made from this curve using some aluminium foil, a
sausage placed along the focal line and put in the sun to cook.
Areas of
Interaction
A possible inter-disciplinary project with Science.
Approaches to
Looking at shapes around them and interpreting their
learning:
use mathematically.
Environments:
How geometry describes, or makes sense of, the
world around us
Human Ingenuity:
:
How man has interpreted shapes and their
relationships to one another,
10
275,
Practical Activity 10:02 245
245
Investigation 10:09A
Investigation10:09B
266
268

Grade 8 - International School of Poznan

Transcription

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