Download MYP-2 - BlooMath

MYP-2
Unit 1:
Number
Duration: 3 weeks
Key Concept: LOGIC
Related Concept: PATTERNS
Global Concept: IDENTITIES AND RELATIONSHIPS
Inquiry Statement: At the end of this unit, students will be able to use logical approaches to find and describe number patterns through an
inquiry into different systems of numbers and the relationships between them.
Inquiry Questions:
1. What the attributes of prime, square and Fibonacci numbers?
2. What does it mean to find the nth term of a sequence of numbers?
3. Which is more accurate, ordinary form or scientific notation?
ATL: Organize time to meet goals and deadlines.
Expectations
Explanatory notes and examples
Textbook
1
2
Problem-Solving Strategies
Activities, IDUs, Explicit
connection to Unit Question,
Explicit connection to AOI
Pascal’s Triangle and Prime
Factorisation
Number Patterns
Pascal’s Triangle
Time: Time zones,
Calendars
Square roots of the perfect
squares from 1 through 225
Writing large and small
numbers using scientific
notation
To understand that the square root is the
inverse operation of to the power of 2 and to
know the square roots of perfect squares 1 to
225
25000 = 2.5
3.28
328
The Calendar Project
Ancient Chinese Number System
Activity
8+1 Connection:
Li: The importance of school
rules and procedures
Operations in scientific
notation
Multiples and Factors
Finding LCM , HCF using
prime factorisation
Matrices
Number Systems: Know
the number system
identifying and giving
examples of each of
Unit 2:
Percents,
Ratios, Rates
and
Proportion
Duration: 4 weeks
Key Concept: RELATIONSHIP
Related Concept: EQUIVALENCE
Global Concept: FAIRNESS AND DEVELOPMENT
Inquiry Statement: At the end of this unit, students will understand the concepts of relative quantity and common frame of reference and
be able to apply these understandings to the study of worldwide distribution of hunger.
Inquiry Questions:
1. How can a fraction be converted to a percentage?
2. What does proportional mean?
3. Is there a universal standard for desirable proportions?
ATL: Begin to take notes, summarize, and paraphrase effectively.
Ensures that all group projects are completed to an acceptable standard.
Expectations
Explanatory notes and examples
Textbook
Activities, IDUs, Explicit connection
to Unit Question, Explicit connection
to AOI
Converting harder
decimals, fractions and
percents
0.375 = 87.35% = 2/7
3:03
UN Day Activity: Posters, to raise
awareness of world issues using decimals,
fractions and percentages (C, D)
REVIEW Finding
- Find 27% of 52Kg
3:04
Use of percentages in the news (D)
1) a percent of an amount
2) an amount given the
percent
3) the percent given the
part and the whole
Using mental and written
strategies
- 15 is 20% of what number?
- An item is advertised as being 25% off. If the
sale price is $42, what was the original price?
- John scored 20 out of 45 in a test what
percent did he get?
3:05
3:06
3:10
Identify and write ratios as
comparisons of part-to-part
and part-to-whole
relationships
Dividing an amount in a
given ratio
There are 10 boys and 12 girls, what is the
ratio of boys to girls? What is the ratio of boys
to the total number of children?
4:01
4:02
4:03
Cutting Rectangles Investigation (B, C, D);
4:04
Scale Drawing Project (A, C)
Solve single- and multi-step
word problems involving
ratios, rates (d = rt), and
percents, and verify the
solutions, including
Currency Conversion.
-Divide 100 into more than two proportional
parts (e.g., 4:3:3)
-Joe, Sam, and Jim completed different
amounts of work. They agree to split the $200
they earned in a ratio of 5:3:2, respectively.
How much did each boy receive?
Julio drove his car 570Km and used 25L of
gasoline. How many Km per L did his car get
during the trip? How many L per Km did his car
travelled? Explain your answer.
- Sally had meeting 100Km away. She drove
there at an average speed of 90 Km per hour,
but when she returned, she averaged only
50Km per hour. How much longer did the
evening trip take than the morning trip? Explain
your reasoning.
Make scale drawings and
solve problems related to
scale.
Represent proportional
relationships using graphs,
tables, and equations, and
- Joe exchanged €200 for Canadian dollars (at
a rate of $1.02 CDN per €1). Then he
exchanged his Canadian dollars for Mexican
pesos (at a rate of 10.8 pesos per $1 CDN).
How many Mexican pesos did Joe get?
On an 80:1 scale drawing of the floor plan the
dimensions of the room are 2.5cm by 3.7cm.
What is the actual area of the room in m 2?
Proportional relationships are linear
relationships whose graphs pass through the
origin and can be written in the form y = kx.
Write ratios to represent a
variety of rates and use unit
rates to solve proportions
Vitruvius: making a human model (A, C and
D)
Proportion in the kitchen (A, C, D)
Vitruvius: making a human model (A, C and
D)
Conversion Graphs (A, C, D)
Conversion Graphs (A, C, D)
8+1 Connection: AI: Caring for others
4:05
Grade 7 Theme Connection:
Environmental Citizenship: Making
4:05
4:06
sure everyone has enough to eat. Not being
wasteful.
make connections among
the representations.
Write proportion equations
to find the value of points
outside the range of the
graph
Write and solve inverse
proportion equations
Determine whether or not a
relationship is proportional
and explain your reasoning.
Write an equation that expresses the length, l,
in terms of the width, w, of similar triangles and
graph the relationship between the two
variables.
Determine whether each situation represents
a proportional relationship and explain your
reasoning.
y = 3x + 2
Is the relationship between heart rate and age
proportional? Explain your reasoning
Draw and interpret straight
line conversion graphs and
distinguish between
proportional and non
proportional quantities.
To understand that the
gradient of a line represents
the rate of change.
Combinatorics: The
Fundamental Counting
Principle
Counting with Restrictions
Factorial Notation
Simple Permutations
Currency conversion (eg. Euros to dollars and
Euros to Moroccan Dirham)
Converting between imperial and metric
system(eg. mi to km)
Converting between the metric system (eg Km
to m, years to centuries)
Time and distance when moving at constant
speed (convert time from decimal to h and min)
9:02
p.213,230
Unit 3:
Algebra
Duration: 7 weeks
Key Concept: IDENTITY
Related Concept: REPRESENTATION
Global Concept: SCIENTIFIC AND TECHNICAL INNOVATION
Inquiry Statement: At the end of this unit, students will understand how to use various algorithms that mathematicians have designed
around the principles of equality and identity in order to represent and solve real-world problems.
Inquiry Questions:
1. What determines the order in which I balance a multi-step equation?
2. How can something be transformed yet stay the same?
3. Does the use of variables make problem-solving more or less straightforward?
ATL: With guidance, begin to identify and state problems, and list solutions to the identified problems.
Expectations
Explanatory notes and examples
Textbook Activities, IDUs, Connections
Know the number system
To understand the diffference between the
Integer Operation Investigation (B, C,
identifying and giving
different types of number and that not all
D)
examples of each of
numbers can be represented as fractions
Compare and order rational
numbers using the number
line, lists, and the symbols
<, >, or =.

Define and determine the
absolute value of a number.
List the numbers
Number Walls Investigation (B, C, D)
Straight Line Investigation (B, C, D)

in increasing order, and graph the numbers
on a number line.
Students define absolute value as the distance
of the number from zero.
Mathematician Research Report
Explain why 5 and –5 have the same absolute
value.
Evaluate |7.8 – 10.3|.
Fluently and accurately
add, subtract, multiply, and
divide rational numbers
using order of operations.
6
Apply the properties
commutative, associative,
distributive (expanding and
factorizing a common
factor) to manipulate
algebraic expressions
involving
coefficients
Write algebraic expressions
from words or diagrams
Identify the identity element
of addition and
multiplication and find the
inverse.
Solve multi-step equations
including decimals &
fractions with variables on
both sides by balancing
Solve equations involving
grouping symbols
Substitute variables by
given values in formulas or
6:06
7:01
91 – 2.5x = 26
7:03
(x – 2) = 119
3x + 34 = 5x
114 = -2x – 8 + 5x
3(x – 2) – 4x = 2(x + 22) – 5
7:04
a=–2
7:05
a + (a – 2)2 –1/2a
expressions
Solve word problems using
equations (including fractions
and decimals).
Graph and solve onevariable inequalities
showing solution on the
number line.
Graph linear patterns and
find general rules from
tables or straight line
graphs including horizontal
and vertical lines.
Graph straight lines and
find the point of intersection
of 2 straight lines.
7:06
Graph the solution of 4x – 21 > 57 on the
number line.
7:07
7:08
-Could the data presented in the table
represent a linear function? Explain your
reasoning.
8:03
8:04
8:05
- Does y  represent a linear function?
Explain your reasoning.
Experimentally through graphing
8:06
Straight Line Graph Investigation (B, C, D)
What is a better deal?
Solve a system of
equations by graphing
Understand the concept of
gradient
9:05
Draw and interpret travel
graphs relating gradient as
speed (travel graphs)
Unit 4:
Geometry:
Area and
Volume
Duration: 4 weeks
Key Concept: FORM
Related Concept: MEASUREMENT
Global Concept: ORIENTATION IN TIME AND SPACE
Inquiry Statement: At the end of this unit, students will understand interrelatedness of space, form and measurement.
Inquiry Questions:
1. What kind of measurement can be used to describe the size of a 3-dimensional solid?
2. What is PI?
3. Is 3.14 a reasonable value to use in calculations involving PI?
ATL: Begin to discuss the effectiveness or feasibility of solutions presented.
Expectations
Explanatory notes and examples
Textbook
Classify quadrilaterals
Solve problems with
quadrilaterals, including
consecutive angles,
diagonals, bisected angles,
perpendicular segments
Classify according to the sides and angles
square, rectangle, parallelogram, trapezium,
rhombus and kite
Determine area and
perimeter of special
quadrilaterals (trapezium,
rhombus, kite)
Know and use the formulas for kite, trapezium
Determine area and
perimeter of simple
quadrilaterals whose
dimensions are given as
simple algebraic
expressions
Definition of a right angle
Definition of a right triangle
Pythagorean’s theorem as it
applies to finding a missing
Activities, IDUs, Explicit
connection to Unit Question,
Explicit connection to AOI
Always Never Sometimes (C, D)
Finding PI Investigation
11:03
Around the Garden Investigation (B,
C, D)
Grade 7 Theme Connection:
Environmental Citizenship: Around
the Garden Investigation (B, C, D)
side of a right triangle.
Simple proof of right
triangle
Know all parts of a circle
Know the properties of
parts of the circle, such as
radius/tangent right angle
relationship, central angle;
inscribed angle
Know and identify the vocabulary related to
circles: circle, diameter, radius, arc, chord,
semicircle, circumference, segment, sector,
tangent
Understand the ratio of
circumference to diameter
to be π, and recognize 22/7
and 3.14 as common
approximations.
Determine circumference
and area of circles and the
areas of sectors
Measure the diameter and circumference of
several circular objects. Divide each
circumference by its diameter. What do you
notice about the results?
Determine the area of a circle with a diameter
of 12cm. Give your answer in m2.
Determine the circumference of a circle with a
radius of 32cm.
Determine the area and
perimeter of composite
shapes
Includes quadrilaterals such as trapezoids or
irregular quadrilaterals, as well as any other
composite figure that can be divided into figures
for which students have calculated areas before.
Example:
Determine the area and perimeter of each of the
following figures,
Construct prisms and
cylinders from nets
The net of a rectangular prism consists of six
rectangles that can then be folded to make the
prism. The net of a cylinder consists of two
circles and a rectangle.
Students may determine surface area by
calculating the area of the faces and adding the
results.
Determine volume and
surface area of prisms and
12:01
12:03
12:04
12:04
11:04
11:05
cylinders.
A net can be used to illustrate the formula for
finding the surface area of a cylinder.
Solve single- and multi-step
word problems involving
area, perimeter and volume
of the above
Alexis needs to paint the four exterior walls of
a rectangular barn. The length of the barn is
80m, the width is 50m, and the height is 30m.
The paint costs $28 per litre, and each litre
covers 420 square meters. How much will it cost
Alexis to paint the barn? Explain your work.
Captain Jenkins determined that the distance
around a circular island is 44 miles. What is the
distance from the shore to the buried treasure
in the centre of the island? What is the area of
the island?
Unit 5:
Angles
Construction
and
Transformati
ons
Duration: 3 weeks
Key Concept: AESTHETICS
Related Concept: PATTERN
Global Concept: PERSONAL AND CULTURAL EXPRESSION
Inquiry Statement: At the end of this unit, students will understand that a culture can be aesthetically represented through mathematical
patterns and designs.
Inquiry Questions:
Factual – What is the formula for finding a single interior angle in a regular polygon?
Conceptual – How can we construct a regular polygon with only a straightedge and a compass?
Debateable – Which are more aesthetically pleasing – regular or irregular shapes?
ATL: Making connections between knowledge, understanding and skills across subjects with guidance.
Expectations
Explanatory notes and examples
Textbook Activities, IDUs, Explicit
connection to Unit Question,
Explicit connection to AOI
In a certain triangle, the measure of one angle is 10:05
Calculate the sum of the
Construction Project
interior angles of polygons
and determine unknown
angle measures knowing
the sum of the interior
angles of polygons
Use constructions for angle
four times the measure of the smallest angle,
and the measure of the remaining angle is the
sum of the measures of the other two angles.
Determine the measure of each angle.
Determine the measure of each interior angle in
a regular pentagon.
Use compass and ruler only to bisect an angle,
10:07
Powerful Dody and Islam Days
Activities
13:01
and line segment
bisections, for 600 angles
and for regular polygons in
a circle
Perform reflections,
rotations, translations of
shapes not using the
coordinate plane
Understanding Symmetry
Explain and perform basic
compass and straightedge
constructions related to
parallel and perpendicular
lines. Perform constructions
using Geometer’s Sketchpad
Unit 6:
Probability
and
Statistics
bisect a line segment and construct a 600 angle.
Understand the information required to perform
each transformation: line of symmetry, angle and
centre of rotation, translation vector
13:02
13:03
Constructions using circles and lines with dynamic
Geometry Example:
• Construct and mathematically justify the steps to:
— Bisect a line segment.
— Drop a perpendicular from a point to a line.
— Construct a line through a point that is parallel to
another line.
13:02 Inv
Transformations from
figures drawn on the
coordinate plane.
Locus
Duration: 4 weeks
Key Concept: COMMUNICATION
Related Concept: GENERALIZATION
Global Concept: GLOBILIZATION AND SUSTAINABILITY
Inquiry Statement: At the end of this unit, students will understand that generalizations about personal and social wellbeing can be
predicted and communicated through probability and statistical analyses.
Inquiry Questions:
Factual: What is sample space?
Conceptual: What is the relationship between theoretical and experimental probability
Debatable: Which is the preferable measure of central tendency
ATL: Evaluate, using appropriate methods, their own performance and outcome whilst showing awareness of their project’s
impact on others or in its intended environment
Expectations
Explanatory notes and examples
Sample Space, Certain and
Impossible events,
Experimental and
Theoretical Probability of
single and compound
events. Probability as a
fraction or decimal,
Probability of
Complementary events
Represent the sample
space using tree diagrams,
grids, sets, lists and Venn
Diagrams
Represent and calculate
probability of single and
combined events using
diagrams, tree diagrams,
grids, sets, lists and Venn
Diagrams.
Determine probabilities for
mutually exclusive,
dependent, and
independent events for
small and large sample
spaces.
Textbook
Activities, IDUs, Explicit
connection to Unit Question,
Explicit connection to AOI
Probability Activity (A, B, C)
Healthy Living Project
Grade 7 Theme Connection:
Environmental Citizenship: Healthy
Living
José flips a penny, Jane flips a nickel, and
Janice flips a dime, all at the same time. List
the possible outcomes of the three
simultaneous coin flips using a tree diagram or
an organised list.
-A triangle with a base of 8 units and a height
of 7 units is drawn inside a rectangle with an
area of 90 square units. What is the probability
that a randomly selected point inside the
rectangle will also be inside the triangle?
-There are 5 blue, 4 green, 8 red, and 3 yellow
marbles in a bag. Rosa draws a marble from
the bag, notes the colour on a sheet of paper,
and puts the marble back in the bag, repeating
the process 200 times. About how many times
would you expect Rosa to draw a red marble?
1. Sample Space with and without Replacement
Examples:


Given a standard deck of 52 playing
cards, what is the probability of drawing
a king or queen? [Some students may
be unfamiliar with playing cards, so
alternate examples may be desirable.]
Leyanne is playing a game at a birthday
party. Beneath ten paper cups, a total of
15:01
15:02

REVIEW:
Measures of Central
Tendency: Mean, Median
and Mode
Measures of Spread:
Range, Maximum, Minimum
Represent data using Stem
& Leaf, Box & Whiskers, Bar
and Pie graphs and scatter
plots
Determine the line of best
fit by finding Point M
Unit 7:
Discrete
Duration: 4 weeks
Key Concept: COMMUNITIES
five pieces of candy are hidden, with one
piece hidden beneath each of five cups.
Given only three guesses, Leyanne
must uncover three pieces of candy to
win all the hidden candy. What is the
probability she will win all the candy?
A bag contains 7 red marbles, 5 blue
marbles, and 8 green marbles. If one
marble is drawn at random and put back
in the bag, and then a second marble is
drawn at random, what is the probability
of drawing first a red marble, then a
blue marble?
Maths
Related Concept: SYSTEM
Global Concept: FAIRNESS AND DEVELOPMENT
Inquiry Statement: At the end of this unit, students will understand that networks are mathematical systems that allow for the optimal
distribution of goods and services between communities.
Inquiry Questions:
Factual: How do we use the order of the vertices in a path to determine if it is Eulerian or not?
Conceptual: Why is the Konigsberg Bridge not a Eulerian Path?
Debatable: How can an understanding of Graph Theory promote fairness and development?
ATL: Making connections between knowledge, understanding and skills across subjects with guidance.
Expectations
Explanatory notes and examples
Textbook Activities, IDUs, Explicit
connection to Unit Question,
Explicit connection to AOI
16:01
Read, interpret and draw
Analyse the graphs of real life networks such as
Motion Stories Activity
graphs used for transport
networks and identify
isomorphism using the
words regions, nodes,
vertices, edges (nodes)
Recognize subgraphs and
minimum spanning trees
Recognize traversable and
non traversable networks
Use graphs to solve
problems
Understand what is meant
by and find Eulerian Paths
and Ciruits and
Hamiltonian Paths and
Circuits
Solve problems by applying
Dykstra’s Theorem to find
metro, rail, road, etc.
16:03
The Knot Investigation (B, C, D)
Networks Investigation (B, C)
Given a graph draw a subgraph that is trees, one
that is not a tree one that has a given number of
edges and one that is disconnected
Mark the odd and even vertices (nodes) in the
networks and relate the findings with Eulerian
trails
weighted graphs in yr9
16:02
The Travelling Salesman Investigation
(B, C, D)
16:03
minimum spanning trees
Big Learning
Unit
Duration: 4 weeks
Selected Investigations that will review concepts learned throughout the year in an integrated, inquiry-based format.