Download UNIT 4: FRACTIONS, RATIOS AND PERCENTS

UNIT 5: FRACTIONS, RATIOS AND PERCENTS
KEY WORDS:
improper fraction
part-to-part ratio
equivalent ratios
mixed number
part-to-whole ratio
percent
ratio
terms of a ratio
KEY MATH LEARNINGS:
Lesson 1: Mixed Numbers
1. An improper fraction represents more than one whole.
2. A mixed number, with a whole number part and a fraction part, is another way of writing
an improper fraction.
Lesson 2: Converting between Mixed Numbers and Improper Fractions
1. Both improper fractions and mixed numbers represent more than one whole.
2. A mixed number can be converted into an improper fraction.
3. An improper fraction can be converted into a mixed number.
Lesson 3: Comparing Mixed Numbers and Improper Fractions
1. A number line can be used to compare mixed numbers and improper fractions.
2. Mixed numbers and improper fractions can be compared by converting the mixed
number to an improper fraction, then writing each improper fraction as an equivalent
fraction with like denominators.
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4: Exploring Ratios
A ratio is a comparison of two quantities with the same units.
The order of the terms of a ratio is important.
A ratio can be used to compare a part of a set to another part of the set.
A ratio can be used to compare a part of a set to the whole set.
Lesson 5: Equivalent Ratios
1. Equal sets of ratios are called equivalent ratios.
2. You can find equivalent ratios by multiplying or dividing the terms of a ratio by the same
non-zero number.
Lesson 6: Problem Solving Strategy
1. When solving a problem, thinking can be represented with words, diagrams, and/or
numbers.
Lesson 7: Exploring Percents
1. Percent means “per hundred” or “out of 100”.
Lesson 8: Relating Fractions, Decimals, and Percents
1. Fractions, decimals, and percents are three ways to describe part of one whole.
2. You can use a percent to describe any part of one whole by writing an equivalent
fraction with hundredths.
UNIT 4: ANGLES AND POLYGONS
KEY WORDS:
angle
arm
acute angle
degree
protractor
diagonal
standard protractor
right angle
obtuse angle
interior angle
straight angle
reflex angle
KEY MATH LEARNINGS:
Lesson 1: Naming Angles
1. An angle is formed when two lines meet.
2. The size of an angle is a measure of the amount of the turn needed to move from one
arm to the other.
3. An angle can be named by the way it relates to a right angle or a straight angle.
Lesson 2: Exploring Angles
1. Concrete, non-standard units can be used to measure and compare angles.
2. Protractors marked with non-standard units can be used to measure and compare angles.
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3: Measuring Angles
Angles can be measured using a standard protractor.
Angles are classified according to their measures in degrees.
To estimate the measure of an angle, we can use 45°, 90°, and 180° as reference angles.
Lesson 4: Drawing Angles
1. An angle of a given measure can be constructed using a standard protractor.
2. Angles of 45°, 90°, and 180° can be drawn without using a protractor.
Lesson 5: Problem Solving Strategy
1. Check and reflect is an important step in solving problems. It helps to ensure that
solutions are accurate and reasonable.
Lesson 6: Investigating Angles in a Triangle
1. The sum of the interior angles in any triangle is 180°.
Lesson 7: Investigating Angles in a Quadrilateral
1. The sum of the angles in a quadrilateral is 360°.
UNIT 6: GEOMETRY AND MEASUREMENT
KEY WORDS:
formula
equilateral triangle
isosceles triangle
scalene triangle
convex polygon
acute triangle
right triangle regular
obtuse triangle
concave polygon
non-polygon
polygon
irregular polygon
congruent
KEY MATH LEARNINGS:
Lesson 1: Exploring Triangles
1. We can name triangles according to the number of equal sides.
2. We can name triangles according to the number of equal angles.
Lesson 2: Naming and Sorting Triangles by Angles
1. We can name triangles according to the types of interior angles.
Lesson 3: Drawing Triangles
1. Triangles can be constructed using a ruler and protractor, given side and angle measures.
2. Two triangles can have congruent angles but different side lengths.
Lesson 4: Investigating Polygons
1. A regular polygon has all sides equal, all angles equal, and line symmetry. An irregular
polygon does not have all sides equal and all angles equal.
2. A convex polygon has all angles less than 180°. A concave polygon has at least one angle
greater than 180°.
Lesson 5: Congruence in Regular Polygons
1. When polygons match exactly, the polygons are congruent.
2. Congruent polygons have all sides equal and all angles equal.
Lesson 6: Problem Solving Strategy
1. Solving a simpler problem and extending a table are two effective strategies to solve
problems.
Lesson 7: Perimeters of Polygons
1. The perimeter of a polygon can be found by adding the side lengths.
2. Formulas can be used to calculate the perimeters of specific polygons.
Lesson 8: Area of a Rectangle
1. The area of a rectangle can be found by using the formula A = l x w, where A represents
the area of a rectangle, l represents its length, and w represents its width.
Lesson 9: Volume of a Rectangular Prism
1. The volume of an object is a measure of the space it takes up.
2. The volume of a rectangular prism can be found using a formula.
UNIT 7: DATA ANALYSIS AND PROBABILITY
KEY WORDS:
fair question
biased question
discrete data
at random
database
line graph
probability
continuous data
electronic media
theoretical probability
experimental probability
KEY MATH LEARNINGS:
Lesson 1: Using a Questionnaire to Gather Data
1. A questionnaire can be used to collect data.
2. A question should be understood in the same way by all, contain a possible answer
for all, and not influence a person to answer in a certain way.
3. A question that might persuade a person to answer in a certain way is biased.
Technology: Using Databases and Electronic Media to Gather Data
1. A database is an organized collection of data. There are two types of databases:
print and electronic.
2. Databases and electronic media can be used to collect data.
Lesson 2: Conducting Experiments to Gather Data
1. Data can be gathered by recording the results of experiments.
2. Data from experiments can be used to draw conclusions.
Lesson 3: Interpreting Graphs
1. Discrete data represent things that can be counted. Continuous data can include
any value between data points. Time, money, temperature, and measurements,
such as length and mass, are continuous.
2. A line graph shows continuous data. Consecutive points are joined by line
segments.
3. A line graph is not appropriate for discrete data. The graph is a series of points
that are not joined.
Lesson 4: Drawing Graphs
1. Graphs can be used to display both continuous and discrete data.
2. When the data are continuous, we join consecutive points with line segments.
Lesson 5: Choosing an Appropriate Graph
1. Different sets of data may require different types of graphs.
Unit 7
Lesson 6: Theoretical Probability
1. Theoretical probability is the likelihood that an outcome will happen.
2. When all outcomes are equally likely, theoretical probability is calculated by
dividing the number of favourable outcomes by the number of possible outcomes.
Lesson 7: Experimental Probability
1. Experimental probabilities are based on the results of an experiment.
2. Experimental probabilities can only be calculated for experiments with outcomes
that are equally likely.
3. The more times an experiment is repeated, the closer the experimental
probability my come to the theoretical probability.
Lesson 8: Strategy
1. There are a variety of ways to explain mathematical thinking. Some examples are
check and reflect, focus on the problem, or represent your thinking with a
picture, table or graph.
UNIT 8: TRANSFORMATIONS
KEY WORDS:
successive translations
successive reflections
successive rotations
KEY MATH LEARNINGS:
Lesson 1: Drawing Shapes on a Coordinate Grid
1. Ordered pairs can be used to describe the position of a shape on a Cartesian plane.
Lesson 2: Transformations on a Coordinate Grid
1. The coordinate of the vertices can be used to describe a transformation image on a
coordinate grid.
2. When points on a transformation image are labelled, an apostrophe after the label refers
to the corresponding image point. For example, A´ is the image of point A.
Technology: Using Technology to Perform Transformations
1. Geometry software can be used to transform shapes on a coordinate grid.
Lesson 3: Successive Transformations
1. The same transformation can be applied to a shape more than once.
Lesson 4: Combining Transformations
1. A combination of 2 or 3 different types of transformations can be applied to a shape on
a grid.
Lesson 5: Creating Designs
1. Transformations of one or more shapes can be used to create a design.
Lesson 6: Problem Solving Strategy
1. Guess and test is a good strategy to use when solving a problem with more than one
possible solution.
Technology: Using a Computer to Make a Design
1. Geometry software and transformations can be used to make designs.