# 6th Grade Math

# Grade Six Math

# Mathematics Education in Alberta*

## GOALS FOR STUDENTS

#### The main goals of mathematics education are to prepare students to:

##### • use mathematics confidently to solve problems

##### • communicate and reason mathematically

##### • appreciate and value mathematics

##### • make connections between mathematics and its applications

##### • commit themselves to lifelong learning

##### • become mathematically literate adults, using mathematics to contribute to society.

## The mathematics curriculum for the province of Alberta identifies four stands in Mathematics.

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#### The Four Strands are:

**NUMBER**

• Develop number sense.

## PATTERNS AND RELATIONS

### Patterns

#### • Use patterns to describe the world and to solve problems.

### Variables and Equations

#### • Represent algebraic expressions in multiple ways.

## SHAPE AND SPACE

### Measurement

#### • Use direct and indirect measurement to solve problems.

### 3-D Objects and 2-D Shapes

#### • Describe the characteristics of 3-D objects and 2-D shapes, and analyze the relationships among them.

### Transformations

#### • Describe and analyze position and motion of objects and shapes.

## STATISTICS AND PROBABILITY

### Data Analysis

• Collect, display and analyze data to solve problems.

### Chance and Uncertainty

• Use experimental or theoretical probabilities to represent and solve problems involving uncertainty.

### These four strands have been part of the elementary program in mathematics. Addition topics covered in Middle School Maths are listed below.

### The additional topics for the general outcome of developing number sense include the following:

##### 1 Explain and apply the order of operations, excluding exponents, with and without technology (limited to whole numbers).

##### 2. Compare and order positive fractions, positive decimals (to thousandths) and whole numbers by using benchmarks, place value, equivalent fractions, and/or decimals.

##### 3. Determine an approximate square root of positive rational numbers that are non-perfect squares.

### The additional topics for the general outcome of developing patterns and relations include the following:

1. Represent and describe patterns and relationships, using graphs and tables.

2. Demonstrate an understanding of the relationships within tables of values to solve problems.

3. Demonstrate an understanding of oral and written patterns and their equivalent linear relations.

4. Create a table of values from a linear relation, graph the table of values, and analyze the graph to draw conclusions and solve problems.

5. Graph and analyze two-variable linear relations.

6. Generalize a pattern arising from a problem-solving context, using a linear equation, and verify by substitution.

7. Graph a linear relation, analyze the graph, and interpolate or extrapolate to solve problems.

### The additional topics for the general outcome of representing algebraic expressions in multiple ways include the following:

##### 1. Represent generalizations arising from number relationships, using equations with letter variables.

##### 2. Express a given problem as an equation in which a letter variable is used to represent an unknown number.

##### 3. Demonstrate and explain the meaning of preservation of equality, concretely and pictorially.

##### 4. Demonstrate an understanding of preservation of equality by modelling preservation of equaliity concretely, pictorially and symbolically and by applying preservation of equality to solve equations.

##### 5. Explain the difference between an expression and an equation.

##### 6. Evaluate an expression, given the value of the variable(s).

##### 7. Model and solve, concretely, pictorially and symbolically, problems that can be represented by one-step linear equations of the form

*, *where *a* and *b* are integers.

*,*

##### 8. Model and solve, concretely, pictorially and symbolically, problems that can be represented by linear equations of the form:

- ,
- ,

##### where a, b and c are whole numbers.

##### 9. Model and solve problems concretely, pictorially and symbolically, using linear equations of the form:

##### where a, b and c are integers.

##### 10. Model and solve problems, using linear equations of the form:

##### where a,b,c,d,e,and f are rational numbers.

11. Explain and illustrate strategies to solve single variable linear inequalities with rational coefficients within a problem-solving context.

12. Demonstrate an understanding of polynomials (limited to polynomials of degree less than or equal to 2).

13. Model, record and explain the operations of addition and subtraction of polynomial expressions, concretely, pictorially and symbolically (limited to polynomials of degree less than or equal to 2).

14. Model, record and explain the operations of multiplication and division of polynomial expressions (limited to polynomials of degree lessthan or equal to 2) by monomials, concretely, pictorially and symbolically.

### The additional topics for the general outcome of using direct and indirect measurement to solve problems include the following:

1. Demonstrate an understanding of angles by:

- identifying examples of angles in the enviroment
- classigying angles according to their measure
- estimating the measure of angles, using and as reference angles
- determining angel measures in degrees
- drawing and labelling angles when the measure is specified

2. Demonstrate that the sum of interior angles is:

- in a triangle
- in a quadrilateral

3. Develop and apply a formula for determining the:

- perimeter of polygons
- area of rectangles
- volume of right rectagular prisms.

4. Demonstrate an understanding of circles by:

- describing the relationships among radius, diameter and circumference
- relating circumference to pi
- determining the sum of the central angles
- constructing circles with given radius or diameter
- solving problems involving the radii, diameters and circumferences of circles.

5. Develop and apply a formula for determining the area of:

- triangles
- parallelograms
- circles.

6. Develop and apply the Pythagorean theorem to solve problems.

7. Draw and construct nets for 3-D objects.

8. Determine the surface area of:

- right rectangular prisms
- right triangular prisms
- right cylinders

to solve problems.

9. Develop and apply formulas for determining the volume of right rectangular prisms, right triangular prisms and right cylinders.

10. Solve problems and justify the solution strategy, using the following circle properties:

- the perpendicular from the centre of a circle to a chord bisects the chord
- the measure of the central angle is equal to twice the measure of the inscribed angle subtended by the same arc
- the inscribed angles subtended by the same arc are congruent
- a tangent to a circle is perpendicular to the radius at the point of tangency.

### The additional topics for the general outcome of describing the characteristics of 3-D objects and 2-D include the following:

1. Construct and compare triangles, including:

- scalene
- isosceles
- equilateral
- right
- obtuse
- acute

in different orientations.

2. Describe and compare the sides and angles of regular and irregular polygons.

3. Perform geometric constructions, including:

- perpendicular line segments
- parallel line segments
- perpendicular bisectors
- angles bisectors

4. Draw and interpret top, front and side views of 3-D objects composed of right rectangular prisms.

5. Determine the surface area of composite 3-D objects to solve problems.

6. Demonstrate an understanding of similarity of polygons.

### The additional topics for the general outcome of describing and analyzing position and motion of objects include the following:

1. Perform a combination of translations, rotations and/or reflections on a single 2-D shape, with and without technology, and draw and describe the image.

2. Perform a combination of successive transformations of 2-D shapes to create a design, and identify and describe the transformations.

3. Identify and plot points in the first quadrant of a Cartesian plane, using whole number ordered pairs.

4. Perform and describe single transformations of a 2-D shape in the first quadrant of a Cartesian plane (limited to whole number vertices).

5. Identify and plot points in the four quadrants of a Cartesian plane, using integral ordered pairs.

6. Perform and describe transformations (translations, rotations or reflections) of a 2-D shape in all four quadrants of a Cartesian plane (limited to integral number vertices).

7. Demonstrate an understanding of the congruence of polygons.

8. Draw and interpret scale diagrams of 2-D shapes.

9. Demonstrate an understanding of line and rotation symmetry.

### The additional topics for the general outcome of collecting, displaying and analyzing data to solve problems include the following:

1. Create, label and interpret line graphs to draw conclusions.

2. Select, justify and use appropriate methods of collecting data, including:

- questionnaires
- experiments
- databases
- electronic media.

3. Graph collected data, and analyze the graph to solve problems.

4. Demonstrate an understanding of central tendency and range by:

- determining the measures of central tendency (mean, median, mode) and range
- determining the most appropriate measures of central tendency to report findings.

5. Determine the effect on the mean, median and mode when an outlier is included in a data set.

6. Construct, label and interpret circle graphs to solve problems.

7. Critique ways in which data is presented in circle graphs, line graphs, bar graphs and pictographs.

8. Describe the effect of:

- bias
- use of language
- ethics
- cost
- time and timing
- privacy
- cultural sensitivity on the collection of data.

9. Select and defend the choice of using either a population or a sample of a population to answer a question.

10. Develop and implement a project plan for the collection, display and analysis of data by:

- formulating a question for investigation
- choosing a data collection method that includes social considerations
- selecting a population or a sample
- collecting the data
- displaying the collected data in an appropriate manner
- drawing conclusion to answer the question.

### The additional topics for the general outcome of using experimental or theoretical probabilities to represent and solve problems involving uncertainty include the following:

1. Demonstrate an understanding of probability by identifying all possible outcomes of a probability experiment, differentiating between experimental and theoretical probability, determining the theoretical probablitiy of outcomes in a probability experiment, and comparing experimental results with the theoretical probability for an experiment.

2. Express probabilities as ratios, fractions and percents.

3. Identify the sample space (where the combined sample space has 36 or fewer elements) for a probability experiment involving two independent events.

4. Conduct a probability experiment to compare the theoretical probability (determined using a tree diagram, table or other graphic organizer) and experimental probability of two independent events.

5. Solve problems involving the probability of independent events.

6. Demonstrate an understanding of the role of probability in society.

## Check out this website to find resources to help you succeed in math.

*Source: education.alberta.ca/media/645594/kto9math.pdf