Skill Descriptor: Describe numbers, ways of representing numbers, relationships among numbers, and number systems.

Global Competencies: CM, CTPS, SASM

Achievement Indicators:

• Provide examples where large numbers and decimals are used
• Explain the properties of prime and composite numbers, including zero and one as neither prime nor composite
• Provide and sort sets of prime and composite numbers
• Explain the pattern of place value for any magnitude
• Identify multiples and factors of whole numbers
• Justify examples of fractions to their decimal equivalents
• Sort sets of fractions representing repeating and terminating decimals
• Predict decimal representations of fractions using patterns
• Explain strategies to find multiples and factors of numbers
• Apply arrays, repeated division, and factor trees to solve problems involving factors and multiples

Skill Descriptor: Describe percentage, ratio, and rate.

Global Competencies: CM, CTPS

Achievement Indicators:

• Explain percentage indicators below within the 0%-100% range such as: 0%, 1%, 10%, 50%, and 100%
• Provide examples where ratios and rates are used
• Represent percent of numbers concretely or pictorially
• Represent part-to-part ratios as part-to-whole fractions
• Represent rates using words or symbolically
• Express ratios as percentages
• Express percentages in decimal and fractional forms and vice-versa
• Explain that percentage represents a ratio out of 100
• Justify when an approximate answer is appropriate
• Solve rate, ratio, and percent problems

Skill Descriptor: Add, subtract, multiply, and divide decimals to solve problems (1-digit whole number multipliers and 1-digit natural number divisors).

Global Competencies: CTPS, SASM

Achievement Indicators:

• Explain decimal indicators below using benchmark decimals such as: 0.1, 0.25, 0.5, 0.75, 0.01, 0.05
• Estimate sums, differences, products, and quotients
• Add, subtract, multiply, and divide decimals with and without models (limited to hundredths)
• Solve problems using decimal operations
• Justify the reasonableness of solutions, by applying the principles of place value (e.g., front-end, magnitude, and value of digit)

Skill Descriptor: Add, subtract, multiply, and divide benchmark fractions and mixed numbers to solve problems (limited to positive sums and differences).

Global Competencies: CTPS

Achievement Indicators:

• Explain fraction indicators below using friendly unit fractions such as: 1/2 , 1/4, 1/8 or 1/2, 1/5, 1/10 or 1/3, 1/6
• Simplify fractions and mixed numbers
• Estimate sums, differences, products, and quotients
• Determine common denominators for sets of positive fractions and mixed numbers
• Add and subtract fractions and mixed numbers with and without the use of models
• Multiply and divide positive fractions by whole numbers with and without the use of models
• Multiply and divide fractions and mixed numbers with and without the use of models
• Justify the reasonableness of solutions

Skill Descriptor: Apply the order of operations (excluding exponents, limited to whole numbers).

Global Competencies: CTPS

Achievement Indicators:

• Apply the order of operations to solve multi-step problems with and without technology

Skill Descriptor: Collect and represent data.

Global Competencies: CM, CTPS

Achievement Indicators:

• Create questions to answer, record results, and draw conclusions
• Design and administer questionnaires for collecting data and recording results
• Justify methods for collecting data to answer questions
• Justify appropriate types of graphs for displaying sets of collected data
• Interpret graphs to draw conclusions about data

Skill Descriptor: Analyze tables of values and graphs of linear relations of the forms: 𝑦=𝑥+𝑎, 𝑦=𝑥−𝑎, 𝑦=𝑎𝑥, y=(x/a), 𝑎≠0.

Global Competencies: CM, CTPS

Achievement Indicators:

• Describe patterns within columns of tables of values
• Calculate values within a table of values given other values
• Create tables of values given a linear relationships and graphs
• Create and label graphs from tables of values or sets of data (limited to linear graphs with discrete elements)
• Explain which sets of data can be represented by line graphs

Skill Descriptor: Identify points and transformations in the first quadrant of the Cartesian Plane using whole number ordered pairs.

Global Competencies: CTPS

Achievement Indicators:

• Label the axes of the first quadrant of the Cartesian Plane and identify the origin
• Plot points in the first quadrant of the Cartesian Plane given ordered pairs
• Match points in the first quadrant of a Cartesian Plane with their corresponding ordered pair
• Create designs using 2D shapes
• Describe direction of turns, fractions of turns, and points of rotation of 2D shapes
• Describe lines of reflection of 2D shapes

Skill Descriptor: Determine the probability of outcomes to solve problems.

Global Competencies: CM, CTPS, ICE

Achievement Indicators:

• Determine theoretical probabilities (sample space) of outcomes occurring
• Predict experimental probabilities of outcomes using theoretical probability
• Conduct probability experiments with and without technology
• Represent probabilities as ratios, fractions, and percentages
• Compare experimental and theoretical probabilities.
• Demonstrate that as the number of trials increases experimental probability approaches theoretical probability
• Explain the difference between theoretical and experimental probability

Skill Descriptor: Develop equations using letter variables.

Global Competencies: CTPS

Achievement Indicators:

• Represent the preservation of equality for addition, subtraction, multiplication, and division concretely and pictorially
• Represent equivalent forms of equations
• Verify the preservation of equality of equations
• Develop equations using letter variables and the commutative property of addition and multiplication

Skill Descriptor: Investigate perimeter, area, volume, and their relationships.

Global Competencies: CM, CTPS

Achievement Indicators:

• Represent perimeter of polygons concretely and pictorially
• Represent area of rectangles, triangles, and parallelograms concretely and pictorially
• Explain the relationship between area of rectangles and area of parallelograms
• Explain the relationship between area of rectangles and area of triangles
• Represent volume of right rectangular prisms concretely and pictorially
• Explain the relationship between area of the base of right concrete 3D objects and the volume of the concrete 3D objects
• Demonstrate that the orientation of concrete right rectangular prisms does not affect its volume

Skill Descriptor: Describe angles.

Global Competencies: CTPS

Achievement Indicators:

• Provide examples of angles found in the environment
• Describe measures of angles as measures of rotation of one of its sides
• Describe the relationship between and sketch 45°, 90°, and 180° angles without the use of a protractor
• Classify angles according to their measure
• Estimate measures of angles
• Measure, create, and label angles in various orientations using a protractor
• Demonstrate that the sum of the interior angles of a triangle is the same for all triangles and that the sum of the interior angles of quadrilaterals is the same for all quadrilaterals

Skill Descriptor: Describe 3D objects.

Global Competencies: CTPS

Achievement Indicators:

• Describe faces and edges of 3D objects using language such as parallel, intersecting, perpendicular, vertical, or horizontal
• Provide examples from the environment with edges, faces, and sides that are parallel, intersecting, perpendicular, vertical, and horizontal
• Sort 3D objects by identifying edges, faces, vertices, length of the sides, shape of the base, etc.
• Construct rectangular and triangular prisms using nets and skeletons
• Compare 3D objects to identify common attributes, different orientations, and different dimensions

Skill Descriptor: Describe numbers, ways of representing numbers, relationships among numbers, and number systems.

Global Competencies: CM, CTPS

Achievement Indicators:

• Provide examples of integers and where they are used
• Explain the pattern on each side of the zero on a number line to compare, order, and verify the position of integers
• Compare integers using the symbols <, >, and =

Skill Descriptor: Add and subtract positive and negative integers to solve problems.

Global Competencies: CM, CTPS

Achievement Indicators:

• Explain the relationship between adding integers and subtracting integers
• Demonstrate that the sum of opposite integers is zero concretely, pictorially, or symbolically
• Add and subtract integers to solve problems

Skill Descriptor: Add, subtract, multiply, and divide decimals to solve problems (1-digit divisors and 2-digit multipliers).

Global Competencies: CTPS

Achievement Indicators:

• Estimate sums, differences, products, and quotients
• Add, subtract, multiply, and divide decimals with and without models (limited to thousandths)
• Solve problems using decimal operations, considering order of operations
• Justify the reasonableness of solutions, by applying the principles of place value. (e.g., front-end, magnitude, and value of digit)
• Multiply or divide 2-digit multipliers or 1-digit divisors (whole numbers or decimals) with and without the use of technology

Skill Descriptor: Add, subtract, multiply, and divide positive fractions and mixed numbers to solve problems.

Global Competencies: CTPS

Achievement Indicators:

• Simplify fractions and mixed numbers
• Estimate sums, differences, products, and quotients
• Determine common denominators for sets of positive fractions and mixed numbers
• Add and subtract fractions and mixed numbers with and without the use of models
• Multiply and divide positive fractions by whole numbers with and without the use of models
• Multiply and divide fractions and mixed numbers with and without the use of models
• Justify the reasonableness of solutions

Skill Descriptor: Calculate measures of central tendency to solve problems.

Global Competencies: CM, CTPS

Achievement Indicators:

• Determine the range of sets of data
• Identify any outliers in sets of data
• Collect data and calculate the mean, the median, and the mode for sets of data
• Provide contexts where mean, median, or mode is the most appropriate measure of central tendency
• Explain why mean, median, and mode for sets of data may be the same or different
• Explain the effect of outliers on measures of central tendency
• Collect data and apply measures of central tendency to identify and solve problems

Skill Descriptor: Analyze linear relations of the forms shown below and compare graphs to solve problems. (e.g., 𝑦=𝑥+𝑎, 𝑦=𝑥−𝑎, 𝑦=𝑎𝑥, y=(x/a), 𝑎≠0).

Global Competencies: CTPS

Achievement Indicators:

• Create tables of values using substitution for variables
• Create tables of values of linear relations involving a single transformation
• Create and label graphs of linear relations from tables of values (limited to discrete elements)
• Describe linear relationships displayed in tables of values and graphs using a mathematical expression
• Predict and verify values of unknown terms using linear mathematical expressions and graphs

Skill Descriptor: Identify points and transformations in the four quadrants of the Cartesian Plane using integral ordered pairs.

Global Competencies: CTPS, ICE

Achievement Indicators:

• Label the axes of the four quadrants of the Cartesian Plane and identify the origin
• Plot points in the four quadrants of the Cartesian Plane given integral ordered pairs
• Match points in the four quadrants of the Cartesian Plane with their corresponding ordered pair
• Determine the distance between points along horizontal and vertical lines
• Describe position, direction, translation, rotation, reflection, and other 2D shape transformations
• Represent 2D shape transformations concretely or pictorially

Skill Descriptor: Determine the probability of outcomes to solve problems.

Global Competencies: CTPS

Achievement Indicators:

• Provide examples of two independent events
• Determine theoretical probabilities (sample space) of outcomes occurring involving two independent events
• Conduct probability experiments with and without technology
• Represent probabilities as ratios, fractions, and percentages
• Compare experimental and theoretical probabilities for outcomes involving two independent events

Skill Descriptor: Solve linear equations.

Global Competencies: CM, CTPS

Achievement Indicators:

• Provide examples of expressions and equations
• Provide examples of contexts where linear relations represent patterns
• Identify constant terms, numerical coefficients, and variables in expressions and equations
• Represent linear equations concretely, pictorially, and symbolically
• Represent relationship and patterns using linear relations
• Evaluate expressions by substituting values for the unknowns
• Apply and explain the process of the preservation of equality for addition, subtraction, multiplication, and division
• Verify the preservation of equality of equations
• Represent problems with linear equations
• Justify the process to solve linear equations

Skill Descriptor: Apply the formulae for perimeter of polygons, area of rectangles, area of triangles, area of parallelograms, and volume of right prisms to solve problems.

Global Competencies: CM, CTPS

Achievement Indicators:

• Generalize rules for determining perimeter of polygons, area of rectangles, area of parallelograms, area of triangles, and volume of right rectangular prisms
• Explain strategies used to estimate area of rectangles, triangles, and parallelograms
• Calculate volumes of right prisms given the area of the base
• Calculate the perimeter of polygons, area of rectangles, area of triangles, area of parallelograms, and volume of right prisms using the appropriate formula to solve problems

Skill Descriptor: Perform geometric constructions.

Global Competencies: CM, CTPS

Achievement Indicators:

• Describe parallel line segments, perpendicular line segments, bisectors of angles, and perpendicular bisectors
• Create line segments parallel and perpendicular to other line segments
• Create bisectors of angles using multiple methods
• Create perpendicular bisectors of line segments using multiple methods
• Verify the equality or congruency of bisectors and perpendicular bisectors

Skill Descriptor: Draw and verify nets.

Global Competencies: CTPS

Achievement Indicators:

• Relate 3D objects to nets and skeletons and vice versa
• Construct 3D objects, including rectangular and triangular prisms, using nets and skeletons
• Match nets to 3D objects
• Create and verify nets for right circular cylinders, right rectangular prisms, and right triangular prisms

Skill Descriptor: Describe numbers, ways of representing numbers, relationships among numbers, and number systems.

Global Competencies: CM, CTPS

Achievement Indicators:

• Provide examples where percentage may be between 0% and 1%, and examples where percentage may be more than 100%.
• Represent percentages greater than 100 using models (e.g., number lines, number frames, )
• Represent proper and improper fractional percentages using models (e.g., number lines, number frames, etc.)
• Record percentages in decimal and fractional forms and vice-versa
• Compare percentage benchmarks to positive fractions, mixed numbers, and decimals
• Solve percentage, combined problems, and percent-of-a-percent problems
• Represent given perfect squares as square regions concretely or pictorially
• Determine the squares of given numbers
• Identify numbers with square roots within a given range
• Determine the square roots of given perfect squares
• Determine all factors of given perfect squares
• Estimate the square root of numbers that are not perfect squares using benchmarks
• Demonstrate if given numbers are perfect squares concretely, pictorially, or symbolically (e.g., prime factorization)

Skill Descriptor: Multiply and divide integers to solve problems (2-digit by 1-digit).

Global Competencies: CTPS

Achievement Indicators:

• Provide examples of contexts that require multiplying and dividing integers
• Represent the multiplication and division of integers concretely, pictorially, or symbolically
• Determine the rule for a sign of a product or quotient of integers (e.g., through patterning)
• Multiply and divide integers to solve problems

Skill Descriptor: Apply the order of operations including whole numbers, positive fractions, and decimals.

Global Competencies: CTPS

Achievement Indicators:

• Apply the order of operations to solve multi-step problems with and without technology
• Apply combinations of operations and number forms to solve problems

Skill Descriptor: Compare and critique graphs and the presentation of data.

Global Competencies: CM, CTPS, SGC

Achievement Indicators:

• Examine and compare representations of data using a variety of circle graphs
• Convert percentages displayed in circle graphs into quantities
• Create and label circle graphs, including title and legend, with and without technology
• Interpret circle graphs to answer questions and solve problems
• Compare strengths and limitations of different types of graphs
• Recognize bias and discrimination, or stereotypes and misconceptions against Wabanaki peoples in graphs and representations of data
• Explain how the format of graphs may misrepresent or lead to misinterpretation of data
• Justify the choice of graphical representations for contexts and their data sets

Skill Descriptor: Analyze linear relations of the forms shown below and compare graphs to solve problems. (e.g., 𝑦=𝑎𝑥+𝑏, 𝑦=𝑎𝑥−𝑏, y=(x/a)+b, 𝑎≠0, y=(x/a)-b, 𝑎≠0).

Global Competencies: CTPS

Achievement Indicators:

• Create tables of values using substitution for variables
• Create tables of values of linear relations involving two transformations
• Determine if the plotted points of graphs should be displayed with solid lines
• Justify the types of number sets used to create linear graphs (i.e., whole numbers, real numbers, integers, etc.)
• Create and label graphs of linear relations from tables of values
• Describe linear relationships displayed in tables of values and graphs using a mathematical expression
• Predict and verify values of unknown terms using linear mathematical expressions and graphs
• Determine a missing coordinate in an ordered pair of a linear relation

Skill Descriptor: Determine the probability of outcomes to solve problems.

Global Competencies: CM, CTPS, ICE

Achievement Indicators:

• Determine theoretical probabilities (sample space) of outcomes occurring involving two independent events
• Distinguish between dependent and independent events
• Conduct probability experiments, with and without technology, for outcomes involving two independent events
• Represent probabilities as ratios, fractions, and percentages
• Compare experimental and theoretical probabilities for outcomes involving two independent events
• Solve probability problems involving two independent events

Skill Descriptor: Solve linear equations.

Global Competencies: CTPS

Achievement Indicators:

• Represent linear equations pictorially and symbolically
• Apply the distributive property to solve linear equations
• Verify solutions to linear equations using different methods
• Solve linear equation problems

Skill Descriptor: Apply the formulae for volume of right cylinders to solve problems.

Global Competencies: CM, CTPS

Achievement Indicators:

• Calculate the volume of right cylinders using the appropriate formula to solve problems
• Explain the relationship between area of the base of a right cylinder and the volume of a right cylinder
• Generalize rules for determining volume of right cylinders
• Apply rules for determining volume of right cylinders
• Demonstrate that the orientation of concrete right cylinders does not affect its volume

Skill Descriptor: Apply properties of circles to solve problems.

Global Competencies: CTPS

Achievement Indicators:

• Demonstrate diameter is twice the radius in circles
• Demonstrate the sum of central angles of circles is 360°
• Demonstrate circumference is approximately three times the diameter in circles
• Demonstrate pi is the ratio of the circumference to the diameter
• Demonstrate the value of pi is approximately 3.14
• Generalize rules to determine area of circles
• Apply formulae to determine the area of circles

Skill Descriptor: Apply the Pythagorean Theorem to solve problems.

Global Competencies: CTPS

Achievement Indicators:

• Represent the Pythagorean Theorem concretely, pictorially, symbolically, or using technology
• Demonstrate that the Pythagorean Theorem only applies to right triangles
• Explain the Pythagorean Theorem
• Apply the Pythagorean Theorem to verify if triangles are right triangles
• Determine the measure of the third side of a right triangle to solve problems, given the measures of the other two sides
• Recognize Pythagorean Triples