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 small decimals are used
• Provide examples of prime and composite numbers
• Explain the pattern of place value for any magnitude
• Identify multiples and factors of numbers
• Match equivalent fractions and decimals
• Sort sets of numbers as prime or composite
• 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
• Explain the properties of prime and composite numbers
• Explain the properties of zero and one as neither prime nor composite
• 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:

• Provide examples where ratios and rates are used
• Represent percent 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
• Explain when an approximate answer is appropriate
• Apply rounding to solutions
• 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:

• Estimate products and quotients
• Apply front-end estimation to place the decimal point in sums, differences, products, and quotients
• Add, subtract, multiply, and divide decimals
• Solve problems including money and measurement

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

Global Competencies: CTPS

Achievement Indicators:

• Express improper fractions as mixed numbers and vice-versa
• Estimate products and quotients
• Determine common denominators for sets of positive fractions and mixed numbers
• Multiply and divide positive fractions by whole numbers
• Add, subtract, multiply, and divide fractions and mixed numbers
• Simplify fractions and mixed numbers

Skill Descriptor: Apply the order of operations (excluding exponents).

Global Competencies: CTPS

Achievement Indicators:

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

Skill Descriptor: Collect 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

Skill Descriptor: Justify elements and compare graphs to solve problems.

Global Competencies: CM, CTPS

Achievement Indicators:

• Describe patterns within columns of tables of values
• Describe relationships in tables of values using mathematical expressions
• Represent pattern rules using mathematical expressions
• Calculate values within table of values given other values and pattern rules
• Create tables of values from patterns
• Create tables of values from graphs
• Create and label graphs from tables of values or sets of data (limited to linear graphs with discrete elements)
• Predict and verify values of unknown terms
• Explain which sets of data can be represented by line graphs or series of points
• Justify appropriate types of graphs for displaying sets of collected data
• Interpret graphs to draw conclusions about data

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 occurring in probability experiments 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 or without technology
• Compare experimental results to theoretical probability of probability experiments
• Demonstrate that as number of trials increases experimental probability approaches theoretical probability
• Explain the difference between theoretical probability 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: Apply formulae to solve problems.

Global Competencies: CM, CTPS

Achievement Indicators:

• Represent perimeter of polygons, volume of right rectangular prisms, and area of rectangles concretely and pictorially
• Generalize rules for determining perimeter of polygons, area of rectangles, area of parallelograms, area of triangles, volume of right rectangular prisms
• Explain strategies used to estimate area of parallelograms
• Calculate volumes of right prisms given the area of the base
• Explain the relationship between area of rectangles and area of triangles
• Explain the relationship between area of rectangles and area of parallelograms
• Explain the relationship between area of the base of right concrete 3D objects and the formula for the volume of the concrete 3D object
• Calculate perimeter of polygons, area of rectangles, area of triangles, area of parallelograms, and volume of right prisms to solve problems

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 angles in various orientations
• 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 concrete 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
• Compare concrete 3D objects to identify common attributes, different orientations, and different dimensions
• Sort concrete 3D objects by identifying edges, faces, vertices, length of the sides, shape of the base, etc.
• Relate concrete 3D objects to nets and skeletons
• Construct rectangular and triangular prisms using nets and skeletons
• Demonstrate that the orientation of concrete 3D objects does not affect volume

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
• Extend number lines to compare and order integers
• Compare integers using the symbols <, >, and =
• Explain the pattern on each side of the zero on a number line to compare and verify the position of integers

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

Global Competencies: CM, CTPS

Achievement Indicators:

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

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
• Apply front-end estimation to place the decimal point in sums, differences, products, and quotients
• Multiply or divide 2-digit multipliers or 1-digit divisors (whole numbers or decimals) with and without the use of technology
• Add, subtract, multiply, and divide decimals (limited to thousandths)

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

Global Competencies: CTPS

Achievement Indicators:

• Express improper fractions as mixed numbers and vice-versa
• Estimate products and quotients
• Multiply and divide positive fractions by whole numbers
• Add, subtract, multiply, and divide fractions and mixed numbers
• Simplify fractions and mixed numbers
• Justify the reasonableness of solutions

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

Global Competencies: CM, CTPS

Achievement Indicators:

• Provide contexts where mean, median, or mode is the most appropriate measure of central tendency
• Determine the range of sets of data
• Identify any outliers in sets of data
• Calculate mean, median, and mode for sets of data
• 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
• Apply measures of central tendency to solve problems

Skill Descriptor: Use tables of values and compare graphs to solve problems.

Global Competencies: CTPS

Achievement Indicators:

• Describe patterns and relationships found in graphs
• Match sets of linear relations and sets of graphs
• Create tables of values using substitution for variables
• Create tables of values using linear relations
• Create graphs of linear relations from tables of values (limited to discrete elements)

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, magnitude, translation, rotation, reflection, and other 2D shape transformations
• Represent 2D shape transformations concretely or pictorially

Skill Descriptor: Determine the probability of outcomes occurring in probability experiments 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
• Compare experimental results to theoretical probability for outcomes involving two independent events
• Express probability as ratio, fraction, and percentage

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, or 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
• Record the process to solve linear equations

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 concrete 3D objects to nets and skeletons
• Construct concrete 3D objects, including rectangular and triangular prisms, using nets and skeletons
• Match nets to concrete 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%
• Identify numbers with square roots that are between two numbers
• Represent given perfect squares as square regions concretely or pictorially
• Represent fractional percentages
• Represent percentages greater than 100
• Estimate the square root of numbers that are not perfect squares using benchmarks
• Determine all factors of given perfect squares
• Determine the square roots of given perfect squares
• Determine the squares of given numbers
• Demonstrate if given numbers are perfect squares concretely, pictorially, or using prime factorization
• Record percentages in decimal and fractional forms and vice-versa
• Solve percentage, combined problems, and percent-of-a-percent problems

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
• Apply a rule for determining the sign of the product and quotient of integers
• Multiply and divide integers
• Solve division of integers problems (2-digit by 2-digit) with the use of technology

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

Global Competencies: CTPS

Achievement Indicators:

• Compare percentage benchmarks to positive fractions, mixed numbers, and decimals
• Estimate sums differences, products, and quotients, using benchmarks
• Add, subtract, multiply, and divide decimals
• Add, subtract, multiply, and divide fractions and mixed numbers
• Apply the order of operations to solve multi-step problems with and without technology
• Apply the order of operations with flexibility, efficiency, and accuracy (fluency)
• 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:

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

Skill Descriptor: Analyze two-variable linear relations and compare graphs to solve problems.

Global Competencies: CTPS

Achievement Indicators:

• Describe relationships between the variables of graphs
• Determine missing values in the ordered pairs of equations
• Determine if plotted points of graphs are shown with solid lines
• Create tables of values by substituting for variables in linear relations
• Graph equations of linear relations (limited to discrete data)

Skill Descriptor: Determine the probability of outcomes occurring in probability experiments 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
• Compare experimental results to theoretical probability 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 or symbolically
• Apply the distributive property to solve linear equations
• Verify solutions to linear equations using different methods
• Solve linear equation problems

Skill Descriptor: Apply formulae to solve problems.

Global Competencies: CM, CTPS

Achievement Indicators:

• Apply the formulae for perimeter of polygons, area of rectangles, area of triangles, area of parallelograms, and volume of right prisms to solve problems
• Generalize rules for determining volume of right cylinders
• Apply rules for determining volume of right cylinders
• Apply formulae for the volume of right cylinders

Skill Descriptor: Apply properties of circles to solve problems.

Global Competencies: CTPS

Achievement Indicators:

• Demonstrate diameter is twice the radius in circles
• 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
• Demonstrate the sum of central angles of circles is 360°
• 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
• Apply the Pythagorean Theorem to verify if triangles are right triangles
• Explain the Pythagorean Theorem
• Demonstrate that the Pythagorean Theorem only applies to right triangles
• Solve Pythagorean Triple problems

Skill Descriptor: No skill descriptors for this year