Progression of Learning

AR.1.2: Fractions

AR.1.2.b: Identifies the different meanings of fractions: part of a whole, division, ratio, operator, measurement

Beam to Moon (Ratios and Proportions)

Dividing Fractions

Dividing Mixed Numbers

Part-to-part and Part-to-whole Ratios

Percents, Fractions, and Decimals

Proportions and Common Multipliers

Solving Algebraic Equations II

AR.1.2.c: Verifies whether two fractions are equivalent

Adding Fractions (Fraction Tiles)

Fractions with Unlike Denominators

Improper Fractions and Mixed Numbers

AR.1.2.e: Orders fractions with the same denominator or where one denominator is a multiple of the other or with the same numerator

Adding Fractions (Fraction Tiles)

Rational Numbers, Opposites, and Absolute Values

AR.1.3: Decimals up to thousandths

AR.1.3.a: Represents decimals in a variety of ways (using objects or drawings) and identifies equivalent representations

Comparing and Ordering Decimals

Multiplying with Decimals

Part-to-part and Part-to-whole Ratios

Percents, Fractions, and Decimals

AR.1.3.b: Reads and writes numbers written in decimal notation

Comparing and Ordering Decimals

AR.1.3.d: Composes and decomposes a number written in decimal notation and recognizes equivalent expressions

Part-to-part and Part-to-whole Ratios

Percents, Fractions, and Decimals

AR.1.3.e: Compares numbers written in decimal notation or arranges them in increasing or decreasing order

Comparing and Ordering Decimals

Rational Numbers, Opposites, and Absolute Values

AR.1.4: Integers

AR.1.4.a: Represents integers in a variety of ways (using objects or drawings)

Adding and Subtracting Integers

AR.1.4.c: Compares integers or arranges integers in increasing or decreasing order

Integers, Opposites, and Absolute Values

Rational Numbers, Opposites, and Absolute Values

AR.1.5: Expresses numbers in a variety of ways (fractional, decimal percentage notation)

Part-to-part and Part-to-whole Ratios

Percents, Fractions, and Decimals

AR.1.6: Represents, reads and writes numbers written in fractional or decimal notation

Comparing and Ordering Decimals

AR.1.7: Approximates, in various contexts, the numbers under study (e.g. estimates, rounds off, truncates)

Estimating Sums and Differences

Multiplying with Decimals

Proportions and Common Multipliers

Sums and Differences with Decimals

AR.1.10: Defines the concept absolute value in context (e.g. difference between two numbers, distance between two points)

Absolute Value with Linear Functions

AR.1.11: Represents and writes

AR.1.11.b: squares and square roots

Simplifying Radical Expressions

Square Roots

AR.1.15: Compares and arranges in order

AR.1.15.a: numbers written in fractional or decimal notation

Adding Fractions (Fraction Tiles)

Comparing and Ordering Decimals

Rational Numbers, Opposites, and Absolute Values

AR.1.15.b: numbers expressed in different ways (fractional, decimal, exponential [integral exponent], percentage, square root, scientific notation)

Comparing and Ordering Decimals

Rational Numbers, Opposites, and Absolute Values

Unit Conversions

Unit Conversions 2 - Scientific Notation and Significant Digits

AR.2.5: Looks for equivalent expressions: decomposing (additive, multiplicative, etc.), equivalent fractions, simplifying and reducing, factoring, etc.

Fractions with Unlike Denominators

Part-to-part and Part-to-whole Ratios

AR.2.6: Translates (mathematizes) a situation using a sequence of operations (no more than two levels of parentheses)

AR.2.7: Anticipates the results of operations

Dividing Fractions

Dividing Mixed Numbers

Estimating Sums and Differences

Multiplying Mixed Numbers

Multiplying with Decimals

Sums and Differences with Decimals

AR.2.8: Interprets the results of operations in light of the context

Adding on the Number Line

Dividing Mixed Numbers

Multiplying Fractions

Multiplying Mixed Numbers

Multiplying with Decimals

Sums and Differences with Decimals

AR.3.5: Approximates the result of an operation or sequence of operations

Dividing Fractions

Dividing Mixed Numbers

Estimating Sums and Differences

Multiplying Mixed Numbers

Multiplying with Decimals

Sums and Differences with Decimals

AR.3.6: Mentally computes the four operations, especially with numbers written in decimal notation, using equivalent ways of writing numbers and the properties of operations

Adding Fractions (Fraction Tiles)

Adding on the Number Line

Improper Fractions and Mixed Numbers

Multiplying Fractions

Multiplying Mixed Numbers

Percents, Fractions, and Decimals

Sums and Differences with Decimals

AR.3.7: Computes, in writing, the four operations with numbers that are easy to work with (including large numbers), using equivalent ways of writing numbers and the properties of operations

AR.3.7.b: positive numbers written in fractional notation, with or without the use of objects or diagrams

Adding Fractions (Fraction Tiles)

Dividing Fractions

Dividing Mixed Numbers

Estimating Sums and Differences

Fractions with Unlike Denominators

Improper Fractions and Mixed Numbers

Multiplying Fractions

Multiplying Mixed Numbers

AR.3.11: Switches, as needed, from one way of writing numbers to another

Percents, Fractions, and Decimals

AR.4.1: Calculates

AR.4.1.a: a certain percentage of a number

Percent of Change

Percents and Proportions

AR.4.1.b: the value corresponding to 100 per cent

Beam to Moon (Ratios and Proportions)

Part-to-part and Part-to-whole Ratios

Percent of Change

Percents and Proportions

Percents, Fractions, and Decimals

AR.4.2: Recognizes ratios and rates

Beam to Moon (Ratios and Proportions)

Geometric Probability

Part-to-part and Part-to-whole Ratios

Percents and Proportions

Proportions and Common Multipliers

AR.4.3: Interprets ratios and rates

Beam to Moon (Ratios and Proportions)

Geometric Probability

Part-to-part and Part-to-whole Ratios

Percents and Proportions

Proportions and Common Multipliers

AR.4.4: Describes the effect of changing a term in a ratio or rate

Beam to Moon (Ratios and Proportions)

Part-to-part and Part-to-whole Ratios

Percents and Proportions

Proportions and Common Multipliers

AR.4.7: Recognizes a proportional situation using the context, a table of values or a graph

Beam to Moon (Ratios and Proportions)

Direct and Inverse Variation

Estimating Population Size

Geometric Probability

Part-to-part and Part-to-whole Ratios

Proportions and Common Multipliers

AR.4.8: Represents or interprets a proportional situation using a graph, a table of values or a proportion

Beam to Moon (Ratios and Proportions)

Direct and Inverse Variation

Part-to-part and Part-to-whole Ratios

Percents and Proportions

Proportions and Common Multipliers

AL.1.A: Algebraic expressions

AL.1.A.1: Describes, using his/her own words and mathematical language, numerical patterns

Compound Interest

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

Using Algebraic Equations

Using Algebraic Expressions

AL.1.A.2: Describes, using his/her own words and mathematical language, series of numbers and family of operations

Arithmetic Sequences

Compound Interest

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

Using Algebraic Equations

Using Algebraic Expressions

Arithmetic Sequences

AL.1.A.4: Describes the role of components of algebraic expressions:

AL.1.A.4.a: unknown

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

Solving Algebraic Equations I

Solving Equations on the Number Line

Using Algebraic Equations

AL.1.A.4.b: variable, constant

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

Solving Algebraic Equations I

Solving Equations on the Number Line

Using Algebraic Equations

AL.1.A.4.c: parameter

AL.1.A.4.d: coefficient, degree, term, constant term, like terms

Compound Interest

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

AL.1.A.5: Constructs an algebraic expression using a register (type) of representation

Compound Interest

Simplifying Algebraic Expressions II

Using Algebraic Equations

AL.1.A.6: Interprets an algebraic expression in light of the context

AL.1.A.7: Recognizes or constructs equivalent algebraic expressions

Dividing Exponential Expressions

Equivalent Algebraic Expressions I

Equivalent Algebraic Expressions II

Exponents and Power Rules

Modeling the Factorization of *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

Multiplying Exponential Expressions

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

Using Algebraic Expressions

AL.1.A.8: Recognizes or constructs

AL.1.A.8.a: equalities and equations

Absolute Value Equations and Inequalities

Linear Functions

Linear Inequalities in Two Variables

Modeling One-Step Equations

Solving Equations on the Number Line

Using Algebraic Equations

AL.1.B: Manipulating algebraic expressions

AL.1.B.1: Calculates the numeric value of an algebraic expression

Compound Interest

Order of Operations

Solving Equations by Graphing Each Side

Solving Equations on the Number Line

AL.1.B.2: Performs the following operations on algebraic expressions, with or without objects or diagrams: addition and subtraction, multiplication and division by a constant, multiplication of first-degree monomials

Dividing Exponential Expressions

Equivalent Algebraic Expressions I

Multiplying Exponential Expressions

AL.1.C: Analyzing situations using equations or inequalities

AL.1.C.1: Recognizes whether a situation can be translated by

AL.1.C.1.a: an equation

Linear Functions

Solving Equations on the Number Line

Using Algebraic Equations

AL.1.C.2: Recognizes or constructs

AL.1.C.2.a: relations or formulas

Introduction to Functions

Linear Functions

AL.1.C.3: Manipulates relations or formulas (e.g. isolates an element)

Area of Triangles

Solving Formulas for any Variable

AL.1.C.4: Represents a situation using

AL.1.C.4.a: a first-degree equation with one unknown

AL.1.C.6: Determines the missing term in an equation (relations between operations): a + b = □, a + □ = c, □ + b = c, a – b = □, a – □ = c, □ – b = c, a × b = □, a × □ = c, □ × b = c, a ÷ b = □, a ÷ □ = c, □ ÷ b = c

Modeling One-Step Equations

Solving Algebraic Equations II

Solving Equations by Graphing Each Side

Solving Equations on the Number Line

AL.1.C.7: Transforms arithmetic equalities and equations to maintain equivalence (properties and rules for transforming equalities) and justifies the steps followed, if necessary

Modeling One-Step Equations

Modeling and Solving Two-Step Equations

Solving Algebraic Equations II

Solving Equations on the Number Line

Solving Two-Step Equations

AL.1.C.9: Uses different methods to solve first-degree equations with one unknown of the form ax + b = cx + d: trial and error, drawings, arithmetic methods (inverse or equivalent operations), algebraic methods (balancing equations or hidden terms)

Modeling One-Step Equations

Modeling and Solving Two-Step Equations

Solving Algebraic Equations II

Solving Equations on the Number Line

Solving Two-Step Equations

AL.2.A: Relations, functions and inverses

AL.2.A.1: Identifies patterns in various situations and in various forms

Arithmetic Sequences

Finding Patterns

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Geometric Sequences

Pattern Finder

AL.2.A.2: Analyzes situations using different registers (types) of representation

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Introduction to Functions

Linear Functions

Points, Lines, and Equations

AL.2.A.3: Represents a situation generally using a graph

Absolute Value with Linear Functions

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Introduction to Functions

Linear Functions

Points, Lines, and Equations

Quadratics in Polynomial Form

P.1.A: Processing data from random experiments

P.1.A.1: Simulates random experiments with or without the use of technological tools

Binomial Probabilities

Geometric Probability

Independent and Dependent Events

Probability Simulations

Theoretical and Experimental Probability

P.1.A.2: Experiments with activities involving chance, using various objects (e.g. spinners, rectangular prisms, glasses, marbles, thumb tacks, 6-, 8- or 12-sided dice)

Binomial Probabilities

Geometric Probability

Independent and Dependent Events

Probability Simulations

Spin the Big Wheel! (Probability)

Theoretical and Experimental Probability

P.1.A.3: In activities involving chance

P.1.A.3.b: recognizes equiprobability (e.g. quantity of objects, symmetry of an object such as a cube)

P.1.A.3.c: becomes aware of the independence of events (e.g. rolling dice, tossing a coin, drawing lots)

Independent and Dependent Events

P.1.A.5: Compares the outcomes of a random experiment with known theoretical probabilities

Geometric Probability

Independent and Dependent Events

Probability Simulations

Spin the Big Wheel! (Probability)

Theoretical and Experimental Probability

P.1.A.6: Distinguishes between prediction and outcome

Independent and Dependent Events

Probability Simulations

Spin the Big Wheel! (Probability)

Theoretical and Experimental Probability

P.1.A.7: Conducts or simulates random experiments involving one or more steps (with or without replacement, with or without order)

Binomial Probabilities

Geometric Probability

Independent and Dependent Events

Probability Simulations

Spin the Big Wheel! (Probability)

Theoretical and Experimental Probability

P.1.A.9: Enumerates the possible outcomes of a random experiment using

P.1.A.9.a: tables, tree diagram

Binomial Probabilities

Permutations and Combinations

P.1.A.10: Defines the sample space of a random experiment

Binomial Probabilities

Independent and Dependent Events

Spin the Big Wheel! (Probability)

P.1.A.11: Recognizes certain, probable, impossible, simple, complementary, compatible, incompatible, dependent, independents events

Geometric Probability

Independent and Dependent Events

Theoretical and Experimental Probability

P.1.A.13: Uses fractions, decimals or percentages to quantify a probability

Estimating Population Size

Independent and Dependent Events

Probability Simulations

Spin the Big Wheel! (Probability)

Theoretical and Experimental Probability

P.1.A.14: Recognizes that a probability is always between 0 and 1

Binomial Probabilities

Geometric Probability

Independent and Dependent Events

P.1.A.15: Predicts qualitatively an outcome or several events using a probability line, among other things

P.1.A.15.a: certain, possible or impossible outcome

Binomial Probabilities

Geometric Probability

Independent and Dependent Events

P.1.A.15.b: more likely, just as likely, less likely event

Probability Simulations

Spin the Big Wheel! (Probability)

Theoretical and Experimental Probability

P.1.B: Analyzing probability situations

P.1.B.1: Represents an event using different registers (types of representation)

Binomial Probabilities

Independent and Dependent Events

Spin the Big Wheel! (Probability)

P.1.B.2: Compares qualitatively the theoretical or experimental probability of an event occurring

Geometric Probability

Independent and Dependent Events

Probability Simulations

Spin the Big Wheel! (Probability)

Theoretical and Experimental Probability

P.1.B.3: Distinguishes between theoretical and experimental probability

Geometric Probability

Independent and Dependent Events

Probability Simulations

Spin the Big Wheel! (Probability)

Theoretical and Experimental Probability

P.1.B.4: Calculates the probability of an event

Binomial Probabilities

Geometric Probability

Independent and Dependent Events

Theoretical and Experimental Probability

P.1.B.9: Interprets probabilities and makes appropriate decisions

Geometric Probability

Independent and Dependent Events

Spin the Big Wheel! (Probability)

Theoretical and Experimental Probability

S.1.A: One-variable distributions

S.1.A.1: Conducts a survey or a census

S.1.A.1.a: Formulates questions for a survey

Correlation

Describing Data Using Statistics

Movie Reviewer (Mean and Median)

Polling: Neighborhood

S.1.A.1.b: Chooses a sampling method:

S.1.A.1.b.i: simple random, systematic

Polling: City

Polling: Neighborhood

Populations and Samples

S.1.A.1.c: Chooses a representative sample

Polling: City

Polling: Neighborhood

S.1.A.1.d: Collects, describes and organizes data (classifies or categorizes) using tables

Describing Data Using Statistics

Stem-and-Leaf Plots

S.1.A.2: Recognizes possible sources of bias

Polling: Neighborhood

Populations and Samples

S.1.A.3: Interprets data presented in a table or a bar graph, a pictograph, a broken-line graph or a circle graph

Forest Ecosystem

Prairie Ecosystem

Reaction Time 1 (Graphs and Statistics)

S.1.A.5: Chooses appropriate register(s) (types) of representation to organize, interpret and present data

Box-and-Whisker Plots

Describing Data Using Statistics

S.1.A.6: Organizes and presents data using

S.1.A.6.a: a table, a bar graph, a pictograph and a broken-line graph

Describing Data Using Statistics

Distance-Time Graphs

Forest Ecosystem

Prairie Ecosystem

Reaction Time 1 (Graphs and Statistics)

Stem-and-Leaf Plots

S.1.A.6.b: a table presenting variables or frequencies, or using a circular graph

S.1.A.7: Compares one-variable distributions

Box-and-Whisker Plots

Describing Data Using Statistics

Movie Reviewer (Mean and Median)

Populations and Samples

Reaction Time 1 (Graphs and Statistics)

Real-Time Histogram

S.1.A.8: Understands and calculates the arithmetic mean

Describing Data Using Statistics

Mean, Median, and Mode

Movie Reviewer (Mean and Median)

Populations and Samples

Stem-and-Leaf Plots

S.1.A.9: Describes the concept of arithmetic mean (leveling or balance point)

Describing Data Using Statistics

Mean, Median, and Mode

Movie Reviewer (Mean and Median)

Populations and Samples

Stem-and-Leaf Plots

S.1.A.10: Calculates and interprets an arithmetic mean

Describing Data Using Statistics

Mean, Median, and Mode

Movie Reviewer (Mean and Median)

Populations and Samples

Sight vs. Sound Reactions

Stem-and-Leaf Plots

S.1.A.11: Determines and interprets

S.1.A.11.b: measures of dispersion:

S.1.A.11.b.i: range

Box-and-Whisker Plots

Describing Data Using Statistics

Mean, Median, and Mode

Movie Reviewer (Mean and Median)

Reaction Time 1 (Graphs and Statistics)

Stem-and-Leaf Plots

S.1.A.11.c: measures of position:

S.1.A.11.c.i: minimum, maximum

S.1.A.12: Chooses the appropriate statistical measures for a given situation

Box-and-Whisker Plots

Describing Data Using Statistics

Movie Reviewer (Mean and Median)

Reaction Time 1 (Graphs and Statistics)

G.1.A: Plane figures

G.1.A.2: Describes and classifies quadrilaterals

Classifying Quadrilaterals

Parallelogram Conditions

Special Parallelograms

G.1.A.3: Describes and classifies triangles

Classifying Triangles

Concurrent Lines, Medians, and Altitudes

Pythagorean Theorem

Pythagorean Theorem with a Geoboard

Similarity in Right Triangles

Triangle Inequalities

G.1.A.4: Describes circles: radius, diameter, circumference, central angle

Chords and Arcs

Circles

Circumference and Area of Circles

Inscribed Angles

G.1.A.6: Decomposes plane figures into circles (sectors), triangles or quadrilaterals

Area of Triangles

Polygon Angle Sum

G.1.A.8: Recognizes and draws main segments and lines

G.1.A.8.a: diagonal, altitude, median, perpendicular bisector, bisector, apothem, radius, diameter, chord

Parallelogram Conditions

Special Parallelograms

G.1.A.9: Identifies the properties of plane figures using geometric transformations and constructions

Circles

Dilations

Reflections

Rock Art (Transformations)

Rotations, Reflections, and Translations

Translations

G.1.A.10: Justifies statements using definitions or properties of plane figures

G.1.B: Solids

G.1.B.2: Determines the possible nets of a solid

Surface and Lateral Areas of Prisms and Cylinders

Surface and Lateral Areas of Pyramids and Cones

G.1.B.3: Names the solid corresponding to a net

Surface and Lateral Areas of Prisms and Cylinders

Surface and Lateral Areas of Pyramids and Cones

G.1.B.4: Describes solids:

G.1.B.4.b: altitude, apothem, lateral face

Surface and Lateral Areas of Prisms and Cylinders

Surface and Lateral Areas of Pyramids and Cones

G.1.B.6: Recognizes solids that can be split into

G.1.B.6.a: right prisms, right cylinders, right pyramids

Surface and Lateral Areas of Prisms and Cylinders

Surface and Lateral Areas of Pyramids and Cones

G.1.C: Geometric constructions and transformations in the Euclidian plane

G.1.C.2: Identifies properties and invariants resulting from geometric constructions and transformations

Circles

Dilations

Reflections

Rock Art (Transformations)

Rotations, Reflections, and Translations

Translations

G.1.C.3: Identifies congruence (translation, rotation and reflection) between two figures

Reflections

Rock Art (Transformations)

Rotations, Reflections, and Translations

Translations

G.1.C.4: Constructs the image of a figure under a translation, rotation and reflection

Holiday Snowflake Designer

Reflections

Rock Art (Transformations)

Rotations, Reflections, and Translations

Similar Figures

Translations

G.1.C.5: Recognizes dilatation with a positive scale factor

G.1.D: Congruent, similar or equivalent figures

G.1.D.3: Recognizes the geometric transformation(s) linking a figure and its image

Dilations

Rotations, Reflections, and Translations

Translations

G.1.D.4: Determines the properties and invariants of congruent or similar figures

Constructing Congruent Segments and Angles

Perimeters and Areas of Similar Figures

Similar Figures

Similarity in Right Triangles

G.1.D.8: Justifies statements using definitions or properties of congruent, similar or equivalent figures, depending on the cycle and year

Constructing Congruent Segments and Angles

Perimeters and Areas of Similar Figures

Similar Figures

Similarity in Right Triangles

G.2.C: Angles

G.2.C.3: Describes the characteristics of different types of angles: complementary, supplementary, adjacent, vertically opposite, alternate interior, alternate exterior and corresponding

Investigating Angle Theorems

Triangle Angle Sum

G.2.C.4: Determines measures of angles using the properties of the following angles: complementary, supplementary, vertically opposite, alternate interior, alternate exterior and corresponding

Investigating Angle Theorems

Similar Figures

Similarity in Right Triangles

Triangle Angle Sum

G.2.C.5: Finds unknown measurements using the properties of figures and relations

G.2.C.5.a: measures of angles in a triangle

Isosceles and Equilateral Triangles

Polygon Angle Sum

Triangle Angle Sum

G.2.C.5.b: degree measures of central angles and arcs

Chords and Arcs

Inscribed Angles

G.2.C.8: Justifies statements using definitions or properties associated with angles and their measures

G.2.D: Length

G.2.D.4: Constructs relations that can be used to calculate the perimeter or circumference of figures

Circumference and Area of Circles

Perimeter and Area of Rectangles

G.2.D.5: Finds the following unknown measurements, using properties of figures and relations

G.2.D.5.a: perimeter of plane figures

Perimeter and Area of Rectangles

G.2.E: Area

G.2.E.1: Chooses the appropriate unit of area for the context

G.2.E.4: Constructs relations that can be used to calculate the area of plane figures: quadrilateral, triangle, circle (sectors)

Area of Parallelograms

Area of Triangles

Chocomatic (Multiplication, Arrays, and Area)

Circumference and Area of Circles

Perimeter and Area of Rectangles

G.2.E.6: Finds unknown measurements, using properties of figures and relations

G.2.E.6.b: area of figures that can be split into circles (sectors), triangles or quadrilaterals

G.2.E.6.c: lateral or total area of right prisms, right cylinders and right pyramids

Surface and Lateral Areas of Prisms and Cylinders

Surface and Lateral Areas of Pyramids and Cones

G.2.E.6.d: lateral or total area of solids that can be split into right prisms, right cylinders or right pyramids

Surface and Lateral Areas of Prisms and Cylinders

Surface and Lateral Areas of Pyramids and Cones

G.2.E.6.f: area of figures resulting from a similarity transformation

G.2.E.7: Justifies statements concerning measures of area

AG.1.A: Locating

AG.1.A.1: Locates objects/numbers on an axis, based on the types of numbers studied

Points in the Coordinate Plane

AG.1.A.2: Locates points in a Cartesian plane, based on the types of numbers studied (x and y-coordinates of a point)

City Tour (Coordinates)

Linear Functions

Point-Slope Form of a Line

Points in the Coordinate Plane

Points, Lines, and Equations

Slope

Correlation last revised: 3/1/2018