Mathematics 10 Pacing Guide - This pacing guide replaces the previous yearly plan. It has been updated to reflect removed outcomes and provide flexibility for responsive instruction.
Warm-ups for Relations and Functions outcomes to elicit prior knowledge *Updated September 2025* (English, French (under development))
Math 10 Retrieval Practice Grid Semester #1 (English, French) *Updated October 2024*
Math 10 Retrieval Practice Grid Semester #2 (English, French) *Updated January 2025*
Mathigon Polypad - Polypad is a collection of free virtual manipulatives including algebra tiles which students can use to model the multiplication of polynomials. The Mathigon 101 webinar for secondary teachers demonstrates a number of available features.
EAL Support - Desmos offers a free suite of math software tools, including the Desmos Graphing Calculator and Scientific Calculator, as well as free digital classroom activities. Click on the globe in the tool bar to access the site in other languages.
RF01 Students will be expected to interpret and explain the relationships among data, graphs, and situations. [C, CN, R, T, V]
RF01.01 Graph, with or without technology, a set of data, and determine the restrictions on the domain and range.
RF01.02 Explain why data points should or should not be connected on the graph for a situation.
RF01.03 Describe a possible situation for a given graph.
RF01.04 Sketch a possible graph for a given situation.
RF01.05 Determine, and express in a variety of ways, the domain and range of a graph, a set of ordered pairs, or a table of values.
RF02 Students will be expected to demonstrate an understanding of relations and functions. [C, R, V]
RF02.01 Explain, using examples, why some relations are not functions, but all functions, are relations.
RF02.02 Determine if a set of ordered pairs represents a function.
RF02.03 Sort a set of graphs as functions or non-functions.
RF02.04 Generalize and explain rules for determining whether graphs and sets of ordered pairs represent functions.
RF04 Students will be expected to describe and represent linear relations, using words, ordered pairs, tables of values, graphs, and equations. [C, CN, R, V]
RF04.01 Identify independent and dependent variables in a given context.
RF04.02 Determine whether a situation represents a linear relation, and explain why or why not.
RF04.03 Determine whether a graph represents a linear relation, and explain why or why not.
RF04.04 Determine whether a table of values or a set of ordered pairs represents a linear relation, and explain why or why not.
RF04.05 Draw a graph from a set of ordered pairs within a given situation, and determine whether the relationship between the variables is linear.
RF04.06 Determine whether an equation represents a linear relation, and explain why or why not.
RF04.07 Match corresponding representations of linear relations.
RF05 Students will be expected to determine the characteristics of the graphs of linear relations, including the intercepts, slope, domain, and range. [CN, PS, R, V]
RF05.01 Determine the intercepts of the graph of a linear relation, and state the intercepts as values or ordered pairs.
RF05.02 Determine the slope of the graph of a linear relation.
RF05.03 Determine the domain and range of the graph of a linear relation.
RF05.04 Sketch a linear relation that has one intercept, two intercepts, or an infinite number of intercepts.
RF05.05 Identify the graph that corresponds to a given slope and y-intercept.
RF05.06 Identify the slope and y-intercept that correspond to a given graph.
RF05.07 Solve a contextual problem that involves intercepts, slope, domain, or range of a linear relation.
RF08 Students will be expected to solve problems that involve the distance between two points and the midpoint of a line segment. [C, CN, PS, T, V]
RF08.01 Determine the distance between two points on a Cartesian plane using a variety of strategies.
RF08.02 Determine the midpoint of a line segment, given the endpoints of the segment, using a variety of strategies.
RF08.03 Determine and endpoint of a line segment, given the other endpoint and the midpoint, using a variety of strategies.
RF08.04 Solve a contextual problem involving the distance between two points or midpoint of a line segment.
RF09 Students will be expected to represent a linear function, using function notation. [CN, ME, V]
RF09.01 Express the equation of a linear function in two variables, using function notation.
RF09.02 Express an equation given in function notation as a linear function in two variables.
RF09.03 Determine the related range value, given a domain value for a linear function. (i.e. find the value of f(x) given a value of x)
RF09.04 Determine the related domain value, given a range value for a linear function. (i.e. find the value of x given a value of f(x))
RF09.05 Sketch the graph of a linear function expressed in function notation.
RF01 On s’attend à ce que les élèves sachent interpréter et expliquer les relations parmi des données, des graphiques et des situations. [C, L, R, T, V]
RF01.01 Tracer, avec ou sans l’aide de la technologie, le graphique d’un ensemble de données et déterminer les restrictions sur le domaine et sur l’image.
RF01.02 Expliquer pourquoi des points de données devraient ou ne devraient pas être reliés dans le graphique d’une situation.
RF01.03 Décrire une situation possible pour un graphique donné.
RF01.04 Esquisser un graphique possible pour une situation donnée.
RF01.05 Déterminer le domaine et l’image à partir du graphique, d’un ensemble de paires ordonnées ou d’une table de valeurs, et les exprimer de diverses façons.
RF02 On s’attend à ce que les élèves montrent qu’ils ont compris les relations et les fonctions. [C, R, V]
RF02.01 Expliquer, à l’aide d’exemples, pourquoi certaines relations ne sont pas des fonctions tandis que toutes les fonctions sont des relations.
RF02.02 Déterminer si un ensemble de paires ordonnées représente une fonction.
RF02.03 Trier un ensemble de graphiques en fonctions et non-fonctions.
RF02.04 Formuler et expliquer des règles générales pour déterminer si des graphiques et des ensembles de paires ordonnées représentent des fonctions.
RF04 On s’attend à ce que les élèves sachent décrire et représenter des relations linéaires à l’aide de descriptions verbales, de paires ordonnées, de tables de valeurs, de graphiques et d’équations. [C, L, R, V]
RF04.01 Reconnaitre les variables indépendante et dépendante dans un contexte donné.
RF04.02 Déterminer si une situation représente une relation linéaire et expliquer pourquoi elle en est une ou non.
RF04.03 Déterminer si un graphique représente une relation linéaire et expliquer pourquoi il en est une ou non.
RF04.04 Déterminer si une table de valeurs ou un ensemble de paires ordonnées représentent une relation linéaire et expliquer pourquoi ils en sont une ou non.
RF04.05 Tracer un graphique à partir d’un ensemble de paires ordonnées tiré d’une situation donnée et déterminer si la relation entre les variables est linéaire.
RF04.06 Déterminer si une équation représente une relation linéaire et expliquer pourquoi elle en est une ou non.
RF04.07 Apparier les représentations correspondantes de relations linéaires.
RF05 On s’attend à ce que les élèves sachent déterminer les caractéristiques des graphiques de relations linéaires, y compris les coordonnées à l’origine, la pente, le domaine et l’image. [L, RP, R, V]
RF05.01 Déterminer les coordonnées à l’origine du graphique d’une relation linéaire et les représenter sous la forme de valeurs numériques ou de paires ordonnées.
RF05.02 Déterminer la pente du graphique d’une relation linéaire.
RF05.03 Déterminer le domaine et l’image du graphique d’une relation linéaire.
RF05.04 Esquisser le graphique d’une relation linéaire ayant une, deux ou une infinité de coordonnées à l’origine.
RF05.05 Déterminer le graphique correspondant à une pente et à une ordonnée à l’origine données.
RF05.06 Déterminer la pente et l’ordonnée à l’origine correspondant à un graphique donné.
RF05.07 Résoudre un problème contextualisé comportant les coordonnées à l’origine, la pente, le domaine ou l’image d’une relation linéaire.
RF08 On s’attend à ce que les élèves sachent résoudre des problèmes comportant la détermination de la distance entre deux points et les coordonnées du point milieu d’un segment de droite. [C, L, RP, T, V]
RF08.01 Déterminer, à l’aide de diverses stratégies, la distance entre deux points situés dans un plan cartésien.
RF08.02 Déterminer, à l’aide de diverses stratégies, les coordonnées du point milieu d’un segment de droite à partir des extrémités du segment.
RF08.03 Déterminer, à l’aide de diverses stratégies, les coordonnées d’une extrémité d’un segment de droite à partir de l’autre extrémité et du point milieu.
RF08.04 Résoudre des problèmes contextualisés qui font intervenir la distance entre deux points ou le point milieu d’un segment de droite.
RF09 On s’attend à ce que les élèves sachent représenter une fonction linéaire par notation fonctionnelle. [L, CE, V]
RF09.01 Exprimer par notation fonctionnelle l’équation d’une fonction linéaire à deux variables.
RF09.02 Exprimer une équation donnée sous la forme d’une fonction linéaire à deux variables par notation fonctionnelle.
RF09.03 Déterminer la valeur de l’image correspondant à une valeur donnée du domaine d’une fonction linéaire.
RF09.04 Déterminer la valeur du domaine correspondant à une valeur donnée de l’image d’une fonction linéaire.
RF09.05 Esquisser le graphique d’une fonction linéaire exprimée par notation fonctionnelle
Additional Resources and Activities for RF01 (Interpreting and sketching graphs):
Graphing Stories - ‘Graphing Stories’ are videos that show a practical situation where a measure, such as height or weight, varies with time. The situation is then replayed at a slower rate to help enable the viewer to assess more clearly how the measurement varies and to then plot a graph of the story.
Desmos Activity: Turtle Crossing (English, French) - Students make connections between scenarios and graphs that represent them.
Oops I Forgot Graphing a Story - Students are read a story and construct a graph (using a dry erase marker on a white board) that might correspond to it. As additional details are added, students revise their graph so it still makes sense. Students could create their own multi-part story as an extension to this activity.
Popcorn Graphs - *Updated June 2025* Students practice writing graph stories describing how four family members eat popcorn.
Desmos Activity: Graphing Stories (English, French) - A collection of short videos. For each video, students will create a graph to describe the action in the video on a handout.
Desmos Activity: Guess My Rule - Students are introduced to the concept of a function by using input-output pairs in a table. They explore different rules, some of which are functions and some of which are not
Desmos Activity: Turtle Time Trials - In this lesson, students explore connections among different representations of proportional relationships, with a glimpse at non-proportional relationships. The lesson centers around a race between turtles of different constant speeds. After encountering the context with an animation, students analyze and create other representations of the scenario: number lines, graphs, tables, and equations.
Canada Flushed Slow Reveal Graph - A "slow reveal" graph to get students thinking about components of a graph.
Desmos Activity: Intro to Domain and Range - Students explore representing, and interpreting Domain and Range for a variety of representations.
Desmos Activity: Domain and Range Introduction (English, French) - In this activity, students adjust shaded regions to identify the domain of a function.
Desmos Activity: Finding Domain and Range (English, French) - In this activity, students describe the domain and range of six relationships. (First verbally and later algebraically.) Later, students use movable points to create three functions whose domain and range match specific criteria.
Domain and Range Challenge - *Updated June 2025* A set of 20 Challenge Questions where students have to identify the domain and range, and if a set of data is continuous or discrete.
Additional Resources and Activities for RF02 (Relations and functions):
Desmos Activity: Function or Not Function? That is the question! - Students will derive the definition of a function as represented by a table, set of ordered pairs, a map, or a graph. They will practice stating whether the given is a function or not a function and why.
Desmos Activity: Cookie Functions - The purpose of this activity is to introduce students to the definition of a function using the example of baking cookies. The students will also learn about domain, range, and the vertical line test.
Function/Not a Function Puzzle Open Middle Problem - Students complete a trio of tables of values in order to make them all a function or all not a function. This could also be done virtually with Google Slides. See more on Sarah Carter's blog.
Function Card Sort - Students sort cards showing functions and non-functions in various representations. You could also do this activity virtually with this Desmos activity. See more on Sarah Carter's blog.
Functions as Vending Machines - A Google Slides selection of photos of vending machines illustrating different types of functions and what they would look like as arrow diagrams.
Desmos Activity: Function Carnival- Students watch a video and describe what they see to uncover misconceptions about graphing. The teacher dashboard allows the teacher to see and record what each student is working on.
Desmos Activity: Polygraph (English, French) - This Custom Polygraph is designed to spark vocabulary-rich conversations about discrete and continuous functions and relations. Key vocabulary that may appear in student questions includes: function, non-function, relation, discrete, continuous, input, output, x-value, and y-value.
Additional Resources and Activities for RF04, RF05, RF07 (Describing linear relations):
Open Middle Problem *Added May 2025* - Linear Function from a Table of Values
Desmos Activity: Representing Linear Relations - Students will become familiar with a variety of ways to represent relations including ordered pairs, table of values, graphs and arrow diagrams. Students will have the opportunity to practice evaluating linear relations using a variety of these different representations.
Domain and Range Lesson Word or PDF - This activity introduces domain and range using a Pictionary activity . The idea is that one student will be given a graph and have to describe it to a partner, who will draw it without looking at it. You make it tougher if you don’t let the describer see what the describe is drawing until the graph is done. This task and resources are also found on the Alberta Assessment Consortium web site. Additional detail from John Scammell.
Rocky Road Activity and Scaffolded Activity- Students analyze the progress of a hiker based on a graphical representation. They determine the equation of a line, and then they create a new story supported by their own graph. From Alberta Assessment Consortium.
Desmos Activity: Representing Linear Relations - Students will become familiar with a variety of ways to represent relations including ordered pairs, table of values, graphs and arrow diagrams. Students will have the opportunity to practice evaluating linear relations using a variety of these different representations.
Linear Relations Add 'Em Up Activity - This is a self-checking activity focused on RF05. These are google slides that can be printed or posted electronically. A series of four sets of questions. Students work in small groups to answer each set. If they correctly complete the set, they move on to the next set.
Additional Resources and Activities for RF08 (Distance and Midpoint):
This outcome was deemed non-Foundational and is no longer included in Mathematics 10.
Additional Resources and Activities for RF09 (Function notation):
Desmos Activity: Warm Up - Functions/ Function Notation - Students identify if different representations are a function or not, then practice working with function notation.
Evaluating Functions War - Students determine the value of a function at two different points to see which is greater. Students get practice evaluating functions from a table, equation, or graph. Additional information at Sarah Carter's blog.
Function Notation Snake - A self-checking activity for students to practice evaluating linear expressions using function notation.
Two-Step Functions Fill in the Blanks activity - Students solve 20 Function Notation problems. They add up all the answers to get a 3 digit code. They check this code with the teacher to see if they have all the right answers. If not, they work to find their mistake (Answers). From Dr. Austin Maths.
Function Notation Crack the Code activity - Students solve 20 Function Notation problems. They add up all the answers to get a 3 digit code. They check this code with the teacher to see if they have all the right answers. If not, they work to find their mistake (Answers). From Dr. Austin Maths.
Function Notation Open Middle Question - Students use the digits 1-9 at most one time each to create a function and evaluate it. What is the largest/smallest function value they can create? Many more open middle questions are available at https://www.openmiddle.com/.
Function Notation Spider - Practice on the function notation involving substituting into a function and finding the value of x given what f(x) equals.
Desmos Activity: Domain and Range in Context - Students explore domain and range in context of linear problems.
Unit 1 Cumulative Review
Student Self-Assessment and Review - Students self-assess their ability to demonstrate the outcomes from Unit 1. Practice questions from the textbook are identified and links to extra practice and review are included.