Mathematics 9 Pacing Guide - This pacing guide replaces the previous yearly plan. It has been updated to remove non-foundational outcomes and provide flexibility for responsive instruction.
Mathematics Progression: Grades 6 - 9
PR01 Students will be expected to generalize a pattern arising from a problem-solving context using a linear equation and verify by substitution. [C, CN, PS, R, V]
Performance Indicators
PR01.01 Write an expression representing a given concrete, pictorial, oral, and/or written pattern.
PR01.02 Write a linear equation to represent a given context.
PR01.03 Describe a context for a given linear equation.
PR01.04 Solve, using a linear equation, a given problem that involves concrete, pictorial, oral, and/or written linear patterns.
PR01.05 Write a linear equation representing the pattern in a given table of values, and verify the equation by substituting values from the table.
PR02 Students will be expected to graph a linear relation, analyze the graph, and interpolate or extrapolate to solve problems. [C, CN, PS, R, T, V]
Performance Indicators
PR02.01 Describe the pattern found in a given graph.
PR02.02 Graph a given linear relation, including horizontal and vertical lines.
PR02.03 Match given equations of linear relations with their corresponding graphs.
PR02.04 Extend a given graph (extrapolate) to determine the value of an unknown element.
PR02.05 Interpolate the approximate value of one variable on a given graph, given the value of the other variable.
PR02.06 Extrapolate the approximate value of one variable from a given graph, given the value of the other variable.
PR02.07 Solve a given problem by graphing a linear relation and analyzing the graph.
PR01 On s’attend à ce que les élèves généralisent une régularité découlant d’un contexte de résolution de problèmes à l’aide d’une équation linéaire et vérifient en faisant des substitutions. [C, L, RP, R, V]
PR01.01 Écrire une expression représentant une régularité donnée sous forme imagée, orale ou écrite.
PR01.02 Écrire une équation linéaire pour représenter un contexte donné.
PR01.03 Décrire un contexte pour une équation linéaire donnée.
PR01.04 Résoudre, en utilisant une équation linéaire, un problème donné faisant intervenir des régularités linéaires sous forme imagée, orale ou écrite.
PR01.05 Écrire une équation linéaire représentant la régularité qui se dégage d’une table de valeurs donnée et vérifier cette équation en y substituant des valeurs tirées de cette table.
PR02 On s’attend à ce que les élèves fassent la représentation graphique d’une relation linéaire, analysent la représentation graphique et fassent des interpolations et des extrapolations pour résoudre des problèmes. [C, L, RP, R, T, V]
PR02.01 Décrire la régularité dans un graphique donné.
PR02.02 Tracer le graphique d’une relation linéaire donnée, y compris les droites verticales et horizontales.
PR02.03 Apparier des relations linéaires données aux graphiques correspondants.
PR02.04 Prolonger un graphique donné (extrapoler) pour déterminer la valeur d’un élément inconnu.
PR02.05 Interpoler la valeur approximative d’une variable sur un graphique donné à partir d’une valeur donnée pour l’autre variable.
PR02.06 Extrapoler la valeur approximative d’une variable sur un graphique donné à partir d’une valeur donnée pour l’autre variable.
PR02.07 Résoudre un problème donné en traçant le graphique d’une relation linéaire et en l’analysant.
Additional Resources and Activities for PR01 (generalize a linear pattern):
Unit 4 Overview Slides English, French - This large file of Google Slides was created to support teaching from home during remote learning in Spring 2020.
Turtle Time Trials Desmos Activity English, French - In this lesson, students explore connections among different representations of 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.
Visual Patterns - Have students describe the patterns from Fawn Nguyen's website using words and then equations. Not all of the patterns on this site are linear. How can students tell if a pattern is linear or not?
Charge! - One evening, with his phone battery nearly depleted, Michael Fenton plugged in and took a series of screenshots to track the percent battery charge (as a function of time). From there, students should have enough information to create a linear model for extrapolation. Some surprising results ensue!
Stacking Paper - Given a photo showing the height of 5 packages of paper stacked against a wall, students are asked to predict (extrapolate) how many packages of paper it will take to reach the ceiling.
Relation Stations - Ask students to create their own linear relation pattern using square tiles. Students then circle the room making a t-chart and function for each pattern.
Determining a Linear Equation from a Pattern NLESD Math 9 Video - This is part of a collection of instructional videos, self-assessments and unit reviews from the Newfoundland and Labrador English School District (NLESD).
Additional Resources and Activities for PR02 (graph and analyze linear relations including interpolation and extrapolation):
Matching graphs and equations: Students are asked to cut, match, paste their matches and explain their strategy and reasoning for why they are a match. Directions are provided in English and French within the document.
Barbie Bungee - Attach rubber bands to a Barbie and measure how far she falls. Record the information to create a linear relationship between the number of rubber bands and the distance fallen. Then use this to predict how many rubber bands are require for a fall from a great height.
Knot Again! - When we tie a knot in a rope we use up a bit of that rope. I took two ropes of different thicknesses and asked my students to guess too low, too high and best guess for how much rope would get used up if we tied a knot. Tie a few knots and measure the rope each time. Use this data to predict the length of the rope with 10 knots tied in it. Ask students to model this relationship symbolically.
Super Racers - Students use pull back cars to collect linear data. They then use this data to plot a linear equation and extrapolate to determine how far to pull back their car to travel a specific distance.
*Updated December 2024* Extrapolating and Interpolating Practice Google Slides English, French - Students can practice extrapolating and interpolating values from a graph. This can be used with technology or printed for each student.
Linear Relations Quizizz formative assessment - 16 questions for students to check their understanding of various forms of linear relations; tables, graphs and functions.
Unit 4 Cumulative Review
Create a Puzzle Activity English, French - Students work with a partner to create 6 puzzles pieces that fit together. Each piece with have a different aspect of a linear relation (table of values, graph, word problem, equation, etc.). Student can then cut the puzzles pieces apart, mix them with other groups puzzles and try to sort them out.
Linear Relations Choice Board English, French - Students are given a sheet with 9 questions on it in a 3x3 grid. Students are asked to select 5 of the 9 questions (including the question in the centre) to solve. Have a conversation with students about how they select the problems they are going to attempt.
Unit 4 Review Pixel Art Activity English, French - This activity uses Google Sheets. As students correctly answer questions, parts of an artwork are revealed. Students know they have completed all the questions correctly when the complete work of art is revealed.
Chasse au trésor - Relations Linéaires (MS Word doc)- Hang these questions around the room and have students individually, or in pairs, complete them. This activity is self checking so students know if they've completed it correctly.
NLESD Math 9 - Linear Relations Unit Review A collection of 10 multiple choice and 4 long answer questions as a summative review of the unit.