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
PR03 Students will be expected to model and solve problems, where a, b, c, d, e, and f are rational numbers, using linear equations of the form.
ax = b
x/a = c, a not equal to 0
ax + b = c
x/a + b = c, a not equal to 0
ax = b + cx
a(x + b) = c
ax + b = cx + d
a(bx + c) = d(ex + f)
a/x = b, x not equal to 0
[C, CN, PS, V]
Performance Indicators
PR03.01 Solve the given linear equation, using concrete and pictorial representations, and record this process symbolically.
PR03.02 Verify by substitution whether a given rational number is a solution to a given linear equation.
PR03.03 Solve a given linear equation symbolically.
PR03.04 Identify and correct an error in a given incorrect solution of a linear equation.
PR03.05 Represent a given problem, using a linear equation. PR03.06 Solve a given problem, using a linear equation, and record the process.
PR04 Students will be expected to explain and illustrate strategies to solve single variable linear inequalities with rational coefficients within a problem-solving context. [C, CN, PS, R, V]
Performance Indicators
PR04.01 Translate a given problem into a single variable linear inequality, using the symbols ≥, >, <, or ≤.
PR04.02 Determine if a given rational number is a possible solution of a given linear inequality.
PR04.03 Generalize and apply a rule for adding or subtracting a positive or negative number to determine the solution of a given inequality.
PR04.04 Generalize and apply a rule for multiplying or dividing by a positive or negative number to determine the solution of a given inequality.
PR04.05 Solve a given linear inequality algebraically, and explain the process orally or in written form.
PR04.06 Compare and explain the process for solving a given linear equation to the process for solving a given linear inequality.
PR04.07 Graph the solution of a given linear inequality on a number line.
PR04.08 Compare and explain the solution of a given linear equation to the solution of a given linear inequality.
PR04.09 Verify the solution of a given linear inequality, using substitution for multiple elements in the solution.
PR04.10 Solve a given problem involving a single variable linear inequality, and graph the solution.
PR03 On s’attend à ce que les élèves modélisent et résolvent des problèmes dans lesquels a, b, c, d, e et f sont des nombres rationnels, à l’aide d’équations linéaires de la forme
ax = b
x/a = c, a not equal to 0
ax + b = c
x/a + b = c, a not equal to 0
ax = b + cx
a(x + b) = c
ax + b = cx + d
a(bx + c) = d(ex + f)
a/x = b, x not equal to 0
[C, CN, PS, V]
PR03.01 Résoudre, à l’aide de représentations concrètes ou imagées, une équation linéaire donnée et prendre en note la marche à suivre sous forme symbolique.
PR03.02 Déterminer, à l’aide de la substitution, si un nombre rationnel donné est la solution pour une équation linéaire donnée.
PR03.03 Résoudre une équation linéaire donnée sous forme symbolique.
PR03.04 Trouver et corriger une erreur dans la solution incorrecte donnée d’une équation linéaire.
PR03.05 Représenter un problème donné à l’aide d’une équation linéaire. PR03.06 Résoudre un problème donné à l’aide d’une équation linéaire et prendre en note la marche à suivre.
PR04 On s’attend à ce que les élèves expliquent et illustrent des stratégies pour résoudre des inéquations linéaires à une seule variable avec des coefficients rationnels dans le cadre de la résolution d’un problème. [C, CN, PS, R, V]
PR04.01 Représenter un problème donné par une inéquation linéaire à une variable en utilisant les symboles ≥, >, < ou ≤.
PR04.02 Déterminer si un nombre rationnel donné est l’une des solutions possibles d’une inéquation linéaire donnée.
PR04.03 Énoncer et appliquer une règle générale pour l’addition ou la soustraction d’un nombre positif ou d’un nombre négatif afin de déterminer la solution d’une inéquation donnée.
PR04.04 Énoncer et appliquer une règle générale pour la multiplication ou la division par un nombre positif ou un nombre négatif afin de déterminer la solution d’une inéquation donnée.
PR04.05 Résoudre une inéquation linéaire donnée algébriquement et expliquer la marche à suivreà l’écrit et à l’oral.
PR04.06 Comparer et expliquer la marche à suivre pour résoudre une équation linéaire donnée à la marche à suivre pour résoudre une inéquation linéaire donnée.
PR04.07 Tracer la solution d’une inéquation linéaire donnée sur une droite numérique.
PR04.08 Comparer la solution d’une équation linéaire donnée à la solution d’une inéquation linéaire donnée et expliquer la solution.
PR04.09 Vérifier la solution d’une inéquation linéaire donnée en substituant à la variable différents éléments de l’ensemblesolution.
PR04.10 Résoudre un problème donné faisant intervenir une inégalité linéaire à une variable et tracer le graphique de la solution.
Additional Resources and Activities for PR03 (solve linear equations):
HRCE Marking Rubric for 9PR03 - This rubric can be used for a variety of purposes such as a resource to create learning goals, a tool for student self assessment and on-going, formative assessment, creating report card comments, summative assessment of achievement, and/or as a support in giving descriptive feedback to students.
Which One Doesn’t Belong? On the graphs page, see Graph #5 or Graph #14, which show a collection of four different linear functions.
Class Warm-up Odd One Out - Four sets of equations are shown on a Google slide. For each set of equations, the value of x is the same in all except one equation. Students try to figure out which equation is the odd one out.
Linear Equations Odd One Out English, French - 8 equations to solve and 9 solutions. Students solve the equations to find out which solution is the "odd one out". A self-checking activity that can be done as a class, in small groups or individually.
Same or Different? Task for Graphs - Show students this image and ask them what is the same between these two graphs and what is different? Same or Different is a routine that provides students opportunities to construct arguments when comparing objects, such as numbers or shapes. More same or different task are available from the Same of Different? website.
Solving Multi-Step Equations Visually - How Many Sour Patch Kids Are In A Bag? a video - Introducing solving linear equations can be challenging when students have a difficult time visualizing the algebra we are using. Start with a visual of candy on a scale, then slowly introduce variables once students get the hang of it! Here, the equation we are looking at is 3x + 6 = 4x + 3.
Would You Rather Math: Reading - Show students this image. Would you rather read 12 pages every night in a book that has 144 pages or read 50 pages three times per week in a book that has 132 pages? Whichever option you choose, justify your reasoning with mathematics.
Treasure Hunt Self-checking worksheet - Review of grade 8 equation solving
Solving Equations Row Game - Student A solves the problems in the left hand column, while Student B solves the problems in the right hand column. As you finish each problem, check your answer with your partner. The answers should be the same! If not, work together to find your mistake.
Matching Equivalent Expressions - A google slides with four sets of equations. For each set, students identify which have the same solution and which have different solutions. The four sets are of increasing level of complexity.
SolveMe Mobiles -SolveMe Mobiles is a free website designed to support and engage students in algebraic reasoning through puzzles. Students determine the value of weights hanging from beams and strings using algebra.
Circuit Training self checking worksheet - Students start by evaluating the first expression. The answer to the first expression leads them to the next question. The final question should complete the circuit and lead them back to the first question.
Tarsia Puzzle Solving Equations - A Tarsia puzzle is a composed of triangles. Each side of the triangle has either and expression or a value. Students cut out all the puzzle pieces so that the side with an expression is adjacent to a side with the corresponding value.
Equations Cross Number Puzzle - Interactive and worksheet
Hidden message activity (French) - A worksheet for French immersion students where they solve a list of equations in order to find the letters to decode a hidden message.
Solving Equations Menu English, French - This is an assessment that can be done virtually. In this set of Google Slides, students select from a menu of options to respond to. Each student answers the questions they have picked and delete any unused slides and pass it in within the Google Classroom.
Additional Resources and Activities for PR04 (solve single variable linear inequalities):
HRCE Marking Rubric for 9PR04 - This rubric can be used for a variety of purposes such as a resource to create learning goals, a tool for student self assessment and on-going, formative assessment, creating report card comments, summative assessment of achievement, and/or as a support in giving descriptive feedback to students.
Inequalities on the Number Line Desmos Activity in English and French - In this activity, students explore linear inequalities and make connections among multiple representations (including algebraic expressions, verbal statements, number line graphs, and solution sets).
Venn Diagram Puzzles for inequalities - Given an inequality for each circle in a Venn Diagram, students find a value for x that would fit in each region. from Mr. Barton Maths
Inequalities Point Collector Desmos Activity - In this activity, students apply (and deepen) their knowledge of one-variable inequalities to "collect" as many points on the number line as they can. The activity focuses on simple and compound inequalities. More advanced inequalities are welcome, but not required.
Inequalities Matching Card Sort - Students match cards with algebraic inequalities to the pictures of their graph on a number line. Cards file to print.
Which One Doesn’t Belong? Inequalities - An WODB image from the How We Teach website.
CEMC Grade 9 Courseware (PR04): Lesson 6: Solving Linear Inequalities This online lesson focuses on solving linear inequalities and solving application problems with and without the linear inequality given.
Unit 6 Cumulative Review
Linear Equations Math Market - Students work in small groups to complete review questions. Student buy the questions from the market and sell back correctly worked solutions for a profit. This activity is self-differentiated as students choose which level of question they'd like to attempt. Student recording sheet.