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
Virtual Algebra Tiles - The Mathigon Polypad site has an set of virtual algebra tiles that is very easy to use. There is also a useful set of virtual algebra tiles at Mathsbot.
PR05 Students will be expected to demonstrate an understanding of polynomials (limited to polynomials of degree less than or equal to 2). [C, CN, R, V]
Performance Indicators
PR05.01 Create a concrete model and/or a pictorial representation for a given polynomial expression.
PR05.02 Write the expression for a given model of a polynomial.
PR05.03 Identify the variables, degree, and number of terms and coefficients, including the constant term, of a given simplified polynomial expression.
PR05.04 Describe a situation for a given first-degree polynomial expression.
PR05.05 Match equivalent polynomial expressions given in simplified form
PR06 Students will be expected to model, record, and explain the operations of addition and subtraction of polynomial expressions, concretely, pictorially, and symbolically (limited to polynomials of degree less than or equal to 2). [C, CN, PS, R, V]
Performance Indicators
PR06.01 Model addition of two given polynomial expressions, concretely and/or pictorially, and record the process symbolically.
PR06.02 Model subtraction of two given polynomial expressions, concretely and/or pictorially, and record the process symbolically.
PR06.03 Identify like terms in a given polynomial expression.
PR06.04 Apply a personal strategy for addition or subtraction of two given polynomial expressions, and record the process symbolically.
PR06.05 Identify equivalent polynomial expressions from a given set of polynomial expressions, including pictorial and symbolic representations.
PR06.06 Identify the error(s) in a given simplification of a given polynomial expression.
PR07 Students will be expected to model, record, and explain the operations of multiplication and division of polynomial expressions (limited to polynomials of degree less than or equal to 2) by monomials, concretely, pictorially, and symbolically. [C, CN, R, V]
Performance Indicators
PR07.01 Model multiplication of a given polynomial expression by a given monomial, concretely or pictorially, and record the process symbolically.
PR07.02 Model division of a given polynomial expression by a given monomial, concretely or pictorially, and record the process symbolically.
PR07.03 Apply a personal strategy for multiplication and division of a given polynomial expression by a given monomial.
PR07.04 Provide examples of equivalent polynomial expressions.
PR07.05 Identify the error(s) in a given simplification of a given polynomial expression.
PR05 On s’attend à ce que les élèves montrent qu’ils comprennent les polynômes (en se limitant aux polynômes de degré inférieur ou égal à deux). [C, L, R, V]
PR05.01 Créer un modèle concret ou une représentation imagée pour une expression polynomiale donnée.
PR05.02 Écrire l’expression qui correspond à un modèle donné de polynôme.
PR05.03 Mettre en évidence dans une expression polynomiale donnée sous forme simplifiée, les variables, le degré, le nombre de termes et les coefficients, y compris le terme constant.
PR05.04 Décrire une situation qui correspond à une expression polynomiale donnée du premier degré.
PR05.05 Apparier des expressions polynomiales équivalentes données sous forme simplifiée.
PR06 On s’attend à ce que les élèves modélisent, enregistrent et expliquent les opérations d’addition et de soustraction d’expressions polynomiales, sous forme concrète, imagée et symbolique (en se limitant aux polynômes de degré inférieur ou égal à deux). [C, L, RP, R, V]
PR06.01 Modéliser l’addition de deux expressions polynomiales données sous forme concrète ou imagée et prendre en note la marche à suivre sous forme symbolique.
PR06.02 Modéliser la soustraction de deux expressions polynomiales données sous forme concrète ou imagée et prendre en note la marche à suivre sous forme symbolique.
PR06.03 Mettre en évidence les termes semblables dans une expression polynomiale donnée.
PR06.04 Appliquer sa propre stratégie pour l’addition et la soustraction d’expressions polynomiales données et prendre en note la marche à suivre sous forme symbolique.
PR06.05 Mettre en évidence des expressions polynomiales équivalentes à partir d’un ensemble donné d’expressions polynomiales, notamment sous forme imagée et symbolique.
PR06.06 Trouver une ou plusieurs erreurs dans une expression polynomiale donnée sous forme simplifiée.
PR07 On s’attend à ce que les élèves modélisent, enregistrent et expliquent les opérations de multiplication et de division d’expressions polynomiales, sous forme concrète, imagée et symbolique (en se limitant aux polynômes de degré inférieur ou égal à deux). [C, L, R, V]
PR07.01 Modéliser la multiplication d’une expression polynomiale donnée par un monôme donné sous forme concrète ou imagée et prendre en note la marche à suivre sous forme symbolique.
PR07.02 Modéliser la division d’une expression polynomiale donnée par un monôme donné de façon concrète ou imagée et prendre en note la marche à suivre sous forme symbolique.
PR07.03 Appliquer ses propres stratégies de multiplication et de division d’une expression polynomiale donnée par un monôme donné.
PR07.04 Fournir des exemples d’expressions polynomiales équivalentes.
PR07.05 Trouver une ou plusieurs erreurs dans une expression polynomiale donnée sous forme simplifiée.
Additional Resources and Activities for PR05 (understanding polynomials):
HRCE Marking Rubric for 9PR05 - 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.
Intro lesson plan on polynomials using algebra tiles - This lesson plan has a corresponding slide show. Students are introduced or re-introduced to algebra tiles using the area model to determine their names. Students create their own pictures followed by writing the unsimplified and simplified polynomial expression. Intro lesson on polynomials using algebra tiles slide show: English, French
Which One Doesn't Belong? - A math routine for students to discuss vocabulary and characteristics of polynomial expressions.
Menu Math: Polynomial Expressions - Menu Math activities ask students to create a set of expressions that satisfy a list of constraints. Students are challenged to make expressions that satisfy several different constraints at once.
Interactive Polynomials Activities - This is a Mimio ink file with a few introductory activities for polynomials. Included are a WODB, Venn diagram problem, dragging expressions to the correct label and modeling expressions with algebra tiles.
Describing and Classifying Polynomials Desmos Activity in English and French - An activity for students to practice classifying polynomials by number of terms and by degree.
Additional Resources and Activities for PR06 (Adding and Subtracting Polynomials):
HRCE Marking Rubric for 9PR06 - 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.
Expression Pyramids with 'p' and Expression Pyramids with 'n' - Students add polynomial expressions together in a pyramid. Each level of the pyramid is the sum of the levels below it. Ask students to complete the pyramids given or even create their own to challenge each other. A google slides with all the pyramids.
Combining like terms tower and Adding polynomials tower - Students complete a tower by combining the terms. The expression in each rectangle is the sum of the expressions in the two rectangles below it. Self-checking, if their sum matches the term a the top of the tower, they've completed it correctly. Students could be challenged to create their own. From Mary Bourassa.
Stacking Tiles Desmos activity - Students will add and subtract polynomial tiles beginning with visual models.
Adding and Subtracting Polynomials Desmos activity in English and French - Students will practice adding and subtracting polynomials pictorially and symbolically in this Desmos activity.
Simplifying Expressions puzzle online - Make each row and each column equal the same amount.
Yohaku Puzzle - In a Yohaku puzzle, your task is to fill in the empty cells such that they give the sum shown in each row and column. There are lots of varieties of this puzzle on the Yohaku website.
Additional Resources and Activities for PR07 (Multiplying and Dividing Polynomials):
HRCE Marking Rubric for 9PR07 - 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.
Check out this awesome video from makemathmoments.com by Kyle Pearce and Jon Orr on the progression of division leading to factoring polynomials. In this video Jon starts with concrete models using Mathigon Polypad and demonstrates how to gradually fade use of the concrete model to more abstract, symbolic representations.
Polynomials Clue Game - Multiplying and Dividing Polynomials: Students must figure out the crime before the timer runs out! The question is WHODUNNIT? The students must solve the clues to find the SOLUTION. Students will follow the clues and eliminate possibilities throughout the slideshow. They will record their work on a student sheet which is provided.
Distributive Law - Practice multiplying a binomial by a number and connecting the expression with the visual representation in Algebra tiles. A handout from startingpointsmath.com.
Multiplying Polynomials Row Game in English and French - A row game for multiplying polynomials by a scalar or monomial. A row game is a self-checking activity for a pair of students.
Multiplying and Dividing Polynomials Desmos activity in English and French - Students will practice multiplying and dividing polynomials pictorially and symbolically in this Desmos activity.
Incorrect Simplification - In this activity, students are asked to identify which polynomial simplification is not correct from a number of choices. From a Don Steward.
Polynomial Area Model slides - Additional practice problems using an area model of polynomials. From an Algebra 2 booklet from startingpointsmath.com.
Yohaku Puzzle - In a Yohaku puzzle, your task is to fill in the empty cells such that they give the product shown in each row and column. There are lots of varieties of this puzzle on the Yohaku website.
Unit 5 Cumulative Review
Polynomials Choice Board - There are 9 activities on this 3x3 grid. Students select three of them to demonstrate their understanding of the outcomes from this unit.
Polynomials Tarsia Puzzle - A Tarsia puzzle is a jigsaw puzzle that students have to solve in order to assemble. They match up sides of triangles with equivalent expressions. By matching up triangles, they will construct a shape like a hexagon or larger triangle. This can be done on paper or digitally on a Jamboard (Teacher version, English student, French student).
Bullseye Polynomials in English and French - An easy to differential activity for students to practice adding, subtracting and multiplying polynomials. After they finish the first page, they create their own using polynomials to give themselves or a friend a challenge.