Mathematics 10 Pacing Guide - *Updated June 2024* This pacing guide replaces the previous yearly plan. It has been updated to reflect removed outcomes and provide flexibility for responsive instruction.
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.
AN01 Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least common multiple, square root, and cube root. [CN, ME, R]
AN01.01 Determine the prime factors of a whole number.
AN01.02 Explain why the numbers 0 and 1 have no prime factors.
AN01.03 Determine, using a variety of strategies, the greatest common factor or least common multiple of a set of whole numbers, and explain the process.
AN01.04 Determine, concretely, whether a given whole number is a perfect square, a perfect cube, or neither.
AN01.05 Determine, using a variety of strategies, the square root of a perfect square, and explain the process.
AN01.06 Determine, using a variety of strategies, the cube root of a perfect cube, and explain the process.
AN01.07 Solve problems that involve prime factors, greatest common factors, least common multiples, square roots, or cube roots.
AN04 Students will be expected to demonstrate an understanding of the multiplication of polynomial expressions (limited to monomials, binomials, and trinomials), concretely, pictorially, and symbolically. [CN, R, V]
AN04.01 Model the multiplication of two given binomials, concretely or pictorially, and record the process symbolically.
AN04.02 Relate the multiplication of two binomial expressions to an area model.
AN04.03 Explain, using examples, the relationship between the multiplication of binomials and the multiplication of two-digit numbers.
AN04.04 Verify a polynomial product by substituting numbers for the variables.
AN04.05 Multiply two polynomials symbolically, and combine like terms in the product.
AN04.06 Generalize and explain a strategy for multiplication of polynomials.
AN04.07 Identify and explain errors in a solution for a polynomial multiplication.
AN05 Students will be expected to demonstrate an understanding of common factors and trinomial factoring, concretely, pictorially, and symbolically. [C, CN, R, V]
AN05.01 Determine the common factors in the terms of a polynomial, and express the polynomial in factored form.
AN05.02 Model the factoring of a trinomial, concretely or pictorially, and record the process symbolically.
AN05.03 Factor a polynomial that is a difference of squares, and explain why it is a special case of trinomial factoring where b = 0.
AN05.04 Identify and explain errors in a polynomial factorization.
AN05.05 Factor a polynomial, and verify by multiplying the factors.
AN05.06 Explain, using examples, the relationship between multiplication and factoring of polynomials.
AN05.07 Generalize and explain strategies used to factor a trinomial.
AN05.08 Express a polynomial as a product of its factors.
AN01 On s’attend à ce que les élèves montrent qu’ils ont compris les facteurs de nombres entiers positifs en déterminant les facteurs premiers, le plus grand diviseur (facteur) commun, le plus petit commun multiple, la racine carrée et la racine cubique. [C, CE, R]
AN01.01 Déterminer les facteurs premiers d’un nombre entier positif.
AN01.02 Expliquer pourquoi les nombres 0 et 1 n’ont pas de facteurs premiers.
AN01.03 Déterminer, en ayant recours à diverses stratégies, le plus grand diviseur (facteur) commun ou le plus petit commun multiple d’un ensemble de nombres entiers positifs et expliquer le processus.
AN01.04 Déterminer concrètement si un nombre entier positif donné est un carré parfait, un cube parfait ou ni l’un ni l’autre.
AN01.05 Déterminer, en ayant recours à diverses stratégies, la racine carrée d’un carré parfait et expliquer le processus.
AN01.06 Déterminer, en ayant recours à diverses stratégies, la racine cubique d’un cube parfait et expliquer le processus.
AN01.07 Résoudre des problèmes comportant des facteurs premiers, le plus grand diviseur commun, le plus petit commun multiple, des racines carrées ou des racines cubiques.
AN04 On s’attend à ce que les élèves montrent qu’ils ont compris la multiplication d’expressions polynomiales (limitées à des monômes, des binômes et des trinômes) de façon concrète, imagée et symbolique. [L, R, V]
AN04.01 Représenter, de façon concrète ou imagée, la multiplication de deux binômes et noter le processus symboliquement.
AN04.02 Établir le rapport entre la multiplication de deux binômes et un modèle d’aire.
AN04.03 Expliquer, à l’aide d’exemples, la relation entre la multiplication de binômes et la multiplication de nombres à deux chiffres.
AN04.04 Vérifier un produit de polynômes en remplaçant les variables par des nombres.
AN04.05 Multiplier deux polynômes symboliquement et regrouper les termes semblables du produit.
AN04.06 Généraliser et expliquer une stratégie de multiplication des polynômes.
AN04.07 Repérer et expliquer les erreurs survenues dans la multiplication de polynômes.
AN05 On s’attend à ce que les élèves montrent qu’ils ont compris les facteurs communs et la décomposition en facteurs de trinômes de façon concrète, imagée et symbolique. [C, L, R, V]
AN05.01 Déterminer les facteurs communs des termes d’un polynôme et exprimer le polynôme sous la forme d’un produit de facteurs.
AN05.02 Représenter, de façon concrète ou imagée, la décomposition en facteurs d’un trinôme et noter le processus symboliquement.
AN05.03 Décomposer en facteurs un polynôme représentant une différence de deux carrés et expliquer pourquoi il s’agit d’un cas particulier de décomposition en facteurs de trinômes où b = 0.
AN05.04 Repérer et expliquer les erreurs survenues dans la décomposition en facteurs d’un polynôme.
AN05.05 Décomposer un polynôme en facteurs et vérifier le résultat en multipliant les facteurs.
AN05.06 Expliquer, à l’aide d’exemples, la relation entre la multiplication et la décomposition en facteurs de polynômes.
AN05.07 Généraliser et expliquer des stratégies de décomposition d’un trinôme en facteurs.
AN05.08 Exprimer un polynôme sous la forme du produit de ses facteurs.
AN01 (prime factors, GCF, LCM, square root, cube root ): This outcome has been removed from Mathematics 10 Curriculum
Additional Resources and Activities for AN04 (multiplication of polynomials):
Polynomial Expressions Menu Task - A Math Menu is a collection of constraints that appear as an unordered list generally about 6-10 constraints long. Each menu prescribes a type of mathematical object that needs to be designed to satisfy these constraints. This task can be used to access students prior knowledge with polynomials.
Same and Different - Area Model - Ask students to compare an image of area model with whole numbers with an image of area model with polynomials. What is alike between the two models? What is different?
Desmos Activity: Multiplying Polynomials- In this activity students will relate the multiplication of two binomial expressions to an area model and then practice multiplying binomial expressions. They will also see the relationship between the multiplication of binomials and the multiplication of two-digit numbers.
Desmos Activity: Multiplying Polynomials - Intro - In this activity students will explore the use of algebra tiles to represent multiplication of polynomials.
From Dr. Austin Maths:
Multiplying Binomials Open Middle Problem - Fill in the boxes with any numbers that make the equation true. From Open Middle.
Writing Polynomial Expressions - Students are asked to create a polynomial expression to describe the area of a polygon given its dimensions. This activity was shared by Miss Konstantine on her blog.
Additional Resources and Activities for AN05 (factoring polynomials):
Desmos Activity: Factoring Trinomials (leading co-efficient other than 1) - Students are guided through this self-checking activity as they explore different polynomial expressions with degree 2, identify factors of coefficients and constants, consider patterns, and make connections between expanded and factored forms of polynomials with degree 2.
Desmos Activity: Factoring Trinomials (leading co-efficient equal to 1) - Students are guided through this self-checking activity as they explore different polynomial expressions with degree 2, identify factors of coefficients and constants, consider patterns, and make connections between expanded and factored forms of polynomials with degree 2.
Factoring Trinomials Math Circuit Worksheet - This worksheet works much like an "I have, who has?" game. Ten problems and ten solutions. Students match up problems with solutions to complete a "circuit" of questions.
Quadratic Area Puzzles - *Updated March 2025* Students need to factor quadratics in order to find the length and width of rectangles to solve each puzzle. (These four area puzzles are inspired by Naoki Inaba‘s Area Maze puzzles, and were shared on TES).
Desmos Activity: Factoring Trinomials - Students are assigned random factoring problems that include an area diagram. The diagram changes based on student answers which reinforces the connection between pictorial and symbolic representations, and provides scaffolding to those that need it.
Factoring Review Practice Grid - A review worksheet with four different levels of questions from Dr. Austin Maths on factoring trinomials. Review Grid Answers.
Multiplying and Factoring Polynomials Spiders - A collection of Google slides with a mixture of practice problems for multiplying and factoring quadratic polynomials.
Row Game: *Updated March 2025* Factoring by Decomposition - Students are in pairs, and factor separate problems, one factor is in common. Students multiply the remaining factors to check their work.
Finding Factors - In a multiplication grid, the headings and the answers have been hidden. Each of the headings is an expression of the form x ± a where a is an integer between 0 and 5, and answers are in the for x^2 + bx + c. By revealing some of the answers, can you work out what each heading must be? From NRICH
Desmos Activity: Open Middle - Factors of Polynomials - Students work together using digits 1 - 9 once to create 3 different polynomials in the form ax^2 + bx + c, then write the polynomials as a product of it's factors.
Factoring a Difference of Squares:
A hands-on version of this activity that demonstrates a square with side length b can be removed from a square with side length a, and the remaining pieces arranged to form a rectangle with dimensions (a + b) and (a - b).
An interactive GeoGebra applet that shows pictorially that a^2 - b^2 = (a+b)(a-b).
Factoring Trinomials Tarsia Puzzle - Have students cut out the triangular puzzle pieces. Put sides together that have corresponding factored and expanded expressions. A self-checking activity that when completed will form a large triangle. Here is the Tarsia file if you'd like to modify or create additional versions of this puzzle at different levels of challenge. Tarsia files can be modified with the free Tarsia Formulator program.
Factoring Trinomials Question Stack - Students are given a double-sided deck of ten cards. One side of the card features a question. The other side features the answer to a DIFFERENT question Students begin the activity by turning over all of the cards to reveal ALL of the answers. This is the students' answer bank. Then, students flip over one card of their choosing. This will be their first problem to solve. When students find the solution, it should be in the answer bank if they have done everything correctly. They pick up the solution card and flip it over to reveal the next question. Check out how Sarah Carter used this activity.
Old Poly Factoring Game - Practice factoring with a polynomial version of the classic "Old Maid" card game. Old Poly Cards pdf file.
Yohaku Algebraic Puzzles - Factoring polynomial expressions using a puzzle. Additional puzzles can be found at https://www.yohaku.ca/algebraic-puzzles.html
Factoring Review "Aim for 16" - A review worksheet with four different levels of factoring questions (1 pt, 2 pt, 3pt an 4 pt). Students do select questions of different levels to make a total of 16 to demonstrate their understanding (i.e. A student might do four 2pt questions and two 4pt questions to make a total of 16).
Desmos Activity: Factoring Breakout Room (Eng., Fre.) - Students complete six different factoring screens. After successfully completing each screen, students receive a part of the lock combination in order to open the safe on the final screen.
Unit 5 Cumulative Review