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.
AN02 Students will be expected to demonstrate an understanding of irrational numbers by representing, identifying, simplifying, and ordering irrational numbers. [CN, ME, R, V]
AN02.01 Sort a set of numbers into rational and irrational numbers.
AN02.02 Determine an approximate value of a given irrational number.
AN02.03 Approximate the locations of irrational numbers on a number line, using a variety of strategies, and explain the reasoning.
AN02.04 Order a set of irrational numbers on a number line.
AN02.05 Express a radical as a mixed radical in simplest form (limited to numerical radicands).
AN02.06 Express a mixed radical as an entire radical (limited to numerical radicands).
AN02.07 Explain, using examples, the meaning of the index of a radical.
AN02.08 Represent, using a graphic organizer, the relationship among the subsets of the real numbers (natural, whole, integer, rational, irrational).
AN03 Students will be expected to demonstrate an understanding of powers with integral and rational exponents. [C, CN, PS, R]
AN03.01 Explain, using patterns, why a^(–n) = 1/(a^n), a ≠ 0 .
AN03.02 Explain, using patterns, why a^(1/n) = nth root (a), n > 0.
AN03.03 Apply the following exponent laws to expressions with rational and variable bases and integral and rational exponents, and explain the reasoning.
(a^m)(a^n ) = a^(m + n)
a^m ÷ a^n = a^(m-n), a ≠ 0
(a^m)^n = a^(mn)
(ab)^m = a^m*b^m
(a/b)^n = a^n/b^n , b ≠ 0
AN03.04 Express powers with rational exponents as radicals and vice versa, when m and n are natural numbers, and x is a rational number.
x^(m/n) = (x^(1/n)) ^m = (nth root (x))^m and x^(m/n) = (x^m) ^(1/n) = nth root (x^m)
AN03.05 Solve a problem that involves exponent laws or radicals.
AN03.06 Identify and correct errors in a simplification of an expression that involves powers.
AN02 On s’attend à ce que les élèves montrent qu’ils ont compris les nombres irrationnels en représentant, en identifiant et en simplifiant des nombres irrationnels, et en mettant en ordre des tels nombres. [L, CE, R, V]
AN02.01 Trier un ensemble de nombres en nombres rationnels et irrationnels.
AN02.02 Déterminer une valeur approximative d’un nombre irrationnel donné.
AN02.03 Déterminer, à l’aide de diverses stratégies, l’emplacement approximatif de nombres irrationnels sur une droite numérique et expliquer le raisonnement suivi.
AN02.04 Mettre en ordre, sur une droite numérique, un ensemble de nombres irrationnels.
AN02.05 Exprimer, sous forme simplifiée, un radical donné sous forme composée (mixte) (limité aux radicandes numériques).
AN02.06 Exprimer, sous forme entière, un radical donné sous forme composée (mixte) (limité aux radicandes numériques).
AN02.07 Expliquer, à l’aide d’exemples, la signification de l’indice d’un radical.
AN02.08 Représenter, à l’aide d’un organisateur graphique, la relation parmi les sous-ensembles des nombres réels (entiers naturels, nombres positifs, entiers, nombres rationnels, nombres irrationnels).
AN03 On s’attend à ce que les élèves montrent qu’ils ont compris les puissances à exposants entiers et rationnels. [C, L, RP, R]
AN03.01 Expliquer, à l’aide de régularités, pourquoi a^(–n) = 1/(a^n), a ≠ 0 .
AN03.02 Expliquer, à l’aide de régularités, pourquoi a^(1/n) = nth root (a), n > 0.
AN03.03 Appliquer les lois des exposants suivants à des expressions ayant des bases rationnelles et variables, des exposants entiers et rationnels, et expliquer le raisonnement.
(a^m)(a^n ) = a^(m + n)
a^m ÷ a^n = a^(m-n), a ≠ 0
(a^m)^n = a^(mn)
(ab)^m = a^m*b^m
(a/b)^n = a^n/b^n , b ≠ 0
AN03.04 Exprimer des puissances ayant des exposants rationnels sous la forme d’un radical et vice versa, quand m et n sont des entiers naturels et x est un nombre rationnel.
x^(m/n) = (x^(1/n)) ^m = (nth root (x))^m and x^(m/n) = (x^m) ^(1/n) = nth root (x^m)
AN03.05 Résoudre un problème faisant appel aux lois des exposants ou des radicaux.
AN03.06 Repérer et corriger les erreurs survenues dans la simplification d’une expression comportant des puissances.
Additional Resources and Activities for AN02 (simplify and order irrational numbers):
Desmos Activity: Polygraph: Rational and Irrational - In this activity, students will ask questions of a partner to discover which card has been chosen.
Desmos Activity: Introduction to Rational Numbers - Students explore representing, identifying, simplifying, and ordering irrational numbers.
Desmos Activity: Simplifying Radicals - Students explore writing entire radicals as mixed radicals.
Desmos Activity: Simplifying Radicals - Students will explore equivalent radical expressions through area and perimeter of squares and rectangles.
Multiplication Madness - A multiplication table puzzle with irrational numbers. From Peter Drysdale.
Multiplication Squares- Complete each multiplication square by filling in the missing number. From MathsPad.
Odd One Out - Pair up the irrational number to find which number has no partner. From MathsPad.
Find the Imposter - A warm-up inspired by the game Among Us. Eight equations are shown. Seven are correct and one is incorrect. Students work to find the "imposter" equation. When finished, you might ask students to create their own "find the imposter" set of equations.
Desmos Activity: Simplify Square Roots Pixel Art - Students will write square roots in simplest form. If the answer is correct, a color will appear in the pixel art.
Irrational Number Spiders - Math "spiders" are a nice math routine to project on the LCD or to print off as a worksheet. From Andy Lutwyche
Simplifying Radicals Tarsia Puzzle - Students cut out the puzzles pieces and then try to assemble them into a large triangle shape. The radical expression on each side of a puzzle piece needs to be placed adjacent to a side with the simplified expression. Solution
Simplifying Radicals Puzzle - *Updated June 2025*: Students cut out the pieces, worked out the problem on each edge in their notebook, and assembled the pieces to make a 4 x 4 square (from Sarah Carter's Blog M+A+T+H = Love)
Additional Resources and Activities for AN03 (powers with integral and rational exponents):
Desmos Activity: Fractional Exponents - Students investigate the nature of fraction exponents by exploring patterns.
Desmos Activity: Zero and Negative Exponents - Students explore patterns with exponents to discover the properties of zero and negative exponents.
Desmos Activity: Zero and Negative Exponent Patterns - Students investigate the nature of negative exponents by exploring patterns.
Exponent Puzzles - A series of 3 sets of problems of increasing complexity for exponential equations. They are all set to print and put into dry erase sleeves for students to work with. From Amy Gruen.
Open Middle Problem - Fill in the boxes with whole numbers 1 through 6, using each number at most once, so that the value of the expression is as large (or as small) as possible. Not challenged yet? Try to find the expression closest to the value of 1.
Open Middle Problem - Using integers between 0 and 9 (whole numbers), fill the blanks to make each box equal to 1. Includes fractional exponents. More detail from John Rowe.
Exponents Spoons Game cards and instructions - This Google Slides file contains a special deck of cards with exponential expressions on them (you can edit this file to make the cards more/less difficult). Students use these cards to play a game of spoons. The first student to collect a set of 4 cards that have the same value grabs a spoon. Additional background from Tina Palmer.
Unit 6 Cumulative Review
Laws of Exponents Math Passport activity - A series of four stations where students work in individually, in pairs or small groups to complete activities at stations. After successfully completing a station, students will get their teacher to "stamp" their passport and then move to the next station.
Roots and Powers Scavenger Hunt review activity - This scavenger hunt contains 14 roots and powers questions. The solution to each question leads students to the next question in the loop. Once students have completed the loop of 12 questions, they are finished.
Desmos Activity: Roots and Powers Review - (English, French) A cumulative review of rational vs irrational numbers, simplifying radicals, and using exponent laws.
Fraction Towers: *Added Jan2025* A tower is built from blocks with exponential expressions. Students take turns, or work in teams, selecting a block then simplifying the exponential expression on that block. If you get a correct answer, you place the block on top of the tower and your turn is over. If you get an incorrect answer, you take another block and try again. The game is over when the tower topples.