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
N01 Students will be expected to demonstrate an understanding of powers with integral bases (excluding base 0) and whole number exponents by: representing repeated multiplication using powers, using patterns to show that a power with an exponent of zero is equal to one, and solving problems involving powers [C, CN, PS, R]
Performance Indicators
N01.01 Demonstrate the differences between the exponent and the base by building models of a given power, such as 2^3 and 3^2 .
N01.02 Explain, using repeated multiplication, the difference between two given powers in which the exponent and base are interchanged.
N01.03 Express a given power as a repeated multiplication.
N01.04 Express a given repeated multiplication as a power.
N01.05 Explain the role of parentheses in powers by evaluating a given set of powers.
N01.06 Demonstrate, using patterns, that a^0 is equal to 1 for a given value of a (a ≠ 0).
N01.07 Evaluate powers with integral bases (excluding base 0) and whole number exponents.
N02 Students will be expected to demonstrate an understanding of operations on powers with integral bases (excluding base 0) and whole number exponents:
(a^m)(a^n) = a^(m+n)
(a^m) ÷ (a^n) = a^(m-n), m>n
(a^m)^n = a^(mn)
(ab)^m = (a^m)(b^m)
(a/b)^n = (a^n)/(b^n), b ≠ 0
[C, CN, PS, R, T]
Performance Indicators
N02.01 Explain, using examples, the exponent laws of powers with integral bases (excluding base 0) and whole number exponents.
N02.02 Evaluate a given expression by applying the exponent laws.
N02.03 Determine the sum of two given powers and record the process.
N02.04 Determine the difference of two given powers and record the process.
N02.05 Identify the error(s) in a given simplification of an expression involving powers.
N04 Students will be expected to explain and apply the order of operations, including exponents, with and without technology. [PS, T]
Performance Indicators
N04.01 Solve a given problem by applying the order of operations without the use of technology.
N04.02 Solve a given problem by applying the order of operations with the use of technology.
N04.03 Identify the error in applying the order of operations in a given incorrect solution.
N01 On s’attend à ce que les élèves montrent qu’ils comprennent les puissances avec des bases qui sont des nombres entiers (autres que 0) et des exposants qui sont des nombres entiers : en représentant des multiplications répétées à l’aide de puissances; en utilisant des régularités pour montrer qu’une puissance avec un exposant 0 est égale à 1; en résolvant des problèmes faisant intervenir des puissances. [C, L, RP, R]
N01.01 Montrer les différences entre l’exposant et la base en concevant des modèles donnés de puissances comme 23 et 32 .
N01.02 Expliquer, à l’aide de la multiplication répétée, la différence entre deux puissances données dans lesquelles la base et l’exposant sont intervertis.
N01.03 Exprimer une puissance donnée sous forme de multiplication répétée.
N01.04 Exprimer une multiplication répétée donnée sous forme de puissance.
N01.05 Expliquer le rôle des parenthèses dans l’évaluation d’un ensemble donné de puissances.
N01.06 Démontrer, à l’aide des régularités, que a0 est égal à 1, pour une valeur donnée de a sachant que a ≠ 0.
N01.07 Évaluer des puissances données ayant des bases qui sont des nombres entiers (autres que 0) et des exposants qui sont des nombres entiers positifs.
N02 On s’attend à ce que les élèves montrent qu’ils comprennent les opérations sur les puissances avec des bases qui sont des nombres entiers (autres que 0) et des exposants qui sont des nombres entiers :
(a^m)(a^n) = a^(m+n)
(a^m) ÷ (a^n) = a^(m-n), m>n
(a^m)^n = a^(mn)
(ab)^m = (a^m)(b^m)
(a/b)^n = (a^n)/(b^n), b ≠ 0
[C, L, RP, R, T]
N02.01 Expliquer, en utilisant des exemples, les lois des exposants ayant des bases qui sont des nombres entiers (autres que 0) et des exposants qui sont des nombres entiers positifs.
N02.02 Évaluer une expression donnée en appliquant les lois des exposants.
N02.03 Déterminer la somme de deux puissances et prendre en note la marche à suivre.
N02.04 Déterminer la différence entre deux puissances et prendre en note la marche à suivre.
N02.05 Trouver les erreurs dans la simplification d’une expression donnée comportant des puissances.
N04 On s’attend à ce que les élèves expliquent et appliquent la priorité des opérations, y compris pour les exposants, avec et sans la technologie. [RP, T]
N04.01 Résoudre un problème donné à l’aide de la priorité des opérations sans l’aide de la technologie.
N04.02 Résoudre un problème donné à l’aide de la priorité des opérations et de la technologie.
N04.03 Trouver, dans une solution incorrecte donnée, l’erreur faite en appliquant la priorité des opérations.
Assessing Prior Knowledge:
Treasure Hunt Review - A self checking review sheet of foundational mathematics 7 and 8 skills.
Additional Resources and Activities for N01 (powers with integral bases, a^0 = 1):
HRCE Marking Rubric for 9N01 - 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.
Circles Desmos Activity in English and French - In this Desmos activity, students review the concepts of whole number exponents in anticipation of extended study of exponent rules
Open Middle: Maximum Value of an Exponent in English and French - Use the digits 1 to 9, at most one time each, to fill in the boxes to make a result that has the greatest value possible. What would be the answer if the solutions could be a four digit number? What would be the answer if you could use digits more than once?
Would You Rather - Would you rather put $3 in the bank and have it triple each week for four weeks or put $4 in the bank and have it quadruple each week for three weeks?
Practice With Rational Bases - This "Which One Doesn't Belong" warm-up prompts students to compare four exponential expressions. Then they practice with exponents in rational bases. from Illustrative Mathematics
Who Wants to Be a Millionaire video - Which of these square numbers also happens to be the sum of two smaller square numbers? 16, 25, 36 or 49? When knowing some math can win you $15,000.
Math Mistakes activity - Students are given 10 different solved mathematical equations with powers. They are all solved incorrectly. Students identify the mistake and make corrections. Inspired by a post from Andrew Stadel.
Why is 2^0 = 1? - This video shows folding paper, a real life example of why 2^0 = 1. When you fold a sheet of paper, you create two regions. Two folds creates 4 regions and 3 folds creates 8 regions. But what about zero folds? When the sheet of paper has zero folds, there is one region of paper (then entire sheet of paper).
Additional Resources and Activities for N02 and N04 (operations with powers and the order of operations):
HRCE Marking Rubric for 9N02 - 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.
HRCE Marking Rubric for 9N04 - 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.
Open Middle: Properties of Integer Exponents in English and French - Using the digits 0 to 9 at most one time each, fill in the boxes to generate equivalent numerical expressions:
Exponent Experimentation 1 from Illustrative Mathematics - Students decide whether each equation is true and explain how they know.
Which One Doesn't Belong: Exponents - The WODB number routine encourages mathematical thinking, reasoning and promotes discourse in the classroom that includes all students. This Google slides file includes a selection of WODB images focused on powers and exponents. Additional WODB images can be found at http://wodb.ca/.
Exponent Rules Row Game - A row game is a self checking activity. A worksheet of problems is organized in two columns. Column A and column B. The pair of problems in each row has to have the same answer. If students don't get the same answer, they work together to find the error(s). Ilona Vashchyshyn created this row game for Exponent Rules.
Exponents and Order of Operations Open Middle Problem - Find 3 positive integers that add up to 10. Place each number into one of the blanks to find the largest possible result. This Open Middle Problem for Exponents and Order of Operations is also available in French.
24 Math Game - This game is excellent practice for order of operations. The original version of 24 is played with an ordinary deck of playing cards with all the face cards removed. The aces are taken to have the value 1 and the basic game proceeds by dealing out 4 cards. The first player that can achieve the number 24 exactly using only allowed operations (such as addition, subtraction, multiplication, division, and parentheses) wins the hand. You can also allow exponentiation, roots, logarithms and/or additional operations. There is also a commercial version of the game. You could play this game as a whole class as well.
Pixel Art (Order of Operations with Powers) : English, French: This self-checking activity reveals an image as students enter the correct answers in the spreadsheet.
Pixel Art How-to guide: A google slide show with step-by-step instructions for making your own pixel art activities.
Unit 1 Cumulative Review
Exponent Laws Quizizz formative assessment - 11 questions for students to check their understanding of the exponent laws and the order of operations.
Powers and Exponent Laws Scavenger Hunt - A scavenger hunt with three different levels of challenge to select from.
Powers and Exponent Laws Math Menu - This Google slides activity is meant to be done online. Students are given a number of different questions to choose from to solve for a cumulative review of powers and exponent laws.