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
N03 Students will be expected to demonstrate an understanding of rational numbers by comparing and ordering rational numbers and solving problems that involve arithmetic operations on rational numbers. [C, CN, PS, R, T, V]
Performance Indicators
N03.01 Order a given set of rational numbers in fraction and decimal form by placing them on a number line.
N03.02 Identify a rational number that is between two given rational numbers.
N03.03 Solve a given problem involving operations on rational numbers in fraction or decimal form.
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.
N03 On s’attend à ce que les élèves montrent qu’ils comprennent les nombres rationnels en comparant et ordonnant des nombres rationnels et en résolvant des problèmes faisant intervenir des opérations arithmétiques sur des nombres rationnels. [C, L, RP, R, T, V]
N03.01 Ordonner un ensemble donné de nombres rationnels, sous forme de fractions et de nombres décimaux, en les plaçant sur une droite numérique.
N03.02 Trouver un nombre rationnel situé entre deux nombres rationnels donnés.
N03.03 Résoudre un problème donné comportant des opérations sur les nombres rationnels, sous forme de fractions et de nombres décimaux.
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.
Additional Resources and Activities for N03 (comparing and ordering rational numbers):
HRCE Marking Rubric for 9N03 - 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.
Adding Fractions Math Menu - In this activity, students are given 8 constraints to try to match when creating addition of fractions questions. Their job is to try to create enough questions to satisfy all 8 constraints collectively. You can also try this in a Desmos Adding Fractions Menu Math Activity.
Dividing Decimals Open Middle problem - Make the smallest (or largest) sum by filling in the boxes using the whole numbers 1-9 no more than one time each.
Placing Fractions on a Number Line - An Open Middle Problem to get students to think about comparing rational numbers. The problem is, "Using the whole numbers 0-9 (one time each) as numerators and denominators, create 5 fractions and correctly place them all on a number line."
Additional Resources and Activities for N04 (apply the order of operations):
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.
What is 1 Anyway? - A collection of short rational expressions. Students decide which are equal to 1 and which are not. A great activity to identify algebraic misconceptions. From Amie Coley.
Order of Operations Open Middle Problem - Directions: Make the largest (or smallest) expression by using the whole numbers 0-9 in the boxes below. You can change around the spaces and brackets to include fractions or other numbers.
24 Game - 24 can be played with an ordinary deck of playing cards with all the face cards removed. The aces are taken to have the value 1. Deal out 4 cards. Try to create a mathematical expression using the numbers on those 4 cards that is equal to 24. Use addition, subtraction, multiplication, division or parentheses.
Using Operations and Parentheses - This task asks what numbers you can make with 1, 2, 3, and 4 using the operations of addition, subtraction, and multiplication. Can you find two different ways to make 9? How about 7 or 11? Can you make 26? After this, you could ask what numbers you can make with 1, 1/2, 1/3, and 1/4. What is the greatest number you can make and what is the smallest number you can make. from Illustrative Mathematics
(Min + Max)imize Number Sense Dice Game - Review of order of operations.
Pixel Art (Rational Numbers): 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.
Desmos: English, French: An interactive self-checking activity to help students practice using the order of operations with rational numbers.
Unit 2 Cumulative Review
Rational Numbers Math Market: English, French - 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.
Rational Numbers 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 rational numbers.