HRCE Updated Pacing Guide *Updated Sept 2025*
Mathematics Progression: Grades 6 - 9
Math 7 Retrieval Practice Grids A: English, French Grids B: English, French
G02 Students will be expected to identify and plot points in the four quadrants of a Cartesian plane, using integral ordered pairs. [C, CN, V]
Performance Indicators
G02.01 Label the axes of a four quadrant Cartesian plane and identify the origin.
G02.02 Identify the location of a given point in any quadrant of a Cartesian plane using an integral ordered pair.
G02.03 Plot the point corresponding to a given integral ordered pair on a Cartesian plane with units of 1, 2, 5, or 10 on its axes.
G02.04 Draw shapes and designs in a Cartesian plane using given integral ordered pairs.
G02.05 Create shapes and designs, and identify the points used to produce the shapes and designs, in any quadrant of a Cartesian plane.
N06 Students will be expected to demonstrate an understanding of addition and subtraction of integers, concretely, pictorially, and symbolically. [C, CN, PS, R, V]
Performance Indicators
N06.01 Explain, using concrete materials such as integer tiles and diagrams, that the sum of opposite integers is zero.
N06.02 Illustrate, using a number line, the results of adding or subtracting negative and positive integers.
N06.03 Add two given integers, using concrete materials and/or pictorial representations, and record the process symbolically.
N06.04 Subtract two given integers, using concrete materials and/or pictorial representations, and record the process symbolically.
N06.05 Illustrate the relationship between adding integers and subtracting integers.
N06.06 Solve a given problem involving the addition and subtraction of integers.
G02 On s’attend à ce que les élèves situent et tracent des points dans les quatre quadrants d’un plan cartésien, à partir de coordonnées qui sont des paires ordonnées de nombres entiers. [C, L, V]
Indicateurs de rendement
G02.01 Annoter les axes d’un plan cartésien à quatre quadrants et indiquer l’origine.
G02.02 Indiquer l’emplacement d’un point donné dans n’importe lequel des quadrants d’un plan cartésien, à partir d’une paire ordonnée de nombres entiers.
G02.03 Tracer un point donné à partir d’une paire ordonnée de nombres entiers dans un plan cartésien dont les axes ont des intervalles de 1, 2, 5 ou 10 unités.
G02.04 Tracer des motifs ou des figures dans un plan cartésien à partir d’une liste donnée de paires ordonnées de nombres entiers
G02.05 Créer des motifs ou des figures dans n’importe lequel des quadrants d’un plan cartésien et indiquer les points utilisés pour produire les motifs et les figures.
N06 On s’attend à ce que les élèves montrent qu’ils comprennent l’addition et la soustraction de nombres entiers, sous forme concrète, imagée et symbolique. [C, L, RP, R, V]
Indicateurs de rendement
N06.01 Expliquer à l’aide de matériel concret, comme des carreaux algébriques et des diagrammes, que la somme de nombres entiers opposés est égale à zéro.
N06.02 Illustrer les résultats d’additions ou de soustractions de nombres entiers négatifs et de nombres entiers positifs en utilisant une droite numérique.
N06.03 Additionner deux nombres entiers donnés à l’aide de matériel concret ou de représentations imagées et prendre en note la marche à suivre sous forme symbolique.
N06.04 Soustraire deux nombres entiers donnés à l’aide de matériel concret ou de représentations imagées et prendre en note la marche à suivre sous forme symbolique.
N06.05 Illustrer le lien entre l’addition de nombres entiers et la soustraction de nombres entiers.
N06.06 Résoudre un problème donné faisant intervenir l’addition et la soustraction de nombres entiers.
Additional Resources and Activities for G02 (plot points in the four quadrants of a Cartesian plane ):
HRCE Marking Rubric for 7G02 - 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.
Desmos Pumpkin carving using cartesian graphing: English, French
Coordinate Grid Battleship from Illustrative Mathematics - A few simple modifications can turn the game of Battleship into a great way to practice plotting points on a Cartesian plane.
Which One Doesn't Belong Coordinates from Eric Simpson - Ask students which of the coordinate pairs doesn't belong and justify it. Every answer is correct as long as there is a sufficient justification to explain it. Find more like this at http://wodb.ca/ .
Coordinate Pictures from Tumshy - Plot and join points on set of axes to make a variety of pictures. Some are just first quadrant and others include all four quadrants. Coordinate pictures handout and solutions.
Ordered Pairs and Coordinate Plane Target Practice Activity and The (Awesome) Coordinate Plane Activity on Desmos from Nathan Kraft - In these online activities students will encounter a series of challenges, each asking them to graph a point on the bullseye of a target. They will plot points in all four quadrants, first by plotting points using a table and then by using ordered pairs.
Battle Boats Desmos Activity - In this activity, students build coordinate plane proficiency through a guess-the-location-style game in all four quadrants of the Cartesian plane. There is also a French translation of this activity.
Treasure Island from Nrich - This could be used as a class warm-up or to assess prior knowledge. It is an activity to practice using coordinates in the first quadrant to find a list of objects. The objects can then be used to find a hidden treasure. Student handout.
Additional Resources and Activities for N06 (addition and subtraction of integers):
HRCE Marking Rubric for 7N06 - 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.
Activity on making generalizations about adding integers. Students read a claim and decide if it is sometimes true, always true, or never true and back up their claim using their own examples. This could be done as a station activity where kids move around the space and discuss in groups. It could be done as a whole class discussion by projecting the slides and talking about it together. (Google Slides version)
Pixel Art: English, French: A self-checking activity for students to practice adding integers. (Picture reveals an "Every Child Matters" orange shirt) Note that each student must have their own copy of the spreadsheet which can be done by making it an assignment in google classroom and generating a copy for each student.
123 Switch! - Tom describes a card game using integers. Students use their cards to make a true equations. First player to get rid of all their cards wins. Here are the instructions, an addition template and a subtraction template.
Adding Integers Desmos Activity (English and French) - In this activity, students practice adding integers in the context of a card game. The goal of the game is to create two groups of cards, each with the same sum. Whoever uses the most cards wins!
Deeper Learning with Integers - Here is a practice handout to give to students to demonstrate their understanding of selected integer expressions in a variety of ways. The four regions on the sheet are for: a solution, a picture to illustrate the expression, a context question and 5 expressions with the same value.
Adding Integers Open Middle Problem - Divide the given integers (-8, -6, -4, -3, 1, 4, 5, 7, 9) into three groups. Try to make the sums of each of the three groups as close as possible. Next ask students to create their own list of integers and repeat the problem.
Integers Clothesline Game - Build and strengthen conceptual understanding of adding & subtracting integers using an integer clothesline. Teams work to land on a target number first by adding or subtracting integers on a number line.
Circle 0 from NLVM - Solve a puzzle by moving numbers around so that the sum of three positive and negative integers is zero.
Which One Doesn't Belong-Integers - Ask students to select one of the four numbers and justify why they think it is different than all the rest. There are no wrong answers as long as a justification accompanies it. Check out http://wodb.ca/ for lots of additional suggestions.
Integer Bingo - Draw random integers (-4 to 4) and add them together. If the sum is on the student's bingo card, they can cross the number off. Start with random bingo cards for the first round and then let them make their own bingo cards for the second round. Great integer addition practice as well as a bit of probability.
Yohaku Puzzles - Fill in the cells with 9 consecutive integers to get the sums shown in each row/column.
Joins (inspired by problem 54 from Mathematical Challenges for Able Pupils) - Join a string of adjacent numbers on a 4x4 grid filled with integers. Find the longest string with a sum of zero. Here is a link to a google doc handout.
Adding and Subtracting Directed Numbers from The Mathematics Assessment Project - This lesson helps students to add and subtract directed numbers (positive, negative and zero) with understanding. It introduces the charge model for directed numbers and asks students to match diagrams with calculations and produce missing diagrams for the remaining calculations. Additional Powerpoint slides.
Pixel Art: English, French: A self-checking activity for students to practice adding and subtracting larger integers. This activity is designed to be used near the end of the unit when students are moving from concrete to symbolic strategies. Note that each student must have their own copy of the spreadsheet which can be done by making it an assignment in google classroom and generating a copy for each student. Pixel Art How-to guide: A google slide show with step-by-step instructions for making your own pixel art activities.
Choice Board for addition and subtraction of integers: English, French: This choice board could be used for formative or summative assessment. A student self-assessment is also included.
Unit 2 Cumulative Review
Adding Integers Dot Game - The classic game of dots and boxes with a twist. Instead of counting the number of boxes won to determine the winner, each box has an integer value that is summed to determine the winner. You could play student vs. student, group vs. group or class vs. teacher.
Integer War - Both players turn over three cards. Evaluate the expression (black cards positive and red cards negative). They player who has the higher total claims all six cards. An Integer war mat can be printed off for students.