HRCE Updated Pacing Guide *Updated Sept 2025*
Mathematics Progression: Grades 6 - 9
Math 7 Retrieval Practice Grids A: English, French Grids B: English, French
N07 Students will be expected to compare, order, and position positive fractions, positive decimals (to thousandths), and whole numbers by using benchmarks, place value, and equivalent fractions and/or decimals. [CN, R, V]
N07.01 Position proper fractions with like and unlike denominators from a given set on a number line, and explain strategies used to determine order.
N07.02 Position a given set of positive fractions, including mixed numbers and improper fractions, on a number line; and explain strategies used to determine order.
N07.03 Position a given set of positive decimals on a number line and explain strategies used to determine order.
N07.04 Compare and order the numbers of a given set that includes positive fractions, positive decimals, and/or whole numbers in ascending or descending order and verify the result using a variety of strategies.
N07.05 Identify a number that would be between two given numbers in an ordered sequence or on a number line.
N07.06 Identify incorrectly placed numbers in an ordered sequence or on a number line.
N07.07 Position the numbers of a given set by placing them on a number line that contains benchmarks, such as 0 and 1 or 0 and 5.
N07.08 Position a given set that includes positive fractions, positive decimals, and/or whole numbers on a number line and explain strategies used to determine order.
N04 Students will be expected to demonstrate an understanding of the relationship between positive terminating decimals and positive fractions and between positive repeating decimals (with one or two repeating digits) and positive fractions. [C, CN, R, T]
N04.01 Predict the decimal representation of a given fraction using patterns.
N04.02 Match a given set of fractions to their decimal representations.
N04.03 Sort a given set of fractions as repeating or terminating decimals.
N04.04 Express a given fraction as a terminating or repeating decimal.
N04.05 Express a given repeating decimal as a fraction.
N04.06 Express a given terminating decimal as a fraction.
N04.07 Provide an example where the decimal representation of a fraction is an approximation of its exact value.
N02 Students will be expected to demonstrate an understanding of the addition, subtraction, multiplication and division of decimals to solve problems (for more than one-digit divisors or more than two-digit multipliers, the use of technology is expected). [ME, PS, T]
N02.01 Use estimation to determine the appropriate place value when calculating the sum or difference.
N02.02 Use estimation to determine the appropriate place value when calculating the product.
N02.03 Use estimation to determine the appropriate place value when calculating the quotient.
N02.04 Represent concretely, pictorially, and symbolically the multiplication and division of decimal numbers.
N02.05 Create and solve a given problem involving the addition of two or more decimal numbers.
N02.06 Create and solve a given problem involving the subtraction of decimal numbers.
N02.07 Create and solve a given problem involving the multiplication of decimal numbers.
N02.08 Create and solve a given problem involving the division of decimal numbers.
N03 Students will be expected to solve problems involving percents from 1% to 100% (limited to whole numbers). [ME, C, CN, PS, R, T]
N03.01 Express a given percent as a decimal or fraction.
N03.02 Use mental mathematics to solve percent problems, when appropriate.
N03.03 Use estimation to determine an approximate answer or the reasonableness of an answer.
N03.04 Solve a given problem that involves finding a percent.
N03.05 Determine the answer to a given percent problem where the answer requires rounding, and explain why an approximate answer is needed (e.g., total cost including taxes).
RAS N07 : On s’attend à ce que les élèves comparent, ordonnent et placent des fractions positives, des nombres décimaux positifs (jusqu’au millième) et des nombres entiers à l’aide de points de repère, de la valeur de position et des fractions équivalentes ou nombres décimaux équivalents. [L, R, V]
N07.01 Placer un ensemble donné de fractions propres avec un dénominateur commun et avec des dénominateurs différents sur une droite numérique et expliquer les stratégies utilisées pour déterminer leur ordre.
N07.02 Placer un ensemble donné de fractions positives incluant des nombres fractionnaires et des fractions impropres sur une droite numérique et expliquer les stratégies utilisées pour déterminer leur ordre.
N07.03 Placer un ensemble donné de nombres décimaux positifs sur une droite numérique et expliquer les stratégies utilisées pour déterminer leur ordre.
N07.04 Comparer et ordonner les nombres d’un ensemble donné comprenant des fractions positives, des nombres décimaux positifs ou des nombres entiers par ordre croissant ou décroissant et vérifier le résultat à l’aide de diverses stratégies.
N07.05 Trouver un nombre situé entre deux nombres donnés dans une suite ordonnée ou sur une droite numérique.
N07.06 Trouver les nombres positifs qui ne sont pas bien placés dans une suite ordonnée ou sur une droite numérique.
N07.07 Ordonner les nombres d’un ensemble donné en les plaçant sur une droite numérique comprenant des points de repère tels que 0 et 1 ou 0 et 5.
N07.08 Placer un ensemble donné comprenant des fractions positives, des nombres décimaux positifs ou des nombres entiers sur une droite numérique et expliquer la stratégie utilisée pour les ordonner.
RAS N04 : On s’attend à ce que les élèves montrent qu’ils comprennent la relation entre les nombres décimaux périodiques positifs et les fractions positives, ainsi qu’entre les nombres décimaux finis positifs (avec un ou deux chiffres qui se répètent) et les fractions positives. [C, L, R, T]
N04.01 Prédire le nombre décimal équivalent à une fraction donnée en ayant recours aux régularités.
N04.02 Apparier les fractions d’un ensemble à leur représentation décimale.
N04.03 Trier les fractions d’un ensemble selon qu’elles sont équivalentes à des nombres décimaux périodiques ou à des nombres décimaux finis.
N04.04 Exprimer une fraction donnée sous la forme d’un nombre décimal fini ou périodique.
N04.05 Exprimer un nombre décimal périodique donné sous la forme d’une fraction.
N04.06 Exprimer un nombre décimal fini donné sous la forme d’une fraction.
N04.07 Fournir un exemple de nombre décimal qui est une représentation approximative de la valeur exacte d’une fraction donnée.
RAS N02 : On s’attend à ce que les élèves montrent qu’ils comprennent l’addition, la soustraction, la multiplication et la division de nombres décimaux et leur application pour résoudre des problèmes. (Pour les diviseurs à plus d’un chiffre et les multiplicateurs à plus de deux chiffres, on s’attend à ce que les élèves utilisent les appareils technologiques.) [CM, RP, T]
N02.01 Se servir d’estimations pour déterminer la valeur de position appropriée quand on calcule la somme ou la différence.
N02.02 Se servir d’estimations pour déterminer la valeur de position appropriée quand on calcule le produit.
N02.03 Se servir d’estimations pour déterminer la valeur de position appropriée quand on calcule le quotient.
N02.04 Représenter sous forme concrète, imagée et symbolique la multiplication et la division de nombres décimaux.
N02.05 Créer et résoudre un problème donné qui comprend l’addition d’au moins deux nombres décimaux.
N02.06 Créer et résoudre un problème donné qui comprend la soustraction de nombres décimaux.
N02.07 Créer et résoudre un problème donné qui comprend la multiplication de nombres décimaux.
N02.08 Créer et résoudre un problème donné qui comprend la division de nombres décimaux.
N02.09 Résoudre un problème donné qui comprend la multiplication par des multiplicateurs à deux chiffres ou la division par des diviseurs à un chiffre (nombres entiers ou décimaux) de nombres décimaux sans l’aide de la technologie.
N02.10 Résoudre un problème donné qui comprend la multiplication par des multiplicateurs à plus de deux chiffres ou la division par des diviseurs à plus qu’un chiffre (nombres entiers ou décimaux) de nombres décimaux sans l’aide de la technologie.
N02.11 Vérifier la vraisemblance de solutions à l’aide d’estimations.
N02.12 Résoudre un problème donné comportant des opérations sur des nombres décimaux, en se limitant aux millièmes et en tenant compte de la priorité des opérations.
RAS N03 : On s’attend à ce que les élèves résolvent des problèmes faisant intervenir des pourcentages de 1 à 100 p. 100 (en se limitant aux nombres entiers). [CM, C, L, RP, R, T]
N03.01 Exprimer un pourcentage donné sous forme décimale ou fractionnaire.
N03.02 Utiliser le calcul mental pour résoudre des problèmes faisant intervenir des pourcentages, quand cela est approprié.
N03.03 Utiliser l’estimation pour déterminer approximativement la réponse ou déterminer la vraisemblance de la réponse.
N03.04 Résoudre un problème donné où il faut déterminer un pourcentage.
N03.05 Déterminer la solution à un problème donné comportant des pourcentages, quand la solution exige un arrondissement, et expliquer pourquoi il est nécessaire de donner une réponse approximative (p. ex. le cout total d’un objet, taxes incluses).
Getting Ready for Unit 3:
Introduction to Fractions base concepts and vocabulary: English, French: Slide show with pictures and vocabulary touching on base concepts for fractions.
Anchor Chart for Place Value: English, French: An anchor chart for student/teacher use to review place value and vocabulary associated with place value.
Base 10 blocks Placemat for Place Value: English, French: A template that is designed to be blown up on large paper and used with base 10 blocks. Note the legend for students to indicate which block represents 1 whole.
Representing and Naming decimal numbers: English, French : A review of how to properly say decimal numbers and represent them using base 10 blocks. Note that students are asked to use different blocs to represent 1 whole. This is essential to students' conceptual understanding of decimals. Throughout the unit it should be reinforced that decimal and fraction names for numbers are the same. This is an important strategy for converting decimals to fractions with denominators of 10, 100, 1000.
Fractions Equality Lab and Game from PhET - Students explore equivalent fractions in using both pictorial and numerical representations.
Additional Resources and Activities for N07 (compare and order positive fractions, decimals, and whole numbers):
HRCE Marking Rubric for 7N07 - 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.
CEMC Video (Teacher Resource N07) Comparing Fractions , Comparing decimals : Videos from the Centre for Education in Mathematics and Computing from the University of Waterloo include a mini-lesson on the target concept as well as a few self-checking questions (review questions) and some sample practice questions.
Comparing Fractions “I can” statements: The Big ideas: English: This graphic organizer could be used for teacher anecdotal observational notes or student self-reflection on the different strategies students are expected to use when comparing fractions. Note that when students have flexibility with a number of strategies, finding a common denominator becomes a strategy that is only used when absolutely needed to compare two fractions that are very close in size.
Fraction Strips Explore intro activity to fractions and benchmarks: English, French: This activity is designed to be an exploration activity in small groups. It is an active way to review important base fraction concepts in a 'new' way as the focus on representing fractions on a number line is often less familiar for students than a picture model such as a pizza. Once students have completed the group activity they are asked to do an analysis to focus on important benchmark fractions. (see below).
Fraction Strips Explore Analysis activity on fractions and benchmarks: English, French: This analysis activity is designed to follow the Fraction Strips Explore activity above.
Compare Decimals Entrance/Exit Slip: English, French. Six quick questions for students to indicate which decimal is greater than, less than or equal to the other.
Clothesline Math - Clothesline math is a math routine where students take turns to place number cards in sequence along a line hanging in the classroom.
Spiralling Decimals from NRICH - Two students take turns placing decimal numbers between 0 and 1 on a spiralled number line. The first to place 3 numbers in a row wins!
Rounding with Decimals - Students have six digits (0,0,0,4,5,6) and a decimal and have to create numbers to satisfy a variety of challenges.
Additional Resources and Activities for N04 (relationships between terminating /repeating decimals and fractions):
Note: N04.07 indicator is no longer a requirement for Mathematics 7. (decimal representation of a fraction is an approximation of its exact value.)
HRCE Marking Rubric for 7N04 - 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.
CMEC Videos (Teacher Resource N07 & N04) Terminating and repeating decimals, comparing decimals : Videos from the Centre for Education in Mathematics and Computing from the University of Waterloo include a mini-lesson on the target concept as well as a few self-checking questions (review questions) and some sample practice questions.
Terminating and Repeating Decimals: English, French: An introduction to vocabulary and explanation of terminating and repeating decimals as well as an opportunity to practice converting fractions to decimals and vice versa.
What’s my value: English, French: This activity helps students connect decimals to money. Teachers can explore different coin values and help students make connections with how we write these numbers as decimals, fractions and in words.
What’s my value extension: English, French: A few extension questions relating decimals to money as well as their fraction equivalents.
Converting a fraction to a decimal from Open Middle: Students use the digits 1 to 9, at most one time each, to place a digit in each box to make a true statement.
Exit Card for Fraction and decimal equivalents: English, French: Exit cards are a quick way to formatively asses what students understand and are able to do. Note: The photo shows decimal numbers without a zero before the decimal point. Taking the time to discuss this with students and why we prefer to have the zero before the decimal point is an excellent classroom discussion.
Pixel Art: (English, French): A self checking digital activity .
Additional Resources and Activities for N02 (Operations with Decimals):
HRCE Marking Rubric for 7N02 - 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 and Subtracting Decimal Numbers using Models and Symbols: English, French: A recording sheet as students explore adding and subtracting decimals using both base ten blocks and symbolic notation. Contains an extension where teachers chose a target or "magic" number for students to create their own addition and subtraction question.
Multiplying Decimals Slide show lessons: English, French: This slide show guides students through modelling multiplication of decimals with base 10 blocks over multiple lessons. The intent is a guided exploration for students with pauses for sharing, questioning and student self-reflection along the way. The slide show also includes student copy and template for base 10 paper manipulatives in speaking notes.
Placemat for multiplying decimals with base ten blocks: This placemat can be blown up on large paper for students to place their base ten blocks on physically. This reinforces students' understanding of the area model for multiplication.
Multiplying Decimals with pictures and symbols: English, French: A graphic organizer for students to use to represent multiplication of decimals using pictures (of base 10 blocks) as well as symbols. Estimation is also included.
Decimal Multiplication Choice Board: English, French: Students chose three questions to solve to make a line on the choice chart. There is also a student recording sheet and a place for student reflection on the learning goal.
Dividing decimals using models: English, French: A slide show that models the division of decimals using base 10 blocks using the area model. There are practice questions imbedded for students to explore and try on their own as well as contextualized word problems to solve at the end.
Additional Resources and Activities for N03 (percentages from 1% to 100%):
HRCE Marking Rubric for 7N03 - 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.
CEMC Videos (Teacher Resource N03) Percentages: Videos from the Centre for Education in Mathematics and Computing from the University of Waterloo include a mini-lesson on the target concept as well as a few self-checking questions (review questions) and some sample practice questions.
Introduction to percent (slides): English, French: A slide show to introduce percent in different ways such as 100 grid and number line.
Percent benchmarks Introduction: English, French: Student recording sheet to accompany/follow-up the introduction to percent slide show. 100 grid, number line and symbolic representations of percent are included.
Benchmarks and percent (contexts for %): English, French: An activity to consider and discuss percentages in real life; specifically when a certain percent represents a large quantity or that same percent represents a small quantity.
Exploring benchmarks on a number line: English, French: This activity has students color percentages on 100 grids and then cut and glue them on a 1m number line. Teachers who completed the fraction number line activity listed for N07 could add to these number lines. The goal is to have students make connections between different representations for percent as well as solidify their understanding that fractions, decimals and percentages are different representations of the same number.
Percent Desmos Activity in English and French: This activity explores percent using a number line and the hundred grid and includes some open-middle challenges at the end.
Percent of a Number Introduction: English, French: An introduction to the percent of a number with a focus on using benchmark percentages on a number line to help students use personal strategies to determine the percent of a number.
Percent of a number, two strategies: English, French: An activity that has students use two strategies for finding the percent of a number (number line and equivalent fractions).
Percent of a number recording sheet for word problems: English, French: A scaffolded recording sheet with two strategies for solving percent discount problems.
Exploring percent using Cuisenaire rods: English, French: A problem solving activity using Cuisenaire rods where students as asked to think about percent in terms of the length of a Cuisenaire rod in relation to another rod. Students must use partitioning skills to break-up and put together percent pieces as they use the rods as a concrete model. Low floor high ceiling activity for all students.
Relating fractions, decimals and percent (slides): English, French: A slide show with shaded images for students to determine the fraction, decimal and percent shaded in each picture. Great for reinforcing the connection between these three representations. Intended to be broken up and done over a period of days as a warm-up or number routine.
Grade 7 N03 Percent tracker: A tracking sheet for teachers to record formative assessment (conversations/ observations/ products) with students as they work through the outcome N03.
"Des-Farm" Desmos Activity in English and French: An interactive self-checking activity where students will find part-to-whole ratios of plants on a farm and use these ratios to determine the equivalent fraction, decimal, or percent representation.
Percent Choice Chart: English: A choice chart for students to make choices about the activities they'd like to complete to demonstrate their understanding of N03.
Unit 3 Cumulative Review
Quizzes on Fractions, Decimals and Percent: English, French: Quizizz is an online assessment tool that is both self-checking for students and provides assessment data for teachers. The multiple choice format also engages students with memes which serve as encouragement after each question. Though there is a time limit option, it is suggested that teachers turn this option off to allow students the time they need to carefully consider their answers. Students using Quizizz for the first time may think it is like Kahoot in that a quicker answer leads to a higher score. This is NOT the case with Quizizz and should be explicitly explained to students. Accuracy and careful thinking is the goal.