HRCE Updated Pacing Guide *Updated Sept 2025*
Mathematics Progression: Grades 6 - 9
Math 7 Retrieval Practice Grids A: English, French Grids B: English, French
SP01 Students will be expected to demonstrate an understanding of central tendency and range by
determining the measures of central tendency (mean, median, mode) and range
determining the most appropriate measures of central tendency to report findings [C, PS, R, T]
Performance Indicators
SP01.01 Determine mean, median, and mode for a given set of data, and explain why these values may be the same or different.
SP01.02 Determine the range for a given set of data.
SP01.03 Provide a context in which the mean, median, or mode is the most appropriate measure of central tendency to use when reporting findings.
SP01.04 Solve a given problem involving the measures of central tendency.
SP02 Students will be expected to determine the effect on the mean, median, and mode when an outlier is included in a data set. [C, CN, PS, R]
Performance Indicators
SP02.01 Analyze a given set of data to identify any outliers.
SP02.02 Explain the effect of outliers on the measures of central tendency for a given data set.
SP02.03 Identify outliers in a given set of data, and justify whether or not they are to be included in reporting the measures of central tendency.
SP02.04 Provide examples of situations in which outliers would and would not be used in reporting the measures of central tendency.
SP03 Students will be expected to construct, label, and interpret circle graphs to solve problems. [C, CN, PS, R, T, V]
Performance Indicators
SP03.01 Identify common attributes of circle graphs, such as
title, label, or legend
the sum of the central angles is 360°
the data is reported as a percent of the total, and the sum of the percents is equal to 100%
SP03.02 Create and label a circle graph, with and without technology, to display a given set of data.
SP03.03 Find and compare circle graphs in a variety of print and electronic media, such as newspapers, magazines, and the Internet.
SP03.04 Translate percentages displayed in a circle graph into quantities to solve a given problem.
SP03.05 Interpret a given or constructed circle graph to answer questions.
SP04 Students will be expected to express probabilities as ratios, fractions, and percents. [C, CN, R, T, V]
Performance Indicators
SP04.01 Determine the probability of a given outcome occurring for a given probability experiment, and express it as a ratio, fraction, and percent.
SP04.02 Provide an example of an event with a probability of 0 or 0% (impossible) and an example of an event with a probability of 1 or 100% (certain).
SP05 Students will be expected to identify the sample space (where the combined sample space has 36 or fewer elements) for a probability experiment involving two independent events. [C, ME, PS]
Performance Indicators
SP05.01 Provide an example of two independent events, such as the following, and explain why they are independent. spinning a four-section spinner and an eight-sided die tossing a coin and rolling a twelve-sided die tossing two coins rolling two dice
SP05.02 Identify the sample space (all possible outcomes) for each of two independent events using a tree diagram, table, or other graphic organizer.
SP06 Students will be expected to conduct a probability experiment to compare the theoretical probability (determined using a tree diagram, table, or other graphic organizer) and experimental probability of two independent events. [C, PS, R, T]
Performance Indicators
SP06.01 Determine the theoretical probability of a given outcome involving two independent events.
SP06.02 Conduct a probability experiment for an outcome involving two independent events, with and without technology, to compare the experimental probability with the theoretical probability.
SP06.03 Solve a given probability problem involving two independent events.
SP01 On s’attend à ce que les élèves montrent qu’ils comprennent la tendance centrale et l’étendue en faisant les choses suivantes:
déterminer les mesures de tendance centrale (moyenne, médiane, mode) et l’étendue;
déterminer les mesures de tendance centrale les plus appropriées pour présenter des conclusions. [C, RP, R, T]
Indicateurs de rendement
SP01.01 Déterminer la moyenne, la médiane et le mode d’un ensemble donné de données et expliquer pourquoi ces mesures peuvent être identiques ou différentes.
SP01.02 Déterminer l’étendue d’un ensemble donné de données.
SP01.03 Fournir un contexte dans lequel la moyenne, la médiane ou le mode d’un ensemble de données est la mesure de tendance centrale la plus appropriée pour présenter des conclusions.
SP01.04 Résoudre un problème donné qui comprend des mesures de tendance centrale.
SP02 On s’attend à ce que les élèves déterminent l’effet sur la moyenne, la médiane et le mode quand on a une valeur aberrante dans un ensemble de données. [C, L, RP, R]
Indicateurs de rendement
SP02.01 Analyser un ensemble donné de données afin d’y mettre en évidence les valeurs aberrantes, s’il y en a.
SP02.02 Expliquer les effets des valeurs aberrantes sur les mesures de tendance centrale pour un ensemble donné de données.
SP02.03 Trouver les valeurs aberrantes dans un ensemble donné de données et expliquer pourquoi il est approprié ou non d’en tenir compte lors de la présentation des mesures de tendance centrale.
SP02.04 Fournir des exemples de situations dans lesquelles des valeurs aberrantes devraient ou ne devraient pas être incluses lors de la présentation des mesures de tendance centrale.
SP03 On s’attend à ce que les élèves construisent, annotent et interprètent des diagrammes circulaires pour résoudre des problèmes. [C, L, RP, R, T, V]
Indicateurs de rendement
SP03.01 Mettre en évidence les caractéristiques communes de diagrammes circulaires :
titre, annotations ou légende;
somme des angles au centre d’un cercle égale à 360°;
données présentées sous la forme de pourcentages d’un tout et somme de ces pourcentages égale à 100.
SP03.02 Créer et annoter un diagramme circulaire pour présenter un ensemble de données avec ou sans l’aide de la technologie.
SP03.03 Trouver et comparer des diagrammes circulaires dans divers médias imprimés et électroniques (quotidiens, magazines, Internet, etc.).
SP03.04 Exprimer les pourcentages présentés dans un diagramme circulaire sous forme de quantités afin de résoudre un problème donné.
SP03.05 Interpréter un diagramme circulaire donné afin de répondre à des questions.
SP04 On s’attend à ce que les élèves expriment les probabilités sous forme de rapports, de fractions et de pourcentages. [C, L, R, T, V]
Indicateurs de rendement
SP04.01 Déterminer la probabilité de l’un des résultats d’une expérience de probabilité et exprimer cette probabilité sous la forme d’un rapport, d’une fraction et d’un pourcentage.
SP04.02 Fournir un exemple d’évènement dont la probabilité est de 0 ou 0 p. 100 (impossible) et un exemple d’évènement dont la probabilité est de 1 ou 100 p. 100 (certain).
SP05 On s’attend à ce que les élèves définissent l’espace d’échantillon (quand l’espace d’échantillon combiné a 36 éléments ou moins) pour une expérience de probabilité faisant intervenir deux évènements indépendants. [C, CM, RP]
Indicateurs de rendement
SP05.01 Fournir un exemple de paire d’évènements indépendants : faire tourner une roulette ayant quatre secteurs et lancer un dé à huit faces; lancer une pièce de monnaie et lancer un dé à douze faces; lancer deux pièces de monnaie; lancer deux dés; et expliquer pourquoi ces évènements sont des évènements indépendants
SP05.02 Définir l’espace d’échantillon (ensemble des résultats possibles) de chacun des deux évènements indépendants dans une expérience donnée en utilisant un diagramme en arbre, un tableau ou un autre outil d’organisation graphique.
SP06 On s’attend à ce que les élèves effectuent une expérience de probabilité afin de comparer la probabilité théorique (déterminée à l’aide d’un diagramme en arbre, d’un tableau ou d’un autre outil d’organisation graphique) et la probabilité expérimentale de deux évènements indépendants. [C, RP, R, T]
Indicateurs de rendement
SP06.01 Déterminer la probabilité théorique d’un résultat donné faisant intervenir deux évènements indépendants.
SP06.02 Mener une expérience de probabilité à la suite de deux évènements indépendants, avec ou sans l’aide de la technologie, afin de comparer la probabilité expérimentale et la probabilité théorique.
SP06.03 Résoudre un problème de probabilité donné faisant intervenir deux évènements indépendants.
Additional Resources and Activities for SP01 and SP02 (mean, median, mode, range, and outliers):
HRCE Marking Rubric for 7SP01 and Marking Rubric for 7SP02 - 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.
Who's Better at Doodle Jump? from Math Arguments - Take a look at this image comparing the Doodle Jump stats for Dan and his friend Mike. Start a class debate. Half the class can give reasons why Dan is the better player and the other half can defend why Mike is the better player. What additional data would help you make your case?
Measures of Central Tendency Puzzles - Ms. Konstantine shared two puzzles for students to practice mean, median, mode and range. Can students solve this puzzle? Is there more than one solution? Can they create their own puzzle? Solutions and google slides template.
Paper Airplanes - Julie Reulbach and Bruno Reddy describe how they each used a paper airplane contest to necessitate the need for calculating an average. Create, throw and collect data to determine which plane is the winner.
Mean, Median, Mode, and Range Spider Puzzles - These puzzles should bring about plenty of discussion. Four "spiders" of increasing difficulty asking students to complete a list of numbers to make the average and range properties true. Sarah Carter describes using this resource in her classroom. from Andy Lutwyche
Which One Doesn't Belong? Statistics - Use mean, median, mode, range, etc. to determine which of the following data sets is not like the other. A variety of WODB discussion prompts are found at http://wodb.ca/.
Range and Median Predictions Activity from David Coffey - Give students 10 playing cards numbered 1 to 10. Shuffle an deal 5 of the cards. Flip over the first 4 cards. Students use their knowledge of probability to predict the range and the median of the five numbers before the final card is turned over. You could play this as a class to see who can get the closest prediction.
Equal Sharing - Students are given a set of towers and asked to make all of the towers have the same height. You must maintain the same number of towers. The only thing you can change is the arrangement of the blocks. Sarah Carter describes using this resource in her classroom. from Don Steward
Additional Resources and Activities for SP03 (circle graphs):
HRCE Marking Rubric for 7SP03 - 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.
Outdoor Circle Graphs - Give each student a random playing card from a deck of cards. Ask your students to gather outside and gather in two groups: students who have a black card and students who have a red card. Next ask them to form a circle staying in their groups. Use several pieces of rope or string to indicate the divisions between groups to create a human circle graph. Ask students how they could take this physical circle graph and use it to draw a circle graph (how to relate the number of objects in each category to how big the angle of each sector is). Next ask students to gather in a different arrangement... perhaps by suit, or odds, evens and face cards, etc. Have a handout for students to record this data and draw these circle graphs (while outside if you have clipboards). If you had a deck of number cards you could do the same activity but with different groups using divisibility rules.
Additional Resources and Activities for SP04, SP05 and SP06 (probability):
SP05 has been removed as an outcome and is no longer evaluated as its own. However, indicator SP06.01 requires students to determine the theoretical probability of a given situation involving two independent events.
CPM Virtual Probability Tools - This website hosts a variety of flexible and easy to use virtual probability tools including spinners, dice, bags of counters, etc.
Probability Stations Google Slides English, French - Students do probability experiments with virtual dice, coins, spinners and bag of squares. These four stations can be done virtually or in person with virtual manipulatives.
Probability Scavenger Hunt - Students can select one of 3 different levels of difficulty and answer 9 questions. Students find the answers to these questions on stations posted around the room (or outside!). Students use the answer to decode a hidden message.
The Two-Dice Sum Game - Each student makes a number line from 2 to 12. Students get to place 11 counters on this number line (you might use multi-link cubes or two color counters). Roll two dice and if there is a counter on that number, remove it. The first student to remove all their counters from their number line wins. Can students find the best way to allocate their counters? Joe Schwartz describes how he used this game in a classroom.
Dibingo - In this game, students have to pick a card with different values on it. Students take turns rolling two dice. If there sum is a number that is on their card, they score a point. Which card will give you the best chance of winning? Megan Schmidt wrote about using this game in her classroom. from Don Steward
Card Game from Mathematical Assessment Project - Students use probability to make predictions about a card game. Ten cards, numbered 1 to 10, are shuffled and placed face down so that the numbers do not show. The cards are turned over one at a time. The class has to find the probability that the next card will have a higher number than the last one turned. The card game task instructions and a scoring rubric.