HRCE Updated Pacing Guide *Updated Sept 2025*
Mathematics Progression: Grades 6 - 9
Math 7 Retrieval Practice Grids A: English, French Grids B: English, French
M01 Students will be expected to demonstrate an understanding of circles by describing the relationships among radius, diameter, and circumference relating circumference to pi
determining the sum of the central angles
constructing circles with a given radius or diameter
solving problems involving the radii, diameters, and circumferences of circles. [C, CN, PS, R, V]
Performance Indicators
M01.01 Illustrate and explain that the diameter is twice the radius in a given circle.
M01.02 Illustrate and explain that the circumference is approximately three times the diameter in a given circle.
M01.03 Explain that, for all circles, pi is the ratio of the circumference to the diameter ( C / d )and its value is approximately 3.14.
M01.04 Explain, using an illustration, that the sum of the central angles of a circle is 360°.
M01.05 Draw a circle with a given radius or diameter, with and without a compass.
M01.06 Solve a given contextual problem involving circles.
M02 Students will be expected to develop and apply a formula for determining the area of triangles, parallelograms, and circles. [CN, PS, R, V]
Performance Indicators
M02.01 Illustrate and explain how the area of a rectangle can be used to determine the area of a triangle.
M02.02 Generalize a rule to create a formula for determining the area of triangles.
M02.03 Illustrate and explain how the area of a rectangle can be used to determine the area of a parallelogram.
M02.04 Generalize a rule to create a formula for determining the area of parallelograms.
M02.05 Illustrate and explain how to estimate the area of a circle without the use of a formula.
M02.06 Generalize a rule to create a formula for determining the area of a given circle.
M02.07 Solve a given problem involving the area of triangles, parallelograms, and/or circles
M01 On s’attend à ce que les élèves montrent qu’ils comprennent les cercles en faisant les choses suivantes :
décrire les relations entre le rayon, le diamètre et la circonférence;
faire le lien entre la circonférence et π; déterminer la somme des angles centraux;
construire des cercles quand on leur donne le rayon ou le diamètre;
résoudre des problèmes faisant intervenir les rayons, les diamètres et les circonférences de cercles. [C, L, RP, R, V]
Indicateurs de rendement
M01.01 Illustrer et expliquer que le diamètre d’un cercle donné est égal au double de son rayon.
M01.02 Illustrer et expliquer que la circonférence d’un cercle donné est approximativement le triple de son diamètre.
M01.03 Expliquer que, pour tout cercle, π est le rapport de la circonférence au diamètre (C / d) , dont la valeur est approximativement égale à 3,14.
M01.04 Expliquer, à l’aide d’une illustration, que la somme des angles au centre de tout cercle est égale à 360°.
M01.05 Tracer un cercle dont le rayon ou le diamètre est donné, avec ou sans l’aide d’un compas.
M01.06 Résoudre un problème contextualisé donné faisant intervenir des cercles.
M02 On s’attend à ce que les élèves mettent au point et mettent en application une formule pour déterminer l’aire de triangles, de parallélogrammes et de cercles.[L, RP, R, V]
Indicateurs de rendement
M02.01 Illustrer et expliquer comment on peut déterminer l’aire d’un triangle à partir de l’aire d’un rectangle.
M02.02 Généraliser une règle pour créer une formule permettant de déterminer l’aire de triangles.
M02.03 Illustrer et expliquer comment on peut déterminer l’aire d’un parallélogramme à partir de l’aire d’un rectangle.
M02.04 Généraliser une règle pour créer une formule permettant de déterminer l’aire de parallélogrammes.
M02.05 Illustrer et expliquer comment on peut estimer l’aire d’un cercle sans avoir recours à une formule.
M02.06 Généraliser une règle pour créer une formule permettant de déterminer l’aire d’un cercle donné.
M02.07 Résoudre un problème donné comportant l’aire de triangles, de parallélogrammes ou de cercles.
Additional Resources and Activities for M01 (radius, diameter, and circumference of circles):
HRCE Marking Rubric for 7M01 - 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 Which One Doesn't Belong - A Which One Doesn't Belong warm-up routine created by Andrew Stadel.
Tile Circle 3-act task. In this problem based lesson, students will explore the relationship between circumference and diameter of a circle to “bump into” Pi, then show how Pi can be used to help find the unknown circumference of a circle and area of a circle.
Dianne's Quill Boxes Desmos Activity - This activity begins with Indigenous knowledge of making Mi'kmaw quill boxes. Baskets have been made from porcupine quills in North American Indigenous communities for thousands of years. To make a basket, Mi'kmaw elder Dianne Toney knew that the relationship between the ring (circumference) and the distance across the circle top (diameter) was equivalent to three measures across and a thumb width. Beginning with this story, students discover the relationship commonly referred to as π. It is important to acknowledge that this relationship was known amongst the Mi'kmaq (and likely many other indigenous peoples) long before contact with European settlers.
Additional Resources and Activities for M02 (area of triangles, parallelograms, and circles):
HRCE Marking Rubric for 7M02 - 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.
Measurement: Discovering Formulas for Area - Using the formula for a rectangle to determine the formula for parallelograms and triangles.
Would You Rather Circle Area and Would You Rather Table Area - A class warm-up routine. Show students the image and ask which option they would rather selection. Ask students to justify their reasoning using area. Check out the images on the Would You Rather website - Circle Area and Table Area.
100 unit^2 Name Activity - Hand out a piece of graph paper to each student. Ask them to write out their name (first, last or perhaps initials) using exactly 100 square units of area. Students can self-differentiate this activity by making the letters in their name a complex as they would like. Check out Ethan and Ken. Inspired by Ilona Vashchyshyn.
Geoboard Triangles - Use an 11 by 11 geoboard to ask students to find triangles with an area of 15. After some right triangles have been found, challenge students to find some other examples. You could then ask students to "Find all the triangles that have one horizontal side, and area 15". Students who need a challenge could be asked to "Find triangles with area 15, such that none of their sides are horizontal or vertical".
Donkey Kong Circles Desmos activity English, French - Students will explore circumference and area of circles. The end challenge has students find circumference, area, and the radius based on given information. The last screen includes computed values of pi.
Circle Area Problem - Squares have circles, semicircles, quadrants drawn inside them. Which design has the largest orange fraction (of the whole square) shaded? This question was from an article by D.B. Eperson in Mathematics in School from January 1992. Additional circle problems can be found on Don Steward's website.
Area of a Circle Increasingly Difficult Questions - A worksheet of questions that start simple and end challenging. Additional sheets in this style are available from Increasingly Difficult Questions.
Circles and Area Scavenger Hunt - A cumulative review activity of outcomes M01 and M02 (foundational outcomes for 2020-2021). In a Scavenger Hunt, students work in small groups to solve mathematics problems posted on station cards. They start at any station card and solve the problem posted on the bottom of it. Once they solve the problem, they find another station card posted around the room (or outside) with that solution located on the top of it. This new station card also includes another problem to solve (on the bottom half of the card). If students solve all of the problems correctly, they’ll move from station to station, then end back up at the station they started at.
Circles and Area Sidewalk Art - With a bit of sidewalk chalk, students can get outside to use the geometry they have learned in this unit to create different styles of art. They might create a mandala to demonstrate their understanding of the features of a circle or stained glass images to show the features of triangles and parallelograms.