Mathematics 8 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
Math 8 Retrieval Practice Grid A English, French Grid B English, French
Desmos Activities: Collection for Math 8 and Collection for Math 8 French Immersion
National Library of Virtual Manipulatives - Virtual Manipulatives sorted by Topic (Number and Operations, Algebra, Geometry, Measurement, Data Analysis & Probability) and grade level (Note: Resource is American, so topics may not align directly with Nova Scotia Curriculum).
M02 Students will be expected to draw and construct nets for 3-D objects. [C, CN, PS, V]
M02.01 Match a given net to the 3-D object it represents.
M02.02 Construct a 3-D object from a given net.
M02.03 Draw nets for a given right cylinder, right rectangular prism, and right triangular prism, and verify by constructing the 3-D objects from the nets.
M02.04 Predict 3-D objects that can be created from a given net, and verify the prediction.
M03 Students will be expected to determine the surface area of right rectangular prisms, right triangular prisms, and right cylinders to solve problems. [C, CN, PS, R, V]
M03.01 Explain, using examples, the relationship between the area of 2-D shapes and the surface area of a given 3-D object.
M03.02 Identify all the faces of a given prism, including right rectangular and right triangular prisms.
M03.03 Identify all the faces of a given right cylinder.
M03.04 Describe and apply strategies for determining the surface area of a given right rectangular or right triangular prism.
M03.05 Describe and apply strategies for determining the surface area of a given right cylinder.
M03.06 Solve a given problem involving surface area.
M04 Students will be expected to develop and apply formulas for determining the volume of right rectangular prisms, right triangular prisms, and right cylinders. [C, CN, PS, R, V]
M04.01 Determine the volume of a given right prism, given the area of the base.
M04.02 Generalize and apply a rule for determining the volume of right cylinders.
M04.03 Explain the connection between the area of the base of a given right 3-D object and the formula for the volume of the object.
M04.04 Demonstrate that the orientation of a given 3-D object does not affect its volume.
M04.05 Apply a formula to solve a given problem involving the volume of a right cylinder or a right prism.
M02 On s’attend à ce que les élèves dessinent et construisent des développements pour des objets à trois dimensions. [C, L, RP, V]
M02.01 Apparier un développement donné à l’objet à trois dimensions qu’il représente.
M02.02 Construire un objet à trois dimensions à partir de son développement.
M02.03 Tracer des développements d’objets à trois dimensions donnés, comme des cylindres droits, des prismes droits à base rectangulaire et des prismes droits à base triangulaire, puis vérifier en construisant l’objet à partir de son développement.
M02.04 Prédire les objets à trois dimensions qui pourraient être construits à partir de développements donnés et vérifier les prédictions.
M03 On s’attend à ce que les élèves déterminent l’aire de la surface de prismes droits à base rectangulaire, de prismes droits à base triangulaire et de cylindres droits pour résoudre des problèmes. [C, L, RP, R, V]
M03.01 Expliquer, à l’aide d’exemples, la relation entre l’aire de figures à deux dimensions et l’aire de la surface d’un objet à trois dimensions donné.
M03.02 Définir toutes les faces d’un prisme donné, notamment d’un prisme droit à base rectangulaire et d’un prisme droit à base triangulaire.
M03.03 Définir toutes les faces d’un cylindre droit donné.
M03.04 Décrire et appliquer des stratégies pour déterminer l’aire de la surface d’un prisme droit donné à base rectangulaire ou triangulaire.
M03.05 Décrire et appliquer des stratégies permettant de déterminer l’aire de la surface d’un cylindre droit donné.
M03.06 Résoudre un problème donné faisant intervenir l’aire de la surface.
M04 On s’attend à ce que les élèves établissent et mettent en application des formules pour déterminer le volume de prismes droits à base rectangulaire, de prismes droits à base triangulaire et de cylindres droits. [C, L, RP, R, V]
M04.01 Déterminer le volume d’un prisme droit donné, étant donné l’aire de la base.
M04.02 Énoncer une règle générale pour déterminer le volume de cylindres droits et l’appliquer.
M04.03 Expliquer la relation entre l’aire de la base d’un objet droit à trois dimensions donné et la formule pour calculer son volume.
M04.04 Démontrer que l’orientation d’un objet à trois dimensions donné n’affecte pas son volume.
M04.05 Appliquer une formule pour résoudre un problème donné faisant intervenir le volume d’un cylindre droit ou d’un prisme droit.
HRCE Rubrics for M02, M03, M04 - These rubrics 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.
Online math tools: Grids, dot grids, expression mats, algebra tiles, base 10 blocks, number lines,
Additional Resources and Activities for M02 (nets for 3D objects):
Pull-Up Nets - A 'pull-up net' uses a loop of string to 'pull up' the 2D net to make a 3D object. Cut out the net for the polyhedron you want to create. Use a ruler to score the edges and make holes to pull the string through. Loop the string through the holes and then gently pull on the string to close the net into the 3D object. Check out the article at ATM. Also see this YouTube video.
The Spider and the Fly from Henry Dudeney's The Canterbury Puzzles - Inside a rectangular room, measuring 30 feet in length and 12 feet in width and height, a spider is at a point on the middle of one of the end walls, 1 foot from the ceiling, as at A; and a fly is on the opposite wall, 1 foot from the floor in the centre, as shown at B. What is the shortest distance that the spider must crawl in order to reach the fly, which remains stationary? Of course the spider never drops or uses its web, but crawls fairly. As a hint, ask students to draw a net of this prism in several different ways (or perhaps use Polydron pieces to explore different nets). Students can use these net drawings and Pythagorean Theorem to solve this.
Net Drawing Relay - Students work in small groups to draw a net given the 3-D image of a rectangular prism. After completing the net, they will add on measurements to each of the sides. The activity is intended to be run outdoors but could be modified to accomplish inside.
Additional Resources and Activities for M03 (surface area of rectangular prisms, triangular prisms, and cylinders):
Hands-on Surface Area Activity - Students work in pairs to create a net of a rectangular or triangular prism on a piece of coverstock. They measure all of the edges and calculate the surface area of each face and the total surface area on the net. Then they cut out the net and tape it together.
Pop Box Design - A three act task investigating surface area of pop boxes. This lesson is also a precursor to this three act task on the volume of different pop cans.
Area Maze Puzzles by Naoki Inaba - A nice class warm-up logic puzzle to get students thinking about area.
Additional Resources and Activities for M04 (volume of rectangular prisms, triangular prisms, and cylinders):
Volume Questions : English, French: A Google slide show with several questions about volume shared by Miss Konstantine on her blog.
Solid Fusing Task - Students are given a set of six solids. Rather than provide them with a pre-ordained arrangement of the solids, the task makes the arrangement the key mathematical decision to be made. Students must combine any number of the six solids provided to create a shape that has a surface area (in square units) as close as possible to its volume (in cubic units).
Would Your Rather... Pools - Would you rather have a pool with dimensions of 40 ft x 9 ft x 4 ft OR 7 yds x 4 yds x 2 yds? Whichever option you choose, justify your reasoning with mathematics.
Unit 4 Cumulative Review
Surface Area and Volume Choice Board : English, French: Students are given 9 problems on a 3x3 grid. They select 3 of these problems to demonstrate their understanding of outcomes M03 and M04.
Passport de Module 5: Une activité pour engager les élèves dans une révision des résultats d'apprentissage M02, M03, M04.