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
HRCE Video - Fractions and Decimals, slideshow
CEMC Grade 7-8 Courseware: Lesson 11: Order of Operations. Lesson 14: Multiplying Fractions, Lesson 15: Dividing Fractions
Online math tools: Grids, dot grids, expression mats, algebra tiles, base 10 blocks, number lines
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).
N06 Students will be expected to demonstrate an understanding of multiplying and dividing positive fractions and mixed numbers, concretely, pictorially, and symbolically. [C, CN, ME, PS]
N06.01 Identify the operation required to solve a given problem involving positive fractions.
N06.02 Provide a context that requires the multiplying of two given positive fractions.
N06.03 Provide a context that requires the dividing of two given positive fractions.
N06.04 Estimate the product of two given positive proper fractions to determine if the product will be closer to 0, 1/2 , or 1.
N06.05 Estimate the quotient of two given positive fractions, and compare the estimate to whole number benchmarks.
N06.06 Express a given positive mixed number as an improper fraction and a given positive improper fraction as a mixed number.
N06.07 Model multiplication of a positive fraction by a whole number concretely and/or pictorially and record the process.
N06.08 Model multiplication of a positive fraction by a positive fraction concretely and/or pictorially, using an area model, and record the process.
N06.09 Model division of a positive proper fraction by a whole number concretely and/or pictorially and record the process.
N06.10 Model division of a whole number by a positive proper fraction concretely and/or pictorially, using an area model, and record the process.
N06.11 Model division of a positive proper fraction by a positive proper fraction pictorially and record the process.
N06.12 Generalize and apply rules for multiplying and dividing positive fractions, including mixed numbers.
N06.13 Symbolically solve a given problem involving positive fractions, taking into consideration order of operations (limited to problems with positive solutions and that exclude exponents).
N06 On s’attend à ce que les élèves montrent qu’ils comprennent la multiplication et la division de fractions et de nombres fractionnaires de signe positif, sous forme concrète, imagée et symbolique. [C, L, CM, RP]
Indicateurs de rendement
N06.01 Définir l’opération appropriée pour résoudre un problème faisant intervenir des fractions positives.
N06.02 Fournir un contexte exigeant la multiplication de deux fractions positives données.
N06.03 Fournir un contexte exigeant la division de deux fractions positives données.
N06.04 Estimer le produit de deux fractions propres positives pour déterminer si le produit est plus près de 0, de 1/2 ou de 1.
N06.05 Estimer le quotient de deux fractions positives données en utilisant des nombres entiers comme points de repère.
N06.06 Exprimer un nombre fractionnaire positif donné sous forme de fraction impropre positive et une fraction impropre positive donnée sous forme de nombre fractionnaire.
N06.07 Modéliser la multiplication d’une fraction positive par un nombre entier positif sous forme concrète ou imagée et prendre en note la marche à suivre.
N06.08 Modéliser la multiplication d’une fraction positive par une fraction positive sous forme concrète ou imagée à l’aide du concept de surface et prendre en note la marche à suivre.
N06.09 Modéliser la division d’une fraction propre positive par un nombre entier sous forme concrète ou imagée et prendre en note la marche à suivre.
N06.10 Modéliser la division d’un nombre entier par une fraction propre positive sous forme concrète ou imagée à l’aide du concept de surface et prendre en note la marche à suivre.
N06.11 Modéliser la division d’une fraction propre positive par une fraction propre positive sous forme imagée et prendre en note la marche à suivre.
N06.12 Énoncer et appliquer des règles générales pour multiplier et diviser des fractions positives, y compris des nombres fractionnaires.
N06.13 Résoudre sous forme symbolique un problème donné comportant des fractions positives, en tenant compte de la priorité des opérations et en se limitant aux problèmes ayant des solutions positives et excluant les exposants.
HRCE Rubric for 8N06 - 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.
Mental Math and Number Routines for N06:
Math Visuals (fractions) - Math Visuals was created as a resource for fellow math educators, and seeks to: uncover patterns that are foundational to Elementary Math, give multiple access points to engage everyone in discussion and inspire educators and students to invent their own visualizations of math concepts
Open Middle - Multiplying fractions to make a whole number , Multiplying Fractions
Would You Rather? - Fraction Multiplication
Additional Resources and Activities for N06 (operations with fractions):
Row Game for multiplying fractions by a whole number (English, French): An activity to promote student collaboration and problem-solving. Students work on questions in their own column (A or B). Their answers should be the same as the answers in their partner's column of questions. If their answers don't match, students work together to figure out the error together.
Adding and Subtracting Fractions Choice Board: This collection of activities would be a good refresher to practice adding/subtracting fractions before moving into multiplying and dividing fractions. It could also be a good review to be used at anytime.
Operations with Fractions Pixel Art (English, French): A self checking activity involving multiplication and division of fractions using modeling and problem solving.
Snowflake Pixel Art: English: French: A self checking activity in a premade Google sheet that uses conditional formatting to change the colour of cells when a student correctly answers a questions.
*Updated December 2024* Multiplying Fractions Google Slides (English, French): Students can use explore multiplying fractions using fraction squares.
*Updated December 2024* Dividing Fractions Google Slides (English, French): Students can use explore dividing fractions using fraction squares.
Open Middle: Order of Operations: Using the integers -5 to 5, at most one time each, write an expression that will have the greatest (or least) value.
Gimme a Break - A three act task on adding and subtracting fractions and an introduction to multiplying and dividing fractions.
Fractions Jigsaw - A nice way to assess prior knowledge of equivalent fractions and fraction addition and subtraction. Download and print out a jigsaw, and cut up the pieces into squares. Ask students to put the jigsaw together with equivalent fractions and touching sides.
Two Fractions Activity - Stretch your students’ number sense skills with a fraction challenge. Use four different digits (from 2-9) and one operation (+, –, •, or ÷) to create two fractions in an expression with the greatest possible value. Also have students try to discover an expression with the least value or the expression closest to 0.
Interpreting Multiplication and Division from the Mathematics Assessment Project - This lesson unit is designed to help students to interpret the meaning of multiplication and division. Students use cards to match multiplication and division situations with pictures.
Rational Number Operations Question Stack - This is a self checking activity popularized by Sarah Carter. Check out her website for additional variations of this activity.
L-Shapes with Fractions - Students find the area and perimeter of l-shaped polygons with fraction length sides.
Modeling Fraction Division- A slide deck that scaffolds the development of students' understanding of faction division using models.
Fraction Division Using Rectangles - A visual way to think of fraction division using rectangles.
Visualizing Division of Fractions - Article from NCTM's Math Teaching in the Middle School. Teachers must be prepared to recognize valid alternative representations of arithmetic problems. Challenging examples involving mixed fractions and division are presented along with teacher's discussion from a professional development workshop. The teachers created, interpreted, and discussed the various representations to develop and enhance their understanding of fraction division.
Dividing Fractions Progression and Practice Desmos Activity - In this activity the idea is that to help students develop tools for fraction division and eventually get to the fraction division algorithm conceptually. One way to do that without just telling them the rules is to use a progression of successively more and more complex problems.
Fraction Thinking Tasks: A collection of great thinking questions for fraction operations.
Formative assessment for fraction multiplication by a whole number and vice versa: English, French: This formative assessment has students demonstrate their understanding using different representations and will help teachers identify next steps for instruction.
Unit 3 Cumulative Review
Fraction Feast - This menu of activities is presented in a Google slides presentation. Students can choose various problems on this menu that span the unit. This would make a productive cumulative project for this unit.
Unit 3 Review Desmos Activity - An self-checking Desmos activity for students to review fraction operations.