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
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).
N01 Students will be expected to demonstrate an understanding of perfect squares and square roots, concretely, pictorially, and symbolically (limited to whole numbers). [C, CN, R, V]
Performance Indicators
N01.01 Represent a given perfect square as a square region, using materials such as grid paper or square shapes.
N01.02 Determine the factors of a given perfect square, and explain why one of the factors is the square root and the others are not.
N01.03 Determine whether or not a given number is a perfect square, using materials and strategies such as square shapes, grid paper or prime factorization, and explain the reasoning.
N01.04 Determine the square root of a given perfect square, and record it symbolically.
N01.05 Determine the square of a given number.
N02 Students will be expected to determine the approximate square root of numbers that are not perfect squares (limited to whole numbers). [C, CN, ME, R, T]
Performance Indicators
N02.01 Estimate the square root of a given number that is not a perfect square, using materials such as square shapes and graph paper and strategies such as using the roots of perfect squares as benchmarks.
N02.02 Approximate the square root of a given number that is not a perfect square using technology (e.g., a calculator or a computer).
N02.03 Explain why the square root of a number shown on a calculator may be an approximation.
N02.04 Identify a number with a square root that is between two given numbers.
M01 Students will be expected to develop and apply the Pythagorean theorem to solve problems. [CN, PS, R, T, V]
Performance Indicators
M01.01 Model and explain the Pythagorean theorem concretely, pictorially, or using technology.
M01.02 Explain, using examples, that the Pythagorean theorem applies only to right triangles.
M01.03 Determine whether or not a given triangle is a right triangle by applying the Pythagorean theorem.
M01.04 Determine the measure of the third side of a right triangle, given the measures of the other two sides, to solve a given problem.
M01.05 Solve a given problem that involves Pythagorean triples.
N01 On s’attend à ce que les élèves montrent qu’ils comprennent les carrés et les racines carrées sous forme concrète, imagée et symbolique (en se limitant aux nombres entiers). [C, L, R, V]
N01.01 Représenter un carré parfait donné sous la forme d’une région carrée à l’aide du matériel de manipulation (papier quadrillé, formes carrées, etc.).
N01.02 Déterminer les facteurs d’un carré parfait donné et expliquer pourquoi l’un de ces facteurs est la racine carrée, tandis que les autres ne la sont pas.
N01.03 Déterminer si un nombre donné est ou n’est pas un carré parfait à l’aide du matériel de manipulation et de stratégies, par exemple en utilisant des formes carrées ou du papier quadrillé ou en décomposant le nombre en facteurs premiers et en expliquant son le raisonnement.
N01.04 Déterminer la racine carrée d’un carré parfait donné et la prendre en note sous forme symbolique.
N01.05 Déterminer le carré d’un nombre donné.
N02 On s’attend à ce que les élèves déterminent la valeur approximative de la racine carrée de nombres qui ne sont pas des carrés (en se limitant aux nombres entiers). [C, L, CM, R, T]
N02.01 Faire une estimation de la racine carrée d’un nombre donné qui n’est pas un carré parfait en utilisant du matériel comme des formes carrées et du papier quadrillé et des stratégies comme l’utilisation des racines de carrés parfaits comme repères.
N02.02 Déterminer la valeur approximative de la racine carrée d’un nombre donné qui n’est pas un carré parfait à l’aide de la technologie (calculatrice ou ordinateur).
N02.03 Expliquer pourquoi la racine carrée d’un nombre déterminé à l’aide d’une calculatrice est parfois une approximation.
N02.04 Trouver un nombre dont la racine carrée se situe entre deux nombres donnés
M01 On s’attend à ce que les élèves établissent et mettent en application le théorème de Pythagore pour résoudre des problèmes. [L, RP, R, T, V]
M01.01 Modéliser et expliquer le théorème de Pythagore de façon concrète et imagée ou à l’aide de la technologie.
M01.02 Expliquer, à l’aide d’exemples, le fait que le théorème de Pythagore s’applique uniquement aux triangles rectangles.
M01.03 Déterminer si un triangle donné est un triangle rectangle ou non à l’aide du théorème de Pythagore.
M01.04 Résoudre un problème donné dans lequel il faut déterminer la longueur du troisième côté d’un triangle rectangle dont on connait la longueur des deux autres côtés.
M01.05 Résoudre un problème donné comportant des triples de Pythagore.
Additional Resources and Activities for N01 and N02 (perfect squares and square roots):
HRCE Rubrics for N01, N02 - 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.
Desmos Activity: Sieve of Eratosthenes - Explore prime numbers using this classic algorithm
Counting Factors - Students work as a class to sort the numbers from 1 to 100 by their total number of factors. Students can then make a number of observations: Only “1” has a single factor, Lots of numbers have only 2 factors (the set of prime numbers), Numbers don’t have as many factors as we thought, Large numbers might have a few factors, and All the numbers with an odd number of factors are perfect squares.
The Locker Problem - A nice review of perfect squares and factors.
Best Square - A three act task exploring how to decide what makes the best square. You can use the videos provided or have a few students create their own "best square".
Amazing circle of numbers challenge problem: English, French: A problem for students to play with using the numbers from 1-32. Arrange the numbers in a circle so that the sum of any two adjacent numbers is a perfect square.
Square Root cards for clothesline math - The Clothesline is a manipulatable number line that makes the facilitation of class discourse on number sense much more efficient and effective.
Pixel Art (N01): English, French: Pixel Art is a self-checking activity that slowly reveals a picture as students enter correct answers into a google sheet. Pixel Art How-to guide: A google slide show with step-by-step instructions for making your own pixel art activities.
Exploring the estimation of square roots using post-it notes- This slideshow describes the activity and provides guiding questions for classroom discussion.
(N02) Introductory Lesson on estimating square roots using models. Student recording sheets are included: English, French
Additional Resources and Activities for M01 (Pythagorean Theorem):
HRCE Rubric for M01 - 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.
An introductory lesson to discovering the Pythagorean Theorem: English, French: This lesson has students make squares using graph paper for the side lengths of different triangles and glue them on a page to make triangles. Students are then given some guiding questions to help them notice and wonder what is similar and different about the triangles and the squares of their sides.
Video - The Pythagorean Theorem Water Demo
Proof Without Words - NCTM Illuminations - Watch a dynamic, geometric "proof without words" of the Pythagorean Theorem. Can you explain the proof?
Taco Truck Desmos Activity in English and French - In this activity, students use the Pythagorean theorem as a tool to solve problems involving diagonal distances. In a quick prelude, students reason with the Pythagorean theorem and with rates in a situation that they may encounter in their daily lives: taking a shortcut to save time. Students then determine the best path to a taco truck from a spot on the beach. The activity culminates in a class-wide race!
Pythagorean Stack Worksheet - A simple worksheet using a stack of triangles. If the final answer is correct, you know you've done the entire sheet correct. A good example of purposeful practice, there is a goal for students to reach by completing these problems. This activity is described by Jan Lichtenberger on her website.
Watson Saves - Watch the video with your class and ask students who ran the greater distance. What other questions might your student wonder after watching the activity?
Pythagorean Theorem Choice Board - A selection of 9 Pythagorean Theorem problems in a 3x3 grid. Students select a set of these problems to work on.
Pythagorean Theorem in Dartmouth Streets in English and French - Students are given a map of streets in downtown Dartmouth. A cable technician working for a local cable company needs to lay down a cable through this grid of streets. Students use Pythagorean Theorem to solve a series to problems to determine how much cable is needed.
Unit 1 Cumulative Review
Legend of Zelda Pythagorean Theorem Desmos Activity - In this activity students will apply Pythagorean Theorem to help Link defeat Ganon and save Zelda.