Mathematics 9 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
N05 Students will be expected to determine the exact square root of positive rational numbers [C, CN, PS, R, T]
Performance Indicators
N05.01 Determine whether or not a given rational number is a square number and explain the reasoning.
N05.02 Determine the square root of a given positive rational number that is a perfect square.
N05.03 Identify the error made in a given calculation of a square root (e.g., is 3.2 the square root of 6.4)?
N05.04 Determine a positive rational number, given the square root of that positive rational number.
N06 Students will be expected to determine an approximate square root of positive rational numbers. [C, CN, PS, R, T]
Performance Indicators
N06.01 Estimate the square root of a given rational number that is not a perfect square, using the roots of perfect squares as benchmarks.
N06.02 Determine an approximate square root of a given rational number that is not a perfect square, using technology (e.g., a calculator, a computer).
N06.03 Explain why the square root of a given rational number as shown on a calculator may be an approximation.
N06.04 Identify a number with a square root that is between two given numbers.
G01 Students will be expected to determine the surface area of composite 3-D objects to solve problems. [C, CN, PS, R, V]
Performance Indicators
G01.01 Determine the area of overlap in a given composite 3-D object, and explain the effect on determining the surface area (limited to right cylinders, right rectangular prisms, and right triangular prisms).
G01.02 Determine the surface area of a given composite 3-D object (limited to right cylinders, right rectangular prisms, and right triangular prisms).
G01.03 Solve a given problem involving surface area.
N05 On s’attend à ce que les élèves déterminent la valeur exacte de la racine carrée de nombres rationnels positifs. [C, L, RP, R, T]
N05.01 Déterminer si un nombre rationnel donné est ou n’est pas un nombre carré et expliquer le raisonnement.
N05.02 Déterminer la racine carrée d’un nombre rationnel positif donné qui est un carré parfait.
N05.03 Trouver l’erreur faite dans le calcul donné d’une racine carrée, p. ex. : un élève pense que 3,2 est la racine carrée de 6,4.
N05.04 Déterminer un nombre rationnel positif à partir de la racine carrée de ce nombre rationnel positif.
N06 On s’attend à ce que les élèves déterminent la valeur approximative de la racine carrée de nombres rationnels positifs. [C, L, RP, R, T]
N06.01 Estimer la racine carrée d’un nombre rationnel donné qui n’est pas un carré parfait en ayant recours à des racines carrées de carrés parfaits comme points de repère.
N06.02 Déterminer approximativement la racine carrée d’un nombre rationnel donné qui n’est pas un carré parfait à l’aide de la technologie, p. ex. une calculatrice ou un ordinateur.
N06.03 Expliquer pourquoi la racine carrée d’un nombre rationnel donné, calculé à l’aide d’une calculatrice, peut être une approximation.
N06.04 Trouver un nombre dont la racine carrée se situe entre deux nombres donnés.
G01 On s’attend à ce que les élèves déterminent l’aire de la surface d’objets composés à 3D pour résoudre des problèmes. [C, L, RP, R, V]
G01.01 Déterminer l’aire de la surface du chevauchement dans un objet à trois dimensions donné et expliquer son effet sur le calcul de l’aire de la surface (en se limitant aux cylindres droits et aux prismes droits à base rectangulaire ou triangulaire).
G01.02 Déterminer l’aire de la surface d’un objet à trois dimensions concret donné (en se limitant aux cylindres droits et aux prismes droits à base rectangulaire ou triangulaire).
G01.03 Résoudre un problème donné faisant intervenir l’aire de la surface.
Additional Resources and Activities for N05 (exact square roots):
HRCE Marking Rubric for 9N05 - 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.
Square Roots of Perfect Squares Student Handout: English, French- Students can work through this handout to discover the visual relationship between the area model of a fraction with a square number denominator and its square root.
Square Roots Clothesline Activity - Use a variety of visuals and benchmarks to locate perfect squares and approximate the value of non-perfect square numbers. A pdf file of cards already constructed for this activity from Andrew Stadel.
Square Roots of Perfect Square Rationals Quizizz Game
Additional Resources and Activities for N06 (approximate square roots):
HRCE Marking Rubric for 9N06 - 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.
Placing a square root on the number line - Ask students to place √28 on a number line, accurate to one decimal point.
Desmos Polygraph Activity with Rational and Irrational Numbers - This Desmos Polygraph is designed to spark vocabulary-rich conversations about functions and relations. Key vocabulary that may appear in student questions includes: positive, negative, fraction, rational, and irrational. A Polygraph activity is an online activity for pairs of students that is similar to the old board game "Guess Who?" where students ask each other yes or no questions.
This is a collection of instructional videos, self-assessments and unit reviews from the Newfoundland and Labrador English School District (NLESD).
NLESD Math 9 Video - Estimating the square root of a decimal
NLESD Math 9 Video - Estimating the square root of a fraction which is not a perfect square
NLESD Math 9 Video - Finding a number with a square root between two numbers
Additional Resources and Activities for G01 (surface area of composite 3-D objects):
HRCE Marking Rubric for 9G01 - This rubric can be used for a variety of purposes such as a resource to help create learning goals (“I can” statements), student self assessments, on-going, formative assessment, Help create report card comments, Summative assessment of achievement, support giving descriptive feedback to students
Exploring overlap Slide Show - English, French: This slide show asks student to explore overlap and think about how overlap affects the total surface area of a composite 3D object.
Surface Area check-in and Surface Area check-in with additional scaffolding - Two different versions of a short check-in for the surface area of composite 3D objects. One includes additional scaffolding for students who benefit from organizational prompts.
Surface Area Stations (English and French) - A series of 8 stations for students to practice calculating the surface are of 3D composite objects. Accompanying student recording sheets for students who benefit from additional organizational support: English, French
How Many Post-It Notes will it take to cover a file cabinet? (Note: this is not a compound shape but would be a good warm-up activity leading into compound shapes)
The Birdhouse Challenge - Design and create a model birdhouse from a single sheet of 8.5” x 11” paper. Here are links for Google Slides with directions for this activity in English and French.
Unit 3 Cumulative Review
NLESD Math 9 - Square Root and Surface Area Unit Review. From the Newfoundland and Labrador English School District site.
Square Roots & Surface Area Math Menu - This Google slides activity is meant to be done online. Students are given a number of different questions to choose from to solve for a cumulative review of square roots and surface area.