Grade Eight Maht Crriculum
Almost on the threshold of high school, Grade 8 is always considered to be the fun grade. This is also the year at which academic competition starts to rise and directions towards future careers begin to be mapped. Strengthening of mathematics concepts in this grade also becomes imperative. Moving from the world of basic decimals and fractions, Grade 8 further explores equations and proportional relationships and introduces the concepts of quadrants and axes. It is in grade 8 that students become familiar with one of the oldest mathematical rules, known as the Pythagorean Rule, whose origin dates to the ancient times.
Table of Contents
Overall and Specific Expectations
A. Number Sense
Students will demonstrate an understanding of numbers and make connections to the way numbers are used in everyday life. They will
1. Rational numbers
- represent and compare very large and very small numbers, including through the use of scientific notation, and describe various ways they are used in everyday life.
- describe, compare, and order numbers in the real number system (rational and irrational numbers), separately and in combination, in various contexts.
- estimate and calculate square roots, in various contexts.
2. Fractions and Decimals,and Percents
- use fractions, decimal numbers, and percents, including percents of more than 100% or less than 1%, interchangeably and flexibly to solve a variety of problems.
Students will use knowledge of numbers and operations to solve mathematical problems encountered in everyday life. They will
1.Properties and Relationships
- use the properties and order of operations, and the relationships between operations, to solve problems involving rational numbers, ratios, rates, and percents, including those requiring multiple steps or multiple operations.
2. Math Facts
- understand and recall commonly used square numbers and their square roots.
3. Mental Math
- use mental math strategies to multiply and divide whole numbers and decimal numbers up to thousandths by powers of ten, and explain the strategies used.
4. Addition and Subtraction
- add and subtract integers, using appropriate strategies, in various contexts.
- add and subtract fractions, using appropriate strategies, in various contexts.
5. Multiplication and Division
- multiply and divide fractions by fractions, as well as by whole numbers and mixed numbers, in various contexts.
- multiply and divide integers, using appropriate strategies, in various contexts.
- compare proportional situations and determine unknown values in proportional situations and apply proportional reasoning to solve problems in various contexts.
A. Patterns and Relationships
Students will identify, describe, extend, create, and make predictions about a variety of patterns, including those found in real-life contexts. They will
- identify and compare a variety of repeating, growing, and shrinking patterns, including patterns found in real-life contexts, and compare linear growing and shrinking patterns on the basis of their constant rates and initial values.
- create and translate repeating, growing, and shrinking patterns involving rational numbers using various representations, including algebraic expressions and equations for linear growing and shrinking patterns.
- determine pattern rules and use them to extend patterns, make and justify predictions, and identify missing elements in growing and shrinking patterns involving rational numbers, and use algebraic representations of the pattern rules to solve for unknown values in linear growing and shrinking patterns.
- create and describe patterns to illustrate relationships among rational numbers.
B. Equations and Inequalities
Students will demonstrate an understanding of variables, expressions, equalities, and inequalities, and apply this understanding in various contexts. They will
1. Variables and Expressions
- add and subtract monomials with a degree of 1 and add binomials with a degree of 1 that involve integers, using tools.
- evaluate algebraic expressions that involve rational numbers.
2. Equalities and Inequalities
- solve equations that involve multiple terms, integers, and decimal numbers in various contexts, and verify solutions.
- solve inequalities that involve integers and verify and graph the solutions.
Students will solve problems and create computational representations of mathematical situations using coding concepts and skills. They will
1. Coding Skills
- solve problems and create computational representations of mathematical situations by writing and executing code, including code that involves the analysis of data in order to inform and communicate decisions.
- read and alter existing code involving the analysis of data in order to inform and communicate decisions and describe how changes to the code affect the outcomes and the efficiency of the code.
D. Mathematical Modelling
Students will apply the process of mathematical modelling to represent, analyse, make predictions, and provide insight into real-life situations.
A. Data Literacy
Students will manage, analyse, and use data to make convincing arguments and informed decisions, in various contexts drawn from real life. They will
1. Data Collection and Organization
- identify situations involving one-variable data and situations involving two-variable data and explain when each type of data is needed.
- collect continuous data to answer questions of interest involving two variables and organize the data sets as appropriate in a table of values.
2. Data Visualization
- select from among a variety of graphs, including scatter plots, the type of graph best suited to represent various sets of data; display the data in the graphs with proper sources, titles, and labels, and appropriate scales; and justify their choice of graphs.
- create an infographic about a data set, representing the data in appropriate ways, including in tables and scatter plots, and incorporating any other relevant information that helps to tell a story about the data.
3. Data Analysis
- use mathematical language, including the terms “strong”, “weak”, “none”, “positive”, and “negative”, to describe the relationship between two variables for various data sets with and without outliers.
- analyse different sets of data presented in various ways, including in scatter plots and in misleading graphs, by asking and answering questions about the data, challenging preconceived notions, and drawing conclusions, then make convincing arguments and informed decisions.
Students will describe the likelihood that events will happen and use that information to make predictions. They will
- solve various problems that involve probability, using appropriate tools and strategies, including Venn and tree diagrams.
- determine and compare the theoretical and experimental probabilities of multiple independent events happening and of multiple dependent events happening.
A. Geometric and Spatial Reasoning
Students will describe and represent shape, location, and movement by applying geometric properties and spatial relationships to navigate the world around them. They will
1. Geometric Reasoning
- identify geometric properties of tessellating shapes and identify the transformations that occur in the tessellations.
- make objects and models using appropriate scales, given their top, front, and side views or their perspective views.
- use scale drawings to calculate actual lengths and areas and reproduce scale drawings at different ratios.
2. Location and Movement
- describe and perform translations, reflections, rotations, and dilations on a Cartesian plane, and predict the results of these transformations.
Students will compare, estimate, and determine measurements in various contexts. They will
1. The Metric System
- represent very large (mega, giga, tera) and very small (micro, nano, pico) metric units using models, base ten relationships, and exponential notation.
- solve problems involving perimeter, area, and volume that require converting from one metric unit of measurement to another.
2. Lines and Angles
- solve problems involving angle properties, including the properties of intersecting and parallel lines and of polygons.
3. Length, Area, and Volume
- solve problems involving the perimeter, circumference, area, volume, and surface area of composite two-dimensional shapes and three-dimensional objects, using appropriate formulas.
- describe the Pythagorean relationship using various geometric models and apply the theorem to solve problems involving an unknown side length for a given right triangle.
A. Money and Finances
Students will demonstrate an understanding of the value of Canadian currency. They will
1. Money Concepts
- describe some advantages and disadvantages of various methods of payment that can be used when dealing with multiple currencies and exchange rates.
2. Financial Management
- create a financial plan to reach a long-term financial goal, accounting for income, expenses, and tax implications.
- identify different ways to maintain a balanced budget and use appropriate tools to track all income and spending, for several different scenarios.
- determine the growth of simple and compound interest at various rates using digital tools and explain the impact interest has on long-term financial planning.
3. Consumer and Civic Awareness
- compare various ways for consumers to get more value for their money when spending, including taking advantage of sales and customer loyalty and incentive programs, and determine the best choice for different scenarios.
- compare interest rates, annual fees, and rewards and other incentives offered by various credit card companies and consumer contracts to determine the best value and the best choice for different scenarios.
List of Skills
Objective evaluation is believed to be one of the most essential parts of teaching mathematics. In Genius Math, we use different tools and methods to evaluate the mathematical knowledge of students and their progress. Our evaluation process consists of three stages: before teaching sessions, during teaching sessions and after teaching sessions.
- Initial Assess ment Test
Before starting our teaching sessions, we administrate an assessment test to obtain some insights on the strengths and weaknesses of students and their previous math knowledge. This key information helps us to come up with a special plan for every single student.
- Standard Problems
During teaching sessions, we use a combination of different resources providing standard problems that are designed by famous mathematicians all over the world to improve the problem-solving skills of students. Among those resources are Math Kangaroo Contests, CEMC (University of Waterloo), AMC (American Mathematics Competitions), and even IMO (International Mathematics Olympiad), the latter might be considered for those who want to tackle more challenging problems or prepare for math olympiads. We use these problems to design homework, quizzes, and tests for our students based on their grades, needs and goals. As a matter of fact, such problems can be used to unveil the depth of students’ mathematical understanding.
- Final Assessment Test
When teaching sessions are over, students are asked to take another assessment test aiming to show their real progress in mathematics.
Most Common Challenging Topics
The followings are among the most common challenges students face in grade 8:
- Rational and irrational numbers
- Mixed operations
- Variables and equations as well as inequalities
- Data analysis
- Mixed transformations and impacts on geometric shapes
- Area and volume
- Pythagorean rule
What We Can Offer
- To review and practice their class notes and handouts
- To be helped with their homework, quizzes, and tests
- To improve their math skills in general
- To level up (e.g., moving from B- to B+)
- To get A+
- To learn topics beyond curriculum
- To prepare for math competitions