Overview
Throughout Grade 8, students will strengthen their mathematical thinking by building on prior knowledge while exploring new concepts through problem solving, collaboration and real-world applications. They will develop a deeper understanding of geometry, linear relationships, functions, statistics, volume, systems of equations and irrational numbers while refining their reasoning, communication and critical thinking skills. Students will also be encouraged to see themselves as capable mathematicians by making connections between mathematics and the world around them. By the end of the year, they will have built a strong foundation of mathematical knowledge and confidence that will prepare them for future success in mathematics.
Unit 1: Math Is...
In Unit 1, Math Is..., students will think and talk about what it means to do math and to see themselves as a "doer of math." They will be encouraged to notice and wonder about how math is used in everyday situations, talk about their mathematical ideas and reflect on their experiences with mathematics.
Students build on their problem-solving as they consider alternative strategies for solving the problem presented.
Students model real-world situations with a range of representations.
Students construct arguments to critique the reasoning of classmates.
Students use appropriate units in their calculations.
Students make generalizations after noticing repeated calculations with operations.
What does it mean to do math?
Ask your child to think about how they use math in everyday life.
Money: Ask your child what math problems they can think of that involve money. For example, they may need to determine how much more money they need to save to buy a new bike.
Games: Ask your child how they might use math in the games they play. For example, they may find by how many points they lead or trail in a game.
Encourage your child to have a positive attitude toward mathematics and learning.
Talk about math in a postivie way. Choosing positive words when talking about math at home can help your child develop positive feelings around learning math.
Celebrate successes (both small and large).
Unit 2: Congruence & Similarity
In Unit 2, Congruence & Similarity, students will draw on their knowledge of graphing on the coordinate plane to transform figures and develop understanding of how transformations affect the x- and y-coordinates of a preimage. They will use transformations to determine whether two figures are similar or congruent.
Student describe the characteristics of translations, reflections, rotations and dilations.
Students translate, reflect, rotate and dilate figures.
Students describe a sequence of transformations that map one figure (a preimage) onto another (the image).
Students explain why two figures are congruent using rigid motions.
Students determine whether a pair of triangles is similar by using Angle-Angle Similarity.
Students find distances or lenths that are difficult to measure directly by using properties of similar triangles.
What does it mean for two objects to be congruent or similar?
Ask your child to identify transformations and congruent and similar figures in everyday life.
Architecture: Discuss with your child how architects and engineers use geometric transformations when designing buildings and bridges. Often, they use reflections to create symmetrical patterns and designs.
Interior Design: Ask your child to identify transformations and congruent or similar figures in the patterns observed on fabrics, floor coverings or wall coverings in your house. For example, floor tiles may be installed using congruent square tiles that are translated.
Encourage your child to have a positive attitude toward mathematics and learning.
Encourage your child to share what he or she has learned in class with you.
Remind your child that making mistakes helps them grow their mathematical and reasoning skills. Encourage them to go back and fix their mistakes as they work through the unit.
Unit 3: Linear Relationships & Equations
In Unit 3, Linear Relationships & Equations, students will use their prior knowledge of unit rates and proportional relationships to develop understanding of slope and linear relationships. They will draw on their knowledge of two-step equations to help them solve more complex equations.
Students graph a proportional relationship and describe the slope as the constant of proportionality.
Students compare two different proportional relationships by comparing the slopes.
Students explain why the hypotenuses of similar triangles have equal slopes.
Students derive the equations y = mx for a line through the origin and y = mx + b for a line intercepting the y-axis at b.
Students solve linear equations with variables on both sides.
Students determine the number of solutions to linear equations.
How are linear relationships related to proportional relationships?
Ask your child to use slope and linear equations in everyday life.
Stairs: Estimate the rise (height) and run (depth) of each stair of a staircase. Discuss how the staircase might be different if the run changed.
Cell phones: Algebraically model the cost c of two cell phone plans to determine after how many months x they will be the cost. For example, if one plan charges $55 per month plus a $30 activation fee (c = 55x +30) and another charges $60 per month (c = 60x), the equation 55x + 30 = 60z represents the situation.
Encourage your child to have a positive attitude toward mathematics and learning.
Encourage them to ask questions (both at home and in class). Sometimes, an answer to a question will generate more questions. That's how you know they are learning!
Encourage your child to embrace challenges and remind them that every challenge is an opportunity to learn something new.
Unit 4: Understand & Analyze Functions
In Unit 4, Understand & Analyze Functions, students will use their prior knowledge of linear relationships to develop an understanding of functions. They will use tables, mapping diagrams, graphs and equations to represent and compare functions.
Students identify and use qualitative features of relationships.
Students determine if a relation is a function by using a table or mapping diagram.
Students represent functions in different forms and determine if a function is linear or nonlinear from multiple representations.
Students analyze functions to interpret their rate of change and initial values.
Students compare functions represented in different forms.
How do you use functions to model relationships?
Ask your child to model real-world situations with functions in everyday life.
TV Streaming: Compare the costs of television streaming from two streaming services, making sure to account for any initial start-up costs. Represent the relationship between total cost c and months m using a table, graph or equation.
Savings Accounts: Compare different interest rates for savings accounts and explain why these relationships are nonlinear functions.
Encourage your child to have a positive attitude toward mathematics and learning.
Encourage your child to draw connections to prior mathematics knowledge, such as slope. New learning is supported by using prior knowledge.
When your child is frustrated, encourage them to take a break. Stepping away from a problem and returning to it with fresh eyes can lead to an "aha!" moment.
Unit 5: Patterns of Association
In Unit 5, Patterns of Association, students will draw on their knowledge of linear functions and percentages to develop an understanding of scatter plots and two-way relative frequency tables. They will use representations to build fluency with statistics.
Students represent bivariate data on a scatterplot.
Students investigate and interpret patterns in bivariate data.
Students draw lines of fit in a scatterplot of bivariate data, assess the closeness of fit of the associations in the data, and use a line of fit or its equation to make predictions.
Students explore how to represent multiple categories of data in two-way tables and analyze the rows and columns to describe patterns of association.
Students display data in two-way tables and interpret patterns in the data.
What kind of patterns can be found in data?
Ask your child to represent and interpret data in everyday life.
Gas Prices: Keep track of the price of a gallon of gasoline at one gas station over a two-week period. Create a scatter plot and find a line of fit if a linear association is suggested.
Surveys: Have your child find a survey that organizes the results by two categories, such as favorite music genre and age group. Have them create a two-way table using the data.
Encourage your child to have a positive attitude toward mathematics and learning.
As they work through problems, ask your child to explain their reasoning. You can ask questions such as " Why did you..." and "How do you know?"
Talk about math in a positive way. Choosing positive words when talking about math at home can help your child develop positive feelings about learning math.
Unit 6: Angles, Triangles & The Pythagorean Theorem
In Unit 6, Angles, Triangles & The Pythagorean Theorem, students will use their prior knowledge of angles and triangles to understand special angle pairs and the Pythagorean Theorem. They will use this understanding to find missing angle measures and the side lengths of right triangles.
Students explore using relationships among angles formed when two parallel lines are crossed by a transversal.
Students explore the relationships between the interior and exterior angles of a triangle.
Students calculate and estimate square roots.
Students apply the Pythagorean Theorem to determine the measures of the sides of a right triangle, to determine the length of a diagonal line on the coordinate plane and in real-world applications.
Students use the converse of the Pythagorean Theorem to analyze triangles.
How can angle relationships and right triangles be used to solve everyday problems?
Ask your child to solve problems involving angles and triangles in everyday life.
Screens: Computer monitors are described by their diagonal length. Discuss the differences between the dimensions of a 24" by 17" screen and a 24" screen.
Home improvement: Have your child explain how they would find the dimensions of a square floor that is being carpeted if they know the area in square feet.
Encourage your child to have a positive attitude toward mathematics and learning.
Remind your child that making mistakes helps them grow their mathematical and reasoning skills. Encourage them to go back and fix their mistakes as they work through the unit.
When working through problems, encourage your child to identify and organize the relevant information. This can help them make sense of problems.
Unit 7: Volume
In Unit 7, Volume, students will draw on their knowledge of finding volumes of prisms to develop understanding of how to find the volumes of cylinders, cones and spheres. They use this understanding to find the volumes of composite figures and solve real-world problems involving solid figures.
Students find the cube root of a value.
Students find volumes of cylinders and use volumes to solve problems.
Students use the volume formula to find the volume of cones.
Students use the volume formula to find the volume of spheres.
Students use volume formulas to solve problems in context.
How can volume be used to solve real-world problems?
Ask your child to find the volume of objects in everyday life.
Containers: Ask your child to find the dimensions of a cylinder, cone or sphere that would hold approximately the same volume as a given rectangular prism. For example, ask for the radius and height of a cylindrical container that would hold the contents of a cereal box.
Sports: Have your child compare the volumes of balls from two different sports. For example, ask how much greater the volume of a basketball with the radius of 9.55 inches is than a soccer ball with a radius of 8.65 inches.
Encourage your child to have a positive attitude toward mathematics and learning.
Encourage your child to share what they have learned in class with you. Discussing mathematics helps to build conceptual understanding.
Encourage your child to connect finding volume to their everyday life. This helps build their math identity and their belief that math can be used in powerful ways in their life.
Unit 8: Systems of Linear Equations
In Unit 8, Systems of Linear Equations, students will draw on their prior knowledge of linear equations to solve systems of two linear equations both graphically and algebraically. They will understand what a solution to a system of equations is and will find the number of solutions to a system. This will lay the foundation for solving more complicated systems of equations and inequalities in later courses.
Students use graphing to find the solution to a system of equations.
Students use graphing to estimate the solution to a system of equations.
Students determine the number of solutions to a system of equations by looking at a graph of the system.
Students use substitution or elimination to solve a system of two linear equations.
How can systems of equations be helpful in solving everyday problems?
Ask your child to apply their knowledge of systems of equations in everyday life.
Coins: Suppose you have $1.55 in quarters q and dimes d and a total of 8 coins. Have your child write a system of equations, such as q + d = 8 and 0.25q + 0.10d = 1.55, to model this situation. Have them solve the system to determine the number of each type of coin.
Memberships: Have your child find when the total cost of two different memberships with different initial and monthly fees will be the same.
Encourage your child to have a positive attitude toward mathematics and learning.
Encourage them to ask questions (both at and in class). Sometimes, an answer to a question will generate more questions.
When your child is frustrated, encourage them to take a break. Stepping away from a problem and returning to it with fresh eyes can lead to an "aha!" moment.
Unit 9: Irrational Numbers, Exponents & Scientific Notation
In Unit 9, Irrational Numbers, Exponents & Scientific Notation, students will use their prior knowledge of exponents to develop understanding of the properties of exponents and scientific notation.
Students explore converting rational numbers into repeating decimals.
Students use a number line to locate, compare and order rational and irrational numbers.
Students generate equivalent expressions using zero and negative exponents and properties of powers.
Students rewrite numbers as products of a number between 1 and 10 times a power of 10.
Students use properties of powers to add, subtract, multiply and divide numbers in scientific notation.
Why are the properties of numbers important?
Ask your child to apply exponents in everyday life.
News Articles: Find a news article with a number represented in billions or trillions, such as 1.2 billion. Have your child write it in standard form and scientific notation.
Computers: A megabyte of storage is equal to 2 to the power of 20 bytes. A gigabyte is equal to 2 to the power of 30 bytes. Ask your child how many megabytes are in a gigabyte.
Encourage your child to have a positive attitude toward mathematics and learning.
Encourage your child to draw connections to mathematics they already know, such as ordering rational numbers. New learning is supported by utilizing prior knowledge.
Celebrate successes (both small and large).
Unit 10: Math Is...
In Unit 10, Math Is..., students will connect mathematics to everyday places, objects and situations. Recognizing connections between everyday life and mathematics reinforces that math is more than just a school subject.
Students discuss the role of math in their and other peoples' lives.
Students discuss approaches for making sense of a problem and determining strategies for solving it.
Students explore different ways to use mathematics to represent real-world problems.
Students construct mathematical arguments and respond to the ideas and arguments of others.
Students consider strategies for uncovering patterns and using patterns to solve problems.
Students use generalizations derived from repeated reasoning to solve problems.
Students decide on classroom norms of interaction for a productive learning environment.
What is math?
Ask your child to child to identify places where they see mathematics in everyday life.
Cooking: Have your child identify how math is used in the kitchen. For example, they may note the difference in volumes of kitchen tools, such as measuring cups, pots or funnels. They may also notice that each measuring cup in a set is a dilation of another cup.
Design: Ask your child what patterns or structure they see in designs and architecture. For example, they may point out similar and congruent shapes or parallel lines in the structure of a building.
Encourage your child to have a positive attitude toward mathematics and learning.
When working through problems, encourage your child to identify and organize the relevant information. This can help them make sense of problems.
Remind your child that making mistakes helps them grow their mathematical and reasoning skills. Encourage them to go back and fix their mistakes.
Encourage your child to connect the mathematics they have learned throughout the course to their everyday life. This helps build their math identity and their belief math can be used in powerful ways in their life.