Overview
The Grade 6 mathematics curriculum is designed to help students develop strong mathematical understanding while building confidence in their ability to think, reason and solve problems. Throughout the year, students explore concepts that connect mathematics to real-world situations, beginning with developing a positive mathematical identity and ending with recognizing how math is part of everyday life. Along the way, they build essential skills in statistics, ratios, percentages, geometry, algebraic thinking, integers, equations and relationshps between variables. Each unit builds on prior knowledge, encouraging students to communicate their mathematical thinking, make meaningful connections and apply what they have learned to authentic situations. By the end of the course, students will have developed both the conceptual understanding and procedural fluency needed for future mathematical success.
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 skills 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 need to determine how much more money they need to save to buy a new bike.
Encourage your child to have a positive attitude toward mathematics and learning.
Talk about math in a positive 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: Understanding The World Around Us Through Statistics
In Unit 2, Understanding The World Around Us Through Statistics, students will use their prior knowledge of representing and interpreting data to develop understanding of statistical measures. Students will also build fluency with dividing multi-digit whole numbers and decimals. By having a solid understanding of statistical measures, data displays and division algorithms, students will be better prepared to analyze data presented in everyday life.
Students understand statistical questions and variability.
Students summarize, describe and interpret data in dot plots, histograms and box plots.
Students determine and use medians and means of data sets.
Students identify and use range, interquartile and MAD to describe a data set and use measures of variation to compare two data sets.
Students divide multi-digit whole numbers and decimals.
Students choose appropriate measures of center and variation to describe and interpret data.
How is data collected, analyzed and displayed?
Ask your child to analyze statistics and divide multi-digit numbers in everyday life.
Weather: Look up the temperature for your area over a certain period. Have your child create a data display and then describe the data set using measures of center and variation. Have them explain why making sense of this data is useful.
Money: Determine how many items you can buy with a given budget. For example, if drinks from a vending machine cost $1.75, find how many drinks you can buy with $11.20. Ask how much change woud be left.
Encourage your child to have a positive attitude toward mathematics and learning.
Encourage your child to draw connetions to mathematics they already know, such as using partial quotient to divide. New learning is supported by utilizing prior knowledge.
When working through problems, encourage your child to identify and organize the relevant information. This can help make sense of problems.
In Unit 3, Ratios and Rates, students will use their prior knowledge of fractions and fraction equivalence to develop understanding of ratios and rates. Ratio reasoning is a foundational topic for middle school mathematics, with applications in algebra, geometry, probability, statistics and everyday life!
Students understand ratios as a comparison of quantities. They apply ratio reasoning to solve problems.
Students understand rates as a kind of ratio that compares quantities that may have different units.
Students understand percents as a kind of ratio with a whole always equal to 100.
How can you describe how two quantities are related?
Ask your child to use ratio reasoning to solve problems in everyday life.
Recipes: Find the quantities of ingredients needed for a recipe if you need to make multiple batches or half a batch.
Driving: Use the speed limit, in miles per hour, to approximate how long it will take to drive a given distance.
Shopping: Compare the unit price of items, such as cost per ounce of different brands of shampoo. Ask which is the better buy.
Encourage your child to have a positive attitude towards mathematics and their 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.
Celebrate successes (both small and large).
In Unit 4, Understand and Use Percentages, students will use their prior understanding of ratios and rates as a comparison of quantities to develop understanding of percentages. Students will estimate, calculate and solve problems involving percentages. Having a solid understanding of percentages will prepare students for their future as they calculate tips, understand taxes and compare sale prices while shopping.
Students understand the meaning of a percent as a rate per 100.
Students understand that percentages greater than 100% represent numbers greater than 1.
Students determine equivalent fractions, decimals and percentages.
Students estimate percent of a number using benchmark percentages and rounding strategies.
Students determine the percent given a part and a whole, and the whole given a part and the percent.
How can you use percentages to solve everyday problems?
Ask your child to use percentages in everyday life.
Shopping: Find an advertisement indicating a sale where a percent is included. Ask your child to explain what it means if a sale advertises 20% off.
Money: It may be challenging to grasp that a percent can be greater that 100%. Place a dollar bill on your kitchen table, and ask your child to find 50% of the dollar (50 cents or $0.50) and 100% of the dollar (100 cents or $1). Place a second dollar bill on the table and ask what percent of the original dollar bill is represented by these two dollars (200%).
Encourage your child to have a positive attitude toward mathematics and learning.
Encourage your child to share what they learned in class with you.
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?"
In Unit 5, Solve Area, Surface Area & Volume Problems, students will use their prior knowledge of polygons and area to develop an understanding of the areas of polygons, volume and surface area. Having a solid understanding of these concepts will prepare students for their future as they encounter landscaping or home improvement projects.
Students find the area of parallelograms, rhombuses, triangles, trapezoids and polygons by composing or decomposing figures into other figures or using a formula.
Students determine volumes of rectangular prisms using unit cubes or a formula.
Students make nets for three-dimensional figures and identify three-dimensional figures based on nets.
Students determine surface area of rectangular prisms, triangular prisms, rectangular pyramids and triangular pyramids.
How can you relate the areas of triangles and rectangles to the areas, surface areas and volumes of other polygons and 3-D figures?
Ask your child to use area, surface area and volume in everyday life.
Home Improvement: Calculate the area(s) of furniture or other features around your home in the shapes of parallelograms, triangles or trapezoids.
Gardening: Determine the amount of cubic feet of soil needed to fill a garden bed.
Encourage your child to have a positive attitude toward mathematics and learning.
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.
Encourage your child to connect geometry and finding area to their everyday life. This helps build their math identity and the belief that math can be used in powerful ways in their life.
Unit 6: Numerical & Algebraic Expressions
In Unit 6, Numerical & Algebraic Expressions, students will build fluency with division of fractions and develop understanding of numercial and algebraic expressions. Having a solid understanding of these concepts will prepare students for determining unknown quantities and totals in everyday life.
Students find quotients of fractions, whole numbers and mixed numbers by using equations and models.
Students write numerical expressions with exponents and algebraic expressions.
Students use the order of operations to evaluate numerical and algebraic expressions.
Students determine whether two expressions are equivalent and create equivalent expressions using properties of operations.
Students find the greatest common factor or least common multiple of two numbers.
How can we communicate algebraic relationships with mathematical symbols?
Ask your child to write and evaluate expressions in everyday life.
Amusement Park: Have your child write and evaluate an expression for the total amount of money needed for your family to spend a day at an amusement park.
Cereal: Consider a 3/4 pound box of cereal that contains 9 servings. Have your child determine how much cereal is in each serving.
Encourage your child to have a positive attitude toward mathematics and learning.
Talk about math in a positive way. Choosing positive words when talking about math at home can help your child develop positive feelings around learning math.
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 7: Integers, Rational Numbers & The Coordinate Plane
In Unit 7, Integers, Rational Numbers & The Coordinate Plane, students will draw on their knowledge of whole numbers and number lines to develop understanding of integers, rational numbers and the coordinate plane. Understanding these concepts prepares students as they encounter integers and rational numbers in their everyday life.
Students explore the locations of rational numbers and their opposites on a number line.
Students explore absolute value.
Students use the number line to compare and order rational numbers.
Students plot points on the coordinate plane and describe the location of points.
Students find the distance between points on the coordinate plane.
Students find side lengths of polygons on the coordinate plane using absolute value.
How are integers and rational numbers related to the coordinate plane?
Ask your child to order and compare rational numbers and integers in everyday life.
Grocery Shopping: Have your child compare the budget for a trip to the grocery store to the actual total cost by using rational numbers to represent the amounts.
Sea Level: Ask your child to find and compare the elevations above and below sea level of several mountains and trenches.
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 graphing on the coordinate plane.
When working through problems, encourage your child to identify and organize the relevant information. This can help make sense of problems.
Unit 8: Equations & Inequalities
In Unit 8, Equations & Inequalities, students draw on their knowledge of expressions and properties of operations to develop understanding or equations and inequalities. They build fluency with solving one-step equations and writing and graphing inequalities.
Students write and solve equations involving one variable.
Students write and solve one-step addition, subtraction, multiplication and division equations.
Students explore writing inequalities to represent real-world and mathematical problems.
Students draw number line graphs to represent inequalities and use substitution to test solutions.
What are the similarities and differences between equations and inequalities?
Ask your child to use equations and inequalities in everyday life.
Shopping: Have your child find the amount of change from a purchase. For example, when buying a gallon of milk at $4.49, the equation 4.49 + c = 5 could be used to find the amount of change, c, from $5.
Catering: At least 50 dinner rolls are needed for an event. Have your child write and graph an inequality for the number of dinner rolls a caterer could supply.
Encourage your child to have a positive attitude toward mathematics and learning.
Encourage them to ask questions (both in home and in class). Sometimes, an answer to a question will generage more questions.
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?"
Unit 9: Relationships Between Two Variables
In Unit 9, Relationships Between Two Variables, students draw on their knowledge of tables, equations and the coordinate plane to develop understanding of relationships between two variables. Having a solid understanding of these concepts will prepare students as they encounter situations where a relationship exists between two variables.
Students identify independent and dependent variables.
Students find the value of the dependent variable given a relationship between two quantities.
Students use tables and graphs to find and analyze the relationship between two quantities and to write an equation to show the relationship between the dependent and independent variables.
Students write an equation to show the relationship between two quantities and use it to solve a problem.
How can you find and represent the relationship between two variables?
Ask your child to identify and represent two-variable relationships in everyday life.
Groceries: Have your child use the price per pound or price per item of different foods to represent or determine the total cost, C, of purchasing, x, pounds or items.
Driving: Given a speed in miles per hour, have your child determine how many miles, d, a car would travel after, t, hours. Have them write an equation and use it to determine how long it would take to travel some number of miles at that speed.
Encourage your child to have a positive attitude toward mathematics and learning.
Encourage your child to share what they learned in class with you. Discussing mathematics helps build conceptual understanding.
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 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 actions, hobbies and activities.
Students explore different ways to use mathematics to represent and find creative solutions to 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 and relationships to solve problems or puzzles.
Students use generalizations derived from repeated reasoning to solve problems.
Students explore math and beauty in nature and geometric design.
What is math?
Encourage your child to identify places where they see mathematics in everyday life.
Nature: Ask your child what patterns or structure they see in the plants and animals around them. For example, they may notice the repetition in a beehive or concentric circles in the rings of a tree.
Hobbies: Have your child identify how math is used in their hobbies or the sports they play. For example, they may find that statistics are an important part of a sport they play.
Encourage your child to have a positive attitude towards mathematics and their learning.
Encourage your child to explore challenges and remind them that every challenge is an opportunity to learn something new.
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.
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 that math can be used in powerful ways in their life.