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Course Standards
General Course Information and Notes
General Notes
MAFS.6In Grade 6, instructional time should focus on four critical areas: (1) connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; (3) writing, interpreting, and using expressions and equations; and (4) developing understanding of statistical thinking.
- Students use reasoning about multiplication and division to solve ratio and rate problems about quantities. By viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative size of quantities, students connect their understanding of multiplication and division with ratios and rates. Thus students expand the scope of problems for which they can use multiplication and division to solve problems, and they connect ratios and fractions. Students solve a wide variety of problems involving ratios and rates.
- Students use the meaning of fractions, the meanings of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for dividing fractions make sense. Students use these operations to solve problems. Students extend their previous understandings of number and the ordering of numbers to the full system of rational numbers, which includes negative rational numbers, and in particular negative integers. They reason about the order and absolute value of rational numbers and about the location of points in all four quadrants of the coordinate plane.
- Students understand the use of variables in mathematical expressions. They write expressions and equations that correspond to given situations, evaluate expressions, and use expressions and formulas to solve problems. Students understand that expressions in different forms can be equivalent, and they use the properties of operations to rewrite expressions in equivalent forms. Students know that the solutions of an equation are the values of the variables that make the equation true. Students use properties of operations and the idea of maintaining the equality of both sides of an equation to solve simple one-step equations. Students construct and analyze tables, such as tables of quantities that are equivalent ratios, and they use equations (such as 3x = y) to describe relationships between quantities.
- Building on and reinforcing their understanding of number, students begin to develop their ability to think statistically. Students recognize that a data distribution may not have a definite center and that different ways to measure center yield different values. The median measures center in the sense that it is roughly the middle value. The mean measures center in the sense that it is the value that each data point would take on if the total of the data values were redistributed equally, and also in the sense that it is a balance point. Students recognize that a measure of variability (interquartile range or mean absolute deviation) can also be useful for summarizing data because two very different set of data can have the same mean and median yet be distinguished by their variability. Students learn to describe and summarize numerical data sets, identifying clusters, peaks, gaps, and symmetry, considering the context in which the data were collected.
Students in Grade 6 also build on their work with area in elementary school by reasoning about relationships among shapes to determine area, surface area, and volume. They find areas of right triangles, other triangles, and special quadrilaterals by decomposing these shapes, rearranging or removing pieces, and relating the shapes to rectangles. Using these methods, students discuss, develop, and justify formulas for areas of triangles and parallelograms. Students find areas of polygons and surface areas of prisms and pyramids by decomposing them into pieces whose area they can determine. They reason about right rectangular prisms with fractional side lengths to extend formulas for the volume of a right rectangular prism to fractional side lengths. They prepare for work on scale drawings and constructions in Grade 7 by drawing polygons in the coordinate plane.
General Information
Student Resources
Original Student Tutorials
Explore reflections on a coordinate plane in epic Capture the Flag tournament with this interactive tutorial.
This is part 2 in a two-part series:
- Open "Capturing Flags on the Coordinate Plane Part 1"
- Open "Capturing Flags on the Coordinate Plane Part 2"
Type: Original Student Tutorial
Explore the coordinate plane in an epic Capture the Flag tournament with this interactive tutorial.
This is part 1 in a two-part series:
- Open "Capturing Flags on the Coordinate Plane Part 1"
- Open "Capturing Flags on the Coordinate Plane Part 2"
Type: Original Student Tutorial
Evaluate numerical expressions with fractions using the order of operations and properties of operations in this interactive tutorial.
Type: Original Student Tutorial
Evaluate numerical expressions with decimals using the order of operations and properties of operations in this interactive tutorial.
Type: Original Student Tutorial
Evaluate numerical expressions with whole numbers using the order of operations and properties of operations in this interactive tutorial.
This is part 2 of a series on evaluating expressions with whole numbers.
Type: Original Student Tutorial
Use the least common multiple to solve real-life problems with Brady and Natalia in this interactive tutorial.
This is part 2 of 2-part series, click HERE to view part 1.
Type: Original Student Tutorial
Evaluate numerical expressions with integers using the order of operations and properties of operations in this interactive tutorial.
Type: Original Student Tutorial
Follow George as he explores the formula for the area of a triangle and uses it to find the area of various triangles in this interactive student tutorial.
Type: Original Student Tutorial
Follow Jamal as he represents algebraic inequalities on a number line while visiting a theme park with his family in this interactive tutorial.
This is part 2 in a two-part series on inequalities. Click HERE to open part 1.
Type: Original Student Tutorial
Help Oscar translate written real-world descriptions of multiplication and division into algebraic expressions in this interactive tutorial.
This is part 2 of 3. Click below to open the other tutorials in this series.
- Algebraic Expressions Part 1: Addition and Subtraction
- Part 3 (Coming Soon)
Type: Original Student Tutorial
Follow Oscar as he writes algebraic expressions of addition and subtraction about his new puppy Scooter in this interactive tutorial.
Type: Original Student Tutorial
Help Cindy find the missing dimension of a rectangular prism in her delivery services job with this interactive tutorial.
This is part 3 in a three-part series. Click below to open the other tutorials in the series.
Type: Original Student Tutorial
Follow Cindy as she explores fractional unit cubes and finds the volume of rectangular prisms that have rational number dimensions in this interactive tutorial.
This is part 2 in a three-part series. Click below to open the other tutorials in the series.
Type: Original Student Tutorial
Follow Cindy as she learns about the volume formulas to create boxes in this interactive tutorial.
This is part 1 in a three-part series. Click below to open the other tutorials in the series.
Type: Original Student Tutorial
Help Lily identify and create equivalent ratios in this interactive tutorial.
Type: Original Student Tutorial
Follow Matteo as he explores opposite numbers, positive and negative rational numbers, and zero in real-world contexts while planning and going on a cruise in Alaska in this interactive tutorial.
Type: Original Student Tutorial
Learn how to identify and calculate unit rates by helping Milo find prices per item at a farmer's market in this interactive tutorial.
Type: Original Student Tutorial
Learn how math models can show why social distancing during a epidemic or pandemic is important in this interactive tutorial.
Type: Original Student Tutorial
Sail through subtracting decimals to the thousandths place using a standard algorithm in this interactive tutorial.
Type: Original Student Tutorial
Learn to add decimals to the thousandths using a standard algorithm at the ice cream shop in this interactive tutorial.
Type: Original Student Tutorial
Learn how to solve 1-step multiplication and division equations with Dr. E. Quation in Part 2 of this series of interactive tutorials. You'll also learn how to check your answers to make sure your answer is the solution to the equation.
Type: Original Student Tutorial
Learn how to solve and check one-step addition and subtraction equations with Dr. E. Quation as you complete this interactive tutorial.
Click here to open Dr. E. Quation Part 2: One-Step Multiplication and Division Equations
Type: Original Student Tutorial
Use models to solve balance problems on a space station in this interactive, math and science tutorial.
Type: Original Student Tutorial
Learn how to interpret histograms to analyze data, and help an inventor predict the range of a catapult in part 2 of this interactive tutorial series. More specifically, you'll learn to describe the shape and spread of data distributions.
Click HERE to open part 1.
Type: Original Student Tutorial
Learn how to create a histogram to display continuous data from projectiles launched by a catapult in this interactive tutorial.
This is part 1 in a 2-part series. Click HERE to open part 2.
Type: Original Student Tutorial
Explore computer coding on the farm by using IF statements and repeat loops to evaluate mathematical expressions. In this interactive tutorial, you'll also solve problems involving inequalities.
Click below to check out the other tutorials in the series.
- MacCoder’s Farm Part 1: Declare Variables
- MacCoder’s Farm Part 2: Condition Statements
- MacCoder's Farm Part 3: IF Statements
Type: Original Student Tutorial
Explore computer coding on the farm by using relational operators and IF statements to evaluate expressions. In this interactive tutorial, you'll also solve problems involving inequalities.
Click below to check out the other tutorials in the series.
- MacCoder’s Farm Part 1: Declare Variables
- MacCoder's Farm Part 2: Condition Statements
- MacCoder's Farm Part 4: Repeat Loops
Type: Original Student Tutorial
Explore computer coding on the farm by using condition and IF statements in this interactive tutorial. You'll also get a chance to apply the order of operations as you using coding to solve problems.
Click below to check out the other tutorials in the series.
- MacCoder's Farm Part 1: Declare Variables
- MacCoder’s Farm Part 3: If Statements
- MacCoder's Farm Part 4: Repeat Loops
Type: Original Student Tutorial
Explore computer coding on the farm by declaring and initializing variables in this interactive tutorial. You'll also get a chance to practice your long division skills.
Type: Original Student Tutorial
Learn how to calculate and interpret the Mean Absolute Deviation (MAD) of data sets in this travel-themed, interactive statistics tutorial.
Type: Original Student Tutorial
Learn how to make and interpret boxplots in this pet-themed, interactive tutorial.
Type: Original Student Tutorial
Learn how arguments are formed with claims, reasons, and evidence. In this interactive tutorial, you'll read several short speeches from students hoping to be elected president of the Student Council. We'll trace the claim made by each student and the reasons and evidence they use to support it.
Type: Original Student Tutorial
Discover how to calculate and interpret the mean, median, mode and range of data sets from the zoo in this interactive tutorial.
Type: Original Student Tutorial
You will organize information in a table and write ratios equivalent to a given ratio in order to solve real-world and mathematical problems in this interactive tutorial.
Type: Original Student Tutorial
Investigate the limiting factors of a Florida ecosystem and describe how these limiting factors affect one native population-the Florida Scrub-Jay-with this interactive tutorial.
Type: Original Student Tutorial
Investigate how temperature affects the rate of chemical reactions in this interactive tutorial.
Type: Original Student Tutorial
Learn what genetic engineering is and some of the applications of this technology. In this interactive tutorial, you’ll gain an understanding of some of the benefits and potential drawbacks of genetic engineering. Ultimately, you’ll be able to think critically about genetic engineering and write an argument describing your own perspective on its impacts.
Type: Original Student Tutorial
Learn how to create and use number lines with positive and negative numbers, graph positive and negative numbers, find their distance from zero, find a number’s opposite using a number line and signs, and recognize that zero is its own opposite with this interactive, golf-themed tutorial.
Type: Original Student Tutorial
Evaluate numerical expressions with whole numbers using the order of operations and properties of operations in this interactive tutorial.
Type: Original Student Tutorial
Follow Jamal as he translates theme park written descriptions into algebraic inequalities in this interactive tutorial.
Type: Original Student Tutorial
Type: Original Student Tutorial
Learn how to find the least common multiple by helping Brady and Natalia work through some homework questions in this interactive student tutorial.
This is part 1 of 2-part series, click HERE to view part 2.
Type: Original Student Tutorial
Educational Games
In this challenge game, you will be solving equations with variables on both sides. Each equation has a real solution. Use the "Teach Me" button to review content before the challenge. After the challenge, review the problems as needed. Try again to get all challenge questions right! Question sets vary with each game, so feel free to play the game multiple times as needed! Good luck!
Type: Educational Game
This fun and interactive game helps practice estimation skills, using various operations of choice, including addition, subtraction, multiplication, division, using decimals, fractions, and percents.
Various levels of difficulty make this game appropriate for multiple age and ability levels.
Addition/Subtraction: The addition and subtraction of whole numbers, the addition and subtraction of decimals.
Multiplication/Division: The multiplication and addition of whole numbers.
Percentages: Identify the percentage of a whole number.
Fractions: Multiply and divide a whole number by a fraction, as well as apply properties of operations.
Type: Educational Game
This is a fun and interactive game that helps students practice ordering rational numbers, including decimals, fractions, and percents. You are planting and harvesting flowers for cash. Allow the bee to pollinate, and you can multiply your crops and cash rewards!
Type: Educational Game
Test your fraction skills by answering questions on this site. This quiz asks you to simplify fractions, convert fractions to decimals and percentages, and answer algebra questions involving fractions. You can even choose difficulty level, question types, and time limit.
Type: Educational Game
In this timed activity, students solve linear equations (one- and two-step) or quadratic equations of varying difficulty depending on the initial conditions they select. This activity allows students to practice solving equations while the activity records their score, so they can track their progress. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.
Type: Educational Game
In this activity, two students play a simulated game of Connect Four, but in order to place a piece on the board, they must correctly solve an algebraic equation. This activity allows students to practice solving equations of varying difficulty: one-step, two-step, or quadratic equations and using the distributive property if desired. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the Java applet.
Type: Educational Game
In this activity, students enter coordinates to make a path to get to a target destination while avoiding mines. This activity allows students to explore Cartesian coordinates and the Cartesian coordinate plane. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.
Type: Educational Game
Problem-Solving Tasks
In this online problem-solving challenge, students apply algebraic reasoning to determine the "costs" of individual types of faces from sums of frowns, smiles, and neutral faces. This page provides three pictorial problems involving solving systems of equations along with tips for thinking through the problem, the solution, and other similar problems.
Type: Problem-Solving Task
Students are asked to use a diagram or table to write an algebraic expression and use the expression to solve problems.
Type: Problem-Solving Task
The goal of this task is to give students a context to investigate large numbers and measurements. Students need to fluently convert units with very large numbers in order to successfully complete this task. The total number of pennies minted either in a single year or for the last century is phenomenally large and difficult to grasp. One way to assess how large this number is would be to consider how far all of these pennies would reach if we were able to stack them one on top of another: this is another phenomenally large number but just how large may well come as a surprise.
Type: Problem-Solving Task
This tasks gives a verbal description for computing the perimeter of a rectangle and asks the students to find an expression for this perimeter. They then have to use the expression to evaluate the perimeter for specific values of the two variables.
Type: Problem-Solving Task
Students are asked to determine if given expressions are equivalent.
Type: Problem-Solving Task
The purpose of this task is to ask students to write expressions and to consider what it means for two expressions to be equivalent.
Type: Problem-Solving Task
Students are asked to explore and then write an expression with an exponent. The purpose of this task is to introduce the idea of exponential growth and then connect that growth to expressions involving exponents. It illustrates well how fast exponential expressions grow.
Type: Problem-Solving Task
This problem asks the student to find a 3% sales tax on a vase valued at $450.
Type: Problem-Solving Task
The purpose of this task is to give students an opportunity to solve a challenging multistep percentage problem that can be approached in several different ways. Students are asked to find the cost of a meal before tax and tip when given the total cost of the meal. The task can illustrate multiple standards depending on the prior knowledge of the students and the approach used to solve the problem.
Type: Problem-Solving Task
Students are asked to determine and illustrate all possible descriptions for the base and height of a given triangle.
Type: Problem-Solving Task
Students are asked to draw a scale model of a building and find related volume and surface areas of the model and the building which are rectangular prisms.
Type: Problem-Solving Task
Students are asked to demonstrate two different strategies for finding the area of polygons shown on grids.
Type: Problem-Solving Task
Students are asked to use the given information to determine the cost of painting a barn.
Type: Problem-Solving Task
The purpose of this task is to gain a better understanding of factors and common factors. Students should use the distributive property to show that the sum of two numbers that have a common factor is also a multiple of the common factor.
Type: Problem-Solving Task
Students are asked to reason about and explain the position of two locations relative to sea level.
Type: Problem-Solving Task
The purpose of this task is for students to solve problems involving decimals in a context involving a concept that supports financial literacy, namely inflation. Inflation is a sustained increase in the average price level. In this task, students are asked to compare the buying power of $20 in 1987 and 2012, at least with respect to movie tickets.
Type: Problem-Solving Task
Given the fact 13 x 17 = 221, students are asked to reason about and explain the decimal placement in multiplication and division problems where some of the numbers involved have been changed by powers of ten.
Type: Problem-Solving Task
Students are asked to reason about and explain the placement of decimals in quotients.
Type: Problem-Solving Task
Students are asked to solve a distance problem involving fractions.
Type: Problem-Solving Task
Students are asked to solve a fraction division problem using both a visual model and the standard algorithm within a real-world context.
Type: Problem-Solving Task
The purpose of this task is converting square units. Use the information provided to answer the questions posed. This task asks students to critique Jada's reasoning.
Type: Problem-Solving Task
Students are asked to use a ratio to determine how much money Jim and Jesse had at the start of their trip.
Type: Problem-Solving Task
Students are asked to determine the percent of the area of a store covered by a security camera. Then, students are asked to determine the "best" place to position the camera and support their answer.
Type: Problem-Solving Task
Use the information provided to find out the original price of Selina's shirt. There are several different ways to reason through this problem; two approaches are shown.
Type: Problem-Solving Task
This problem is the fifth in a series of seven about ratios. Even though there are three quantities (the number of each candidates' votes), they are only considered two at a time.
Type: Problem-Solving Task
This is the sixth problem in a series of seven that use the context of a classroom election. While it still deals with simple ratios and easily managed numbers, the mathematics surrounding the ratios are increasingly complex. In this problem, the students are asked to determine the difference in votes received by two of the three candidates.
Type: Problem-Solving Task
This is the last problem of seven in a series about ratios set in the context of a classroom election. Since the number of voters is not known, the problem is quite abstract and requires a deep understanding of ratios and their relationship to fractions.
Type: Problem-Solving Task
This problem is the third in a series of tasks set in the context of a class election. Students are given a ratio and total number of voters and are asked to determine the difference between the winning number of votes received and the number of votes needed for victory.
Type: Problem-Solving Task
This is the first and most basic problem in a series of seven problems, all set in the context of a classroom election. Students are given a ratio and total number of voters and are asked to determine the number of votes received by each candidate.
Type: Problem-Solving Task
This is the second in a series of tasks that are set in the context of a classroom election. It requires students to understand what ratios are and apply them in a context. The simple version of this question just asked how many votes each gets. This has the extra step of asking for the difference between the votes.
Type: Problem-Solving Task
This is the fourth in a series of tasks about ratios set in the context of a classroom election. Given only a ratio, students are asked to determine the fractional difference between votes received and votes required.
Type: Problem-Solving Task
Students are given a context and a dotplot and are asked a number of questions regarding shape, center, and spread of the data.
Type: Problem-Solving Task
Students are given a context and a series of questions and are asked to identify whether each question is statistical and to provide their reasoning. Students are asked to compose an original statistical question for the given context.
Type: Problem-Solving Task
Using the information provided, create an appropriate graphical display and answer the questions regarding shape, center and variability.
Type: Problem-Solving Task
The purpose of this task is meant to reinforce students' understanding of rational numbers as points on the number line and to provide them with a visual way of understanding that the sum of a number and its additive inverse (usually called its "opposite") is zero.
Type: Problem-Solving Task
Students are asked a series of questions involving a fraction and a whole number within the context of a recipe. Students are asked to solve a problem using both a visual model and the standard algorithm.
Type: Problem-Solving Task
Students are asked to solve a distance problem involving fractions. The purpose of this task is to help students extend their understanding of division of whole numbers to division of fractions, and given the simple numbers used, it is most appropriate for students just learning about fraction division because it lends itself easily to a pictorial solution.
Type: Problem-Solving Task
The purpose of this task is for students to solve problems involving multiplication and division of decimals in the real-world context of setting financial goals. The focus of the task is on modeling and understanding the concept of setting financial goals, so fluency with the computations will allow students to focus on other aspects of the task.
Type: Problem-Solving Task
Students are asked to solve a real-world problem involving common multiples.
Type: Problem-Solving Task
Students are asked to use fractions to determine how many hours it will take a car to travel a given distance.
Type: Problem-Solving Task
Students are asked to use fractions to determine how long a video game can be played.
Type: Problem-Solving Task
The purpose of this task is to have students convert multiple currencies to answer the problem. Students may find the CDN abbreviation for Canada confusing. Teachers may need to explain the fact that money in Canada is also called dollars, so to distinguish them, we call them Canadian dollars.
Type: Problem-Solving Task
Use the information provided to find out what percentage of Dana's lot won't be covered by the house.
Type: Problem-Solving Task
This task asks the students to solve a real-world problem involving unit rates (data per unit time) using units that many teens and pre-teens have heard of but may not know the definition for. While the computations involved are not particularly complex, the units will be abstract for many students. The first solution relies more on reasoning about the meaning of multiplication and division, while the second solution uses units to help keep track of the steps in the solution process.
Type: Problem-Solving Task
Students are asked to use knowledge of rates and ratios to answer a series of questions involving time, distance, and speed.
Type: Problem-Solving Task
Students are asked to write complete sentences to describe ratios for the context.
Type: Problem-Solving Task
The purpose of the task is for students to compare signed numbers in a real-world context.
Type: Problem-Solving Task
The purpose of this task is to help students explore the meaning of fraction division and to connect it to what they know about whole-number division. Students are asked to explain why the quotient of two fractions with common denominators is equal to the quotient of the numerators of those fractions.
Type: Problem-Solving Task
This task builds on a fifth grade fraction multiplication task, "Drinking Juice." This task uses the identical context, but asks the corresponding "Number of Groups Unknown" division problem. See "Drinking Juice, Variation 3" for the "Group Size Unknown" version.
Type: Problem-Solving Task
Students are asked to solve a fraction division problem using a visual model and the standard algorithm.
Type: Problem-Solving Task
Students are asked to solve problems from context by using multiplication or division of decimals.
Type: Problem-Solving Task
This instructional task requires that the students model each problem with some type of fractions manipulatives or drawings. This could be pattern blocks, student or teacher-made fraction strips, or commercially produced fraction pieces. At a minimum, students should draw pictures of each. The above problems are meant to be a progression which require more sophisticated understandings of the meaning of fractions as students progress through them.
Type: Problem-Solving Task
The purpose of this task is for students to get a better understanding of the relative positions and values of positive and negative numbers.
Type: Problem-Solving Task
The purpose of this task is for students to apply their knowledge of integers in a real-world context.
Type: Problem-Solving Task
Students are asked to add or subtract decimals to solve problems in context.
Type: Problem-Solving Task
Students are asked to write and solve an equation in one variable to answer a real world question.
Type: Problem-Solving Task
In this task students use different representations to analyze the relationship between two quantities and to solve a real world problem. The situation presented provides a good opportunity to make connections between the information provided by tables, graphs and equations. In the later part of the problem, the numbers are big enough so that using the formula is the most efficient way to solve the problem; however, creative use of the table or graph will also work.
Type: Problem-Solving Task
This task asks students to find equivalent expressions by visualizing a familiar activity involving distance. The given solution shows some possible equivalent expressions, but there are many variations possible.
Type: Problem-Solving Task
Students are asked to use properties of operations to match expressions that are equivalent and to write equivalent expressions for any expressions that do not have a match.
Type: Problem-Solving Task
In this task students are asked to write an equation to solve a real-world problem.
Type: Problem-Solving Task
Students are asked to write and graph two inequalities described in context: one discrete and one continuous.
Type: Problem-Solving Task
Students are asked to solve an inequality in order to answer a real-world question.
Type: Problem-Solving Task
Students are asked to write an equation with one variable in order to find the distance walked.
Type: Problem-Solving Task
This purpose of this task is to help students understand the absolute value of a number as its distance from 0 on the number line. The context is not realistic, nor is meant to be; it is a thought experiment to help students focus on the relative position of numbers on the number line.
Type: Problem-Solving Task
Students are asked to determine if two different ratios are both appropriate for the same context.
Type: Problem-Solving Task
Given a ratio, students are asked to determine how much of each ingredient is needed to make concrete.
Type: Problem-Solving Task
This problem provides an interesting geometric context to work on the notion of percent. Two different methods for analyzing the geometry are provided: the first places the two squares next to one another and then moves one so that they overlap. The second solution sets up an equation to find the overlap in terms of given information which reflects the mathematical ideas reason about and solve one-variable equations and inequalities.
Type: Problem-Solving Task
Students are asked to use a given ratio to determine if two different interpretations of the ratio are correct and to determine the maximum quantity that could be purchased within a given context.
Type: Problem-Solving Task
Students are asked apply knowledge of ratios to answer several questions regarding speed, distance and time.
Type: Problem-Solving Task
Student Center Activity
Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.
Type: Student Center Activity
Tutorials
In this video, you will practice describing the shape of distributions as skewed left, skewed right, or symmetrical.
Type: Tutorial
In this video, you will see two ways to find the Mean Absolute Deviation of a data set.
Type: Tutorial
Students will learn that non-zero numbers to the zero power equal one. They will also learn that zero to any positive exponent equals zero.
Type: Tutorial
In this tutorial, you will compare rational numbers using a number line.
Type: Tutorial
In this video, you will practice using arithmetic properties with integers to determine if expressions are equivalent.
Type: Tutorial
You will discover rules to help you determine the sign of an exponential expression with a base of -1.
Type: Tutorial
The focus of this video is to help you understand the core concepts of arithmetic mean, median, and mode.
Type: Tutorial
This video shows how to find the value of a missing piece of data if you know the mean of the data set.
Type: Tutorial
This video demonstrates how to construct a box plot, formerly known as a box and whisker plot.
Type: Tutorial
In this tutorial, you will see how mixed numbers can be divided.
Type: Tutorial
This tutorial demonstrates how the area of an irregular geometric shape may be determined by decomposition to smaller familiar shapes.
Type: Tutorial
In this video, discover another way of finding the volume of a rectangular prism involves dividing it into fractional cubes, finding the volume of one, and then multiplying that area by the number of cubes that fit into the rectangular prism.
Type: Tutorial
This video shows how to solve a word problem involving rectangular prisms.
Type: Tutorial
This video demonstrates how to construct nets for 3-D shapes.
Type: Tutorial
Students will graph the given coordinates of three of the polygon vertices, then locate and graph the fourth vertex.Â
Type: Tutorial
This video demonstrates using a net to find surface area.
Type: Tutorial
In this example, students are given the coordinates of the vertices and asked to construct the resulting polygon, specifically a quadrilateral. Â
Type: Tutorial
In this video, we organize data into frequency tables and dot plots (sometimes called line plots).
Type: Tutorial
Learn how to create histograms, which summarize data by sorting it into groups.
Type: Tutorial
Here's an introduction to basic algebraic equations of the form ax = b in this tutorial.
Type: Tutorial
In this tutorial, we will solve equations in one step by multiplying or dividing a number on both sides.
Type: Tutorial
Learn how to test if a certain value of a variable makes an inequality true in this tutorial.
Type: Tutorial
Learn how to test if a certain value of a variable makes an equation true in this tutorial.
Type: Tutorial
This video demonstrates how to write and solve a one-step addition equation.
Type: Tutorial
To find the value of a variable, you have to get it on one side of the equation alone. To do that, you'll need to do something to BOTH sides of the equation.
Type: Tutorial
This video provides a conceptual explanation of why one needs to divide both sides of an equation to solve for a variable.
Type: Tutorial
In an equation with 2 variables, we will be able to determine which is the dependent variable, and which is the independent variable.
Type: Tutorial
Learn how to write basic algebraic expressions.
Type: Tutorial
Learn how to write inequalities to model real-world situations.
Type: Tutorial
Given a graph, we will be able to find the equation it represents.
Type: Tutorial
Learn how to write simple algebraic expressions.
Type: Tutorial
Learn how to write basic expressions with variables to portray situations described in word problems.
Type: Tutorial
Learn how to apply the distributive law of multiplication over addition and why it works. This is sometimes just called the distributive law or the distributive property.
Type: Tutorial
Learn how to apply the distributive property of multiplication over subtraction. This is sometimes just called the distributive property or distributive law.
Type: Tutorial
Learn how to apply the distributive property to algebraic expressions.
Type: Tutorial
This video demonstrates solving word problems involving the coordinate plane.
Type: Tutorial
The focus here is understanding that a variable is just a symbol that can represent different values in an expression.
Type: Tutorial
Learn how to evaluate an expression with variables using a technique called substitution.
Type: Tutorial
This video demonstrates evaluating expressions with two variables.
Type: Tutorial
Explore how the value of an algebraic expression changes as the value of its variable changes.
Type: Tutorial
In this example, we have a formula for converting a Celsius temperature to Fahrenheit.
Type: Tutorial
Students will simplify an expression by combining like terms. Â
Type: Tutorial
Students will plot an ordered pair on the x (horizontal) axis and y (vertical) axis of the coordinate plane.
Type: Tutorial
This tutorial is an explanation on how to combine like terms in algebra.
Type: Tutorial
This video demonstrates the prime factorization method to find the lcm (least common multiple).
Type: Tutorial
This video contains examples of plotting coordinate pairs and identifying their quadrant.
Type: Tutorial
This video discusses the negative sign as meaning "opposite."
Type: Tutorial
Locate fractions and decimals on the same number line in this tutorial.
Type: Tutorial
Let's order negative numbers from least to greatest in this video.
Type: Tutorial
In this tutorial, you will learn how to order rational numbers using a number line.
Type: Tutorial
In this tutorial you will compare the absolute value of numbers using the concepts of greater than (>), less than (<), and equal to (=).
Type: Tutorial
This video guides you through comparisons of values, including opposites.
Type: Tutorial
This video demonstrates sorting values including absolute value from least to greatest using a number line.
Type: Tutorial
This video demonstrates evaluating inequality statements, some involving absolute value, using a number line.
Type: Tutorial
This is an introduction to combining like terms in this tutorial.
Type: Tutorial
This video demonstrates solving absolute value inequality statements.
Type: Tutorial
Students will evaluate expressions using the order of operations.
Type: Tutorial
This video is about interpreting absolute value in a real-life situation.
Type: Tutorial
Students will learn how to identify the four quadrants in the coordinate plane.
Type: Tutorial
This video uses a number line to describe the opposite of a number.
Type: Tutorial
Work through a challenging order of operations example with only positive numbers.
Type: Tutorial
Work through a challenging order of operations example with only positive numbers.
Type: Tutorial
This video will show how to evaluate expressions with exponents using the order of operations.
Type: Tutorial
This video demonstrates dividing two numbers that are decimals.
Type: Tutorial
This video portrays a proof of the formula for area of a parallelogram.
Type: Tutorial
This video demonstrates how to evaluate expressions with whole number exponents.
Type: Tutorial
A trapezoid is a type of quadrilateral with one set of parallel sides. Here we explain how to find its area.
Type: Tutorial
We will be able to find the area of a triangle in a coordinate grid. The formula for the area of a triangle is given in this tutorial.
Type: Tutorial
Students will learn the basics of finding the perimeter and area of squares and rectangles.
Type: Tutorial
This video demonstrates adding decimal numbers to solve a word problem.
Type: Tutorial
Let's show subtracting with digits up to the thousandths place in this tutorial.
Type: Tutorial
Watch as we align decimals before subtracting in this tutorial.
Type: Tutorial
Learn how to add decimals and use place value in this tutorial.
Type: Tutorial
In this video, watch as we solve this word problem using what we know about equivalent ratios.
Type: Tutorial
In this video, a ratio is given and then applied to solve a problem.
Type: Tutorial
In the video, we find the percent when given the part and the whole.
Type: Tutorial
This video demonstrates how to find percent of a whole number.
Type: Tutorial
You're asked to find the whole when given the part and the percent.
Type: Tutorial
Evaluating Expressions with Two Variables
Type: Tutorial
This video demonstrates how to write a decimal as a percent.
Type: Tutorial
This video demonstrates solving a unit price problem using equivalent ratios.
Type: Tutorial
In this example we have a formula for converting Celsius temperature to Fahrenheit. Let's substitute the variable with a value (Celsius temp) to get the degrees in Fahrenheit. Great problem to practice with us!
Type: Tutorial
Learn how to evaluate an expression with variables using a technique called substitution (or "plugging in").
Type: Tutorial
This video deals with what percent really means by looking at a 10 by 10 grid.
Type: Tutorial
This video demonstrates a visual model of a percent greater than 100.
Type: Tutorial
Great question. In algebra, we do indeed avoid using the multiplication sign. We'll explain it for you here.
Type: Tutorial
Our focus here is understanding that a variable is just a letter or symbol (usually a lower case letter) that can represent different values in an expression. We got this. Just watch.
Type: Tutorial
The distributive property states that the terms of addition or subtraction statements within parentheses may be separately multiplied by a value outside the parentheses. In this tutorial, students will learn the distributive property, which is very helpful with mental math calculations and solving equations.
Type: Tutorial
The Cartesian Coordinate system, formed from the Cartesian product of the real number line with itself, allows algebraic equations to be visualized as geometric shapes in two or three dimensions. While this tutorial includes the basis of Coordinate system, it also includes ideas beyond fifth grade standards. Most likely only advanced fifth graders would find the video engaging.
Type: Tutorial
The first fractions used by ancient civilizations were "unit fractions." Later, numerators other than one were added, creating "vulgar fractions" which became our modern fractions. Together, fractions and integers form the "rational numbers."
Type: Tutorial
Take a look at the logic behind the associative and distributive properties of multiplication.
Type: Tutorial
A look behind the fundamental properties of the most basic arithmetic operation, addition
Type: Tutorial
Number systems evolved from the natural "counting" numbers, to whole numbers (with the addition of zero), to integers (with the addition of negative numbers), and beyond. These number systems are easily understood using the number line.
Type: Tutorial
The commutative property is common to the operations of both addition and multiplication and is an important property of many mathematical systems.
Type: Tutorial
Students will be able to see examples of addition of integers while watching a short video, and practice adding integers using an online quiz.
Type: Tutorial
This lesson introduces students to linear equations in one variable, shows how to solve them using addition, subtraction, multiplication, and division properties of equalities, and allows students to determine if a value is a solution, if there are infinitely many solutions, or no solution at all. The site contains an explanation of equations and linear equations, how to solve equations in general, and a strategy for solving linear equations. The lesson also explains contradiction (an equation with no solution) and identity (an equation with infinite solutions). There are five practice problems at the end for students to test their knowledge with links to answers and explanations of how those answers were found. Additional resources are also referenced.
Type: Tutorial
This resource helps the user learn the three primary colors that are fundamental to human vision, learn the different colors in the visible spectrum, observe the resulting colors when two colors are added, and learn what white light is. A combination of text and a virtual manipulative allows the user to explore these concepts in multiple ways.
Type: Tutorial
The user will learn the three primary subtractive colors in the visible spectrum, explore the resulting colors when two subtractive colors interact with each other and explore the formation of black color.
Type: Tutorial
This Khan Academy presentation models solving two-step equations with one variable.
Type: Tutorial
In this lesson, students will be viewing a Khan Academy video that will show how to convert ratios using speed units.
Type: Tutorial
The video describes how to multiply fractions and state the answer in lowest terms.
Type: Tutorial
The video demonstrates rewriting given numbers in a common format (as decimals), so they can be compared and ordered.
Type: Tutorial
Introduction to solving one variable multiplication equations of the form px = q.
Type: Tutorial
Video/Audio/Animations
When working with fractions, divisions can be converted to multiplication by the divisor's reciprocal. This chapter explains why.
Type: Video/Audio/Animation
This short video provides a clear explanation why we perform the same steps on each side of an equation when solving for the variable/unknown.
Type: Video/Audio/Animation
This short video provides a clear explanation about the "why" of performing the same steps on each side of an equation when solving for the variable/unknown.
Type: Video/Audio/Animation
Percentages are one method of describing a fraction of a quantity. the percent is the numerator of a fraction whose denominator is understood to be one-hundred.
Type: Video/Audio/Animation
Ratio errors confuse one of the coaches as two teams face off in an epic dodgeball tournament. See how mathematical techniques such as tables, graphs, measurements and equations help to find the missing part of a proportion.
Atlantean Dodgeball addresses number and operations standards, the algebra standard, and the process standard, as established by the National Council of Teachers of Mathematics (NCTM). It guides students in:
- Understanding and using ratios and proportions to represent quantitative relationships.
- Relating and comparing different forms of representation for a relationship.
- Developing, analyzing, and explaining methods for solving problems involving proportions, such as scaling and finding equivalent ratios.
- Representing, analyzing, and generalizing a variety of patterns with tables, graphs, words, and, when possible, symbolic rules.
Type: Video/Audio/Animation
Virtual Manipulatives
In this online activity, students apply their understanding of proportional relationships by adding circles, either colored or not, to two different piles then combine the piles to produce a required percentage of colored circles. Students can play in four modes: exploration, unknown part, unknown whole, or unknown percent. This activity also includes supplemental materials in tabs above the applet, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the Java applet.
Type: Virtual Manipulative
In this activity, students use preset data or enter in their own data to be represented in a box plot. This activity allows students to explore single as well as side-by-side box plots of different data. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the Java applet.
Type: Virtual Manipulative
This is an online graphing utility that can be used to create box plots, bubble graphs, scatterplots, histograms, and stem-and-leaf plots.
Type: Virtual Manipulative
Users select a data set or enter their own data to generate a box plot.
Type: Virtual Manipulative
This tool helps students better understand that equality is a relationship and not an operational command to "find the answer." The applet features a pan balance that allows the student to input each half of an equation in the pans, which responds to the numerical expression's value by raising, lowering or balancing.
Type: Virtual Manipulative
This virtual manipulative histogram tool can aid in analyzing the distribution of a dataset. It has 6 preset datasets and a function to add your own data for analysis.
Type: Virtual Manipulative
In this activity, students practice solving algebraic expressions using order of operations. The applet records their score so the student can track their progress. This activity allows students to practice applying the order of operations when solving problems. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.
Type: Virtual Manipulative
In this activity, students can create and view a histogram using existing data sets or original data entered. Students can adjust the interval size using a slider bar, and they can also adjust the other scales on the graph. This activity allows students to explore histograms as a way to represent data as well as the concepts of mean, standard deviation, and scale. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.
Type: Virtual Manipulative
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