# Access M/J Mathematics 1   (#7812015)

## General Course Information and Notes

### General Notes

Access Courses: Access courses are intended only for students with a significant cognitive disability. Access courses are designed to provide students with access to the general curriculum. Access points reflect increasing levels of complexity and depth of knowledge aligned with grade-level expectations. The access points included in access courses are intentionally designed to foster high expectations for students with significant cognitive disabilities.

Access points in the subject areas of science, social studies, art, dance, physical education, theatre, and health provide tiered access to the general curriculum through three levels of access points (Participatory, Supported, and Independent). Access points in English language arts and mathematics do not contain these tiers, but contain Essential Understandings (or EUs). EUs consist of skills at varying levels of complexity and are a resource when planning for instruction.

### General Information

Course Number: 7812015
Course Path:
Abbreviated Title: Access M/J Math 1
Course Length: Year (Y)
Course Attributes:
• Class Size Core Required
Course Status: Course Approved

## Educator Certifications

One of these educator certification options is required to teach this course.

## Student Resources

Vetted resources students can use to learn the concepts and skills in this course.

## Original Student Tutorials

Join in on creating a delicious sundae by adding decimals to the thousandths, using the standard algorithm, in this interactive tutorial.

Type: Original Student Tutorial

Dr. E. Quation Part 2: One Step Multiplication & Division Equations:

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

Dr. E. Quation Part 1: One Step Addition & Subtraction Equations:

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

Balancing the Machine:

Use models to solve balance problems on a space station in this interactive, math and science tutorial.

Type: Original Student Tutorial

Castles, Catapults and Data: Histograms Part 2:

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.

Type: Original Student Tutorial

Castles, Catapults and Data: Histograms Part 1:

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

MacCoder's Farm Part 4: Repeat Loops:

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.

Type: Original Student Tutorial

MacCoderâ€™s Farm Part 3: If Statements:

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.

Type: Original Student Tutorial

MacCoderâ€™s Farm Part 2: Condition Statements:

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.

Type: Original Student Tutorial

MacCoderâ€™s Farm Part 1: Declare Variables:

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

It's Raining....Cats and Dogs:

Learn how to make and interpret boxplots in this pet-themed, interactive tutorial.

Type: Original Student Tutorial

What's for Lunch?:

Learn how writers and speakers create arguments by stating a claim and backing it up with reasons and evidence. In this interactive tutorial, you'll hear speeches from candidates for Student Council President and complete practice exercises.

Type: Original Student Tutorial

It Can Be a Zoo of Data!:

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

Helping Chef Ratio:

Learn how to identify explicit evidence and understand implicit meaning in a text.

You will be able to organize information in a table and write ratios equivalent to a given ratio in order to solve real-world and mathematical problems.

Type: Original Student Tutorial

Where Have All the Scrub-Jays Gone?:

Investigate the limiting factors of a Florida ecosystem and describe how these limiting factors affect one native population-the Florida Scrub-Jay.

Type: Original Student Tutorial

Hot on the Trail:

Investigate how temperature affects the rate of chemical reactions in this interactive tutorial.

Type: Original Student Tutorial

Yes or No to GMO?:

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

Golf: Where Negative Numbers are a Positive Thing:

Learn how to 1) create and use number lines with positive and negative numbers, 2) use those number lines to graph positive and negative numbers, 3)  find their distance from zero, 4) find a number’s opposite using a number line and using number signs, and 5) recognize that zero is its own opposite.

Type: Original Student Tutorial

## Educational Games

Solving Equations: Same Variable, Both Sides, One Solution:

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

Graphing Points and Lines:

Challenge yourself with this Prodigi game to see if you can answer questions about points and lines in graphs. Practice using slope-intercept form of a line. Try the "Teach Me" button to prepare yourself. When you are ready, play Prodigi! Be sure to use the review function at the end for any incorrect answers! Have fun!

Type: Educational Game

Negative Number Mission:

Play this robot game to improve your negative number skills. Order and compare negative and positive numbers to complete missions in order to weaken the robots who have taken over the world.

Type: Educational Game

Ice Ice Maybe: An Operations Estimation 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.

Multiplication/Division: The multiplication and addition of fractions and decimals.

Percentages: Identify the percentage of a whole number.

Fractions: Multiply and divde a whole number by a fraction, as well as apply properties of operations.

Type: Educational Game

Flower Power: An Ordering of Rational Numbers 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

This addition game uses mixed decimals to the tenths place. This game encourages some logical analysis as well as addition skills. There may be several ways to make the first couple of circles sum to 3, but there is only one way to combine all the given numbers so that every circle sums to 3.

Type: Educational Game

Fraction Quiz:

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

This addition game encourages some logical analysis as well as addition skills. This particular circle game uses positive and negative integers. There is only one way to combine all the given numbers so that every circle sums to zero.
(source: NLVM grade 6-8 "Circle 0")

Type: Educational Game

Timed Algebra Quiz:

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

Algebra Four:

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

Number Puzzles:

This virtual manipulative poses problems requiring the students to position numbers in a diagram, so all numbers in a line add up to a given value.

Type: Educational Game

Maze 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

Smiles:

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.

Triangular Tables:

Students are asked to use a diagram or table to write an algebraic expression and use the expression to solve problems.

Pennies to Heaven:

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.

Rectangle Perimeter 1:

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.

Rectangle Perimeter 2:

Students are asked to determine if given expressions are equivalent.

Rectangle Perimeter 3:

The purpose of this task is to ask students to write expressions and to consider what it means for two expressions to be equivalent.

The Djinniâ€™s Offer:

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.

Kendall's Vase - Tax:

This problem asks the student to find a 3% sales tax on a vase valued at \$450.

Anna in D.C.:

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.

Base and Height:

Students are asked to determine and illustrate all possible descriptions for the base and height of a given triangle.

Christoâ€™s Building:

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.

Finding Areas of Polygons, Variation 1:

Students are asked to demonstrate two different strategies for finding the area of polygons shown on grids.

Painting a Barn:

Students are asked to use the given information to determine the cost of painting a barn.

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.

Mile High:

Students are asked to reason about and explain the position of two locations relative to sea level.

Movie Tickets:

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.

Reasoning about Multiplication and Division and Place Value, Part 1:

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.

Reasoning about Multiplication and Division and Place Value, Part 2:

Students are asked to reason about and explain the placement of decimals in quotients.

Running to School, Variation 2:

Students are asked to solve a distance problem involving fractions.

Making Hot Cocoa, Variation 1:

Students are asked to solve a fraction division problem using both a visual model and the standard algorithm within a real-world context.

Converting Square Units:

The purpose of this task is converting square units. Use the information provided to answer the questions posed. Since this task asks students to critique Jada's reasoning, it provides an opportunity to work on Standard for Mathematical Practice MAFS.K12.MP.3.1 - Construct Viable Arguments and Critique the Reasoning of Others.

Jim and Jesse's Money:

Students are asked to use a ratio to determine how much money Jim and Jesse had at the start of their trip.

Security Camera:

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.

Shirt Sale:

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.

Voting for Three, Variation 1:

This problem is the fifth in a series of seven about ratios. At first glance the problem may look to be beyond MAFS.6.RP.1.3, which limits itself to "describe a ratio relationship between two quantities." However, even though there are three quantities (the number of each candidates' votes), they are only considered two at a time.

Voting for Three, Variation 2:

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.

Voting for Three, Variation 3:

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.

Voting for Two, Variation 3:

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.

Voting for Two, Variation 1:

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.

Voting for Two, Variation 2:

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.

Voting for Two, Variation 4:

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.

Electoral College:

Students are given a context and a dotplot and are asked a number of questions regarding shape, center, and spread of the data.

Buttons: Statistical Questions:

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.

Puppy Weights:

Using the information provided, create an appropriate graphical display and answer the questions regarding shape, center and variability.

Distances on the Number Line 2:

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.

Making Hot Cocoa, Variation 2:

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.

Running to School, Variation 3:

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.

Setting Goals:

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.

The Florist Shop:

Students are asked to solve a real-world problem involving common multiples.

Traffic Jam:

Students are asked to use fractions to determine how many hours it will take a car to travel a given distance.

Video Game Credits:

Students are asked to use fractions to determine how long a video game can be played.

Currency Exchange:

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.

Dana's House:

Use the information provided to find out what percentage of Dana's lot won't be covered by the house.

Data Transfer:

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.

Friends Meeting on Bicycles:

Students are asked to use knowledge of rates and ratios to answer a series of questions involving time, distance, and speed.

Games at Recess:

Students are asked to write complete sentences to describe ratios for the context.

Comparing Temperatures:

The purpose of the task is for students to compare signed numbers in a real-world context.

Danâ€™s Division Strategy:

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.

Drinking Juice, Variation 2:

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.

Drinking Juice, Variation 3:

Students are asked to solve a fraction division problem using a visual model and the standard algorithm.

Students are asked to solve problems from context by using multiplication or division of decimals.

How Many _______ Are In. . . ?:

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.

Integers on the Number Line 2:

The purpose of this task is for students to get a better understanding of the relative positions and values of positive and negative numbers.

It's Warmer in Miami:

The purpose of this task is for students to apply their knowledge of integers in a real-world context.

Jaydenâ€™s Snacks:

Students are asked to add or subtract decimals to solve problems in context.

Busy Day:

Students are asked to write and solve an equation in one variable to answer a real world question.

Chocolate Bar Sales:

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.

Distance to School:

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.

Equivalent Expressions:

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.

Firefighter Allocation:

In this task students are asked to write an equation to solve a real-world problem.

Students are asked to write and graph two inequalities described in context: one discrete and one continuous.

Log Ride:

Students are asked to solve an inequality in order to answer a real-world question.

Morning Walk:

Students are asked to write an equation with one variable in order to find the distance walked.

Jumping Flea:

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.

Mangos for Sale:

Students are asked to determine if two different ratios are both appropriate for the same context.

Mixing Concrete:

Given a ratio, students are asked to determine how much of each ingredient is needed to make concrete.

Overlapping Squares:

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 described in cluster MAFS.6.EE.2 - Reason about and solve one-variable equations and inequalities.

Price Per Pound and Pounds Per Dollar:

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.

Running at a Constant Speed:

Students are asked apply knowledge of ratios to answer several questions regarding speed, distance and time.

Models for the Multiplication and Division of Fractions:

This site uses visual models to better understand what is actually happening when students multiply and divide fractions. Using area models -- one that superimposes squares that are partitioned into the appropriate number of regions, and shaded as needed -- students multiply, divide, and translate the processes to decimals. The lesson uses an interactive simulation that allows students to create their own area models and is embedded with problems throughout for students to solve.

Measuring Henry's Cabin:

This resource introduces students to the aspects a builder must think about before constructing a building. Students will study the cabin blueprint of Henry David Thoreau and then will find the surface area of the walls and how much paint would be needed. Then, students will find the volume of the cabin to determine the home heating needs. Third, students will study the blueprint and will create a 1/10 scale of it on graph paper and then will use art supplies to create a model of the cabin. Last, students will design and create models of furniture to scale for the cabin.

## 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

Shapes of Distributions:

In this video, you will practice describing the shape of distributions as skewed left, skewed right, or symmetrical.

Type: Tutorial

Mean Absolute Deviation Example:

In this video, you will see two ways to find the Mean Absolute Deviation of a data set.

Type: Tutorial

Powers of zero:

Students will learn that non-zero numbers to the zero power equals one. They will also learn that zero to any positive exponent equals zero. They will then investigate what happens when you have zero to the zero power.

Type: Tutorial

Comparing Rational Numbers:

In this tutorial, you will compare rational numbers using a number line.

Type: Tutorial

Applying Arithmetic Properties with Negative Numbers:

In this video, you will practice using arithmetic properties with integers to determine if expressions are equivalent.

Type: Tutorial

Patterns in Raising 1 and -1 to Different Powers:

You will discover rules to help you determine the sign of an exponential expression with a base of -1.

Type: Tutorial

Statistics Introduction: Mean, Median, and Mode:

The focus of this video is to help you understand the core concepts of arithmetic mean, median, and mode.

Type: Tutorial

Find a Missing Value Given the Mean:

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

Constructing a Box and Whisker Plot:

This video demonstrates how to construct a box and whisker plot.

Type: Tutorial

Interpreting box and whisker plots:

Students will interpret data presented in a box and whisker plot.

Type: Tutorial

Exponents with Negative Bases:

In this tutorial, you will apply what you know about multiplying negative numbers to determine how negative bases with exponents are affected and what patterns develop.

Type: Tutorial

Dividing Mixed Numbers:

In this tutorial, you will see how mixed numbers can be divided.

Type: Tutorial

Finding Area by Decomposing a Shape:

This tutorial demonstrates how the area of an irregular geometric shape may be determined by decomposition to smaller familiar shapes.

Type: Tutorial

Volume of a Rectangular Prism: Fractional Cubes:

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. Watch this explanation.

Type: Tutorial

Volume of a Rectangular Prism: Word Problem:

This video shows how to solve a word problem involving rectangular prisms.

Type: Tutorial

Nets of 3-Dimensional Figures:

This video demonstrates how to construct nets for 3-D shapes.

Type: Tutorial

Graphing a parallelogram on the coordinate plane:

Students will graph the given coordinates of three of the polygon vertices, then locate and graph the fourth vertex.

Type: Tutorial

Finding Surface Area: Net of a Rectangular Prism :

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.

Type: Tutorial

Frequency tables and dot plots:

In this video, we organize data into frequency tables and dot plots (sometimes called line plots).

Type: Tutorial

Histograms:

Learn how to create histograms, which summarize data by sorting it into groups (buckets).

Type: Tutorial

How to Solve Equations of the Form ax = b:

Here's an introduction to basic algebraic equations of the form ax = b. Remember that you can check to see if you have the right answer by substituting it for the variable!

Type: Tutorial

How to Solve One-Step Multiplication and Division Equations with Fractions and Decimals:

Learn how to solve equations in one step by multiplying or dividing a number on both sides. These problems involve decimals and fractions.

Type: Tutorial

Statistical questions:

Discover what makes a question a "statistical question"?

Type: Tutorial

How to Test Solutions to Inequalities:

A solution to an inequality makes that inequality true. Learn how to test if a certain value of a variable makes an inequality true.

Type: Tutorial

How to Test Solutions to Equations Using Substitution:

A solution to an equation makes that equation true. Learn how to test if a certain value of a variable makes an equation true.

Type: Tutorial

How to Represent a Relationship with a Simple Equation:

This video demonstrates how to write and solve a one-step addition equation.

Type: Tutorial

Solving One-Step Equations Using Division:

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

Why to Divide on both Sides of an Equation:

This video provides a conceptual explanation of why one needs to divide both sides of an equation to solve for a variable.

Type: Tutorial

Dependent and Independent Variables Exercise: The Basics:

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

How to Write Basic Expressions with Variables:

Learn how to write basic algebraic expressions.

Type: Tutorial

How to Represent Real-World Situations with Inequalities:

Learn how to write inequalities to model real-world situations.

Type: Tutorial

Dependent and Independent Variables Exercise: Express the Graph as an Equation:

Given a graph, we will be able to find the equation it represents.

Type: Tutorial

How to Write Expressions with Variables:

Learn how to write simple algebraic expressions.

Type: Tutorial

How to Write Basic Algebraic Expressions from Word Problems:

Learn how to write basic expressions with variables to portray situations described in word problems.

Type: Tutorial

The Distributive Law of Multiplication over Addition:

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

The Distributive Law of Multiplication over Subtraction:

Learn how to apply the distributive property of multiplication over subtraction. This is sometimes just called the distributive property or distributive law.

Type: Tutorial

How to Use the Distributive Property with Variables:

Learn how to apply the distributive property to algebraic expressions.

Type: Tutorial

Coordinate Plane: Word Problem Exercises:

This video demonstrates solving word problems involving the coordinate plane.

Type: Tutorial

What Is a Variable?:

The focus here is understanding that a variable is just a symbol that can represent different values in an expression.

Type: Tutorial

How to Evaluate an Expression with Variables:

Learn how to evaluate an expression with variables using a technique called substitution.

Type: Tutorial

How to Evaluate Expressions with Two Variables:

This video demonstrates evaluating expressions with two variables.

Type: Tutorial

Thinking About the Changing Values of Variables and Expressions:

Explore how the value of an algebraic expression changes as the value of its variable changes.

Type: Tutorial

How to Evaluate an Expression Using Substitution:

In this example, we have a formula for converting a Celsius temperature to Fahrenheit.

Type: Tutorial

How to simplify an expression by combining like terms:

Students will simplify an expression by combining like terms.

Type: Tutorial

The Coordinate Plane, plotting an ordered pair:

Students will plot an ordered pair on the x (horizontal) axis and y (vertical) axis of the coordinate plane.

Type: Tutorial

How to combine like terms:

This tutorial is a good explanation on how to combine like terms in algebra.

Type: Tutorial

Least Common Multiple Exercise:

This video demonstrates the prime factorization method to find the lcm (least common multiple).

Type: Tutorial

Coordinate plane examples:

Students will become familiar with the x/y coordinate plane, both from the perspective of plotting points and interpreting the placement of points on a plane.

Type: Tutorial

Coordinate Plane: Graphing Points and Naming Quadrants:

This video contains several examples of plotting coordinate pairs and identifying their quadrant.

Type: Tutorial

Negative Symbol as Opposite:

This video discusses the negative sign as meaning "opposite."

Type: Tutorial

Decimals and Fractions on a Number Line:

We're mixing it up by placing both fractions and decimals on the same number line. Great practice because you need to move effortlessly between the two.

Type: Tutorial

Ordering Negative Numbers:

Is -40 bigger than -10? When ordering negative numbers from least to greatest, be careful that you don't get hung up on the "amount" of the number. Think about what that negative sign really means!

Type: Tutorial

Ordering Rational Numbers:

In this tutorial, you will learn how to order rational numbers using a number line.

Type: Tutorial

Comparing Absolute Values:

In this tutorial you will compare the absolute value of numbers using the concepts of greater than (>), less than (<), and equal to (=).

Type: Tutorial

Comparing Variables with Negatives:

This video guides you through comparisons of values, including opposites.

Type: Tutorial

Sorting Values on Number Line:

This video demonstrates sorting values including absolute value from least to greatest using a number line.

Type: Tutorial

Comparing Values on Number Line:

This video demonstrates evaluating inequality statements, some involving absolute value, using a number line.

Type: Tutorial

Combining Like Terms Introduction:

In simple addition we learned to add all the numbers together to get a sum. In algebra, numbers are sometimes attached to variables and we need to make sure that the variables are alike before we add the numbers. This tutorial is an introduction to combining like terms.

Type: Tutorial

Values to Make Absolute Value Inequality True:

This video demonstrates solving absolute value inequality statements.

Type: Tutorial

Introduction to order of operations:

Students will evaluate expressions using the order of operations.

Type: Tutorial

Interpreting Absolute Value:

Practice 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

Opposite of a Number:

This video uses a number line to describe the opposite of a number.

Type: Tutorial

Order of operations: PEMDAS:

Work through another challenging order of operations example with only positive numbers.

Type: Tutorial

Order of Operations :

Work through a challenging order of operations example with only positive numbers.

Type: Tutorial

Order of Operations :

This video will show how to evaluate expressions with exponents using the order of operations.

Type: Tutorial

Dividing by a Multi-Digit Decimal:

This video demonstrates dividing two decimal numbers.

Type: Tutorial

Area of a parallelogram:

This video portrays a proof of the formula for area of a parallelogram.

Type: Tutorial

Introduction to Exponents:

This video demonstrates how to evaluate expressions with whole number exponents.

Type: Tutorial

Area of a trapezoid:

A trapezoid is a type of quadrilateral with one set of parallel sides. Here we explain how to find its area.

Type: Tutorial

The Zero Power:

Learn why a number raised to the zero power equals 1.

Type: Tutorial

Multiplying Decimals Example:

This video demonstrates how to multiply two decimal numbers.

Type: Tutorial

Area of triangle in grid:

Students 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

Perimeter and Area: the basics:

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

Subtracting Decimals Example 2:

This video shows an example of subtracting with digits up to the thousandths place.

Type: Tutorial

Subtracting Decimals Example 1:

Just like when add, be sure you align decimals before subtracting.

Type: Tutorial

Learn how to add 9.087 to 15.31. Be careful to use place value!

Type: Tutorial

Ratio word problem: centimeters to kilometers:

Let's solve this word problem using what we know about equivalent ratios.

Type: Tutorial

Ratio word problem: boys to girls:

In this example, we are given a ratio and then asked to apply that ratio to solve a problem. No problem!

Type: Tutorial

Finding a Percent:

You are asked to find the percent when given the part and the whole.

Type: Tutorial

Percent of a Whole Number:

This video demonstrates how to find percent of a whole number.

Type: Tutorial

Percent Word Problem Example 3:

You're asked to find the whole when given the part and the percent.

Type: Tutorial

Percent word problem example 2:

It's nice to practice conversion problems, but how about applying our new knowledge of percentages to a real life problem like recycling? Hint: don't forget your long division!

Type: Tutorial

Example: Evaluating expressions with 2 variables:

Evaluating Expressions with Two Variables

Type: Tutorial

Solving Unit Price Problem:

This video demonstrates solving a unit price problem using equivalent ratios.

Type: Tutorial

How to evaluate an expression using substitution:

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

How to evaluate an expression with variables:

Learn how to evaluate an expression with variables using a technique called substitution (or "plugging in").

Type: Tutorial

The Meaning of Percent:

This video talks about what percent really means by looking at a 10 by 10 grid.

Type: Tutorial

Why aren't we using the multiplication sign?:

Great question. In algebra, we do indeed avoid using the multiplication sign. We'll explain it for you here.

Type: Tutorial

What is a variable?:

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 and Mental Math:

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

Order of Operations:

This tutorial reviews the mathematical order of operations and reminds students why common memory tricks might be misleading.

Type: Tutorial

The Cartesian Coordinate System:

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.

Type: Tutorial

Pre-Algebra - Fractions and Rational Numbers:

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

Pre-Algebra - Associative & Distributive Properties of Multiplication:

Take a look at the logic behind the associative and distributive properties of multiplication.

Type: Tutorial

Pre-Algebra - Commutative & Associative Properties of Addition:

A look behind the fundamental properties of the most basic arithmetic operation, addition

Type: Tutorial

Pre-Algebra - Whole Numbers, Integers, and the Number Line:

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

Pre-Algebra - Commutative Property of Multiplication:

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

Linear Equations in One Variable:

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

Primary Subtractive Colors:

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

Solving Equations with One Variable :

This Khan Academy presentation models solving two-step equations with one variable.

Type: Tutorial

Converting Speed Units:

In this lesson, students will be viewing a Khan Academy video that will show how to convert ratios using speed units.

Type: Tutorial

Multiplying Fractions:

The video describes how to multiply fractions and state the answer in lowest terms.

Type: Tutorial

Ordering Numeric Expressions :

The video demonstrates rewriting given numbers in a common format (as decimals), so they can be compared and ordered.

Type: Tutorial

Simple Equations:

Introduction to solving one variable multiplication equations of the form px = q.

Type: Tutorial

## Video/Audio/Animations

Reciprocals and Divisions of Fractions:

When working with fractions, divisions can be converted to multiplication by the divisor's reciprocal. This chapter explains why.

Type: Video/Audio/Animation

Why Do We Divide Both Sides?:

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

Solving Simple Equations:

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

Exponentiation:

Exponentiation can be understood in terms of repeated multiplication much like multiplication can be understood in terms of repeated addition. Properties of multiplication and division of exponential expressions with the same base are derived.

Type: Video/Audio/Animation

Understanding Percentages:

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

Atlantean Dodge Ball (An entetaining look at appropriate use of ratios and proportions):

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

Algebra Balance Scales-Negatives:

This virtual manipulative allows the learners to solve simple linear equations through the use of a balance beam. Unit blocks and x-boxes are placed on the pans of a balance beam to balance it.

Type: Virtual Manipulative

Sorting Numbers with a Venn Diagram:

This drag and drop Venn diagram simulation gives students the opportunity to solve a mathematical problem based on number properties using a range of different Venn diagrams. There are five different levels involving a range of multiples and simply odds and evens. The three core layouts cover simple separate sets, two intersecting sets, and a three way intersecting Venn Diagram. The odds and evens layout is limited to two intersecting sets, of course.

Type: Virtual Manipulative

Bar Chart:

This virtual manipulative is intended to introduce users to the idea of visual representation of data by means of a bar chart. This manipulative is also useful for letting the students categorize collections of familiar objects, (shoes, dry food items, coins etc.) separate them into sub-categories, and describe.

Type: Virtual Manipulative

Space Blocks:

This virtual manipulative allows students to manipulate blocks, add or remove blocks, and connect them together to form solids. They can also experiment with counting the number of exposed faces, seeing what happens to the surface area when blocks are added or removed, and "unfolding" a block to create a net .

Type: Virtual Manipulative

Percentages:

This virtual manipulative allows the student to enter any two of the three quantities involved in percentage computation: the whole, a part and the percent. This manipulative can also be used for the discussions of relations among fractions, decimals, ratios and percentages.

Type: Virtual Manipulative

Histogram vs. Box Plot:

This simulation allows the student to create a box plot and a histogram for the same set of data and toggle between the two displays. Maximum, minimum, median and mean are shown for the data set. The student can change the cell width to explore how the histogram is affected.

Type: Virtual Manipulative

Converting Units Through Dimensional Analysis:

Using this virtual manipulative, students apply dimensional analysis (AKA factor-label method or unit-factor method) to solve unit conversion problems. There is also the opportunity to create your own unit conversion problems.

Type: Virtual Manipulative

Mixtures:

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

Factor Tree:

This virtual manipulative will help the students in exploring the prime factorization of numbers and see how to use the factorization of a pair of numbers to find the greatest common factor (GCF) and the least common factor (LCM). In the manipulative, the number pairs are presented randomly, so that a student returning to the factor tree will most likely begin with a pair of numbers not seen before.

Type: Virtual Manipulative

Geoboard:

This extremely versatile manipulative can be used by learners of different grades. At early grades, this manipulative will help the students recognize, name, build, draw, and compare two-dimensional shapes. As they progress students can classify and understand relationships among types of two-dimensional objects using their defining properties. The application computes perimeter and area allowing students to explore patterns as dimensions change.

Type: Virtual Manipulative

Box Plot:

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

Algebra Balance Scales - with Negatives:

This site provides a virtual balance on which the student can represent (and then solve) simple linear equations with integer answers. Conceptually, positive weights (unit-blocks and x-boxes) push the pans of the scale downward. Negative values are represented by balloons which can be attached to the pans of the scale. The student can then manipulate the weights to solve the equation while simultaneously seeing a visual display of these effects on the equation.

Type: Virtual Manipulative

Number Line Bars:

A versatile tool that can be used to illustrate the operations of addition, subtraction, multiplication, and division.

Type: Virtual Manipulative

Box Plotter:

Users select a data set or enter their own data to generate a box plot.

Type: Virtual Manipulative

Volt Meter (positive and negative numbers):

The user drags batteries to create a circuit. The voltage of the batteries that are placed will be displayed on the voltmeter, and an equation will be displayed in a list on the right, giving an example of how positive and negative numbers work together.

Type: Virtual Manipulative

Pan Balance - Numbers:

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

Histogram Tool:

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

Exploring Mean and Median Using Box Plots:

Using an interactive applet, students can compare and contrast properties of measures of central tendency, specifically the influence of changes in data values on the mean and median. As students change the data values by dragging the red points to the left or right, the interactive figure dynamically adjusts the mean and median of the new data set.
(NCTM's Illuminations)

Type: Virtual Manipulative

Order of Operations Quiz:

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

Histogram:

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

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this course.

## Educational Games

This addition game uses mixed decimals to the tenths place. This game encourages some logical analysis as well as addition skills. There may be several ways to make the first couple of circles sum to 3, but there is only one way to combine all the given numbers so that every circle sums to 3.

Type: Educational Game

This addition game encourages some logical analysis as well as addition skills. This particular circle game uses positive and negative integers. There is only one way to combine all the given numbers so that every circle sums to zero.
(source: NLVM grade 6-8 "Circle 0")

Type: Educational Game

Number Puzzles:

This virtual manipulative poses problems requiring the students to position numbers in a diagram, so all numbers in a line add up to a given value.

Type: Educational Game

Smiles:

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.

Triangular Tables:

Students are asked to use a diagram or table to write an algebraic expression and use the expression to solve problems.

Pennies to Heaven:

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.

Rectangle Perimeter 1:

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.

Rectangle Perimeter 2:

Students are asked to determine if given expressions are equivalent.

Rectangle Perimeter 3:

The purpose of this task is to ask students to write expressions and to consider what it means for two expressions to be equivalent.

The Djinniâ€™s Offer:

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.

Kendall's Vase - Tax:

This problem asks the student to find a 3% sales tax on a vase valued at \$450.

Anna in D.C.:

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.

The purpose of this task is two-fold. One is to provide students with a multi-step problem involving volume. The other is to give them a chance to discuss the difference between exact calculations and their meaning in a context. It is important to note that students could argue that whether the new pan is appropriate depends in part on how accurate Leo's estimate for the needed height is.

Base and Height:

Students are asked to determine and illustrate all possible descriptions for the base and height of a given triangle.

Christoâ€™s Building:

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.

Finding Areas of Polygons, Variation 1:

Students are asked to demonstrate two different strategies for finding the area of polygons shown on grids.

Painting a Barn:

Students are asked to use the given information to determine the cost of painting a barn.

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.

Bake Sale:

The purpose of this task requires students to apply the concepts of factors and common factors in a context. A version of this task could be adapted into a teaching task to help motivate the need for the concept of a common factor.

Mile High:

Students are asked to reason about and explain the position of two locations relative to sea level.

Movie Tickets:

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.

Reasoning about Multiplication and Division and Place Value, Part 1:

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.

Reasoning about Multiplication and Division and Place Value, Part 2:

Students are asked to reason about and explain the placement of decimals in quotients.

Running to School, Variation 2:

Students are asked to solve a distance problem involving fractions.

Making Hot Cocoa, Variation 1:

Students are asked to solve a fraction division problem using both a visual model and the standard algorithm within a real-world context.

Converting Square Units:

The purpose of this task is converting square units. Use the information provided to answer the questions posed. Since this task asks students to critique Jada's reasoning, it provides an opportunity to work on Standard for Mathematical Practice MAFS.K12.MP.3.1 - Construct Viable Arguments and Critique the Reasoning of Others.

Jim and Jesse's Money:

Students are asked to use a ratio to determine how much money Jim and Jesse had at the start of their trip.

Security Camera:

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.

Shirt Sale:

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.

Voting for Three, Variation 1:

This problem is the fifth in a series of seven about ratios. At first glance the problem may look to be beyond MAFS.6.RP.1.3, which limits itself to "describe a ratio relationship between two quantities." However, even though there are three quantities (the number of each candidates' votes), they are only considered two at a time.

Voting for Three, Variation 2:

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.

Voting for Three, Variation 3:

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.

Voting for Two, Variation 3:

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.

Voting for Two, Variation 1:

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.

Voting for Two, Variation 2:

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.

Voting for Two, Variation 4:

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.

Electoral College:

Students are given a context and a dotplot and are asked a number of questions regarding shape, center, and spread of the data.

Buttons: Statistical Questions:

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.

Puppy Weights:

Using the information provided, create an appropriate graphical display and answer the questions regarding shape, center and variability.

Distances on the Number Line 2:

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.

Making Hot Cocoa, Variation 2:

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.

Running to School, Variation 3:

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.

Setting Goals:

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.

The Florist Shop:

Students are asked to solve a real-world problem involving common multiples.

Traffic Jam:

Students are asked to use fractions to determine how many hours it will take a car to travel a given distance.

Video Game Credits:

Students are asked to use fractions to determine how long a video game can be played.

Currency Exchange:

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.

Dana's House:

Use the information provided to find out what percentage of Dana's lot won't be covered by the house.

Data Transfer:

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.

Friends Meeting on Bicycles:

Students are asked to use knowledge of rates and ratios to answer a series of questions involving time, distance, and speed.

Games at Recess:

Students are asked to write complete sentences to describe ratios for the context.

The purpose of this task is to help students get a better understanding of multiplying and dividing using fractions.

There are two aspects to fluency with division of multi-digit numbers: knowing when it should be applied, and knowing how to compute it. While this task is very straightforward, it represents the kind of problem that sixth graders should be able to recognize and solve relatively quickly. Easily recognizing contexts that require division is a necessary conceptual prerequisite to more complex modeling problems that students will be asked to solve later in middle and high school.

This task also has a natural carryover to work with ratios and rates, so students should also be building connections between these kinds of division problems and finding unit rates.

Comparing Temperatures:

The purpose of the task is for students to compare signed numbers in a real-world context.

Danâ€™s Division Strategy:

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.

Drinking Juice, Variation 2:

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.

Drinking Juice, Variation 3:

Students are asked to solve a fraction division problem using a visual model and the standard algorithm.

Students are asked to solve problems from context by using multiplication or division of decimals.

How Many _______ Are In. . . ?:

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.

Integers on the Number Line 2:

The purpose of this task is for students to get a better understanding of the relative positions and values of positive and negative numbers.

It's Warmer in Miami:

The purpose of this task is for students to apply their knowledge of integers in a real-world context.

Jaydenâ€™s Snacks:

Students are asked to add or subtract decimals to solve problems in context.

Busy Day:

Students are asked to write and solve an equation in one variable to answer a real world question.

Chocolate Bar Sales:

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.

Distance to School:

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.

Equivalent Expressions:

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.

Firefighter Allocation:

In this task students are asked to write an equation to solve a real-world problem.

Students are asked to write and graph two inequalities described in context: one discrete and one continuous.

Log Ride:

Students are asked to solve an inequality in order to answer a real-world question.

Morning Walk:

Students are asked to write an equation with one variable in order to find the distance walked.

Jumping Flea:

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.

Mangos for Sale:

Students are asked to determine if two different ratios are both appropriate for the same context.

Mixing Concrete:

Given a ratio, students are asked to determine how much of each ingredient is needed to make concrete.

Overlapping Squares:

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 described in cluster MAFS.6.EE.2 - Reason about and solve one-variable equations and inequalities.

Price Per Pound and Pounds Per Dollar:

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.

Running at a Constant Speed:

Students are asked apply knowledge of ratios to answer several questions regarding speed, distance and time.

Ratio - Make Some Chocolate Crispies:

In this activity students calculate the ratio of chocolate to cereal when making a cake. Students then use that ratio to calculate to amount of chocolate and cereal necessary to make 21 cakes.

## Teaching Ideas

Design a Powerful Bird Wing:

In this hands-on and web interactive project, students design and build a bird wing powerful enough to spin them in an office chair when it is flapped. By modifying the shape, size, and/or materials used in their design based on observations of natural and man-made transportation methods, students will learn about thrust, forces, durability, and energy use.

Type: Teaching Idea

Build a Mighty Machine:

In this hands-on and web interactive project, students design and build a machine inspired by animals where the entire structure flips or jumps (vertically or horizontally) using basic materials such as sticks and rubber bands. The students will explore concepts including power amplification, elastic potential energy, and kinetic energy by manipulating physical objects.

Type: Teaching Idea

## Tutorials

The Distributive Property and Mental Math:

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

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

Multiplying Fractions:

The video describes how to multiply fractions and state the answer in lowest terms.

Type: Tutorial

Ordering Numeric Expressions :

The video demonstrates rewriting given numbers in a common format (as decimals), so they can be compared and ordered.

Type: Tutorial

Simple Equations:

Introduction to solving one variable multiplication equations of the form px = q.

Type: Tutorial

## Video/Audio/Animation

Atlantean Dodge Ball (An entetaining look at appropriate use of ratios and proportions):

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

Algebra Balance Scales-Negatives:

This virtual manipulative allows the learners to solve simple linear equations through the use of a balance beam. Unit blocks and x-boxes are placed on the pans of a balance beam to balance it.

Type: Virtual Manipulative

Sorting Numbers with a Venn Diagram:

This drag and drop Venn diagram simulation gives students the opportunity to solve a mathematical problem based on number properties using a range of different Venn diagrams. There are five different levels involving a range of multiples and simply odds and evens. The three core layouts cover simple separate sets, two intersecting sets, and a three way intersecting Venn Diagram. The odds and evens layout is limited to two intersecting sets, of course.

Type: Virtual Manipulative

Bar Chart:

This virtual manipulative is intended to introduce users to the idea of visual representation of data by means of a bar chart. This manipulative is also useful for letting the students categorize collections of familiar objects, (shoes, dry food items, coins etc.) separate them into sub-categories, and describe.

Type: Virtual Manipulative

Space Blocks:

This virtual manipulative allows students to manipulate blocks, add or remove blocks, and connect them together to form solids. They can also experiment with counting the number of exposed faces, seeing what happens to the surface area when blocks are added or removed, and "unfolding" a block to create a net .

Type: Virtual Manipulative

Percentages:

This virtual manipulative allows the student to enter any two of the three quantities involved in percentage computation: the whole, a part and the percent. This manipulative can also be used for the discussions of relations among fractions, decimals, ratios and percentages.

Type: Virtual Manipulative

Histogram vs. Box Plot:

This simulation allows the student to create a box plot and a histogram for the same set of data and toggle between the two displays. Maximum, minimum, median and mean are shown for the data set. The student can change the cell width to explore how the histogram is affected.

Type: Virtual Manipulative

Converting Units Through Dimensional Analysis:

Using this virtual manipulative, students apply dimensional analysis (AKA factor-label method or unit-factor method) to solve unit conversion problems. There is also the opportunity to create your own unit conversion problems.

Type: Virtual Manipulative

Factor Tree:

This virtual manipulative will help the students in exploring the prime factorization of numbers and see how to use the factorization of a pair of numbers to find the greatest common factor (GCF) and the least common factor (LCM). In the manipulative, the number pairs are presented randomly, so that a student returning to the factor tree will most likely begin with a pair of numbers not seen before.

Type: Virtual Manipulative

Geoboard:

This extremely versatile manipulative can be used by learners of different grades. At early grades, this manipulative will help the students recognize, name, build, draw, and compare two-dimensional shapes. As they progress students can classify and understand relationships among types of two-dimensional objects using their defining properties. The application computes perimeter and area allowing students to explore patterns as dimensions change.

Type: Virtual Manipulative

Algebra Balance Scales - with Negatives:

This site provides a virtual balance on which the student can represent (and then solve) simple linear equations with integer answers. Conceptually, positive weights (unit-blocks and x-boxes) push the pans of the scale downward. Negative values are represented by balloons which can be attached to the pans of the scale. The student can then manipulate the weights to solve the equation while simultaneously seeing a visual display of these effects on the equation.

Type: Virtual Manipulative

Number Line Bars:

A versatile tool that can be used to illustrate the operations of addition, subtraction, multiplication, and division.

Type: Virtual Manipulative