General Course Information and Notes

General Notes

MAFS.7

In Grade 7,instructional time should focus on four critical area: (1) developing understanding of and applying proportional relationships; (2) developing understanding of operations with rational numbers and working with expressions and linear equations; (3) solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume; and (4) drawing inferences about populations based on samples.

1. Students extend their understanding of ratios and develop understanding of proportionality to solve single- and multi-step problems. Students use their understanding of ratios and proportionality to solve a wide variety of percent problems, including those involving discounts, interest, taxes, tips, and percent increase or decrease. Students solve problems about scale drawings by relating corresponding lengths between the objects or by using the fact that relationships of lengths within an object are preserved in similar objects. Students graph proportional relationships and understand the unit rate informally as a measure of the steepness of the related line, called the slope. They distinguish proportional relationships from other relationships.
2. Students develop a unified understanding of number, recognizing fractions, decimals (that have a finite or a repeating decimal representation), and percents as different representations of rational numbers. Students extend addition, subtraction, multiplication, and division to all rational numbers, maintaining the properties of operations and the relationships between addition and subtraction, and multiplication and division. By applying these properties, and by viewing negative numbers in terms of everyday contexts (e.g., amounts owed or temperatures below zero), students explain and interpret the rules for adding, subtracting, multiplying, and dividing with negative numbers. They use the arithmetic of rational numbers as they formulate expressions and equations in one variable and use these equations to solve problems.
3. Students continue their work with area from Grade 6, solving problems involving area and circumference of a circle and surface area of three-dimensional objects. In preparation for work on congruence and similarity in Grade 8 they reason about relationships among two-dimensional figures using scale drawings and informal geometric constructions, and they gain familiarity with the relationship between angles formed by intersecting lines. Students work with three-dimensional figures, relating them to two-dimensional figures by examining cross-sections. They solve real-world and mathematical problems involving area, surface area, and volume of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes and right prisms.
4. Students build on their previous work with single data distributions to compare two data distributions and address questions about difference between populations. They begin informal work with random sampling to generate data sets and learn about the importance of representative samples for drawing inferences.

English Language Development ELD Standards Special Notes Section:
Teachers are required to provide listening, speaking, reading and writing instruction that allows English language learners (ELL) to communicate information, ideas and concepts for academic success in the content area of Mathematics. For the given level of English language proficiency and with visual, graphic, or interactive support, students will interact with grade level words, expressions, sentences and discourse to process or produce language necessary for academic success. The ELD standard should specify a relevant content area concept or topic of study chosen by curriculum developers and teachers which maximizes an ELL's need for communication and social skills. To access an ELL supporting document which delineates performance definitions and descriptors, please click on the following link:

A.V.E. for Success Collection is provided by the Florida Association of School Administrators: http://www.fasa.net/4DCGI/cms/review.html?Action=CMS_Document&DocID=139. Please be aware that these resources have not been reviewed by CPALMS and there may be a charge for the use of some of them in this collection.

Florida Standards Implementation Guide Focus Section:

The Mathematics Florida Standards Implementation Guide was created to support the teaching and learning of the Mathematics Florida Standards. The guide is compartmentalized into three components: focus, coherence, and rigor.Focus means narrowing the scope of content in each grade or course, so students achieve higher levels of understanding and experience math concepts more deeply. The Mathematics standards allow for the teaching and learning of mathematical concepts focused around major clusters at each grade level, enhanced by supporting and additional clusters. The major, supporting and additional clusters are identified, in relation to each grade or course. The cluster designations for this course are below.

Major Clusters

MAFS.7.RP.1 Analyze proportional relationships and use them to solve real-world and mathematical problems.

MAFS.7.NS.1 Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

MAFS.7.EE.1 Use properties of operations to generate equivalent expressions.

MAFS.7.EE.2 Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Supporting Clusters

MAFS.7.SP.1 Use random sampling to draw inferences about a population.

MAFS.7.SP.3 Investigate chance processes and develop, use, and evaluate probability models.

MAFS.7.G.1 Draw, construct, and describe geometrical figures and describe the relationships between them.

MAFS.7.G.2 Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

MAFS.7.SP.2 Draw informal comparative inferences about two populations.

Note: Clusters should not be sorted from major to supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting and additional clusters.

General Information

Course Number: 1205040
Course Path:
Abbreviated Title: M/J GRADE 7 MATH
Course Attributes:
• Class Size Core Required
Course Level: 2
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

Working With Proportions:

Roll up your sleeves and learn how proportions can be used in everyday life, in this interactive tutorial.

Type: Original Student Tutorial

Order of Operations with Rational Numbers Part 2: Decimals:

Evaluate numerical expressions with rational numbers expressed as decimals using the order of operations and properties of operations in this interactive tutorial.

Type: Original Student Tutorial

Order of Operations with Rational Numbers Part 1: Fractions:

Evaluate numerical expressions with rational numbers expressed as fractions using the order of operations and properties of operations in this interactive tutorial.

This is part 1 in a two-part series.

Type: Original Student Tutorial

Estimating Tax and Tip:

Follow Hailey and Kenna as they estimate tips and sales tax at the mall, restaurants, and the hair salon in this interactive tutorial.

Type: Original Student Tutorial

Math at the Mall: Markups and Markdowns:

Let's calculate markups and markdowns at the mall and follow Paige and Miriam working in this interactive tutorial.

Type: Original Student Tutorial

Simple Interest:

Calculate simple interest and estimate monthly payments alongside a loan officer named Jordan in this interactive tutorial.

Type: Original Student Tutorial

Taxes, Fees, and Commission:

Explore sales tax, fees, and commission by following a customer service representative named Julian in this interactive tutorial.

Type: Original Student Tutorial

The Percent Times: Percent Increase and Decrease:

Learn to solve percent change problems involving percent increases and decreases in in this interactive tutorial.

Type: Original Student Tutorial

Playground Angles Part 1:

Explore complementary and supplementary angles around the playground with Jacob in this interactive tutorial.

This is Part 1 in a two-part series. Click HERE to open Playground Angles: Part 2.

Type: Original Student Tutorial

Playground Angles: Part 2:

Help Jacob write and solve equations to find missing angle measures based on the relationship between angles that sum to 90 degrees and 180 degrees in this playground-themed, interactive tutorial.

This is Part 2 in a two-part series. Click HERE to open Playground Angles: Part 1.

Type: Original Student Tutorial

Math Models and Social Distancing:

Learn how math models can show why social distancing during a epidemic or pandemic is important in this interactive tutorial.

Type: Original Student Tutorial

Professor E. Qual Part 2: Two-Step Equations & Rational Numbers:

Practice solving and checking two-step equations with rational numbers in this interactive tutorial.

This is part 2 of the two-part series on two-step equations. Click HERE to open Part 1.

Type: Original Student Tutorial

Professor E. Qual Part 1: 2 Step Equations:

Professor E. Qual will teach you how to solve and check two-step equations in this interactive tutorial.

This is part 1 of a two-part series about solving 2-step equations. Click HERE to open Part 2.

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

Math Soup: Creating Equivalent Expressions by Combining Like Terms :

Learn how to combine like terms to create equivalent expressions in this cooking-themed, interactive tutorial.

Type: Original Student Tutorial

Pizza Pi: Circumference:

Explore the origins of Pi as the ratio of Circumference to diameter of a circle. In this interactive tutorial you'll work with the circumference formula to determine the circumference of a circle and work backwards to determine the diameter and radius of a circle.

Type: Original Student Tutorial

Introduction to Probability:

Learn how to calculate the probability of simple events, that probability is the likeliness of an event occurring, and that some events may be more likely than others to occur in this interactive tutorial.

Type: Original Student Tutorial

Exploring Mean Absolute Deviation: Lionfish:

Compare multiple samples of lionfish to make generalizations about the population by analyzing the samples’ mean absolute deviations (MAD) and their distributions in this interactive tutorial.

Type: Original Student Tutorial

Alice in Mathematics-Land:

Help Alice discover that compound probabilities can be determined through calculations or by drawing tree diagrams in this interactive tutorial.

Type: Original Student Tutorial

Pizza Pi: Area:

Explore how to calculate the area of circles in terms of pi and with pi approximations in this interactive tutorial. You will also experience irregular area situations that require the use of the area of a circle formula.

Type: Original Student Tutorial

Predicting Outcomes at the Carnival:

Learn how to use probability to predict expected outcomes at the Carnival in this interactive tutorial.

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-with this interactive tutorial.

Type: Original Student Tutorial

Learn how to explain the meaning of additive inverse, identify the additive inverse of a given rational number, and justify your answer on a number line in this original tutorial.

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

Swimming in Circles:

Learn to solve problems involving the circumference and area of circle-shaped pools in this interactive tutorial.

Type: Original Student Tutorial

Scale Round Up:

Learn to use architectural scale drawings to build a new horse arena and solve problems involving scale drawings in this interactive tutorial. By the end, you should be able to calculate actual lengths using a scale and proportions.

Type: Original Student Tutorial

Why Does a Negative Times a Negative Equal a Positive?:

Use mathematical properties to explain why a negative factor times a negative factor equals a positive product instead of just quoting a rule with this interactive tutorial.

Type: Original Student Tutorial

Arguing Mars :

Practice identifying and examining the evidence used to support a specific argument. In this interactive tutorial, you'll read several short texts about the exploration of Mars to practice distinguishing relevant from irrelevant evidence. You'll also practice determining whether the evidence presented is sufficient or insufficient

Type: Original Student Tutorial

Educational Games

Integers Jeopardy Game:

This interactive game has 4 categories: adding integers, subtracting integers, multiplying integers, and dividing integers. Students can play individually or in teams.

Type: Educational Game

Estimator Four:

In this activity, students play a game of connect four, but to place a piece on the board they have to correctly estimate an addition, multiplication, or percentage problem. Students can adjust the difficulty of the problems as well as how close the estimate has to be to the actual result. This activity allows students to practice estimating addition, multiplication, and percentages of large numbers (100s). 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

Estimator Quiz:

In this activity, students are quizzed on their ability to estimate sums, products, and percentages. The student can adjust the difficulty of the problems and how close they have to be to the actual answer. This activity allows students to practice estimating addition, multiplication, or percentages of large numbers. 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

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

Educational Software / Tool

Glossary:

This resource is an online glossary to find the meaning of math terms. Students can also use the online glossary to find words that are related to the word typed in the search box. For example: Type in "transversal" and 11 other terms will come up. Click on one of those terms and its meaning is displayed.

Type: Educational Software / Tool

Perspectives Video: Experts

Mathematically Exploring the Wakulla Caves:

The tide is high!  How can we statistically prove there is a relationship between the tides on the Gulf Coast and in a fresh water spring 20 miles from each other?

Type: Perspectives Video: Expert

MicroGravity Sensors & Statistics:

Statistical analysis played an essential role in using microgravity sensors to determine location of caves in Wakulla County.

Type: Perspectives Video: Expert

Practical Use of Area and Circumference:

A math teacher describes the relationship between area and circumference and gives examples in nature.

Type: Perspectives Video: Expert

Using Statistics to Estimate Lionfish Population Size:

It's impossible to count every animal in a park, but with statistics and some engineering, biologists can come up with a good estimate.

Type: Perspectives Video: Expert

Tow Net Sampling to Monitor Phytoplankton Populations:

How do scientists collect information from the world? They sample it! Learn how scientists take samples of phytoplankton not only to monitor their populations, but also to make inferences about the rest of the ecosystem!

Type: Perspectives Video: Expert

Perspectives Video: Professional/Enthusiasts

Modeling with Polygons for 3D Printers:

Understand 3D modeling from a new angle when you learn about surface geometry and 3D printing.

Type: Perspectives Video: Professional/Enthusiast

Building Scale Models to Solve an Archaeological Mystery:

An archaeologist describes how mathematics can help prove a theory about mysterious prehistoric structures called shell rings.

Type: Perspectives Video: Professional/Enthusiast

Ratios and Proportions in Mixing Ceramic Glazes:

Ceramic glaze recipes are fluid and not set in stone, but can only be formulated consistently with a good understanding of math!

Type: Perspectives Video: Professional/Enthusiast

Sampling Bird Populations to Track Environmental Restoration:

Sometimes scientists conduct a census, too! Learn how population sampling can help monitor the progress of an ecological restoration project.

Type: Perspectives Video: Professional/Enthusiast

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.

The Titanic 1:

This task asks students to calculate probabilities using information presented in a two-way frequency table.

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.

Discounted Books:

This purpose of this task is to help students see two different ways to look at percentages both as a decrease and an increase of an original amount. In addition, students have to turn a verbal description of several operations into mathematical symbols. This requires converting simple percentages to decimals as well as identifying equivalent expressions without variables.

Equivalent Expressions?:

Students are asked to determine if two expressions are equivalent and explain their reasoning.

Students are asked to write and solve an inequality to determine the number of people that can safely rent a boat.

Guess My Number:

This problem asks the students to represent a sequence of operations using an expression and then to write and solve simple equations. The problem is posed as a game and allows the students to visualize mathematical operations. It would make sense to actually play a similar game in pairs first and then ask the students to record the operations to figure out each other's numbers.

Miles to Kilometers:

In this task students are asked to write two expressions from verbal descriptions and determine if they are equivalent. The expressions involve both percent and fractions. This task is most appropriate for a classroom discussion since the statement of the problem has some ambiguity.

Shrinking:

Students are asked to determine the change in height in inches when given a constant rate of change in centimeters. The answer is rounded to the nearest half inch.

Sports Equipment Set:

The student is asked to write and solve an inequality to match the context.

Eight Circles:

Students are asked to find the area of a shaded region using a diagram and the information provided. The purpose of this task is to strengthen student understanding of area.

Floor Plan:

The purpose of this task is for students to translate between measurements given in a scale drawing and the corresponding measurements of the object represented by the scale drawing. If used in an instructional setting, it would be good for students to have an opportunity to see other solution methods, perhaps by having students with different approaches explain their strategies to the class. Students who can only solve this by first converting the linear measurements will have a hard time solving problems where only area measures are given.

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.

Comparing Freezing Points:

In this task, students answer a question about the difference between two temperatures that are negative numbers.

Coupon Versus Discount:

In this task, students are presented with a real-world problem involving the price of an item on sale. To answer the question, students must represent the problem by defining a variable and related quantities, and then write and solve an equation.

Operations on the Number Line:

The purpose of this task is to help solidify students' understanding of signed numbers as points on a number line and to understand the geometric interpretation of adding and subtracting signed numbers. There is a subtle distinction in the academic standards between a fraction and a rational number. Fractions are always positive, and when thinking of the symbol ab as a fraction, it is possible to interpret it as a equal-sized pieces where b pieces make one whole.

Repeating Decimal as Approximation:

The student is asked to complete a long division which results in a repeating decimal, and then use multiplication to "check" their answer. The purpose of the task is to have students reflect on the meaning of repeating decimal representation through approximation.

Sharing Prize Money:

Students are asked to determine how to distribute prize money among three classes based on the contribution of each class.

Sand Under the Swing Set:

The 7th graders at Sunview Middle School were helping to renovate a playground for the kindergartners at a nearby elementary school. City regulations require that the sand underneath the swings be at least 15 inches deep. The sand under both swing sets was only 12 inches deep when they started. The rectangular area under the small swing set measures 9 feet by 12 feet and required 40 bags of sand to increase the depth by 3 inches. How many bags of sand will the students need to cover the rectangular area under the large swing set if it is 1.5 times as long and 1.5 times as wide as the area under the small swing set?

Art Class, Variation 1:

Students are asked to use ratios and proportional reasoning to compare paint mixtures numerically and graphically.

Chess Club:

This problem includes a percent increase in one part with a percent decrease in the remaining and asks students to find the overall percent change. The problem may be solved using proportions or by reasoning through the computations or writing a set of equations.

Comparing Years:

Students are asked to make comparisons among the Egyptian, Gregorian, and Julian methods of measuring a year.

Cooking with the Whole Cup:

Students are asked to use proportional reasoning to answer a series of questions in the context of a recipe.

Gotham City Taxis:

The purpose of this task is to give students an opportunity to solve a multi-step ratio problem that can be approached in many ways. This can be done by making a table, which helps illustrate the pattern of taxi rates for different distances traveled and with a little persistence leads to a solution which uses arithmetic. It is also possible to calculate a unit rate (dollars per mile) and use this to find the distance directly without making a table.

Finding a 10% Increase:

5,000 people visited a book fair in the first week. The number of visitors increased by 10% in the second week. How many people visited the book fair in the second week?

Friends Meeting on Bikes:

Using the information provided find out how fast Anya rode her bike.

Molly's Run:

This task asks students to solve a problem in a context involving constant speed. This task provides a transition from working with ratios involving whole numbers to ratios involving fractions. This problem can be thought of in several ways; in particular, this problem also provides an opportunity for students to work with the "How many in one group?'' interpretation of division.

Molly's Run, Assessment Variation:

Use the information provided to find out how long it will take Molly to run one mile.

Music Companies, Variation 1:

This problem requires a comparison of rates where one is given in terms of unit rates, and the other is not. See "Music Companies, Variation 2" for a task with a very similar setup but is much more involved and so illustrates .

Music Companies, Variation 2:

This problem has multiple steps. In order to solve the problem it is necessary to compute: the value of the TunesTown shares; the total value of the BeatStreet offer of 20 million shares at \$25 per share; the difference between these two amounts; and the cost per share of each of the extra 2 million shares MusicMind offers to equal to the difference.

Robot Races:

Students should use information provided to answer the questions regarding robot races.

Sale!:

Students are asked to determine which sale option results in the largest percent decrease in cost.

Selling Computers:

The sales team at an electronics store sold 48 computers last month. The manager at the store wants to encourage the sales team to sell more computers and is going to give all the sales team members a bonus if the number of computers sold increases by 30% in the next month. How many computers must the sales team sell to receive the bonus? Explain your reasoning.

Sore Throats, Variation 1:

Students are asked to decide if two given ratios are equivalent.

Stock Swaps, Variation 2:

Students are asked to solve a problem using proportional reasoning in a real world context to determine the number of shares needed to complete a stock purchase.

Stock Swaps, Variation 3:

Students are asked to solve a multistep ratio problem in a real-world context.

Tax and Tip:

After eating at your favorite restaurant, you know that the bill before tax is \$52.60 and that the sales tax rate is 8%. You decide to leave a 20% tip for the waiter based on the pre-tax amount. How much should you leave for the waiter? How much will the total bill be, including tax and tip?

The purpose of this task is for students to calculate the percent increase and relative cost in a real-world context. Inflation, one of the big ideas in economics, is the rise in price of goods and services over time. This is considered in relation to the amount of money you have.

Track Practice:

This activity asks the student to use unit rate and proportional reasoning to determine which of two runners is the fastest.

Two-School Dance:

The purpose of this task is to see how well students students understand and reason with ratios.

Mr. Brigg's Class Likes Math:

In a poll of Mr. Briggs's math class, 67% of the students say that math is their favorite academic subject. The editor of the school paper is in the class, and he wants to write an article for the paper saying that math is the most popular subject at the school. Explain why this is not a valid conclusion and suggest a way to gather better data to determine what subject is most popular.

Offensive Linemen:

In this task, students are able to conjecture about the differences and similarities in the two groups from a strictly visual perspective and then support their comparisons with appropriate measures of center and variability. This will reinforce that much can be gleaned simply from visual comparison of appropriate graphs, particularly those of similar scale.

Tossing Cylinders:

The purpose of this task is to provide students with the opportunity to determine experimental probabilities by collecting data. The cylindrical objects used in this task typically have three different resting positions but not all of these may be equally likely and some may be extremely unlikely or impossible when the object is tossed. Furthermore, obtaining the probabilities of the outcomes is perhaps only possible through the use of long-run relative frequencies. This is because these cylinders do not have the same types of symmetries as objects that are often used as dice, such as cubes or tetrahedrons, where each outcome is equally likely.

How Many Buttons?:

This resource involves a simple data-gathering activity which furnishes data that students organize into a table. They are then asked to refer to the data and determine the probability of various outcomes.

Election Poll, Variation 2:

This task introduces the fundamental statistical ideas of using data summaries (statistics) from random samples to draw inferences (reasoned conclusions) about population characteristics (parameters). In the task built around an election poll scenario, the population is the entire seventh grade class, the unknown characteristic (parameter) of interest is the proportion of the class members voting for a specific candidate, and the sample summary (statistic) is the observed proportion of voters favoring the candidate in a random sample of class members. Variation 2 leads students through a physical simulation for generating sample proportions by sampling, and re-sampling, marbles from a box.

Election Poll, Variation 1:

This task introduces the fundamental statistical ideas of using data summaries (statistics) from random samples to draw inferences (reasoned conclusions) about population characteristics (parameters). There are two important goals in this task: seeing the need for random sampling and using randomization to investigate the behavior of a sample statistic. These introduce the basic ideas of statistical inference and can be accomplished with minimal knowledge of probability.

Waiting Times:

As the standards in statistics and probability unfold, students will not yet know the rules of probability for compound events. Thus, simulation is used to find an approximate answer to these questions. In fact, part b would be a challenge to students who do know the rules of probability, further illustrating the power of simulation to provide relatively easy approximate answers to wide-ranging problems.

Rolling Dice:

This task is intended as a classroom activity. Students pool the results of many repetitions of the random phenomenon (rolling dice) and compare their results to the theoretical expectation they develop by considering all possible outcomes of rolling two dice. This gives them a concrete example of what we mean by long term relative frequency.

Rolling Twice:

The purpose of this task is for students to compute the theoretical probability of a compound event. Teachers may wish to emphasize the distinction between theoretical and experimental probabilities for this problem. For students learning to distinguish between theoretical and experimental probability, it would be good to find an experimental probability either before or after students have calculated the theoretical probability.

Sitting Across From Each Other:

The purpose of this task is for students to compute the theoretical probability of a seating configuration. There are 24 possible configurations of the four friends at the table in this problem. Students could draw all 24 configurations to solve the problem but this is time consuming and so they should be encouraged to look for a more systematic method.

Log Ride:

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

Tutorials

Finding the Measure of Complementary Angles:

The video will use algebra to find the measure of two angles whose sum equals 90 degrees, better known as complementary angles.

Type: Tutorial

Find Measure of Complementary Angles:

Watch as we use algebra to find the measure of two complementary angles.

Type: Tutorial

Find Measure of Supplementary Angles:

Watch as we use algebra to find the measure of supplementary angles, whose sum is 180 degrees.

Type: Tutorial

Thinking About the Sign of Expressions:

This video shows some examples that test your understanding of what happens when positive and negative numbers are multiplied and divided.

Type: Tutorial

Solving Percentage Problems with Linear Equations:

Many real world problems involve involve percentages. This lecture shows how algebra is used in solving problems of percent change and profit-and-loss.

Type: Tutorial

Age word problem:

This tuptorial shows students how to set up and solve an age word problem. The tutorial also shows how tp check your work using substitution.

Type: Tutorial

Age word problem :

Students will learn how to set up and solve an age word problem.

Type: Tutorial

Converting repeating decimals to fractions :

Students will learn how to convert difficult repeating decimals to fractions.

Type: Tutorial

Converting repeating decimals to fractions :

This tutorial shows students how to convert basic repeating decimals to fractions.

Type: Tutorial

Finding Probability:

This video demonstrates several examples of finding probability of random events.

Type: Tutorial

The Limits of Probability:

This video discusses the limits of probability as between 0 and 1.

Type: Tutorial

Comparing Theoretical to Experimental Probabilites:

This video compares theoretical and experimantal probabilities and sources of possible discrepancy.

Type: Tutorial

Converting a fraction to a repeating decimal:

Students will learn how to convert a fraction into a repeating decimal. Students should know how to use long division before starting this tutorial.

Type: Tutorial

Impact of a Radius Change on the Area of a Circle:

This video shows how the area and circumference relate to each other and how changing the radius of a circle affects the area and circumference.

Type: Tutorial

Circles: Radius, Diameter, Circumference, and Pi:

In this video, students are shown the parts of a circle and how the radius, diameter, circumference and Pi relate to each other.

Type: Tutorial

Circumference of a Circle:

This video shows how to find the circumference, the distance around a circle, given the area.

Type: Tutorial

Finding Probability of a Simple Event:

This video demonstrates how to find the probability of a simple event.

Type: Tutorial

Making Predictions with Probability:

Watch the video as it predicts the number of times a spinner will land on a given outcome.

Type: Tutorial

Constructing Probability Model from Observations:

This video demonstrates development and use of a probability model.

Type: Tutorial

Compound Sample Spaces:

This video explores how to create sample spaces as tree diagrams, lists and tables.

Type: Tutorial

Probability of Compound Events:

This video shows how to use a sample space diagram to find probability.

Type: Tutorial

Die Rolling Probability:

The video will show how to use a table to find the probability of a compound event.

Type: Tutorial

Count Outcomes Using a Tree Diagram:

This video shows an example of using a tree diagram to find the probability of a compound event.

Type: Tutorial

Find Measure of Vertical Angles:

This video uses knowledge of vertical angles to solve for the variable and the angle measures.

Type: Tutorial

Introduction to Vertical Angles:

This video uses facts about supplementary and adjacent angles to introduce vertical angles.

Type: Tutorial

Find Measure of Angles in a Word Problem:

This video demonstrates solving a word problem involving angle measures.

Type: Tutorial

Construct a Right Isosceles Triangle:

This video discusses constructing a right isosceles triangle with given constraints and deciding if the triangle is unique.

Type: Tutorial

Construct a Triangle with Given Side Lengths:

This video demonstrates drawing a triangle when the side lengths are given.

Type: Tutorial

Area of a Circle:

In this video, watch as we find the area of a circle when given the diameter.

Type: Tutorial

Factor a Linear Expression by Taking a Common Factor:

This video demonstrates how to factor a linear expression by taking a common factor.

Type: Tutorial

Basic Linear Equation Word Problem:

This video shows how to construct and solve a basic linear equation to solve a word problem.

Type: Tutorial

Proportion Word Problem:

This introductory video demonstrates the basic skill of how to write and solve a basic equation for a proportional relationship.

Type: Tutorial

Adding and Subtracting Numbers in Different Formats:

In this example, we will work with three numbers in different formats: a percent, a decimal, and a mixed number.

Type: Tutorial

Changing a Fraction to Decimal Form:

In this video, you will practice changing a fraction into decimal form.

Type: Tutorial

Multiplying and Dividing Even and Odd Numbers of Negatives:

You will learn how multiplication and division problems give us a positive or negative answer depending on whether there are an even or odd number of negative integers used in the problem.

Type: Tutorial

Interpreting Graphs of Proportional Relationships:

This video shows how to recognize and understand graphs of proportional relationships to find the constant of proportionality.

Type: Tutorial

Combining Like Terms Introduction:

This introductory video teaches about combining like terms in linear equations.

Type: Tutorial

Find the Volume of an Object in a Rectangular Prism:

Find the volume of an object, given dimensions of a rectangular prism filled with water, and the incremental volume after the object is dropped into the water.

Type: Tutorial

Volume of a Rectangular Prism Problem:

This video involves packing a larger rectangular prism with smaller ones which is solved in two different ways.

Type: Tutorial

Find the Volume of a Triangular Prism and Cube:

This video will show to find the volume of a triangular prism, and a cube by applying the formula for volume.

Type: Tutorial

Complementary and Supplementary Angles:

The video will demonstrate the difference between supplementary angles and complementary angles, by using the given measurements of angles.

Type: Tutorial

Simplifying Expressions with Rational Numbers:

In this tutorial, you will simplify expressions involving positive and negative fractions.

Type: Tutorial

Making Sense of Complex Fractions:

In this tutorial, you will see how to simplify complex fractions.

Type: Tutorial

Solving a Proportion with an Unknown Variable :

Here's an introductory video explaining the basic reasoning behind solving proportions and shows three different methods for solving proportions which you will use later on to solve more difficult problems.

Type: Tutorial

Setting up Proportions to Solve Word Problems:

This introductory video shows some basic examples of writing two ratios and setting them equal to each other. This is just step 1 when solving word problems with proportions.

Type: Tutorial

Determining Rates with Fractions:

This video demonstrates finding a unit rate from a rate containing fractions.

Type: Tutorial

Rate Problem With Fractions:

Watch as we solve a rate problem finding speed in meters per second using distance (in meters) and time (in seconds).

Type: Tutorial

Multi-Step Word Problem :

Solve a multi-step word problem in the context of a cab fare.

Type: Tutorial

Rational Number Word Problem with Fractions:

In this example, you determine the volume of frozen water and express the answer as a fraction.

Type: Tutorial

Rational Number Word Problem with Decimals:

This video demonstrates adding and subtracting decimals in the context of an overdrawn checking account.

Type: Tutorial

Multiplying and Dividing Inequalities :

The video will solve the inequality and graph the solution.

Type: Tutorial

Negative Signs in Numerators and Denominators:

In this tutorial, you will evaluate fractions involving negative numbers and variables to determine if expressions are equivalent.

Type: Tutorial

Dividing Negative Fractions:

In this tutorial, you will see how to divide fractions involving negative integers.

Type: Tutorial

Multiplying Negative and Positive Fractions:

In this tutorial you will practice multiplying and dividing fractions involving negative numbers.

Type: Tutorial

Multiplying Positive and Negative Numbers:

In this tutorial, you will learn rules for multiplying positive and negative integers.

Type: Tutorial

Dividing Positive and Negative Numbers:

In this tutorial you will learn how to divide with negative integers.

Type: Tutorial

Why a Negative Times a Negative Makes a Positive:

In this tutorial you will use the repeated addition model of multiplication to help you understand why multiplying negative numbers results in a positive answer.

Type: Tutorial

Why a Negative Times a Negative is a Positive:

In this tutorial, you will use the distributive property to understand why the product of two negative numbers is positive.

Type: Tutorial

Dividing Fractions Example 2:

This video demonstrates dividing fractions as multiplying by the reciprocal.

Type: Tutorial

Dividing Whole Numbers and Fractions: T-shirts:

This video demonstrates dividing a whole number by a fraction by multiplying by the reciprocal.

Type: Tutorial

Proof: Vertical Angles are Equal:

This 5 minute video gives the proof that vertical angles are equal.

Type: Tutorial

Substitution with negative numbers:

Practice substituting positive and negative values for variables.

Type: Tutorial

Finding the absolute value as distance between numbers:

In this video, we will find the absolute value as distance between rational numbers.

Type: Tutorial

Even More Negative Number Practice:

This video uses the number line to find unknown values in subtraction statements with negative numbers.

Type: Tutorial

Adding Negative Numbers on Number Line Examples:

This video asks you to select the model that matches the given expression.

Type: Tutorial

Negative Number Word Problem:

Use a number line to solve a word problem that includes a negative number.

Type: Tutorial

Finding Initial Temperature from Temperature Changes:

In this video, we figure out the temperature in Fairbanks, Alaska by adding and subtracting integers.

Type: Tutorial

Percent Word Problem:

Learn how to find the full price when you know the discount price in this percent word problem.

Type: Tutorial

This video demonstrates how to add and subtract negative fractions with unlike denominators.

Type: Tutorial

This video demonstrates use of a number line and absolute value to add negative numbers.

Type: Tutorial

This video demonstrates use of a number line to add numbers with positive and negative signs.

Type: Tutorial

Subtracting a Negative = Adding a Positive:

Find out why subtracting a negative number is the same as adding the absolute value of that number.

Type: Tutorial

Negative Number Practice:

This video demonstrates adding and subtracting integers using a number line.

Type: Tutorial

Vertical, Adjacent and Linearly Paired Angles:

This resource will allow students to have a good understanding about vertical, adjacent and linear pairs of angles.

Type: Tutorial

Solving One-Step Equations Using Multiplication and Division:

This tutorial will help you to solve one-step equations using multiplication and division. For practice, take the quiz after the lesson!

Type: Tutorial

Examples of Evaluating Variable Expressions:

This video tutorial shows examples of writing expressions in simplified form and evaluating expressions.

Type: Tutorial

Direct and Inverse Variation:

This video provides assistance with understanding direct and inverse variation.

Type: Tutorial

Solving Two-Step Equations:

This short video uses both an equation and a visual model to explain why the same steps must be used on both sides of the equation when solving for the value of a variable.

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 - Multiplying Negative Numbers:

When number systems were expanded to include negative numbers, rules had to be formulated so that multiplication would be consistent regardless of the sign of the operands.

Type: Tutorial

Pre-Algebra - Commutative & Associative Properties of Addition:

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

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

Using the Proportion Method to Solve Percent Problems:

This site explicitly outlines the steps for using the proportion method to solve three different kinds of percent problems. It also includes sample problems for practice determining the part, the whole or the percent.

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 the Variable on Both Sides.:

This video models solving equations in one variable with variables on both sides of the equal sign.

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

Video/Audio/Animations

Solving Motion Problems with Linear Equations:

Based upon the definition of speed, linear equations can be created which allow us to solve problems involving constant speeds, time, and distance.

Note: This video exceeds basic expectations for the mathematical concept(s) at this grade level. The video is intended for students who have demonstrated mastery within the scope of instruction who may be ready for a more rigorous extension of the mathematical concept(s). As with all materials, ensure to gauge the readiness of students or adapt according to student's needs prior to administration.

Type: Video/Audio/Animation

Solving Problems with Linear Equations:

The video explains the process of creating linear equations to solve real-world problems.

Type: Video/Audio/Animation

Compound Probability of Independent Events:

This 6-minute video provides an example of how to work with compound probability of independent events through the example of flipping a coin. If you flip a coin and it lands on heads, is the next flip more likely to be tails? Or are those events independent?

Type: Video/Audio/Animation

Probability Explained:

This 8-minute video provides an introduction to the concept of probability through the example of flipping a coin and rolling a die.

Type: Video/Audio/Animation

Converting Fractions to Decimal Numbers:

Any fraction can be converted into an equivalent decimal number with a sequence of digits after the decimal point, which either repeats or terminates. The reason can be understood by close examination of the number line.

Type: Video/Audio/Animation

Averages:

This Khan Academy video tutorial introduces averages and algebra problems involving averages.

Type: Video/Audio/Animation

Virtual Manipulatives

Spinner:

In this activity, students adjust how many sections there are on a fair spinner then run simulated trials on that spinner as a way to develop concepts of probability. A table next to the spinner displays the theoretical probability for each color section of the spinner and records the experimental probability from the spinning trials. This activity allows students to explore the topics of experimental and theoretical probability by seeing them displayed side by side for the spinner they have created. 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

Cross Section Flyer - Shodor:

With this online Java applet, students use slider bars to move a cross section of a cone, cylinder, prism, or pyramid. This activity allows students to explore conic sections and the 3-dimensional shapes from which they are derived. 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

Circle Tool:

This applet allows students to investigate the relationships between the area and circumference of a circle and its radius and diameter. There are three sections to the site: Intro, Investigation, and Problems.

• In the Intro section, students can manipulate the size of a circle and see how the radius, diameter, and circumference are affected. Students can also play movie clip to visually see how these measurements are related.
• The Investigation section allows students to collect data points by dragging the circle radius to various lengths, and record in a table the data for radius, diameter, circumference and area. Clicking on the x/y button allows students to examine the relationship between any two measures. Clicking on the graph button will take students to a graph of the data. They can plot any of the four measures on the x-axis against any of the four measures on the y-axis.
• The Problems section contains questions for students to solve and record their answers in the correct unit.

(NCTM's Illuminations)

Type: Virtual Manipulative

Linear Function Machine:

In this activity, students plug values into the independent variable to see what the output is for that function. Then based on that information, they have to determine the coefficient (slope) and constant(y-intercept) for the linear function. This activity allows students to explore linear functions and what input values are useful in determining the linear function rule. 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

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

Graphing Lines:

Allows students access to a Cartesian Coordinate System where linear equations can be graphed and details of the line and the slope can be observed.

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

Interactive Marbles:

This online manipulative allows the student to simulate placing marbles into a bag and finding the probability of pulling out certain combinations of marbles. This allows exploration of probabilities of multiple events as well as probability with and without replacement. The tabs above the applet provide access to 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

The students will play a classic game from a popular show. Through this they can explore the probability that the ball will land on each of the numbers and discover that more accurate results coming from repeated testing. The simulation can be adjusted to influence fairness and randomness of the results.

Type: Virtual Manipulative

Curve Fitting:

With a mouse, students will drag data points (with their error bars) and watch the best-fit polynomial curve form instantly. Students can choose the type of fit: linear, quadratic, cubic, or quartic. Best fit or adjustable fit can be displayed.

Type: Virtual Manipulative

Box Plotter:

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

Type: Virtual Manipulative

Random Drawing Tool - Individual Trials (Probability Simulation):

This virtual manipulative allows one to make a random drawing box, putting up to 21 tickets with the numbers 0-11 on them. After selecting which tickets to put in the box, the applet will choose tickets at random. There is also an option which will show the theoretical probability for each ticket.

Type: Virtual Manipulative

Scale Factor:

Explore the effect on perimeter and area of two rectangular shapes as the scale factor changes.

Type: Virtual Manipulative

Parent Resources

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