Fundamental Explorations in Mathematics 1   (#7912110)

Version for Academic Year:
The course was/will be terminated at the end of School Year 2016 - 2017

Course Standards

General Course Information and Notes

General Notes

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:  http://www.cpalms.org/uploads/docs/standards/eld/MA.pdf.

General Information

Course Number: 7912110
Course Path:
Abbreviated Title: FUND EXPLORS IN MATH 1
Course Length: Year (Y)
Course Status: Terminated

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

Rational Numbers in Alaska:

Follow Matteo as he explores opposite numbers, positive and negative rational numbers, and zero in real-world contexts while planning and going on a cruise in Alaska in this interactive tutorial. 

Type: Original Student Tutorial

Farmers Market: Ratios, Rates and Unit Rates:

Learn how to identify and calculate unit rates by helping Milo find prices per item at a farmer's market in this interactive tutorial.  

Type: Original Student Tutorial

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

Sailing Through Subtracting Decimals:

Sail through subtracting decimals to the thousandths place using the standard algorithm in this interactive tutorial.

Type: Original Student Tutorial

Add Another Topping: Adding Decimals:

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. 

Click here to open Part 1

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.

Click HERE to open part 1.

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

MacCoder’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

MacCoder’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

MacCoder’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

Moving MADness:

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

Helping Chef Ratio:

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

Type: Original Student Tutorial

Comparing Mitosis and Meiosis:

Compare and contrast mitosis and meiosis in this interactive tutorial. You'll also relate them to the processes of sexual and asexual reproduction and their consequences for genetic variation.

Type: Original Student Tutorial

Golf: Where Negative Numbers are a Positive Thing:

Learn how to create and use number lines with positive and negative numbers, graph positive and negative numbers, find their distance from zero, find a number’s opposite using a number line and signs, and recognize that zero is its own opposite with this interactive, golf-themed tutorial.

Type: Original Student Tutorial

Cancer: Mutated Cells Gone Wild!:

Explore the relationship between mutations, the cell cycle, and uncontrolled cell growth which may result in cancer with this interactive tutorial.

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

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.

Addition/Subtraction: The addition and subtraction of whole numbers, the addition and subtraction of decimals.

Multiplication/Division: The multiplication and addition of whole numbers.

Percentages: Identify the percentage of a whole number.

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

Type: Educational Game

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

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

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

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

Problem-Solving Tasks

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.

Type: Problem-Solving Task

Triangular Tables:

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

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

Rectangle Perimeter 2:

Students are asked to determine if given expressions are equivalent.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

The Djinni’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.

Type: Problem-Solving Task

Kendall's Vase - Tax:

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

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

Base and Height:

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

Type: Problem-Solving Task

Christo’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.

Type: Problem-Solving Task

Finding Areas of Polygons, Variation 1:

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

Type: Problem-Solving Task

Painting a Barn:

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

Type: Problem-Solving Task

Adding Multiples:

The purpose of this task is to gain a better understanding of factors and common factors. Students should use the distributive property to show that the sum of two numbers that have a common factor is also a multiple of the common factor.

Type: Problem-Solving Task

Mile High:

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

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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

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

Type: Problem-Solving Task

Running to School, Variation 2:

Students are asked to solve a distance problem involving fractions.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

Puppy Weights:

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

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

The Florist Shop:

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

Type: Problem-Solving Task

Traffic Jam:

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

Type: Problem-Solving Task

Video Game Credits:

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

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

Dana's House:

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

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

Games at Recess:

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

Type: Problem-Solving Task

Comparing Temperatures:

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

Type: Problem-Solving Task

Dan’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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

Drinking Juice, Variation 3:

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

Type: Problem-Solving Task

Gifts from Grandma, Variation 3:

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

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

It's Warmer in Miami:

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

Type: Problem-Solving Task

Jayden’s Snacks:

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

Type: Problem-Solving Task

Busy Day:

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

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

Firefighter Allocation:

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

Type: Problem-Solving Task

Log Ride:

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

Type: Problem-Solving Task

Morning Walk:

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

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

Mangos for Sale:

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

Type: Problem-Solving Task

Mixing Concrete:

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

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

Running at a Constant Speed:

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

Type: Problem-Solving Task

Student Center Activity

Edcite: Mathematics Grade 6:

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 equal one. They will also learn that zero to any positive exponent equals zero.

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

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

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:

In this video, discover another way of finding the volume of a rectangular prism involves dividing it into fractional cubes, finding the volume of one, and then multiplying that area by the number of cubes that fit into the rectangular prism.

Type: Tutorial

Volume of a Rectangular Prism: Word Problem:

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

Type: Tutorial

How to Solve Equations of the Form ax = b:

Here's an introduction to basic algebraic equations of the form ax = b in this tutorial.

Type: Tutorial

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

In this tutorial, we will solve equations in one step by multiplying or dividing a number on both sides.

Type: Tutorial

Statistical Questions:

Discover what makes a question a "statistical question."

Type: Tutorial

How to Test Solutions to Inequalities:

Learn how to test if a certain value of a variable makes an inequality true in this tutorial.

Type: Tutorial

How to Test Solutions to Equations Using Substitution:

Learn how to test if a certain value of a variable makes an equation true in this tutorial.

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:

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

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:

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 an explanation on how to combine like terms in algebra. 

Type: Tutorial

Least Common Multiple:

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

Type: Tutorial

Coordinate Plane:

Students will become familiar with the coordinate plane.

Type: Tutorial

Graphing Points and Naming Quadrants:

This video contains 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:

Locate fractions and decimals on the same number line in this tutorial.

Type: Tutorial

Ordering Negative Numbers:

Let's order negative numbers from least to greatest in this video.

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:

This is an introduction to combining like terms in this tutorial.

 

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:

This video is about interpreting absolute value in a real-life situation.

Type: Tutorial

Coordinate Plane: Quadrants:

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 a 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 numbers that are decimals.

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:

This video demonstrates how to multiply two decimal numbers.

Type: Tutorial

Area of Triangle on a Grid:

We will be able to find the area of a triangle in a coordinate grid. The formula for the area of a triangle is given in this tutorial.  

Type: Tutorial

Perimeter and Area:

Students will learn the basics of finding the perimeter and area of squares and rectangles.  

Type: Tutorial

Adding Decimals Word Problem:

This video demonstrates adding decimal numbers to solve a word problem.

Type: Tutorial

Subtracting Decimals 2:

Let's show subtracting with digits up to the thousandths place in this tutorial.

Type: Tutorial

Subtracting Decimals 1:

Watch as we align decimals before subtracting in this tutorial.

Type: Tutorial

Adding Decimals Example:

Learn how to add decimals and use place value in this tutorial. 

Type: Tutorial

Ratio Word Problem: Centimeters to Kilometers:

In this video, watch as we solve this word problem using what we know about equivalent ratios.

Type: Tutorial

Ratio Word Problem:

In this video, a ratio is given and then applied to solve a problem. 

Type: Tutorial

Finding a Percent:

In the video, we 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:

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

Type: Tutorial

Percent Word Problem:

Use long division to find the percent in this tutorial.

Type: Tutorial

Example: Evaluating expressions with 2 variables:

Evaluating Expressions with Two Variables

Type: Tutorial

Converting Decimals to Percents:

This video demonstrates how to write a decimal as a percent.

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 deals with what percent really means by looking at a 10 by 10 grid.

Type: Tutorial

The Meaning of Percent over 100:

This video demonstrates a visual model of a percent greater than 100.

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

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.  While this tutorial includes the basis of Coordinate system, it also includes ideas beyond fifth grade standards.  Most likely only advanced fifth graders would find the video engaging.  

Type: Tutorial

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

Adding Integers:

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

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

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

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

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

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

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

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

Parent Resources

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