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# Seventh Grade Mathematics Resources

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**Commutative and Associative Properties of Addition**

**Source: PBS Learning Media**

**Resource Type: Video**

Generate equivalent expressions using two additive properties. This video focuses on using the associative and commutative properties of addition to combine like terms, simplify expressions, and create equivalent expressions.

*Skill: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.*

*Georgia Standard: 7.EE.1*

**Linear Equations in One Variable**

**Source: PBS Learning Media**

**Resource Type: Interactive Lesson**

Visualize solutions to one-variable equations by performing a balancing act. This interactive exercise focuses on linear equations and mathematical reasoning to show how one-variable equations need to stay balanced to be solved correctly then you get to model your own problems and solve them.

*Skills: Use variables to represent quantities in a real world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.*

*Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently.*

*Georgia Standards: 7.EE.4, 7.EE.4a*

**Solving Linear Inequalities with Negative Numbers**

**Source: PBS Learning Media**

**Resource Type: Video**

Solve an inequality that has negative numbers and a variable. This video focuses on using inverse operations to solve for a variable and the importance of flipping the inequality when multiplying or dividing by a negative number.

*Skill: Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem*

*Georgia Standard: 7.EE.4b*

**Source: PBS Learning Media**

**Resource Type: Interactive**

Observe what happens to an image when the scale changes. This interactive exercise focuses on visually comparing multiplicative and additive relationships.

*Skill: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.*

*Georgia Standard: 7.G.1*

**Source: PBS Learning Media**

**Resource Type: Interactive**

Attempt to build a variety of different triangles using virtual linkage strips. This interactive exercise focuses on the appearance and manipulation of triangles.

*Skill: Explore various geometric shapes with given conditions. Focus on creating triangles from three measures of angles and/or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.*

*Georgia Standard: 7.G.2*

**Source: PBS Learning Media**

**Resource Type: Interactive**

Cut through a cube with a virtual sword and observe the resulting cross sections. This interactive exercise focuses on discovering the relationships between two and three-dimensional shapes.

*Skill: Describe the two-dimensional figures (cross sections) that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms, right rectangular pyramids, cones, cylinders, and spheres.*

*Georgia Standard: 7.G.3*

**Square-Wheeled Tricycle: Radius and Circumference**

**Source: PBS Learning Media**

**Resource Type: Interactive Lesson**

Uncover the secret behind how a square-wheeled tricycle can work at the National Museum of Mathematics. This interactive exercise focuses on working with the radius of various circles to find the circumference and area as well as challenging you to find the distance a square wheel travels around the track.

*Skill: Given the formulas for the area and circumference of a circle, use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.*

*Georgia Standard: 7.G.4*

**Source: PBS Learning Media**

**Resource Type: Video**

Learn how to solve problems that involve finding unknown supplementary, complementary, vertical, and adjacent angles in this Math Shorts video from the Utah Education Network and Planet Nutshell, Inc.

*Skill: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.*

*Georgia Standard: 7.G.5*

**Thinkport: Multiplying a Positive Integer with a Negative Integer**

**Source: PBS Learning Media**

**Resource Type: Interactive**

Explore integer multiplication by considering the trajectory of a hot air balloon as it rises and falls in this interactive from MPT. In the accompanying classroom activity, students play a game in which they find the product of two integers and move a button the corresponding distance and direction along a number line. Next, they use the interactive. To get the most from the lesson, students should be comfortable using a number line to add positive and negative integers, and they should be familiar with the notion that numerical opposites sum to 0. For a longer self-paced student tutorial using this media, see "Multiplying a Positive Integer with a Negative Integer"on Thinkport from Maryland Public Television.

*Skill: Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.*

*Georgia Standard: 7.NS.2a*

**Multiplying and Dividing with Negatives**

**Source: PBS Learning Media**

**Resource Type: Interactive Lesson**

Deepen your understanding of multiplication and division of rational numbers. This interactive exercise focuses on the rules for finding the products and quotients of positive numbers, negative numbers, and fractions and then finding the solutions on a number line.

*Skill: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non‐zero divisor) is a rational number. If p and q are integers then – (p/q) = (– p)/q = p/(–q).*

*Georgia Standard: 7.NS.2b*

**Source: PBS Learning Media**

**Resource Type: Video**

In this video, learn how to use division and place value to convert fractions to decimals. In the accompanying classroom activity, students watch the video to help them learn how to convert a fraction to a decimal using division. Then, they turn their attention to placing rational numbers on a number line. Practicing the placement of these numbers reinforces students’ number sense. It also gives them practice converting among the different representations of a single rational number.

*Skill: Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.*

*Georgia Standard: 7.NS.2d*

**Source: PBS Learning Media**

**Resource Type: Video**

This animated Math Shorts video from the Utah Education Network explains the term additive inverse and provides several examples that demonstrate the concept. In the accompanying classroom activity, students create equations and solve problems that involve adding groups of negative and positive integers that sum to zero. To get the most out of this activity, students should be familiar with plotting positive and negative integers on a number line.

*Skill: Show that a number and its opposite have a sum of 0 (are additive inverses). Describe situations in which opposite quantities combine to make 0.*

*Georgia Standard: 7.NS1a*

**Logical Leaps: Adding Rational Numbers on the Number Line**

**Source: PBS Learning Media**

**Resource Type: Interactive**

In this interactive, use logic to solve riddles involving a wallaby jumping contest. Add two consecutive jumps and place them on a number line, finding equivalent fractions and common denominators to do so. Backward jumps represent negative numbers, and forward jumps represent positive numbers. Numbers are randomized so that riddles can be answered and wallabies placed on the number line multiple times. The accompanying classroom activity includes a fraction/decimal concept review and a response sheet handout to support the online work.

*Skill: Understand p + q as the number located a distance from p, in the positive or negative direction depending on whether q is positive or negative. Interpret sums of rational numbers by describing real world contexts.*

*Georgia Standard: 7.NS1b*

**Subtracting Negative Numbers: School Yourself Algebra**

**Source: PBS Learning Media**

**Resource Type: Interactive**

It turns out that subtracting negatives is the same as adding positives! Learn why with this interactive video from the School Yourself Algebra series.

*Skill: Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (– q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real‐world contexts.*

*Georgia Standard: 7.NS1c*

**Multiplying Fractions by Whole Numbers: Recipes**

**Source: PBS Learning Media**

**Resource Type: Interactive Lesson**

In this blended lesson supporting literacy skills, students watch videos and complete interactive activities to learn about fractions and learn how to perform certain operations with fractions. Students develop their literacy skills as they explore a mathematics focus on multiplying fractions by whole numbers. During this process, they read informational text, learn and practice vocabulary words, and explore content through videos and interactive activities.

*Skill: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.*

*Georgia Standard: 7.RP.1*

**Source: PBS Learning Media**

**Resource Type: Video**

Watch as the National Museum of Mathematics creates an interesting series of images using ratios. This video focuses on the proportional relationship observed in fractals and challenges you to do some critical thinking using ratios and scale factors.

*Skill: Recognize and represent proportional relationships between quantities.*

*Georgia Standard: 7.RP.2*

**Source: PBS Learning Media**

**Resource Type: Interactive Lesson**

Dan has to run on a different track in the winter, how can he figure out his split time for the smaller track? This interactive exercise focuses on using what you know about ratios to calculate the correct split time for the different track, then challenges you to use ratios to solve similar problems.

*Skill: Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.*

*Georgia Standard: 7.RP.2a*

**Area and Volume in Kapa Cloth Making**

**Source: PBS Learning Media**

**Resource Type: Video**

A Hawaiian kapa artist explains how she uses area and measurements as part of her art-making process in this video from the Center for Asian American Media. In the accompanying classroom activity, students watch the video and learn how the artist finds the area of cloth that she can create with one cup of tree bark fiber. Next, students find how many cups of tree bark fiber they would need for kapa cloth to cover various surfaces around the classroom. To get the most from this lesson, students should have experience using a constant of proportionality to find proportional relationships.

*Skill: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.*

*Georgia Standard: 7.RP.2b*

**The Lowdown Percents Combined: Proportional Relationships with Multistep Ratio and Percent Problems**

**Source: PBS Learning Media**

**Resource Type: Video**

Learn how to calculate sale price when combining two “percent-off” discounts in this video from KQED. In the accompanying classroom activity, students develop and share a variety of strategies, including modeling with a 10 x 10 grid to determine a total discount and sale price when two percent-off discounts are combined. They compare their strategies with the approach demonstrated in a video. To get the most out of the activity, students should be comfortable calculating discount as a percent off a dollar amount (e.g., 20% off an item priced at $50) and familiar with the concept of a ratio.

*Skill: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, and fees.*

*Georgia Standard: 7.RP.3*

**Source: PBS Learning Media**

**Resource Type: Interactive Lesson**

In this blended lesson supporting literacy skills, students watch videos and complete interactive activities to learn how the Ojibwe tribe in Minnesota measure the abundance of various fish in their lake, how they interpret the data they collect, and how they make predictions about future populations based on their findings. Students develop their literacy skills as they explore a mathematics focus on population sampling. During this process, they read informational text, learn and practice vocabulary words, and explore content through videos and interactive activities.

*Skill: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions*

*Georgia Standard: 7.SP.2*

**Using Sampling and Statistics to Get Rid of the Trash in Perfectamundo**

**Source: PBS Learning Media**

**Resource Type: Interactive Lesson**

Learn how the CyberSquad uses sampling and data analysis to help solve a city's trash problem in this interactive from WNET. In the accompanying classroom activity, students watch a series of video clips in which the CyberSquad works to get rid of a mountain of trash by reducing, reusing, and recycling. Students use sampling, multiplication, and fractions to help determine the amount of trash for each method of removal and then complete a sampling and data analysis activity of their own design.

*Skill: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions*

*Georgia Standard: 7.SP.2*

**Source: PBS Learning Media**

**Resource Type: Interactive**

Flip a virtual coin to introduce or explore the concept of probability. This interactive exercise focuses on determining probabilities associated with repeated coin tosses and building tree diagrams to take math out of the classroom and into the real world.

*Skill: Develop a probability model and use it to find probabilities of events. Compare experimental and theoretical probabilities of events. If the probabilities are not close, explain possible sources of the discrepancy.*

*Georgia Standard: 7.SP.7*

**Source: PBS Learning Media**

**Resource Type: Video**

Explore basic probability by visualizing all possible outcomes in the sample space. This video focuses on charting the sample space for rolling two dice and then calculating the probability of rolling an 8 using the charted sample space.

*Skill: Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events*

*Georgia Standard: 7.SP.7a*

**Source: PBS Learning Media**

**Resource Type: Video**

Introducing Cardano's contribution to the concept of theoretical probability. This video provides a visual representation of sample space for random events and explains how to calculate probability.

*Skills: Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.*

*Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event*

*Georgia Standards: 7.SP.7b, 7.SP.8b*

**Source: PBS Learning Media**

**Resource Type: Interactive**

Use a tree diagram to find the probability that a set of triplets will be all girls in this interactive from MPT. In the accompanying classroom activity, students find the probability of various outcomes of compound events involving a set of dice, such as the probability of rolling doubles and the probability of rolling at least one “2.” They share solution strategies, including methods of representing sample spaces for these compound events. To get the most from the lesson, students should have experience developing and using uniform probability models.

*Skill: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.*

*Georgia Standard: 7.SP.8*

**Menu Toss-up: Choice and Data Sets**

**Source: PBS Learning Media**

**Resource Type: Video**

Investigate how you may be using math without realizing it when you choose food at a restaurant. This video focuses on the statistics involved when a restaurant offers combinations on their menus.

*Skill: Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.*

*Georgia Standard: 7.SP.8a*

**Your Odds of Winning Powerball: Probabilities of Compound Events Using Visuals**

**Source: PBS Learning Media**

**Resource Type: Video**

In this video, explore the odds of winning the Powerball lottery and learn what few people realize about their chances of winning: they are miniscule. In the accompanying classroom activity, students create simple lottery models to help them understand the probability of compound events. Though the probability of success at these experiments is better than that of Powerball, students will quickly see that the odds of winning any lottery-type game are seldom in their favor.

*Skill: Explain ways to set up a simulation and use the simulation to generate frequencies for compound events.*

*Georgia Standard: 7.SP.8c*