(7.MP) Ratios and Proportional Relationships

(7.RP) The Number System

(7.NS) Expressions and Equations

(7.EE) Geometry

(7.G) Statistics and Probability

(7.SP)

Standard 7.MP.1

Make sense of problems and persevere in solving them. Explain the meaning of a problem and look for entry points to its solution. Analyze givens, constraints, relationships, and goals. Make conjectures about the form and meaning of the solution, plan a solution pathway, and continually monitor progress asking, "Does this make sense?" Consider analogous problems, make connections between multiple representations, identify the correspondence between different approaches, look for trends, and transform algebraic expressions to highlight meaningful mathematics. Check answers to problems using a different method.

Standard 7.MP.2

Reason abstractly and quantitatively. Make sense of the quantities and their relationships in problem situations. Translate between context and algebraic representations by contextualizing and decontextualizing quantitative relationships. This includes the ability to decontextualize a given situation, representing it algebraically and manipulating symbols fluently as well as the ability to contextualize algebraic representations to make sense of the problem.

Standard 7.MP.3

Construct viable arguments and critique the reasoning of others. Understand and use stated assumptions, definitions, and previously established results in constructing arguments. Make conjectures and build a logical progression of statements to explore the truth of their conjectures. Justify conclusions and communicate them to others. Respond to the arguments of others by listening, asking clarifying questions, and critiquing the reasoning of others.

Standard 7.MP.4

Model with mathematics. Apply mathematics to solve problems arising in everyday life, society, and the workplace. Make assumptions and approximations, identifying important quantities to construct a mathematical model. Routinely interpret mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

Standard 7.MP.5

Use appropriate tools strategically. Consider the available tools and be sufficiently familiar with them to make sound decisions about when each tool might be helpful, recognizing both the insight to be gained as well as the limitations. Identify relevant external mathematical resources and use them to pose or solve problems. Use tools to explore and deepen their understanding of concepts.

Standard 7.MP.6

Attend to precision. Communicate precisely to others. Use explicit definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose. Specify units of measure and label axes to clarify the correspondence with quantities in a problem. Calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context.

Standard 7.MP.7

Look for and make use of structure. Look closely at mathematical relationships to identify the underlying structure by recognizing a simple structure within a more complicated structure. See complicated things, such as some algebraic expressions, as single objects or as being composed of several objects.For example, see 5 - 3(x - y)^{2}as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.

Standard 7.MP.8

Look for and express regularity in repeated reasoning. Notice if reasoning is repeated, and look for both generalizations and shortcuts. Evaluate the reasonableness of intermediate results by maintaining oversight of the process while attending to the details.

- Ratios and Proportional Relationships (7.RP) - 7th Grade Core Guide

The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for Mathematics Grade 7 Cluster "Analyze Proportional Relationships and Use Them to Solve Real-World and Mathematical Problems." / Standards 1, 2 and 3.

- Chapter 4 - Mathematical Foundation (UMSMP)

This is Chapter 4 of the Utah Middle School Math: Grade 7 textbook. It provides a Mathematical Foundation for Proportional Relationships and Solving Problems. - Chapter 4 - Student Workbook (UMSMP)

This is Chapter 4 of the Utah Middle School Math: Grade 7 student workbook. It focuses on these topics: Proportional Relationships and Solving Problems. Engage NY - Grade 7 Math Module 1:Ratios and Proportional Relationship (EngageNY)

In this 30-day Grade 7 module, students build upon sixth grade reasoning of ratios and rates to formally define proportional relationships and the constant of proportionality. Students explore multiple representations of proportional relationships by looking at tables, graphs, equations, and verbal descriptions. Students extend their understanding about ratios and proportional relationships to compute unit rates for ratios and rates specified by rational numbers. The module concludes with students applying proportional reasoning to identify scale factor and create a scale drawing. - Grade 7 Math Module 4: Percent and Proportional Relationships (EngageNY)

In Module 4, students deepen their understanding of ratios and proportional relationships from Module 1 by solving a variety of percent problems. They convert between fractions, decimals, and percents to further develop a conceptual understanding of percent and use algebraic expressions and equations to solve multi-step percent problems. An initial focus on relating 100% to the whole serves as a foundation for students. Students begin the module by solving problems without using a calculator to develop an understanding of the reasoning underlying the calculations. - Grade 7 Unit 3: Ratio and Proportional Relationships (Georgia Standards)

The units in this instructional framework emphasize key standards that assist students to develop a deeper understanding of numbers. They learn to express different representations of rational numbers (e.g., fractions, decimals, and percents), discover how to identify and explain the constant of proportionality, and represent proportional relationships and scale drawings within real-world contexts. The Big Ideas that are expressed in this unit are integrated with such routine topics as estimation, mental and basic computation. All of these concepts need to be reviewed throughout the year.

- Anna in D.C.

The purpose of this task is to give students an opportunity to solve a multi-step percentage problem that can be approached in many ways. - Art Class, Assessment Variation

This task is part of a set of three assessment tasks for 7.RP.2. - Art Class, Variation 1

Given a table about paint mixtures students are asked to answer questions about the mixture proportions and plot points on a plane to represent each mixture. - Art Class, Variation 2

Given a table about paint mixtures students are asked to answer questions about the mixture proportions and write an equation that relates y, the number of parts of yellow paint, and b, the number of parts of blue paint for each of the different shades of paint on the table. - Buying Bananas, Assessment Version

This task is part of a set of three assessment tasks for 7.RP.2. - Buying Coffee

The purpose of this task is for students to find a unit rate in a context where two quantities are in a proportional relationship and to draw the graph of that proportional relationship. - Buying Protein Bars and Magazines

The task reads "Tom wants to buy some protein bars and magazines for a trip. He has decided to buy three times as many protein bars as magazines. Each protein bar costs $0.70 and each magazine costs $2.50. The sales tax rate on both types of items is 6Â½%. How many of each item can he buy if he has $20.00 to spend?" - 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. - Cider versus Juice - Variation 1

This task asks students to compute multiple unit rates, aligning with standard 7.RP.A.1. The problem also has a real-world context, which requires students to compare two rates in different units in order to reach a conclusion on buying two different products. - Cider versus Juice - Variation 2

The goal of this task is to apply proportional reasoning to determine which of two ways of buying apple juice/cider is a better deal. This task is a second variation to 7.RP.A.1, 7.RP.A.2.b Cider Versus Juice - Variation 1. This version offers a less directed approach to one of the questions posed in that task. - Climbing the steps of El Castillo

The purpose of this task is for students to solve a straight-forward problem involving a proportional relationship in a context. In order to solve the problem, students must assume that the steps are of uniform height, which looks reasonable given the picture. - Comparing Years

This task asks students to compare two quantities and calculate the percent decrease between the larger and smaller value. - Cooking with the Whole Cup

While the task as written does not explicitly use the term "unit rate," most of the work students will do amounts to finding unit rates. A recipe context works especially well since there are so many different pair-wise ratios to consider. - Double Discounts

The goal of this problem is to calculate percent decreases in the context of several (sequential) discounts. - Drill Rig

The purpose of this task is to provide a context for multiplying and dividing signed rational numbers, providing a means for understanding why the signs behave the way they do when finding products. - Dueling Candidates

The goal of this task is to have students examine some properties of ratios (and fractions) in an important real world context. Students will gain practice working with ratios while investigating some of the complexities of voting theory. - Finding a 10% increase

Students are asked to complete this task: "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?" - Framing a House - student task

This task has students recreate house plans on graph paper and then determine how many linear feet of wall plate material will be needed. - Friends Meeting on Bikes

Students are asked to complete this task: "Taylor and Anya are friends who live 63 miles apart. Sometimes on a Saturday, they ride toward each other's houses on their bikes and meet in between. One day they left their houses at 8 am and met at 11 am. Taylor rode at 12.5 miles per hour. How fast did Anya ride?" - 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. - Gym Membership Plans

In this task, students are presented with two situations in a single context and asked which one represents a proportional relationship. Students are asked to understand this proportional relationship from a variety of perspectives -- a table, a graph, a verbal context, and an equation. - How Fast is Usain Bolt?

This task involves a multi-step conversion between two rates, going from meters per second to miles per hour. - Lincoln's Math Problem

The purpose of this task is for students to solve a multi-step problem involving simple interest. What is most interesting about this task is that it was one that Abraham Lincoln worked on in his youth (probably around the age of 17 years); it was discovered in some old papers that were authenticated as Lincoln's. - Measuring the area of a circle

This goal of this task is to give students familiarity using the formula for the area of a circle while also addressing measurement error and addresses both 7.G.4 and 7.RP.3. - Mixtures

This activity will help students understand percentages and mixture problems by working with two piles of colored chips. - 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. - Molly's Run, Assessment Variation

This task is part of a set of three assessment tasks that address various aspects of 6.RP domain and help distinguish between 6th and 7th grade expectations. - 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 "7.RP Music Companies, Variation 2" for a task with a very similar setup but is much more involved and so illustrates 7.RP.3. - Music Companies, Variation 2

Given a scenario about share prices students are asked to calculate the value of individual shares, the value of groups of shares, and the difference between the two group amounts. - Proportionality

The task has two main purposes. (1) Students make sense out of the definition of direct proportionality. (2) They engage in SMP 3 "Make a viable argument and critique the reasoning of others" and SMP 6 "Attend to precision". - Robot Races

Given a graph of line segments that show the distance d, in meters, that each of three robots traveled after t seconds, students are asked to answer specific questions about the graph. - Robot Races, Assessment Variation

This task is part of a set of three assessment tasks for 7.RP.2. This task asks students to "explain what a point (x,y) on the graph of a proportional relationship means in terms of the situation" and to "compute unit rates associated with ratios of fractions." Students also need to compare the speeds of the robots. - Sale!

The purpose of this task is to engage students in Standard for Mathematical Practice 4, "Model with mathematics." The teacher might use this task after formally teaching 7.RP.1-3. Students could be given the task and asked to collaborate in small groups to solve the questions posed using all the formal instruction on ratio and proportional reasoning. - Sand Under the Swing Set

The purpose of this task is for students to solve a contextual problem where there are multiple entry points to this geometry based concept. The student can choose to solve the problem using a scale factor or a unit rate, but must first must analyze the context of the problem to understand the situation and choose their approach. This task provides opportunities for students to reason about their computations to see if they make sense. This task could be used as an assessment question or for guided instruction on scale factoring and/or unit rate. - Scaling

An interactive from Annenberg asks students to scale a picture by using the math strategies of multiplicative and additive relationships. Students then use those strategies to compare photocopies and rectangles in different scales. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Scaling angles and polygons

The goal of this task is to gather together knowledge and skills from the seventh grade in a context which prepares students for the important eighth grade notion of similarity. - Selling Computers

Given this scenario: "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," students must determine how many computers the sales team needs to sell to get the bonus. - Sore Throats, Variation 1

Given the scenario of mixing salt and water students must identify which of a set of equations best relates that information. - Stock Swaps, Variation 2

Given the price of two stocks to be swapped, students must determine how many shares of stock they need to offer to get an even swap. - Stock Swaps, Variation 3

Given the price of two stocks to be swapped, students must determine how many shares of stock they need to offer to get an even swap. - Tax and Tip

Given this scenario: "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," students must calculate the tip amount and the total bill including it. - Temperature Change

The goal of this task is to provide a context for interpreting the expressions that match the last part of the standard 7.NS.2.b, ''Interpret quotients of rational numbers by describing real-world contexts,'' though in this case the numerator and denominator are integers. Because of the context, students will also gain experience working with rates. - The Price of Bread

The purpose of this task is for students to calculate the percent increase and relative cost in a real-world context. - Thunder and Lightning

The purpose of this task is to work on performing unit conversions in a real world context about the speed of sound. - Track Practice

This task asks students to find the unit rates that one can compute in a context. - Two-School Dance

The purpose of this task is to see how well students students understand and reason with ratios. - Walk-a-thon 2

The purpose of this task is for students to translate information about a context involving constant speed into information presented in a table and to find the time it takes to travel a unit distance as well as the distance traveled per unit time. Students then have to translate the information to equations and graphs and then use these mathematical tools to make predictions about the future.

- Estimating: Counting Trees

This lesson unit is intended to help educators assess how well students are able to solve simple problems involving ratio and direct proportion, choose an appropriate sampling method, and collect discrete data and record them using a frequency table. - Framing a House - student task

This task has students recreate house plans on graph paper and then determine how many linear feet of wall plate material will be needed. - Grid and Percent It

This lesson plans provides a 10 x 10 model so that students can understand how to solve percent problems. - Hay Bale Farmer

This lesson helps students understand volume by having them measure round and square hay bales. - Holes

After watching a clip of the movie Holes from Walt Disney Pictures students will answer a series of questions, such as "If Stanley and X-Ray both dig one hole per day for a year, how much extra dirt will Stanley have dug than X-Ray?" and "How many times could that extra dirt fill one of the holes X-Ray digs?" - IXL Game: Ratios and proportions

This game for seventh graders is designed to help them understand ratios and proportions, specifically by estimating population size using proportions. This is just one of many online games that supports the Utah Math core. Note: The IXL site requires subscription for unlimited use. - Intercepts of Linear Equations video

This video introduces the topic. - Inverse Proportions and Shadows in Practice

in this interactive a figure's shadow is projected on to a screen. Students then observe how the shadow changes as the figure moves farther away . Students also complete a chart that shows the distance of the figure from the light source and the height of the shadow helping them understand inverse proportions. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Inverse Proportions and Shadows in the Real World

A tour of drive-in theaters is the focus of this video. Students are asked to observe how the size of an object relates to its distance from the light source. In the classroom activity students do a hands-on experiments using a projector of other light source. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Linear Functions video

This video compares proportional and non-proportional linear functions. - Living Wages in CA: Ratio and Rate in the Real World

The use of infographics helps us understand the costs of basic living expenses. The classroom activity has students look at real-life examples and data to calculate whether the minimum wage in their state can be a living wage. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Manipulating Graphs

This video demonstrates how to use the slope-intercept of a line to the graph of that line. The classroom activity has them demonstrate their understanding by finding equations for a set of lines through the origin. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Mixtures

This activity will help students understand percentages and mixture problems by working with two piles of colored chips. - One-Dimensional Scaling To Find Unknown Heights

An interactive activity helps students understand real-world application of ratios and asks them to scale a model of a T-Rex for a diorama. In the classroom activity students are asked to draw scale models. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Point Slope Form and Standard Form of Linear Equations video

This a video explanation of the topic. - Proportional Functions video

This video introduces proportional functions. - Rate of Change and Slope video

This video introduces the concepts. - Real-World Proportional Relationships: Gender Wage Gap

Students use an infographic to understand how wages of today compare with those of 50 years ago in this lesson plan. The classroom activity helps students understand and calculate the wage gap using media salaries for men and women. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Scale Models and Three-Dimensional Scaling in Practice

Students can use this interactive to explore how an object changes when enlarged by a factor of 10. They put this understanding to use in the activity when they compare two cubes of different sizes by volume and surface area. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Scale Models in the Real World

This video show scale models of railroads, dollhouses, and architecture to explain what the ratios represent. The hands-on classroom activity then has students create their own models. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Scaling

An interactive from Annenberg asks students to scale a picture by using the math strategies of multiplicative and additive relationships. Students then use those strategies to compare photocopies and rectangles in different scales. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Scaling Up Rectangles Using Simulations

This interactive allows students to create murals in different sizes by understanding two-dimensional scaling. The activity for the classroom has students use graph paper to draw and compare squares with different proportional dimensions and record the data as they change. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Scaling Up Rectangles in the Real World

By looking at murals in this video students see how artists use proportion and measurement to create them. The class then does an activity where they enlarge a drawing by using scale and then create a classroom mural. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Similar Figures and Unknown Heights in Practice

Students will learn about proportional reasoning in this interactive and how it can help find an unknown height as well as exploring proportional relationships among similar triangles. The classroom activity uses the interactive as a catalyst into a discussion of these math concepts. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Similar Figures in the Real World

A visit to the Louisville Slugger Museum and Factory shows students how measurement and engineering are involved in the creation of new baseball bats. The math skills of proportional reasoning and equivalent ratios are used in the classroom activity involving an oversized bat and a player. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.

Standard 7.RP.1

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction^{1/2}/_{1/4}miles per hour, equivalently 2 miles per hour.Standard 7.RP.2

Recognize and represent proportional relationships between quantities.

- 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.
- Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
- Represent proportional relationships by equations.
For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed ast = pn.- Explain what a point (
x,y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1,r) whereris the unit rate.Standard 7.RP.3

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

- The Number System (7.NS) - 7th Grade Core Guide

The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for Mathematics Grade 7 - The Number System

- Chapter 1 - Mathematical Foundation (UMSMP)

This is Chapter 1 of the Utah Middle School Math: Grade 7 textbook. It provides a Mathematical Foundation for Probability, Percent, Rational Number Equivalence. - Chapter 1 - Student Workbook (UMSMP)

This is Chapter 1 of the Utah Middle School Math: Grade 7 student workbook. It covers the following topics: Probability, Percent, Rational Number Equivalence. - Chapter 2 - Mathematical Foundation (UMSMP)

This is Chapter 2 of the Utah Middle School Math: Grade 7 textbook. It provides a Mathematical Foundation for Rational Number Operations. - Chapter 2 - Student Workbook (UMSMP)

This is Chapter 2 of the Utah Middle School Math: Grade 7 student workbook. It covers Rational Number Operations. Engage NY - Grade 7 Math Module 2: Rational Numbers (EngageNY)

In Grade 6, students formed a conceptual understanding of integers through the use of the number line, absolute value, and opposites and extended their understanding to include the ordering and comparing of rational numbers.This module uses the Integer Game: a card game that creates a conceptual understanding of integer operations and serves as a powerful mental model students can rely on during the module. Students build on their understanding of rational numbers to add, subtract, multiply, and divide signed numbers. Previous work in computing the sums, differences, products, and quotients of fractions serves as a significant foundation. - Grade 7 Unit 1: Operations with Rational Numbers (Georgia Standards)

The units in this instructional framework emphasize key standards that assist students to develop a deeper understanding of numbers. They learn to express different representations of rational numbers (e.g., fractions, decimals, and percents) and interpret negative numbers in everyday context (e.g., sea level change). The big ideas that are expressed in this unit are integrated with such previous knowledge as estimation, mental and basic computation. All of these concepts need to be reviewed throughout the year.

- Bookstore Account

The purpose of this task is for students to use algebra and the number line to understand why it makes sense that we sometimes represent debt using negative numbers. If we agree that depositing money in an account adds a positive number to the balance, and buying somethings subtracts a positive number from the balance, then it is natural to represent debt with negative numbers. - Comparing Freezing Points

This task is appropriate for assessing student's understanding of differences of signed numbers. - Decimal Expansions of Fractions

The goal of this task is to convert some fractions to decimals and then make conjectures about which fractions have terminating decimal expansions (as well as the length of those decimals). - Differences and Distances

The purpose of this task is to help students connect the distance between points on a number line with the difference between the numbers. This task assumes that students are familiar with the idea that differences between integers correspond to distances between them on the number line and asks them to analyze a situation involving non-integer quantities. - Differences of Integers

The goal of this task is to subtract integers in a real world context. It will be very helpful for students to use number lines for this task. - Distances Between Houses

The purpose of this task is for students to solve a problem involving distances between objects whose positions are defined relative to a specified location and to see how this kind of situation can be represented with signed numbers. - 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. Students should have lots of opportunities to represent adding specific rational numbers before they work on answering this one. - Distributive Property of Multiplication

The goal of this task is to study the distributive property for products of whole numbers, focusing on using geometry to help understand why (-1) x (-1) = 1. - Drill Rig

The purpose of this task is to provide a context for multiplying and dividing signed rational numbers, providing a means for understanding why the signs behave the way they do when finding products. - Equivalent fractions approach to non-repeating decimals

This task is most suitable for instruction. The purpose of the task is to get students to reflect on the definition of decimals as fractions (or sums of fractions), at a time when they are seeing them primarily as an extension of the base-ten number system and may have lost contact with the basic fraction meaning. Students also have their understanding of equivalent fractions and factors reinforced. - Framing a House - student task

This task has students recreate house plans on graph paper and then determine how many linear feet of wall plate material will be needed. - Modeling Fraction and Mixed Number Division Using Arrays

Students will learn how to solve word problems that involve dividing fractions and mixed numbers by using a visual model. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - 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. - Repeating decimal as approximation

The purpose of the task is to have students reflect on the meaning of repeating decimal representation through approximation. A formal explanation requires the idea of a limit to be made precise, but 7th graders can start to wrestle with the ideas and get a sense of what we mean by an "infinite decimal." Students can make observations which reinforce the topic at hand as well as lay groundwork for later developments. - Repeating or Terminating?

The purpose of this task is to understand, in some concrete cases, why terminating decimal numbers can also be written as repeating decimals where the repeating part is all 9's. - Rounding and Subtracting

This task addresses what happens to rounding discrepancies when arithmetic is performed on rounded numbers and would be a good problem for classroom discussion. - Sharing Prize Money

This task requires students to be able to reason abstractly about fraction multiplication as it would not be realistic for them to solve it using a visual fraction model. Even though the numbers are too messy to draw out an exact picture, this task still provides opportunities for students to reason about their computations to see if they make sense - Temperature Change

The goal of this task is to provide a context for interpreting the expressions that match the last part of the standard 7.NS.2.b, ''Interpret quotients of rational numbers by describing real-world contexts,'' though in this case the numerator and denominator are integers. Because of the context, students will also gain experience working with rates. - Why is a Negative Times a Negative Always Positive?

The purpose of this task is for students to understand the reason it makes sense for the product of two negative numbers to be positive.

- Access Ramp - Student Task

This task has students design an access ramp, which complies with the Americans with Disabilities Act (ADA) requirements and include pricing based on local costs. - Adding Integers

This Teaching Channel video and presentation help students to add and subtract integers using a number line and a song with motions. (14 min.) - Adding Rational Numbers on the Number Line

In this interactive students must solve riddles about a wallaby jumping contest. But they must find equivalent fractions and common denominators to complete the riddle. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Addition and Subtraction of Integers

A card game in which positive and negative numbers are added together is the subject of this video teaching students how to add and subtract integers. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Framing a House - student task

This task has students recreate house plans on graph paper and then determine how many linear feet of wall plate material will be needed. - IXL Game: Rational numbers

This game for seventh graders will help them understand rational numbers, specifically how to add and subtract rational numbers. This is just one of many online games that supports the Utah Math core. Note: The IXL site requires subscription for unlimited use. - Modeling Fraction Division Using Comparison, Group Number Unknown

In this lesson students will learn how to solve a word problem involving the division of fractions by viewing an animation about a hedgehog's hibernation. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Modeling Fraction Division, Equal Groups, Group Size Unknown

The skill of dividing two fractions by groups of unknown size is the focus of this video. Students will learn how to solve a word problem using this process. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Modeling Fraction Division, Equal Groups, Number of Groups Unknown

This animated video shows students a model they can use to solve word problems involving the division of fractions. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Modeling Fraction and Mixed Number Division Using Arrays

Students will learn how to solve word problems that involve dividing fractions and mixed numbers by using a visual model. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Number Sets video

The video introduces and explains the topic. - Repeating Decimal Rings

In this interactive activity you will explore the patterns that occur when expanding seventh and thirteenth fractions into decimals. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - What's Your Sign: Integer Addition

In this filmed lesson students master integer addition using number lines as a visual tool. (5 minutes) - Zero Pairs, Manipulatives, and a Real-World Scenario

In this filmed lesson, students use manipulatives and zero pairs to understand integer subtraction. (6 minutes)

Standard 7.NS.1

Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

- Describe situations in which opposite quantities combine to make 0.
For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.- Understand
p+qas the number located a distance |q| fromp, in the positive or negative direction depending on whetherqis positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.- 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.- Apply properties of operations as strategies to add and subtract rational numbers.
Standard 7.NS.2

Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

- 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.
- 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
pandqare integers, then –(p/q) = (–p)/q=p/(–q). Interpret quotients of rational numbers by describing real-world contexts.- Apply properties of operations as strategies to multiply and divide rational numbers.
- 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.
Standard 7.NS.3

Solve real-world and mathematical problems involving the four operations with rational numbers. Computations with rational numbers extend the rules for manipulating fractions to complex fractions.

- Expressions & Equations (7.EE) - 7th Grade Core Guide

The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for Mathematics Grade 7 Cluster "Use properties of operations to generate equivalent expressions." - The Number System (7.NS) - 7th Grade Core Guide

The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for Mathematics Grade 7 - The Number System

- Chapter 3 - Mathematical Foundation (UMSMP)

This is Chapter 3 of the Utah Middle School Math: Grade 7 textbook. It provides a Mathematical Foundation for Expressions and Equations I. - Chapter 3 - Student Workbook (UMSMP)

This is Chapter 3 of the Utah Middle School Math: Grade 7 student workbook. It covers Expressions and Equations I. - Chapter 6 - Mathematical Foundation (UMSMP)

This is Chapter 6 of the Utah Middle School Math: Grade 7 textbook. It provides a Mathematical Foundation for Expressions and Equations II - Real-world equations, Inequalities. - Chapter 6 - Student Workbook (UMSMP)

This is Chapter 6 of the Utah Middle School Math: Grade 7 textbook. It focuses on these topics: Real-world equations and Inequalities. Engage NY - Grade 7 Math Module 2: Rational Numbers (EngageNY)

In Grade 6, students formed a conceptual understanding of integers through the use of the number line, absolute value, and opposites and extended their understanding to include the ordering and comparing of rational numbers.This module uses the Integer Game: a card game that creates a conceptual understanding of integer operations and serves as a powerful mental model students can rely on during the module. Students build on their understanding of rational numbers to add, subtract, multiply, and divide signed numbers. Previous work in computing the sums, differences, products, and quotients of fractions serves as a significant foundation. - Grade 7 Math Module 3: Expressions and Equations (EngageNY)

This module consolidates and expands upon students understanding of equivalent expressions as they apply the properties of operations to write expressions in both standard form and in factored form. They use linear equations to solve unknown angle problems and other problems presented within context to understand that solving algebraic equations is all about the numbers. Students use the number line to understand the properties of inequality and recognize when to preserve the inequality and when to reverse the inequality when solving problems leading to inequalities. They interpret solutions within the context of problems. Students extend their sixth-grade study of geometric figures and the relationships between them as they apply their work with expressions and equations to solve problems involving area of a circle and composite area in the plane, as well as volume and surface area of right prisms. - Grade 7 Unit 2: Expressions and Equations (Georgia Standards)

The units in this instructional framework emphasize key standards that assist students to develop a deeper understanding of numbers. They learn how to solve multi- step equations and discuss the difference between equations and expressions. The Big Ideas that are expressed in this unit are integrated with such routine topics as estimation, mental and basic computation. All of these concepts need to be reviewed throughout the year.

- Commutative and Associative Equations

This lesson focuses on how to rearrange and combine parts of algebraic expressions by using the commutative and associative properties of addition. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Equivalent Expressions?

The purpose of this task is to directly address a common misconception held by many students who are learning to solve equations. Because a frequent strategy for solving an equation with fractions is to multiply both sides by a common denominator (so all the coefficients are integers), students often forget why this is an "allowable" move in an equation and try to apply the same strategy when they see an expression. - 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. - 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. - Ticket to Ride

The purpose of this instructional task is to illustrate how different, but equivalent, algebraic expressions can reveal different information about a situation represented by those expressions. This task can be used to motivate working with equivalent expressions, which is an important skill for solving linear equations and interpreting them in contexts. The task also helps lay the foundation for students' understanding of the different forms of linear equations they will encounter in 8th grade. - Writing Expressions

This task requires students to write an expression for a sequence of operations.

- Additive Inverse

This lesson begins with students viewing this UEN-produced video which demonstrates the term additive inverse. The accompanying activity has students play a die game and create an equation equal to 0 as well as a word problem using additive inverse. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Commutative and Associative Equations

This lesson focuses on how to rearrange and combine parts of algebraic expressions by using the commutative and associative properties of addition. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Linear Function Machine

By putting different values into the linear function machine students will explore simple linear functions. - Repeating Decimal Rings

In this interactive activity you will explore the patterns that occur when expanding seventh and thirteenth fractions into decimals. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Solving Linear Equations with Negative Numbers

This video is designed for students to learn a strategy to solve a linear equation that has a negative number as a solution. The classroom activity builds on this knowledge by requiring them to use the strategy to solve a series of equations with both positive and negative coefficients and solutions. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Solving Linear Inequalities with Negative Numbers

Students will learn how to solve linear equations that have a negative number solution. They then solve a series of equations with both positive and negative coefficients and solutions in the classroom activity. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.

Standard 7.EE.1

Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.Standard 7.EE.2

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”

- The Number System (7.NS) - 7th Grade Core Guide

The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for Mathematics Grade 7 - The Number System

- Chapter 1 - Mathematical Foundation (UMSMP)

This is Chapter 1 of the Utah Middle School Math: Grade 7 textbook. It provides a Mathematical Foundation for Probability, Percent, Rational Number Equivalence. - Chapter 3 - Mathematical Foundation (UMSMP)

This is Chapter 3 of the Utah Middle School Math: Grade 7 textbook. It provides a Mathematical Foundation for Expressions and Equations I. - Chapter 3 - Student Workbook (UMSMP)

This is Chapter 3 of the Utah Middle School Math: Grade 7 student workbook. It covers Expressions and Equations I. - Chapter 6 - Mathematical Foundation (UMSMP)

This is Chapter 6 of the Utah Middle School Math: Grade 7 textbook. It provides a Mathematical Foundation for Expressions and Equations II - Real-world equations, Inequalities. - Chapter 6 - Student Workbook (UMSMP)

This is Chapter 6 of the Utah Middle School Math: Grade 7 textbook. It focuses on these topics: Real-world equations and Inequalities. Engage NY - Grade 7 Math Module 1:Ratios and Proportional Relationship (EngageNY)

In this 30-day Grade 7 module, students build upon sixth grade reasoning of ratios and rates to formally define proportional relationships and the constant of proportionality. Students explore multiple representations of proportional relationships by looking at tables, graphs, equations, and verbal descriptions. Students extend their understanding about ratios and proportional relationships to compute unit rates for ratios and rates specified by rational numbers. The module concludes with students applying proportional reasoning to identify scale factor and create a scale drawing. - Grade 7 Math Module 2: Rational Numbers (EngageNY)

In Grade 6, students formed a conceptual understanding of integers through the use of the number line, absolute value, and opposites and extended their understanding to include the ordering and comparing of rational numbers.This module uses the Integer Game: a card game that creates a conceptual understanding of integer operations and serves as a powerful mental model students can rely on during the module. Students build on their understanding of rational numbers to add, subtract, multiply, and divide signed numbers. Previous work in computing the sums, differences, products, and quotients of fractions serves as a significant foundation. - Grade 7 Math Module 3: Expressions and Equations (EngageNY)

This module consolidates and expands upon students understanding of equivalent expressions as they apply the properties of operations to write expressions in both standard form and in factored form. They use linear equations to solve unknown angle problems and other problems presented within context to understand that solving algebraic equations is all about the numbers. Students use the number line to understand the properties of inequality and recognize when to preserve the inequality and when to reverse the inequality when solving problems leading to inequalities. They interpret solutions within the context of problems. Students extend their sixth-grade study of geometric figures and the relationships between them as they apply their work with expressions and equations to solve problems involving area of a circle and composite area in the plane, as well as volume and surface area of right prisms. - Grade 7 Math Module 4: Percent and Proportional Relationships (EngageNY)

In Module 4, students deepen their understanding of ratios and proportional relationships from Module 1 by solving a variety of percent problems. They convert between fractions, decimals, and percents to further develop a conceptual understanding of percent and use algebraic expressions and equations to solve multi-step percent problems. An initial focus on relating 100% to the whole serves as a foundation for students. Students begin the module by solving problems without using a calculator to develop an understanding of the reasoning underlying the calculations. - Grade 7 Unit 2: Expressions and Equations (Georgia Standards)

The units in this instructional framework emphasize key standards that assist students to develop a deeper understanding of numbers. They learn how to solve multi- step equations and discuss the difference between equations and expressions. The Big Ideas that are expressed in this unit are integrated with such routine topics as estimation, mental and basic computation. All of these concepts need to be reviewed throughout the year.

- Solving Equations video

Answers the questions "what are equations?" and "how do we solve them?" - Solving Linear Equations with Negative Numbers

This video is designed for students to learn a strategy to solve a linear equation that has a negative number as a solution. The classroom activity builds on this knowledge by requiring them to use the strategy to solve a series of equations with both positive and negative coefficients and solutions. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Writing and Using Inequalities video

This video introduces and explains the topic.

Standard 7.EE.3

Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.Standard 7.EE.4

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=randp(x+q) =r, wherep,q, andrare specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?- Solve word problems leading to inequalities of the form
px+q>rorpx+q<r, wherep,q, andrare specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

- Geometry (7.G) - 7th Grade Core Guide

The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for Mathematics Grade 7 - Geometry.

- Chapter 5 - Mathematical Foundation (UMSMP)

This is Chapter 5 of the Utah Middle School Math: Grade 7 textbook. It provides a Mathematical Foundation for Geometry I - Scale Drawings, Geometric Figures. - Chapter 5 - Student Workbook (UMSMP)

This is Chapter 5 of the Utah Middle School Math: Grade 7 student workbook. It focuses on these topics: Geometry I - Scale Drawings and Geometric Figures. Engage NY - Grade 7 Math Module 1:Ratios and Proportional Relationship (EngageNY)

In this 30-day Grade 7 module, students build upon sixth grade reasoning of ratios and rates to formally define proportional relationships and the constant of proportionality. Students explore multiple representations of proportional relationships by looking at tables, graphs, equations, and verbal descriptions. Students extend their understanding about ratios and proportional relationships to compute unit rates for ratios and rates specified by rational numbers. The module concludes with students applying proportional reasoning to identify scale factor and create a scale drawing. - Grade 7 Math Module 4: Percent and Proportional Relationships (EngageNY)

In Module 4, students deepen their understanding of ratios and proportional relationships from Module 1 by solving a variety of percent problems. They convert between fractions, decimals, and percents to further develop a conceptual understanding of percent and use algebraic expressions and equations to solve multi-step percent problems. An initial focus on relating 100% to the whole serves as a foundation for students. Students begin the module by solving problems without using a calculator to develop an understanding of the reasoning underlying the calculations. - Grade 7 Math Module 6: Geometry (EngageNY)

In Module 6, students delve further into several geometry topics they have been developing over the years. Grade 7 presents some of these topics, (e.g., angles, area, surface area, and volume) in the most challenging form students have experienced yet. Module 6 assumes students understand the basics. The goal is to build a fluency in these difficult problems. The remaining topics, (i.e., working on constructing triangles and taking slices (or cross-sections) of three-dimensional figures) are new to students. - Grade 7 Unit 3: Ratio and Proportional Relationships (Georgia Standards)

The units in this instructional framework emphasize key standards that assist students to develop a deeper understanding of numbers. They learn to express different representations of rational numbers (e.g., fractions, decimals, and percents), discover how to identify and explain the constant of proportionality, and represent proportional relationships and scale drawings within real-world contexts. The Big Ideas that are expressed in this unit are integrated with such routine topics as estimation, mental and basic computation. All of these concepts need to be reviewed throughout the year. - Grade 7 Unit 4: Geometry (Georgia Standards)

The units in this instructional framework emphasize key standards that assist students to develop a deeper understanding of numbers. In this unit they will be engaged in using what they have previously learned about drawing geometric figures using rulers and protractor with an emphasis on triangles, students will also write and solve equations involving angle relationships, area, volume, and surface area of fundamental solid figures.

- A task related to standard 7.G.A.2

When students successfully complete this task, they will have shown that there is more than one triangle with a 30-degree angle adjacent to a side of length 4 units and opposite to a side of length 3 units. This task can be part of a more general study directed at "noticing when" "three measures of angles or sides" "determine a unique triangle, more than one triangle, or no triangle." - Approximating the area of a circle

The goal of this task is twofold: Use the idea of scaling to show that the ratio Area of Circle: (Radius of Circle)2 does not depend on the radius. Use formulas for the area of squares and triangles to estimate the value a real number. - Circumference of a Circle

The goal of this task is to study the circumferences of different sized circles, both using manipulatives and from the point of view of scaling. - 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. - Framing a House - student task

This task has students recreate house plans on graph paper and then determine how many linear feet of wall plate material will be needed. - Map Distance

The purpose of this task is for students to translate between information provided on a map that is drawn to scale and the distance between two cities represented on the map. - Rescaling Washington Park

The goal of this task is to get students to think critically about the effect that changing from one scaling to another has on an image, and then to physically produce the desired image. - Scaling

An interactive from Annenberg asks students to scale a picture by using the math strategies of multiplicative and additive relationships. Students then use those strategies to compare photocopies and rectangles in different scales. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Scaling angles and polygons

The goal of this task is to gather together knowledge and skills from the seventh grade in a context which prepares students for the important eighth grade notion of similarity.

- AAS Triangle construction exploration

If you know two angles of a triangle and a side not between those two angles, will you create a unique triangle? This activity will help you to explore the answer to that question. - ASA Exploration

If you know two angles of a triangle and a side between those two angles, will you create a unique triangle? This activity will help you to explore the answer to that question. - Access Ramp - Student Task

This task has students design an access ramp, which complies with the Americans with Disabilities Act (ADA) requirements and include pricing based on local costs. - Boxed In and Wrapped Up

This lesson asks students to find the volume and surface area of a rectangular box and then convert it into a cubical box with the same volume. - Constructing Quadrilaterals

The Annenberg interactive in this lesson gives the students a chance to manipulate linkage strips to form quadrilaterals. In the activity students are given side lengths and then must build different types of quadrilaterals. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Constructing Triangles

In this interactive students manipulate line segments on a grid to see if they can make a triangle. Students then work with straw segments to discover which side length combinations are able to make a triangle. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Fences - student task

This task has students design a fence that meets the city ordinances and the client's specifications. - Formulas for Circle Area and Circumference: Simple as Pie

A video from Cyberchase shows Bianca undertaking the selling of pies. She has to understand the relationship between the diameter and the circumference of pie pans. In the classroom activity you will learn how to calculate the circumference of wheels. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Formulas for a Circle

The 3 videos in this lesson teach students about the parts of a circle, how to label a circle, and define pi. Students must then test the theories presented in the videos in the classroom activity. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Framing a House - student task

This task has students recreate house plans on graph paper and then determine how many linear feet of wall plate material will be needed. - Maximizing Area: Gold Rush

This lesson unit is intended to help educators assess how well students are able to interpret a situation and represent the variables mathematically, select appropriate mathematical methods to use, explore the effects on the area of a rectangle of systematically varying the dimensions whilst keeping the perimeter constant, as well as interpret and evaluate the data generated and identify the optimum case. - Measuring Henry's cabin

In this lesson and activity students will determine the surface area and volume of a house and also reconstruct it on a smaller scale. - Miniature Golf - student task

This task requires students to redesign a miniature golf course to make it more challenging. - SAS Exploration

If you know two sides of a triangle and the angle between those two sides, will you create a unique triangle? This activity will help you to explore the answer to that question. - SSA Exploration

If you know two sides of a triangle and an angle not between those two sides, will you create a unique triangle? This activity will help you to explore the answer to that question. - Scale Models in the Real World

This video show scale models of railroads, dollhouses, and architecture to explain what the ratios represent. The hands-on classroom activity then has students create their own models. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Scaling

An interactive from Annenberg asks students to scale a picture by using the math strategies of multiplicative and additive relationships. Students then use those strategies to compare photocopies and rectangles in different scales. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Scaling Up Rectangles Using Simulations

This interactive allows students to create murals in different sizes by understanding two-dimensional scaling. The activity for the classroom has students use graph paper to draw and compare squares with different proportional dimensions and record the data as they change. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Scaling Up Rectangles in the Real World

By looking at murals in this video students see how artists use proportion and measurement to create them. The class then does an activity where they enlarge a drawing by using scale and then create a classroom mural. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Stairway - Student Task

This task students to design a stairway for a custom home. They will need to gather information regarding design, safety, and the utility of staircases. - Student Task: Photographs

In this task, students need to figure out how to fit three different-sized photographs on a single sheet. - Student Task: Sports Bag

In this task, students must figure out how to cut out the material to make a cylindrical sports bag. - Student Task: Triangular Frameworks

In this task students determine how many different triangles can be made that follow a set of rules. - Triangle Explorer

The applet in this lesson allows students to draw triangles and calculate their area. - Triangle construction exploration: Version 1

Triangle construction exploration: If you know three sides of a triangle, will you create a unique triangle? This activity will help you to explore the answer to that question. - Triangle construction exploration: Version 2

Triangle construction exploration: If you know three sides of a triangle, will you create a unique triangle? This activity will help you to explore the answer to that question. - Using Dimensions: Designing a Sports Bag

This lesson unit is intended to help educators assess how well students are able to recognize and use common 2D representations of 3D objects, as well as identify and use the appropriate formula for finding the circumference of a circle.

Standard 7.G.1

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.Standard 7.G.2

Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

- Geometry (7.G) - 7th Grade Core Guide

The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for Mathematics Grade 7 - Geometry.

- Chapter 5 - Mathematical Foundation (UMSMP)

This is Chapter 5 of the Utah Middle School Math: Grade 7 textbook. It provides a Mathematical Foundation for Geometry I - Scale Drawings, Geometric Figures. - Chapter 5 - Student Workbook (UMSMP)

This is Chapter 5 of the Utah Middle School Math: Grade 7 student workbook. It focuses on these topics: Geometry I - Scale Drawings and Geometric Figures. - Chapter 8 - Mathematical Foundation (UMSMP)

This is Chapter 8 of the Utah Middle School Math Grade 7 textbook. It provides a Mathematical Foundation for Measurement in 2-3 Dimensions and Cross-Sections of Solids. - Chapter 8 - Student Workbook (UMSMP)

This is Chapter 8 of the Utah Middle School Math Grade 7 student workbook. It focuses on Measurement in 2-3 Dimensions and Cross-Sections of Solids. Engage NY - Grade 7 Math Module 6: Geometry (EngageNY)

In Module 6, students delve further into several geometry topics they have been developing over the years. Grade 7 presents some of these topics, (e.g., angles, area, surface area, and volume) in the most challenging form students have experienced yet. Module 6 assumes students understand the basics. The goal is to build a fluency in these difficult problems. The remaining topics, (i.e., working on constructing triangles and taking slices (or cross-sections) of three-dimensional figures) are new to students. - Grade 7 Unit 4: Geometry (Georgia Standards)

The units in this instructional framework emphasize key standards that assist students to develop a deeper understanding of numbers. In this unit they will be engaged in using what they have previously learned about drawing geometric figures using rulers and protractor with an emphasis on triangles, students will also write and solve equations involving angle relationships, area, volume, and surface area of fundamental solid figures.

- Cube Ninjas!

The purpose of this task is to have students explore various cross sections of a cube and use precise language to describe the shape of the resulting faces. - Escaramuza: 2D Drawing

The real-life equestrian event known as Escaramuza is used to help student make 2D drawings to make triangles. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Escaramuza: Coordinates, Reflection, Rotation

A real-life equestrian event known as Escaramuza is used to demonstrate how to draw a two-dimensional diagram and then represent it on a coordinate plane. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.

- Comparing Volumes of Cylinders, Spheres, and Cones

This interactive explains how to calculate the volumes of cylinders, cones and spheres. Students then apply this understanding to an activity where cylinders, cones and spheres are filled with water so that their volumes can be compared. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Cross Sections of a Cube

In this interactive cubes are sliced in different ways in order to explore cross sections. Students then create cubes out of play dough and slice them with dental floss to create cross-sections of specific shapes. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Holes

After watching a clip of the movie Holes from Walt Disney Pictures students will answer a series of questions, such as "If Stanley and X-Ray both dig one hole per day for a year, how much extra dirt will Stanley have dug than X-Ray?" and "How many times could that extra dirt fill one of the holes X-Ray digs?" - Maximizing Area: Gold Rush

This lesson unit is intended to help educators assess how well students are able to interpret a situation and represent the variables mathematically, select appropriate mathematical methods to use, explore the effects on the area of a rectangle of systematically varying the dimensions whilst keeping the perimeter constant, as well as interpret and evaluate the data generated and identify the optimum case. - Slicing Three Dimensional Figures

In this video students are shown how 2 dimensional figures are created by slicing 3 dimensional ones. Play dough is used in the classroom activity with students slicing figures and then describing the shape that results. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Student Task: Photographs

In this task, students need to figure out how to fit three different-sized photographs on a single sheet. - Student Task: Triangular Frameworks

In this task students determine how many different triangles can be made that follow a set of rules. - Three-Dimensional Printing

Via this video students will obtain an understanding of how 3-D printing works and is used in manufacturing. These printers use the basic shape of the triangle to build complex polygon shapes. Students will then create two-dimensional drawings to represent 3-D figures. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Using Dimensions: Designing a Sports Bag

This lesson unit is intended to help educators assess how well students are able to recognize and use common 2D representations of 3D objects, as well as identify and use the appropriate formula for finding the circumference of a circle.

Standard 7.G.3

Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

- 2D Nets and 3D Decorative Boxes

Calculating the surface area of cardboard boxes is the focus of this interactive activity. The classroom activity takes this knowledge and asks the students for figure out how many square inches of wrapping paper is needed to wrap a gift. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Angles

Students are introduced to all kinds of angles in this lesson plan, including acute, obtuse, right, vertical, adjacent, and corresponding among others. - Applying Angle Theorems

This lesson unit is intended to help educators assess how well students are able to use geometric properties to solve problems. - Area

This lesson is designed to help students be able to calculate the area of a random shape on a grid, explain the correlation between the size of the perimeter and the number of different possible areas that can be contained within that perimeter. - Area Explorations

In this lesson, students will explore the area of irregular shapes to find multiple different methods for calculating area - Boxed In and Wrapped Up

This lesson asks students to find the volume and surface area of a rectangular box and then convert it into a cubical box with the same volume. - Chris McCloud's Lesson: Expert Analysis

This Teaching Channel video highlights and critiques the techniques used in a lesson on cylinders. (14 min.) - Estimating: Counting Trees

This lesson unit is intended to help educators assess how well students are able to solve simple problems involving ratio and direct proportion, choose an appropriate sampling method, and collect discrete data and record them using a frequency table. - Estimations and Approximations: The Money Munchers

This lesson unit is intended to help educators assess how well students are able to model a situation, make sensible, realistic assumptions and estimates, and use assumptions and estimates to create a chain of reasoning, in order to solve a practical problem. - Fences - student task

This task has students design a fence that meets the city ordinances and the client's specifications. - Finding Unknown Angles

In this Math Shorts video from the Utah Education Network students learn to find unknown supplementary, complementary, vertical and adjacent angles. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Formulas for Circle Area and Circumference: Simple as Pie

A video from Cyberchase shows Bianca undertaking the selling of pies. She has to understand the relationship between the diameter and the circumference of pie pans. In the classroom activity you will learn how to calculate the circumference of wheels. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Great Modeling Tasks in Three Acts - File Cabinet

This surface area activity has students answer the question: How many stickies cover the cabinet? - Holes

After watching a clip of the movie Holes from Walt Disney Pictures students will answer a series of questions, such as "If Stanley and X-Ray both dig one hole per day for a year, how much extra dirt will Stanley have dug than X-Ray?" and "How many times could that extra dirt fill one of the holes X-Ray digs?" - Maximizing Area: Gold Rush

This lesson unit is intended to help educators assess how well students are able to interpret a situation and represent the variables mathematically, select appropriate mathematical methods to use, explore the effects on the area of a rectangle of systematically varying the dimensions whilst keeping the perimeter constant, as well as interpret and evaluate the data generated and identify the optimum case. - Measuring Henry's cabin

In this lesson and activity students will determine the surface area and volume of a house and also reconstruct it on a smaller scale. - Miniature Golf - student task

This task requires students to redesign a miniature golf course to make it more challenging. - Mr. McCloud: Discovering Surface Area of a Cylinder

This Teaching Channel video and lesson plan will help students discover and apply the formula for the surface area of a cylinder. (27 minutes) - Solving Linear Inequalities with Negative Numbers

Students will learn how to solve linear equations that have a negative number solution. They then solve a series of equations with both positive and negative coefficients and solutions in the classroom activity. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Student Task: Roman Mosaic

In this task, students have to decide how you would describe the design of a mosaic pattern over the telephone. - Student Task: Circle Pattern

In this task, the student will look at a pattern of black and white circles and describe, mathematically, what is happening to the areas of black and white as the pattern develops. - Student Task: Historic Bicycle

In this task, students will figure out some problems about a strange old bicycle. - Student Task: Octagon Tile

In this task, students will explore the geometry of a pattern made by arranging squares within an octagon. - Surface Area of Prisms

In this lesson students will understand surface area and how solve for the surface area of triangular prisms. - Surface Area of a Rectangular Prisms

This lesson will help students understand surface area and solve problems using the surface area of a rectangular prism. - The Largest Container: Problems Using Volume and Shape

By using a single sheet of paper this interactive leads students to construct shapes, calculate volume, and think about the relationships between different shapes. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Volume of Prisms

This is a lesson designed to help students understand how to solve problems for the volume of triangular prisms. - Volume of Rectangular Prisms

This lesson is designed to help students understand how to solve for the volume of rectangular prisms.

- Chapter 5 - Mathematical Foundation (UMSMP)

This is Chapter 5 of the Utah Middle School Math: Grade 7 textbook. It provides a Mathematical Foundation for Geometry I - Scale Drawings, Geometric Figures. - Chapter 5 - Student Workbook (UMSMP)

This is Chapter 5 of the Utah Middle School Math: Grade 7 student workbook. It focuses on these topics: Geometry I - Scale Drawings and Geometric Figures. - Chapter 6 - Mathematical Foundation (UMSMP)

This is Chapter 6 of the Utah Middle School Math: Grade 7 textbook. It provides a Mathematical Foundation for Expressions and Equations II - Real-world equations, Inequalities. - Chapter 6 - Student Workbook (UMSMP)

This is Chapter 6 of the Utah Middle School Math: Grade 7 textbook. It focuses on these topics: Real-world equations and Inequalities. - Chapter 8 - Mathematical Foundation (UMSMP)

This is Chapter 8 of the Utah Middle School Math Grade 7 textbook. It provides a Mathematical Foundation for Measurement in 2-3 Dimensions and Cross-Sections of Solids. - Chapter 8 - Student Workbook (UMSMP)

This is Chapter 8 of the Utah Middle School Math Grade 7 student workbook. It focuses on Measurement in 2-3 Dimensions and Cross-Sections of Solids. Engage NY - Grade 7 Math Module 3: Expressions and Equations (EngageNY)

This module consolidates and expands upon students understanding of equivalent expressions as they apply the properties of operations to write expressions in both standard form and in factored form. They use linear equations to solve unknown angle problems and other problems presented within context to understand that solving algebraic equations is all about the numbers. Students use the number line to understand the properties of inequality and recognize when to preserve the inequality and when to reverse the inequality when solving problems leading to inequalities. They interpret solutions within the context of problems. Students extend their sixth-grade study of geometric figures and the relationships between them as they apply their work with expressions and equations to solve problems involving area of a circle and composite area in the plane, as well as volume and surface area of right prisms. - Grade 7 Math Module 6: Geometry (EngageNY)

In Module 6, students delve further into several geometry topics they have been developing over the years. Grade 7 presents some of these topics, (e.g., angles, area, surface area, and volume) in the most challenging form students have experienced yet. Module 6 assumes students understand the basics. The goal is to build a fluency in these difficult problems. The remaining topics, (i.e., working on constructing triangles and taking slices (or cross-sections) of three-dimensional figures) are new to students. - Grade 7 Unit 4: Geometry (Georgia Standards)

The units in this instructional framework emphasize key standards that assist students to develop a deeper understanding of numbers. In this unit they will be engaged in using what they have previously learned about drawing geometric figures using rulers and protractor with an emphasis on triangles, students will also write and solve equations involving angle relationships, area, volume, and surface area of fundamental solid figures.

- Angles

Students are introduced to all kinds of angles in this lesson plan, including acute, obtuse, right, vertical, adjacent, and corresponding among others. - Approximating the area of a circle

The goal of this task is twofold: Use the idea of scaling to show that the ratio Area of Circle: (Radius of Circle)2 does not depend on the radius. Use formulas for the area of squares and triangles to estimate the value a real number. - Circumference of a Circle

The goal of this task is to study the circumferences of different sized circles, both using manipulatives and from the point of view of scaling.

Standard 7.G.4

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.Standard 7.G.5

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.Standard 7.G.6

Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

- Statistics and Probability (7.SP) - 7th Grade Core Guide

The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for Mathematics Grade 7 - Statistics and Probability.

- Chapter 7 - Mathematical Foundation (UMSMP)

This is Chapter 7 of the Utah Middle School Math: Grade 7 textbook. It provides a Mathematical Foundation for Expressions and Equations II - Real-world equations, Inequalities. - Chapter 7 - Student Workbook (UMSMP)

This is Chapter 7 of the Utah Middle School Math: Grade 7 student workbook. It focuses on Probability and Statistics. Engage NY - Grade 7 Math Module 5: Statistics and Probability (EngageNY)

In this module, students begin their study of probability, learning how to interpret probabilities and how to compute probabilities in simple settings. They also learn how to estimate probabilities empirically. Probability provides a foundation for the inferential reasoning developed in the second half of this module. Additionally, students build on their knowledge of data distributions that they studied in Grade 6, compare data distributions of two or more populations, and are introduced to the idea of drawing informal inferences based on data from random samples. - Grade 7 Unit 5: Inferences (Georgia Standards)

The units in this instructional framework emphasize key standards that assist students in developing a deeper understanding of numbers. They have learned to recognize and express different representations of rational numbers. Now they will learn how to apply the statistical aspect of mathematics to the measures of center, variability and population. The Big Ideas that are expressed in this unit are integrated with such routine topics as estimation, mental and basic computation. All of these concepts need to be reviewed throughout the year.

- 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). - Mr. Briggs'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. - Valentine Marbles

For this task, Minitab software was used to generate 100 random samples of size 16 from a population where the probability of obtaining a success in one draw is 33.6% (Bernoulli). Given that multiple samples of the same size have been generated, students should note that there can be quite a bit of variability among the estimates from random samples and that on average, the center of the distribution of such estimates is at the actual population value and most of the estimates themselves tend to cluster around the actual population value.

- Create a Graph

This applet allows students to create bar, line, area, pie, and XY graphs. - Designing Experiments: Physicians' Health Study

How do scientists and doctors use data to deal with and control disease? This video from Annenberg's Learners Learning Math show how data was used to design an trial dealing with epidemiology. Students then apply their new understanding to take part in an experiment and design a trial of their own. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Estimating: Counting Trees

This lesson unit is intended to help educators assess how well students are able to solve simple problems involving ratio and direct proportion, choose an appropriate sampling method, and collect discrete data and record them using a frequency table. - Estimation from Random Sampling

By taking random samples of the number of penguins in a sub-region in this interactive students understand how those samples can be used to estimate the total penguin population in the region. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Events and Outcomes (Counting) video

This video introduces and explains the topic. - Gathering Data for a Line Plot

Two interactives are used in this lesson and both involve counting raisins in boxes and then plotting a graph. Students extend their understanding of mean, median, mode, and range after creating line plots in the classroom activity. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Making Random Samples

Students learn about population samples in this interactive by comparing various circles. They are then given a statistical population and have to decide what would make a random sample in the classroom activity. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Marbles

This activity helps the student understand randomness and probability by pulling marbles out of a bag. - Random Sampling and Estimation: Lake Victoria

An Annenberg Learner's Learning Math video shows students a real-life application of random sampling by scientists studying fish in Lake Victoria. Students then apply their understanding by designing their own study using random sampling to make predictions and draw conclusions. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Random Sampling: How Many Fish?

Goldfish crackers stand in for real fish as this video demonstrates the use of random sampling by scientists to make predictions and inferences about wildlife populations. The classroom activity has students make calculations related to the capture-recapture process used by scientists. They also explore other research methods using random sampling. - Recognize and Represent Proportional Relationships Between Quantities: Ratio, Proportion, Cross Mult

Four videos are included in this lesson explaining ratio, proportion and how to use the shortcut of cross multiply and divide. Students then play the game "Pom-Pom Nose Push" to collect data and determine the ratio of time to distance. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Responses to a Court Verdict: Analyzing Samples to Gain Understanding

The infographic basis of this activity pulls the Trayvon Martin case out of the headlines to examine the data collected from a poll about the case. The students need to analyze the responses to conclude whether the results fall along racial lines. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Scatter Plot

An understanding of how a scatter plot works is the focus of this interactive. Students interpret a scatter plot representing the relationship of height to arm length. They then create their own plot by measuring foot and forearm lengths. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Storage Shed - student task

Students are going to build storage sheds as a fund raising project, but before they can start they must determine the best dimensions for the shed, make scale drawings and decide on how much to charge for each shed. - Student Task: Candy Bars

In this task, students analyze a survey to decide how many candy bars students typically eat in a week. - Variation About the Mean: The Boston Harbor Project

The use and statistical analysis of data in the efforts to improve the water quality in Boston Harbor is the subject of this video. Students then apply an understanding of mean absolute deviation to examine data. They also use data about bacteria found in a river in an analysis of what that data set tells. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.

Standard 7.SP.1

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling is more likely to produce representative samples and support valid inferences.Standard 7.SP.2

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.For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

- Chapter 7 - Mathematical Foundation (UMSMP)

This is Chapter 7 of the Utah Middle School Math: Grade 7 textbook. It provides a Mathematical Foundation for Expressions and Equations II - Real-world equations, Inequalities. - Chapter 7 - Student Workbook (UMSMP)

This is Chapter 7 of the Utah Middle School Math: Grade 7 student workbook. It focuses on Probability and Statistics. Engage NY - Grade 7 Math Module 5: Statistics and Probability (EngageNY)

In this module, students begin their study of probability, learning how to interpret probabilities and how to compute probabilities in simple settings. They also learn how to estimate probabilities empirically. Probability provides a foundation for the inferential reasoning developed in the second half of this module. Additionally, students build on their knowledge of data distributions that they studied in Grade 6, compare data distributions of two or more populations, and are introduced to the idea of drawing informal inferences based on data from random samples. - Grade 7 Unit 5: Inferences (Georgia Standards)

The units in this instructional framework emphasize key standards that assist students in developing a deeper understanding of numbers. They have learned to recognize and express different representations of rational numbers. Now they will learn how to apply the statistical aspect of mathematics to the measures of center, variability and population. The Big Ideas that are expressed in this unit are integrated with such routine topics as estimation, mental and basic computation. All of these concepts need to be reviewed throughout the year.

- Designing Experiments: Physicians' Health Study

How do scientists and doctors use data to deal with and control disease? This video from Annenberg's Learners Learning Math show how data was used to design an trial dealing with epidemiology. Students then apply their new understanding to take part in an experiment and design a trial of their own. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Estimation from Random Sampling

By taking random samples of the number of penguins in a sub-region in this interactive students understand how those samples can be used to estimate the total penguin population in the region. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Line Plot Representation of Deviation from the Mean

The concepts of means and deviations are the focus of this interactive from Annenberg. Students manipulate dots on a line graph to experiments with deviation. The classroom activity helps them understand positive and negative deviation. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Student Task: Temperatures

In this task, students will use graphs and box diagrams to compare temperatures in California and Washington - The Hunger Games

By analyzing the lottery system used in the novel Hunger Games students will learn about probability. Students then create their own lottery system based on criteria from the novel in the accompanying classroom activity. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Variation About the Mean: The Boston Harbor Project

The use and statistical analysis of data in the efforts to improve the water quality in Boston Harbor is the subject of this video. Students then apply an understanding of mean absolute deviation to examine data. They also use data about bacteria found in a river in an analysis of what that data set tells. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.

Standard 7.SP.3

Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability.For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, approximately twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.Standard 7.SP.4

Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

- The Number System (7.NS) - 7th Grade Core Guide

The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for Mathematics Grade 7 - The Number System

- Chapter 1 - Mathematical Foundation (UMSMP)

This is Chapter 1 of the Utah Middle School Math: Grade 7 textbook. It provides a Mathematical Foundation for Probability, Percent, Rational Number Equivalence. - Chapter 7 - Mathematical Foundation (UMSMP)

This is Chapter 7 of the Utah Middle School Math: Grade 7 textbook. It provides a Mathematical Foundation for Expressions and Equations II - Real-world equations, Inequalities. - Chapter 7 - Student Workbook (UMSMP)

This is Chapter 7 of the Utah Middle School Math: Grade 7 student workbook. It focuses on Probability and Statistics. Engage NY - Grade 7 Math Module 5: Statistics and Probability (EngageNY)

In this module, students begin their study of probability, learning how to interpret probabilities and how to compute probabilities in simple settings. They also learn how to estimate probabilities empirically. Probability provides a foundation for the inferential reasoning developed in the second half of this module. Additionally, students build on their knowledge of data distributions that they studied in Grade 6, compare data distributions of two or more populations, and are introduced to the idea of drawing informal inferences based on data from random samples. - Grade 7 Unit 6: Statistics (Georgia Standards)

In this unit students will: Analyze data from many different sources such as organized lists, box-plots, bar graphs, histograms and dot plots. Understand that responses to statistical questions may vary. Understand that data can be described by a single number. Determine quantitative measures of center (median and/or mean). Determine quantitative measures of variability (interquartile range and range).

- Beat the Odds

Students will develop and use models of probability in this online game interactive. The classroom activity has them explore the experimental side of probability and probability and randomness. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Compound Probability

This video shows students how to calculate the probability of drawing a particular card from a deck of cards. The students continue to work with cards in the classroom activity where they calculate the probability of drawing specific cards and explain their strategy for the calculation. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Conditional Probability and Probability of Simultaneous Events

This lesson plan is designed to help students understand and use the formula for probability of simultaneous independent events. - Evaluating Statements About Probability

This lesson unit addresses common misconceptions relating to probability of simple and compound events. The lesson will help educators assess how well students understand concepts of equally likely events, randomness, and sample sizes. - Experimental Probability

Using devices such as spinners and dice, students can conduct probability experiments in this lesson plan's applet. - Fire: Modeling Probability

This lesson is designed to help students understand probability and chance and understand it in real life situations. - Introduction to the Concept of Probability

The goals of this lesson are that students will understand the definition of probability, outcomes in probability, and know how to calculate experimental probability. - Marbles

This activity helps the student understand randomness and probability by pulling marbles out of a bag. - Probability

Students learn about probability in this lesson by predicting the outcome of experiments and playing racing games. - Probability Space

In this video students learn the meaning of the phrase "probability space for random events." They learn about the origin of the idea in the 16th century and then apply their understanding via a dice game in the classroom activity. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Probability and Geometry (elementary)

This lesson asks students to practice calculating probability and understand how probability problems can be solved with the help of geometry. - Probability of Dependent Events video

This is a video introduction and explanation of the topic. - Probability of Dependent and Independent Events

This Teaching Channel video shows how students can identify and create examples of independent and dependent events. (Common Core Standards Math.7.SP.8a) (5 minutes) - Probability of Independent Events video

This video introduces and explains the concept. - Probability with Dice

Given 2 dice students learn how to find the probability of rolling a specific number in this video. They then use 2 dice in the classroom activities to apply their understanding of probability. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Probability: Playing with Fire

This lesson is designed to help students understand possible outcomes of a probability experiment. - Probability: Tell the Future

A Flocabulary hip-hop song explains and demonstrates ways to express probability in this lesson. To expand their understanding students toss coins and record the results in the classroom activity. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Racing Game with One Die

Students can simulate a race between two cars with the roll of a die and learn about probability through this activity. - Racing Game with Two Dice

By using the applet embedded in this lesson plan, students can simulate a race and learn about probability. - Random Coin Toss

In this interactive from Annenberg students use a tree diagram to record the results of coin tosses to help them understand probability. The classroom activity extends this understanding to compare theoretical and experimental probability. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Replacement and Probability

This lesson will help students learn the difference between sampling with and without replacement. - Spinner

By manipulating a spinner and its pointer students will learn about probability in this activity. - Student Task: Card Game

In this task, students will use probability to make predictions about a card game. - Student Task: Charity Fair

Ann is in charge of a "Lucky Dip" game to raise money for charities. In this task, students use the rules of probability to advise Ann on how to improve the game so that it raises more money. - Student Task: Spinner Bingo

In this task, students must use math to figure out the best way to play a number bingo game. - Students Task: Lottery

In this task, students must use math to decide whether a lottery idea will make money. - The Hunger Games

By analyzing the lottery system used in the novel Hunger Games students will learn about probability. Students then create their own lottery system based on criteria from the novel in the accompanying classroom activity. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Your Odds of Winning Powerball: Probabilities of Compound Events Using Visuals

The sobering odds of winning at Powerball are made clear in this video. Students then create their own models of lotteries to help them understand the probability of compound events. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.

Standard 7.SP.5

Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.Standard 7.SP.6

Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.Standard 7.SP.7

Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

- Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.
For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.- Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.
For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?Standard 7.SP.8

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

- 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.
- 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.
- Design and use a simulation to generate frequencies for compound events.
For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

The Online Core Resource pages are a collaborative project between the Utah State Board of Education and the Utah Education Network. If you would like to recommend a high quality resource, contact Trish French (Elementary) or Lindsey Henderson (Secondary). If you find inaccuracies or broken links contact resources@uen.org.