Math - Seventh Grade

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Seventh Grade
Instructional Tasks

Stand alone tasks are organized to support learning of content standards. These tasks can be used as initial instruction or to support students who are struggling with a particular topic.

 

Strand: MATHEMATICAL PRACTICES (7.MP)
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Strand: RATIOS AND PROPORTIONAL RELATIONSHIPS (7.RP)
Analyze proportional relationships and use them to solve real-world and mathematical problems (Standards 7.RP.1–3).
  • 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 6½%. 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.
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Strand: THE NUMBER SYSTEM (7.NS)
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers (Standards 7.NS.1–3).
  • 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.
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Strand: EXPRESSIONS AND EQUATIONS (7.EE)
Use properties of operations to generate equivalent expressions (Standards 7.EE.1–2).
  • 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.
Solve real-life and mathematical problems using numerical and algebraic expressions and equations (Standards 7.EE.3–4).
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Strand: GEOMETRY (7.G)
Draw, construct, and describe geometrical figures, and describe the relationships between them (Standards 7.G.1–3)
  • 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.
Draw informal comparative inferences about two populations (Standards 7.SP.3–4).
  • 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.
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume (Standards 7.G.4–6).
  • 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.
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Strand: STATISTICS AND PROBABILITY (7.SP)
Use random sampling to draw inferences about a population (Standards 7.SP.1–2).
  • 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.
Draw informal comparative inferences about two populations (Standards 7.SP.3–4).
Investigate chance processes and develop, use, and evaluate probability models (Standards 7.SP.5–8).
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