Illustrative Mathematics
Illustrative Mathematics: 8.f Function Rules
Four tables showing different types of input and output values are presented and students are asked to describe function rules for them and fill in any missing values. Aligns with 8.F.A.1.
Illustrative Mathematics
Illustrative Mathematics: 8.f Modeling With a Linear Function
For this task, 8th graders are presented with the equation for a linear function and asked to identify which of six problem situations the equation could represent. Aligns with 8.F.B.
Illustrative Mathematics
Illustrative Mathematics: 8.f Delivering the Mail, Assessment Variation
This task assesses a student's ability to construct a linear function and interpret its parameters within the context of a mail truck's mileage. Aligns with 8.F.B.4.
Illustrative Mathematics
Illustrative Mathematics: 8.f Heart Rate Monitoring
In this task, 8th graders are asked to draw a graph that represents heart rate as a function of time from a verbal description of that function. Then they use the graph to draw conclusions about the context. Aligns with 8.F.B.
Illustrative Mathematics
Illustrative Mathematics: 8.f Distance Across the Channel
This task asks students to find a linear function that models the relationship between water depth and distance across a channel at water level. After finding the equation, they have to verbalize the meaning of the slope and intercept of...
Illustrative Mathematics
Illustrative Mathematics: 8.f Downhill
For this task, a car is traveling down a steep hill. Students are given the function for elevation versus distance from the start and are asked to find and explain the slope and intercepts of the graph. Aligns with 8.F.B.4.
Illustrative Mathematics
Illustrative Mathematics: 8.f Us Garbage, Version 1
Eighth graders work with input values (the year) and output values (the amount of garbage that year) in a table about the garbage produced in the US. They study the table to answer specific questions, state whether it represents a linear...
Illustrative Mathematics
Illustrative Mathematics: 8.ee How Many Solutions?
Eighth graders are given a linear equation and instructed to find a second linear equation in order to make a system of equations that fits different criteria related to its possible solutions. Aligns with 8.EE.C.8.
Illustrative Mathematics
Illustrative Mathematics: 8.ee Two Lines
This task presents students with two line graphs. They are asked to find the linear equations and to identify points unique to each graph. Aligns with 8.EE.C.
Illustrative Mathematics
Illustrative Mathematics: 8.ee Stuffing Envelopes
Eighth graders are asked to compare the income earned from two summer jobs stuffing envelopes. They are to draw graphs, write equations, and interpret the graphs. This task provides students with an opportunity to take the step from unit...
Illustrative Mathematics
Illustrative Mathematics: 8.ee Slopes Between Points on a Line
Eighth graders work with slopes and similar triangles in this problem and will learn why the calculated slope will be the same for any two points on a given line. Aligns with 8.EE.B.6.
Illustrative Mathematics
Illustrative Mathematics: 8.ee Proportional Relationships, Lines, and Equations
In this task, 8th graders are shown the graphs of two lines with the same slope. They are given the equation for the first line and the coordinates of a point on the second and are asked to find the equation for the second line. Aligns...
Illustrative Mathematics
Illustrative Mathematics: 8.ee Dvd Profits, Variation 1
Eighth graders examine the costs of producing DVDs, taking into account the cost of building a factory. They need to look at units costs for DVDs, fixed prices, and building costs. They are asked to compare the costs for producing them...
Illustrative Mathematics
Illustrative Mathematics: 8.ee Coffee by the Pound
In this task about the cost of coffee, 8th graders find the cost per pound, how much can be purchased for one dollar, what the graph will look like, and what the slope means. Aligns with 8.EE.B.5.
Illustrative Mathematics
Illustrative Mathematics: 8.ee Giantburgers
Eighth graders are asked to investigate a newspaper claim about the number of Americans said to eat at Giantburger restaurants every day. They work with large numbers expressed using scientific notation in order to perform their...
Illustrative Mathematics
Illustrative Mathematics: 8.ee Ant and Elephant
In this problem comparing the mass of an ant to that of an elephant, 8th graders are contrasting a very small quantity with a very large quantity. They need to convert between grams and metric tons so as to work with the same units, and...
Illustrative Mathematics
Illustrative Mathematics: 8.ee Fixing the Furnace
In this task, 8th graders examine the fee structures for three furnace-repair companies to determine which one offers the best deal. They need to support their reasoning with equations, tables, and/or graphs. Aligns with 8.EE.C.8.
Illustrative Mathematics
Illustrative Mathematics: 8.ee Find the Change
In this task, 8th graders work with linear functions and learn how to discuss and make calculations with slope and x- and y-intercepts. Aligns with 8.EE.B.
Illustrative Mathematics
Illustrative Mathematics: 8.ee Cell Phone Plans
For this task, 8th graders examine the fee structures and features of three cell phone plans to highlight the advantages of each. They will need to write linear equations and draw graphs for each. They then choose the best plan for a...
Illustrative Mathematics
Illustrative Mathematics: 8.ee Extending Definitions of Exponents, Variation 1
In this task, 8th graders examine the changes in the size of a population of bacteria during an experiment studying its growth. They learn how to talk about negative integer exponents and negative time. Aligns with 8.EE.A.1.
Illustrative Mathematics
Illustrative Mathematics: 8.ee Folding a Square Into Thirds
This exercise begins with students folding a square piece of paper according to directions and aligning it on a coordinate grid. They then must find and solve a pair of linear equations which can be used to understand how to fold a piece...
Illustrative Mathematics
Illustrative Mathematics: 8.ee Sammy's Chipmunk and Squirrel Observations
In the context of this task, a student is observing a squirrel and a chipmunk for their acorn-hiding habits. The problem requires students to use a linear equation to find out how many acorns the chipmunk hid. Aligns with 8.EE.C.7.
Illustrative Mathematics
Illustrative Mathematics: 8.ee Sore Throats, Variation 2
In this task where two saltwater solutions are compared, 8th graders must find equivalent ratios, write an equation that works for both solutions, draw the equation's graph, and interpret the slope as a unit rate. Aligns with 8.EE.B.5.
Illustrative Mathematics
Illustrative Mathematics: 8.ee Solving Equations
This task models how a drawing can be used to represent a linear equation in one variable. Students are then asked to solve equations using algebraic symbols as well as pictures and to comment on issues they see. They are then asked to...