Illustrative Mathematics
Illustrative Mathematics: 8.g Cutting a Rectangle Into Two Congruent Triangles
This task shows the congruence of two triangles formed by cutting a rectangle in half along the diagonal. Students are asked to investigate elements of congruence and transformations among the shapes. Aligns with 8.G.A.2.
Illustrative Mathematics
Illustrative Mathematics: 8.f Introduction to Linear Functions
This task lets students explore the differences between linear and non-linear functions. By contrasting the two, it reinforces the properties of linear functions. Aligns with 8.F.A.3.
Illustrative Mathematics
Illustrative Mathematics: 8.ns Calculating and Rounding Numbers
In this task, 8th graders investigate how numbers are rounded when using a calculator and what effects this can have. Aligns with 8.NS.A.
Illustrative Mathematics
Illustrative Mathematics: 8.ns Estimating Square Roots
This task asks students to estimate the square root of 800 without using a calculator. To do it, they must examine perfect squares that are higher and lower than 800. Aligns with 8.NS.A.
Illustrative Mathematics
Illustrative Mathematics: 8.ns Irrational Numbers on the Number Line
This task presents students with four irrational numbers and asks them to place them on a real number line without referring to a calculator. Aligns with 8.NS.A.2.
Illustrative Mathematics
Illustrative Mathematics: 8.ns Comparing Rational and Irrational Numbers
For this task, 8th graders are presented with pairs of rational or irrational numbers. They must state which number in the pair is higher and explain their thinking. Aligns with 8.NS.A.2.
Illustrative Mathematics
Illustrative Mathematics: 8.ns Converting Decimal Rational Numbers to Fractions
Eighth graders are presented with three repeating decimal numbers and must convert them to fraction format. Aligns with 8.NS.A.1.
Illustrative Mathematics
Illustrative Mathematics: 8.ns Converting Repeating Decimals to Fractions
The purpose of this task is to study some concrete examples of repeating decimals and find a way to convert them to fractions. Aligns with 8.NS.A.1.
Illustrative Mathematics
Illustrative Mathematics: 8.sp Animal Brains
This task looks at a possible relationship between the weight of an animal's body and the weight of its brain. Students make a scatter plot of data, look for outliers, make a second scatter plot without the outliers, and describe the...
Illustrative Mathematics
Illustrative Mathematics: 8.sp.4 Music and Sports
This task looks at a possible relationship between playing a sport and playing a musical instrument. Students collect data from classmates, summarize the data into a two-way table, make some observations, and construct a bar graph of the...
Illustrative Mathematics
Illustrative Mathematics: 8.sp.1 Hand Span and Height
This task looks at a possible relationship between height and hand size. Students collect data from classmates, make a scatter plot, and explain the relationship as linear or nonlinear. Aligns with 8.SP.A.1.
Illustrative Mathematics
Illustrative Mathematics: 8.sp.1 Texting and Grades I
This task looks at a possible relationship between how many text messages high school students send and their grade point average. The data is presented in a scatter plot which students must examine for patterns and deviations. Aligns...
Illustrative Mathematics
Illustrative Mathematics: 8.sp Birds' Eggs
A scatter plot showing data for the sizes of birds' eggs is presented. Students are to look for correlations and make predictions whose values fall within the data range. They are also to make generalizations about the characteristics of...
Illustrative Mathematics
Illustrative Mathematics: 8.sp Laptop Battery Charge
This task looks at how long it takes for a laptop battery to fully charge. Students make a scatter plot of data, draw a 'line of best fit,' and predict the time it will take to reach a full charge. Aligns with 8.SP.A.2.
Illustrative Mathematics
Illustrative Mathematics: 8.ns Identifying Rational Numbers
For this task, 8th graders are presented with a mixed set of eight different numbers and must identify them as rational or irrational and explain how they know. Aligns with 8.NS.A.1.
Illustrative Mathematics
Illustrative Mathematics: 8.ns Placing a Square Root on the Number Line
This task develops students' number sense of squares and square roots. They are to find an approximation of a less obvious square root of a number to see where it would fall on a number line. To do this, they must examine perfect squares...
Illustrative Mathematics
Illustrative Mathematics: 8.f Foxes and Rabbits
In this problem about the predator-prey relationship between the fox and rabbit populations, 8th graders are asked to identify and explain any functions that they see. Aligns with 8.F.A.1.
Illustrative Mathematics
Illustrative Mathematics: 8.f Riding by the Library
For this task, 8th graders draw the graphs of two functions from verbal descriptions. Both functions describe the same situation but changing the viewpoint of the observer changes where the function has output value zero. This forces the...
Illustrative Mathematics
Illustrative Mathematics: 8.f Bike Race
Eighth graders are presented with the distance-time graphs of two bike riders in a race. They are to identify the winner and write a story describing what is happening during the race based on the shapes of the graphs. Aligns with 8.F.B.5.
Illustrative Mathematics
Illustrative Mathematics: 8.f Distance
Eighth graders are presented with the graphs of two cars traveling. One shows distance from home versus time and the other shows speed versus time. Students are to write a description of what might be happening during each car's...
Illustrative Mathematics
Illustrative Mathematics: 8.f Tides
In this problem, 8th graders are presented with a graph showing high and low tides and are asked to analyze it. Aligns with 8.F.B.5.
Illustrative Mathematics
Illustrative Mathematics: 8.f Chicken and Steak, Variation 2
This task has students write an equation to calculate the amount of chicken and steak that can be purchased while staying within a given budget. Students then graph the function and analyze it, discussing the dependent relationship...
Illustrative Mathematics
Illustrative Mathematics: 8.f Baseball Cards
This task has the context of a baseball card collection. Students are shown four equations that might represent the number of cards in the collection where the total is a function of time. They are asked to explain what we can learn...
Illustrative Mathematics
Illustrative Mathematics: 8.f Chicken and Steak, Variation 1
This task has students find a linear function that will calculate the amount of chicken and steak to purchase in order to stay within a given budget. Students then graph the function and interpret it. Aligns with 8.F.B.4.