Illustrative Mathematics
Cynthia's Perfect Punch
Using a real-world example, this problem illustrates the thought process that learners need to engage in to understand adding mixed numbers with common denominators. First by looking at estimation, and then by drawing models that...
Illustrative Mathematics
Is This a Parallelogram?
If both pairs of opposite sides of a quadrilateral are congruent, is the quadrilateral a parallelogram? This task asks learners to determine the answer and to support their answer with a proof. The resource includes a commentary for...
Illustrative Mathematics
Warming and Cooling
Is it too hot to go hiking? This task asks learners to refer to a graph that shows temperature as a function of time and answer five questions about the scenario depicted by the graph. The exercise could be used for instruction to help...
Illustrative Mathematics
Reflections and Isosceles Triangles
Geometers explore symmetries of isosceles triangles by using rigid transformations of the plane. They complete four tasks, including congruence proofs, which illustrate the relationship between congruence and rigid transformations. The...
Illustrative Mathematics
Pizza Place Promotion
The longer you wait to try the new pizza place, the more it's going to cost you! This real-world problem about how the cost of pizza varies with respect to time is a good example of how piecewise functions are used to describe...
Illustrative Mathematics
Interpreting the graph
The purpose of this exercise is to give practice in reading information about a function from its graph. Learners are given graphs of two functions on the same axes. The task is to locate and label various key points on the graph that...
Illustrative Mathematics
Graphs of Power Functions
This activity consists of three exercises in which learners sketch the graphs of various power functions on the same axes. They use their sketches to make comparisons and observations which lead to generalizations about the graphs of...
Illustrative Mathematics
How is the Weather?
This activity asks learners to interpret data displayed on a graph within the context of the problem. Students are given three graphs that show solar radiation, or intensity of the sun, as a function of time. They are also given three...
Illustrative Mathematics
Same Base and Height, Variation 1
Four triangles are depicted for learners to construct on a geoboard. They compute and compare the areas, and so meet one of the sixth grade Common Core standards for geometry. Note that the set of triangles does not include a right...
Illustrative Mathematics
Words and Music I
What type of music is best to listen to while learning? In a short writing prompt, learners must determine if a scenario involving listening to music while memorizing material is an experiment or an observational study. The prompt also...
Illustrative Mathematics
Sarah, the chimpanzee
Is Sarah, the chimpanzee, smart or just a lucky guesser? Here, learners set up a simulation and read a dotplot to find out the likelihood of getting 7 out of 8 questions correct. One suggested modification would be to have your class...
Illustrative Mathematics
Identifying Even and Odd Functions
Use a worksheet to give learners practice in identifying even and odd functions. The problems on this page are also appropriate for use as assessment items, or you can use them with GeoGebra to interactively present concepts. The task is...
Illustrative Mathematics
Comparing Products
How can 5th graders show understanding that 30 x 225 is half of 60 x 225 without completing the computation? They can use an area model and draw it out. An array, or an open array, is an area model that allows for young learners to...
Illustrative Mathematics
Words to Expressions 1
Designed as a follow-up to the lesson plan titled Watch Out for Parenthesis 1, this activity asks young learners to write an equation for the calculation described with words rather than numbers and symbols. The treasure that 5th graders...
Illustrative Mathematics
Watch Out for Parentheses 1
Parentheses are an important tool in the algebraic toolbox in regard to the structure of the algebraic equation. They are the beginning of the standard order of operations rule, the P in PEMDAS. The central question that 5th graders are...
Illustrative Mathematics
Haircut Costs
Who pays more for haircuts, men or women? Given quartile values, learners construct box and whiskers plots and interpret the results. They compare the mean and median, and discuss which is more appropriate under particular conditions....
Illustrative Mathematics
SAT Scores
If you earned a score of 610 on the math portion of the SAT, what would be your percentile ranking? Given the mean and standard deviation of normally distributed data, find the probability of getting a particular score, or that your...
Illustrative Mathematics
Finding a Chair
Here is an activity that incorporates subtraction in word problems. Youngsters are provided with six word problems that essentially deal with the same numbers in each problem, yet use different comparison language. These problems are...
Illustrative Mathematics
A Pencil and a Sticker
How much do a pencil and sticker cost? Youngsters use a bar diagram to find the cost of a sticker that is twenty cents less than the cost of a pencil. Given the prices, learners must find the cost of the sticker in order to find the cost...
Illustrative Mathematics
Operations with Rational and Irrational Numbers
Learners complete addition and multiplication tables that include rational and irrational numbers. They also answer a series of questions about the sums and products of irrational and rational numbers. One suggested modification would be...
Illustrative Mathematics
Speed Trap
In which direction is traffic moving faster, north or south? Use box and whisker plots to organize data and interpret the results. Detailed solutions are included. This activity would be good as a warm up or quick assessment at the end...
Illustrative Mathematics
Do You Fit In This Car?
A short activity that focuses on the normal distribution as a model for data distribution. Using given means and standard deviations, your budding statisticians can use statistical tables, calculators, or other statistical software to...
Illustrative Mathematics
Complex number patterns
Start off with the definition of the imaginary number i, then have your class practice simplifying expressions involving powers of i and look for patterns. See how the cyclic nature of powers of i translate to sums of powers of i.
Illustrative Mathematics
How Much is a Penny Worth?
Are pennies really worth one cent? Here, learners use rates to calculate the price per pound of copper that would result in pennies that are exactly one cent's worth of copper. Might work best as a group or whole-class activity since the...