Illustrative Mathematics
Illustrative Mathematics: Peyton and Presley Discuss Addition
The purpose of this task is to support students in developing an understanding of a place value strategy for adding numbers. By using a representation to visualize the abstract notation, students will make sense of the strategy, adding...
Illustrative Mathematics
Illustrative Mathematics: Reflections, Rotations, and Translations
This task uses GeoGebra software, which can be freely downloaded, to explore what happens to the line segments and angles of a triangle when it is reflected, rotated, and translated. Includes printable task sheet for students and a...
Illustrative Mathematics
Illustrative Mathematics: N q.a.1 and N q.a.3: Felicia's Drive
This task requires learners to make some sensible approximations of the amount of gas needed for a drive. They must choose a level of accuracy appropriate to limitations on measurement when reporting quantities. Aligns with N-Q.A.1 and...
Illustrative Mathematics
Illustrative Mathematics: 5.md: Breaking Apart Composite Solids
This exercise helps students understand how volume in figured, even when two or more parts of a prism are not overlapping. There is a teacher view, with a description of the activity and commentary, and a student view, with just the...
Illustrative Mathematics
Illustrative Mathematics: 4.g the Geometry of Letters
Letters can be thought of as geometric figures. Aligns with 4.G.A.1.
Illustrative Mathematics
Illustrative Mathematics: 4.nf Explaining Fraction Equivalence With Pictures
The purpose of this task is to provide students with an opportunity to explain fraction equivalence through visual models in a particular example. Part (c) should be approached as a discussion before students are asked to write an...
Illustrative Mathematics
Illustrative Mathematics: 4.nf Using Benchmarks to Compare Fractions
Melissa gives her classmates the following explanation for comparing fractions.
Illustrative Mathematics
Illustrative Mathematics: Rounding to Tenths and Hundredths
The purpose of this task is for students to use the position of a number on the number line to round the number without knowing its exact value. Though this task deals most directly with rounding, it also requires students to understand...
Illustrative Mathematics
Illustrative Mathematics: 7.rp Proportionality
This lesson plan explores how to recognize and represent proportional relationships between quantities.
Illustrative Mathematics
Illustrative Mathematics: G Mg Hexagonal Pattern of Beehives
Beehives are made of walls, each of the same size, enclosing small hexagonal cells where honey and pollen are stored and bees are raised. This problem examines some of the mathematical advantages of the hexagonal tiling in a beehive....
Illustrative Mathematics
Illustrative Mathematics: G Mg Toilet Roll
Picture a roll of toilet paper; assume that the paper in the roll is very tightly rolled. Assuming that the paper in the roll is very thin, find a relationship between the thickness of the paper, the inner and outer radii of the roll,...
Illustrative Mathematics
Illustrative Mathematics: G Mg How Many Cells Are in the Human Body?
About how many cells are in the human body? The purpose of this task is for young scholars to apply the concepts of mass, volume, and density in a real-world context. Aligns with G-MG.A.2.
Illustrative Mathematics
Illustrative Mathematics: G Mg Paper Clip
A paper clip is just over 4 cm long. How many paper clips like this may be made from a straight piece of wire 10 meters long? This high level task is an example of applying geometric methods to solve design problems and satisfy physical...
Illustrative Mathematics
Illustrative Mathematics: N Q Giving Raises
A small company wants to give raises to their 5 employees. They have $10,000 available to distribute. Imagine you are in charge of deciding how the raises should be determined. What method would be fair to everyone? Aligns with HSN-Q.A.2.
Illustrative Mathematics
Illustrative Mathematics: N Rn Sums of Rational and Irrational Numbers
The goal of this task is to examine sums and products of rational and irrational numbers. One important property of rational numbers is that their decimals always terminate or repeat: using a slightly different formulation, a rational...
Illustrative Mathematics
Illustrative Mathematics: N Cn Complex Distance
In this problem, you will compute some values related to the complex numbers 2 + i and 5 - 3i. Aligns with N-CN.B.6.
Illustrative Mathematics
Illustrative Mathematics: 7.sp, S Cp, S Md but Mango Is My Favorite
A seven-year-old boy has a favorite treat, Super Fruity Fruit Snax. Of the 5 fruit flavors, he likes mango the best. When the boy found no mango in his fruit pouch, his mother (a statistician) assured him that this was no big deal and...
Illustrative Mathematics
Illustrative Mathematics: S Cp Breakfast Before School
On school days, Janelle sometimes eats breakfast and sometimes does not. After studying probability for a few days, Janelle says, "The events 'I eat breakfast' and 'I am late for school' are independent." Explain what this means in terms...
Illustrative Mathematics
Illustrative Mathematics: s.ic.4 the Marble Jar
Sometimes hotels, malls, banks, and other businesses will present a display of a large, clear container holding a large number of items and ask customers to estimate some aspect of the items in the container as a contest. In some cases,...
Illustrative Mathematics
Illustrative Mathematics: S Md Fred's Fun Factory
A famous arcade in a seaside resort town consists of many different games of skill and chance. In order to play a popular "spinning wheel" game at Fred's Fun Factory Arcade, a player is required to pay a small, fixed amount of 25 cents...
Illustrative Mathematics
Illustrative Mathematics: S Md.2, 5 Sounds Really Good! (Sort Of)
A friend of yours, Phil, writes to you asking about a new scratch-off lottery game. It costs $10 to play this game. There are two outcomes for the game (win, lose) and the probability that a player wins a game is 60%. A win results in...
Illustrative Mathematics
Illustrative Mathematics: Counting Dots in Arrays
This activity addresses CCSS 2.OA.C.4 where students count dots in an array using repeated addition. This skill lays the foundation for an understanding of multiplication.
Illustrative Mathematics
Illustrative Mathematics: 4.oa Comparing Money Raised
The purpose of this task is for students to solve three comparisons problems that are related by their context but are structurally different. Multiplicative comparison is purposefully excluded from third grade (see 3.OA.3 and 3.MD.2),...
Illustrative Mathematics
Illustrative Mathematics: 4.nf Cynthia's Perfect Punch
Cynthia is making her famous "Perfect Punch" for a party. After looking through the recipe, Cynthia explores mixed numbers to create it.