Illustrative Mathematics
Illustrative Mathematics: N q.a.3 and S id.a: Accuracy of Carbon 14 Dating I
This task examines, from a mathematical and statistical point of view, how scientists measure the age of organic materials by measuring the ratio of Carbon 14 to Carbon 12. The focus here is on the statistical nature of such dating....
Illustrative Mathematics
Illustrative Mathematics: G Co Defining Rotations
The goal of this task is to encourage learners to be precise in their use of language when making mathematical definitions. After working on this problem, they are asked to give a proper definition of a rotation by an angle about a...
Illustrative Mathematics
Illustrative Mathematics: Measuring Cups
This task could form part of a classroom activity where students are encouraged to find as many different ways as possible to make different fractions such as 1/12 and then share their methods. While measuring cups would be helpful to...
Illustrative Mathematics
Illustrative Mathematics: N rn.a.1: Evaluating a Special Exponential Expression
The purpose of this task is to study the rules of exponents in the context of trying to make sense of a challenging mathematical expression. Teachers will critically analyze each student's argument. Aligns with N-RN.A.1.
Illustrative Mathematics
Illustrative Mathematics: F Tf Hours of Daylight 1
In order to determine how effective solar panels would be at various times of the year, it is important to know the amount of daylight at a given location. Students are asked to find an appropriate function that serves as a mathematical...
Illustrative Mathematics
Illustrative Mathematics: F Le Dido and the Foundation of Carthage
According to ancient legend, Dido made a deal with a local ruler to obtain as much land as she could cover with an oxhide. Dido interpreted "cover" in an imaginative way and the land she obtained became the site of the important ancient...
Illustrative Mathematics
Illustrative Mathematics: A Rei Reasoning With Linear Inequalities
Students are presented with a solution to an inequality and are asked to find two mathematical errors and explain why they are incorrect. Aligns with A-REI.B.3 and A-REI.A.1.
Illustrative Mathematics
Illustrative Mathematics: Toll Bridge Puzzle
You are on a trip and need to cross a bridge, but you have to pay tolls in coins. Solve this puzzle by making your way to the island only using 100 coins.
Illustrative Mathematics
Illustrative Mathematics: G Mg Ice Cream Cone
You have been hired by the owner of a local ice cream parlor to assist in his company's new venture. The company will soon sell its ice cream cones in the freezer section of local grocery stores. The manufacturing process requires that...
Student Achievement Partners
Illustrative Mathematics: Three Composing/decomposing Problems [Pdf]
In this grade 2 lesson, students use base ten blocks to compose and decompose numbers.
Illustrative Mathematics
Illustrative Mathematics: 6.ns Gifts From Grandma, Variation 3
This task presents three problems about money spent on grandchildren at a fair. The first problem involves decimal multiplication and the other two require decimal division. The lesson includes two additional lesson attachments that...
Illustrative Mathematics
Illustrative Mathematics: Hsa ced.a.2 Create Equations in Two or More Variables
Choose from a variety of creative problems (tasks) to teach how to create equations in two or more variables to represent relationships between quantities and graph equations on coordinate axes with labels and scales. Explanations and...
Illustrative Mathematics
Illustrative Mathematics: Look for and Express Regularity in Repeated Reasoning
The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important 'Processes and Proficiency' with longstanding...
Illustrative Mathematics
Illustrative Mathematics: A Sse the Physics Professor
In this task, students are asked to study the structure of an algebraic expression, draw conclusions, and explain their thinking. Aligns with A-SSE.A.1 and A-SSE.A.1.b.
Illustrative Mathematics
Illustrative Mathematics: G Co Origami Regular Octagon
After successive folds of a piece of origami paper, a student must explain why the shape made is a regular octagon. Aligns with G-CO.A.3 and G-CO.D.12.
Illustrative Mathematics
Illustrative Mathematics: G Co Seven Circles Ii
In this task, seven pennies are placed in a circle so that they are all touching one in the center and their neighbors. Learners are asked to find as many rigid motions of the plane as they can which are symmetries of this configuration...
Illustrative Mathematics
Illustrative Mathematics: N q.a: New Cuyama
On a road trip in California, Lisa saw a sign which made her laugh and take a picture: Aligns with N-Q.A.
Illustrative Mathematics
Illustrative Mathematics: N Rn and 8 Ns: Calculating the Square Root of 2
Jessica evaluates $\sqrt{2}$ on her calculator which shows a value of $$ 1.4142136. $$ She then writes $$ \sqrt{2} = 1.4142136. $$ Aligns with 8.NS.A.
Illustrative Mathematics
Illustrative Mathematics: N q.a.1: Ice Cream Van
The purpose of this task is to engage students, probably working in groups, in a substantial and open-ended modeling problem. Students will have to brainstorm or research several relevant quantities, and incorporate these values into...
Illustrative Mathematics
Illustrative Mathematics: S cp.b.9: Alex, Mel, and Chelsea Play a Game
Alex, Mel, and Chelsea play a game that has 6 rounds. In each round there is a single winner, and the outcomes of the rounds are independent. For each round the probability that Alex wins is $\frac{1}{2}$, and Mel is twice as likely to...
Illustrative Mathematics
Illustrative Mathematics: G Co Are the Triangles Congruent?
In each of the following diagrams, two triangles are shaded. Based on the information given about each diagram, decide whether there is enough information to prove that the two triangles are congruent. Aligns with G-CO.B.
Illustrative Mathematics
Illustrative Mathematics: G Co Building a Tile Pattern by Reflecting Octagons
This task applies reflections to a regular octagon to construct a pattern of four octagons enclosing a quadrilateral. The focus of the task is on using the properties of reflections to deduce that the quadrilateral is actually a square....
Illustrative Mathematics
Illustrative Mathematics: G Co Defining Perpendicular Lines
Three students have proposed three ways to describe when two lines are perpendicular. Students are asked to analyze their statements. Aligns with G-CO.A.1.
Illustrative Mathematics
Illustrative Mathematics: G Co Defining Parallel Lines
Alex and his friends are studying for a geometry test and one of the main topics covered is parallel lines. They each write down what they think it means for two distinct lines in a plane to be parallel. Young scholars are asked to...