Illustrative Mathematics
Illustrative Mathematics: Which Is Heavier?
Students will learn the concept of weight by practicing weighing items on a balance scale and recording their results. Students can record their answers on the black line masters included in the Illustrated Mathematics lesson "How Heavy?".
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 Reflections
The goal of this task is to compare and contrast the visual intuition we have of reflections with their technical mathematical definition. Aligns with G-CO.A.4.
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: A Rei Solution Sets
For this task, students are shown the graphs of two equations, with areas bounded by their lines and intersections shaded in different colors. They are asked to write a system of equations or inequalities for each shaded area and explain...
Illustrative Mathematics
Illustrative Mathematics: Origami Stars
The purpose of this task is to present students with a situation in which they need to divide a whole number by a unit fraction in order to find a solution. Calculating the number of origami stars that Avery and Megan can make...
Illustrative Mathematics
Illustrative Mathematics: G Mg How Many Leaves on a Tree?
This is a mathematical modeling task aimed at making a reasonable estimate for something which is too large to count accurately, the number of leaves on a tree, taking into account the tree size and the density of the leaves. Aligns with...
Illustrative Mathematics
Illustrative Mathematics: F Bf 1,000 Is Half of 2,000
This task is about an online mathematics organization that is trying, over a four-year period, to generate 2,000 math problems that cover all grades. This real-life modeling task could serve as a summative exercise that draws on many...
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: Converting Fractions of a Unit Into a Smaller Unit
Note that in each of these problems we are given a set of a specified size and a specified number of subsets into which it is to be divided. The questions ask the student to find out the size of each of the subsets. Students are not...
Illustrative Mathematics
Illustrative Mathematics: 6.ee
The purpose of this task is to introduce the idea of exponential growth and then connect that growth to expressions involving exponents. It illustrates well how fast exponential expressions grow. Learners who are just learning about...
Illustrative Mathematics
Illustrative Mathematics: Painting a Room
The purpose of this task is to provide students with a situation in which it is natural for them to divide a unit fraction by a non-zero whole number. Determining the amount of paint that Kulani needs for each wall illustrates an...
Illustrative Mathematics
Illustrative Mathematics: 7.rp Two School Dance
The purpose of this task is to see how well middle schoolers students understand and reason with ratios. This task was adapted from problem #14 on the 2011 American Mathematics Competition (AMC) 8 Test. Aligns with 7.RP.A.3. The site...
Illustrative Mathematics
Illustrative Mathematics: S Id Sat Scores
Young scholars will find solutions for a series of questions based on the assumption that SAT mathematics scores for a particular year are approximately normally distributed with a mean of 510 and a standard deviation of 100. Explanation...
Illustrative Mathematics
Illustrative Mathematics: A sse.a.2 & N cn.a: Computations With Complex Numbers
This task requires learners to rewrite mathematical expressions involving complex numbers. Aligns with A-SSE.A.2 and N-CN.A.
Illustrative Mathematics
Illustrative Mathematics: N q.a.1: Runners' World
This task provides students with an opportunity to engage in Standard for Mathematical Practice 6, attending to precision. It intentionally omits some relevant information. Aligns with N-Q.A.1.
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: G Srt Ask the Pilot
In the July 2013 issue of United Airlines' Hemisphere Magazine, a pilot responded to a question about how far in the distance he could see at different altitudes. The solution involved right triangles, lines of tangency to a circle, and...
Illustrative Mathematics
Illustrative Mathematics: A ced.a.3 and a rei.d.12: Fishing Adventures 3
During this illustrated lesson, students will write and solve inequalities, and they will represent their solutions graphically. Aligns with A-CED.A.3 and A-REI.D.12.
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: A sse.b.3: Ice Cream
This task illustrates the process of rearranging the terms of an expression to reveal different aspects about the quantity it represents. Aligns with A-SSE.B.3.
Illustrative Mathematics
Illustrative Mathematics: 3.oa Patterns in the Multiplication Table
The goal is to look for structure and identify patterns in the multiplication table and then try to find the mathematical explanation for this. Aligns with CCSS.Math.Content.3.OA.D.9 Identify arithmetic patterns, and explain them using...
Illustrative Mathematics
Illustrative Mathematics: A rei.c.6: Accurately Weighing Pennies Ii
This illustrated math lesson shows how important levels of accuracy in measurement are. The answer can be different since a scale only accurately weighs to the nearest tenth of a gram instead of to the nearest hundredth of a gram. Aligns...
Illustrative Mathematics
Illustrative Mathematics: g.co Reflections and Isosceles Triangles
This task has learners link their intuitive notions of symmetries of a triangle with statements proving that said triangle is unmoved by applying certain rigid transformations. The mechanism through which students do this is via...