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: Boys and Girls, Variation 1
This word problem focuses on the Put Together/Take Apart contexts for addition and subtraction. Learners may use objects, pictures, or equations to represent their solutions. Examples and explanations are provided.
University of Texas
Inside Mathematics: Cubes [Pdf]
This task challenges a student to use knowledge of concepts of volume and its attributes to solve problems with rectangular prisms.
University of Toronto (Canada)
University of Toronto: Deductive and Inductive Reasoning
Part of a University of Toronto website, this page defines and describes deductive and inductive reasoning in solving mathematical problems.
Illustrative Mathematics
Illustrative Mathematics: 7.ns Sharing Prize Money
In this lesson, 7th graders solve real world problems using the four operations.
Illustrative Mathematics
Illustrative Mathematics: G C, G Srt Setting Up Sprinklers
In this task, students must decide where to place sprinklers on a lawn so that the maximum area of the lawn will be watered. To solve it, they must find areas of sectors of circles and use trigonometric ratios to solve right triangles....
Illustrative Mathematics
Illustrative Mathematics: A rei.c.6: Accurately Weighing Pennies I
In this problem, young scholars will use the number of decimal places in the coefficients to motivate writing and solving a system of equations. Aligns with A-REI.C.6.
Illustrative Mathematics
Illustrative Mathematics: G Gmd Centerpiece
This problem presents a wedding reception scenario. The bride is creating centerpieces for the tables and must calculate how many marbles she needs to partly fill the vases and stay within her budget at the same time. Aligns with G-GMD.A.3.
Illustrative Mathematics
Illustrative Mathematics: 6.rp, 7.rp.3 Climbing the Steps of El Castillo
A performance task in which students solve a problem involving a proportional relationship. The problem is: The temple at the top of the pyramid is approximately 24 meters above the ground, and there are 91 steps leading up to the...
Illustrative Mathematics
Illustrative Mathematics: 6.ns Making Hot Cocoa, Variation 2
In this task, 6th graders solve a fraction division problem by drawing a picture, interpreting it, identifying an equation that represents the problem, and verifying that the equation gives the same answer as the picture. Aligns with...
Illustrative Mathematics
Illustrative Mathematics: 7.rp Dueling Candidates
Seventh graders use proportional reasoning to solve word problems regarding an election.
Illustrative Mathematics
Illustrative Mathematics: Running to School
This is the easiest problem in a series of three tasks involving fraction multiplication that can be solved with pictures or number lines. Aligns with 5.NF.B.6.
Illustrative Mathematics
Illustrative Mathematics: A Apr Egyptian Fractions Ii
In this task, learners will rewrite fractions as a sum of distinct unit fractions. To solve the problem, students will rewrite a simple rational expression and will need to study the arithmetic of these unit fractions with a variable in...
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: 6.ns Video Game Credits
Sixth graders solve problems requiring fraction division in this task about video game credits. Aligns with 6.NS.A.1.
Illustrative Mathematics
Illustrative Mathematics: 6.rp Converting Square Units
In this task, 6th graders must inches to feet in order to find the area of a rectangular board and explain the error in the calculations made by the board owner. Aligns with 6.RP.A.3.
Illustrative Mathematics
Illustrative Mathematics: 6.g Painting a Barn
This task asks students to determine the area of the exterior walls of a barn and to calculate how many gallons of paint would be needed to cover them, as well as the cost of the paint. Aligns with 6.G.A and 6.RP.A.3.
Illustrative Mathematics
Illustrative Mathematics: 6.ns Distances Between Points
The purpose of this task is for students to find the distance between points that lie in all four quadrants of the coordinate plane. Aligns with 6.NS.C.8.
Illustrative Mathematics
Illustrative Mathematics: Valentine Marbles
Explore estimation through this lesson designed to engage middle schoolers.
AdLit
Ad lit.org: Cross Disciplinary Proficiencies: American Diploma Project Benchmarks
Students must graduate from high school with not only a firm foundation in mathematics and English, but also with the ability to approach with confidence new and unfamiliar tasks and challenges in college, the workplace and life....
Illustrative Mathematics
Illustrative Mathematics: G Gpe, G Srt Slope Criterion for Perpendicular Lines
The goal of this task is to use similar triangles to establish the slope criterion for perpendicular lines. Aligns with HSG-GPE.B.5 and HSG-SRT.B.5.
Illustrative Mathematics
Illustrative Mathematics: G Gpe.5 Triangles Inscribed in Circle
In this task, students use ideas about linear functions to determine when certain angles are right angles. They use the fact that two lines (if not vertical or horizontal) are perpendicular when their slopes are inverse reciprocals, as...
Illustrative Mathematics
Illustrative Mathematics: G Srt Shortest Line Segment From a Point P to a Line L
For this task, students develop an understanding that the shortest path from a point to a line always meets the line at a right angle. Aligns with G-SRT.C.8.
Illustrative Mathematics
Illustrative Mathematics: G Srt Tangent Line to Two Circles
The purpose of this task is to use similar triangles and setting up a proportion in order to calculate a side length. Aligns with G-SRT.B.5.