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: G C Placing a Fire Hydrant
You have been asked to place a fire hydrant so that it is an equal distance from three locations on a map. Students must fold a paper so that this point is where two folds intersect, and they must explain why their construction works and...
Illustrative Mathematics
Illustrative Mathematics: G C Inscribing a Triangle in a Circle
This problem introduces the circumcenter of a triangle and shows how it can be used to inscribe the triangle in a circle. It also shows that there cannot be more than one circumcenter. Aligns with G-C.A.3.
Illustrative Mathematics
Illustrative Mathematics: G C Circumcenter of a Triangle
The goal of this task is to construct the circumcenter of a triangle, that is, the point which is the same distance from each of the triangle's three vertices. This task shows that the three perpendicular bisectors of the sides of a...
Illustrative Mathematics
Illustrative Mathematics: How Heavy
Learners will have fun learning about weights with this hands-on activity. Students will use a balance scale to compare the weights of two different objects. Recording sheets are provided.
Illustrative Mathematics
Illustrative Mathematics: Which Weighs More? Which Weighs Less?
Students will use a block to compare with other objects to decide which is heavier/lighter. They will fill in a chart by drawing a picture of it under "Heavier" or "Lighter" depending which applies.
Illustrative Mathematics
Illustrative Mathematics:size Shuffle
Students will learn about height and comparable language with this task that will get your class moving around!
Illustrative Mathematics
Illustrative Mathematics: Make 9
Students will make 9 in as many ways as they can by adding two numbers between 0 and 9. This is a good introduction to the commutative property.
Illustrative Mathematics
Illustrative Mathematics: Christina's Candies
The teacher will pose a sequence of questions for students to solve using objects, pictures, or equations. Students will develop a sense of quantities and how they are related to a problem situation.
Illustrative Mathematics
Illustrative Mathematics: Which Is Heavier?
Learners 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: Which Is Longer?
Students are introduced to the concept of length with this hands-on activity. Each student will choose two objects to compare by laying them next to each other and comparing which is longer. Students will record and discuss their findings.
Illustrative Mathematics
Illustrative Mathematics: Many Ways to Do Addition 1
Students will learn that there are multiple ways to solve math problems, such as drawing a picture, using counters, using fingers, using a number line, and memorizing facts. The teacher writes a simple addition problem on the whiteboard...
Illustrative Mathematics
Illustrative Mathematics: Longer and Shorter
Students will use their shoe as a measuring item to learn about length. Students will compare classroom items by holding their shoe against the item and deciding if it is longer or shorter than their shoe. Students will record their...
Illustrative Mathematics
Illustrative Mathematics: G C Similar Circles
In this task, students are asked to show that all circles are similar using two different methods, a visual one and an algebraic one. Includes a GeoGebra worksheet that can be used by the instructor to demonstrate the material. Aligns...
Illustrative Mathematics
Illustrative Mathematics: G Srt Shortest Line Segment From a Point P to a Line L
In 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.
Illustrative Mathematics
Illustrative Mathematics: G Srt, G Mg Coins in a Circular Pattern
In this task, students investigate how many coins will fit around a central coin when they are all of the same denomination, and if there is room left over. The teacher is given a chart of four coin denominations and their diameters, but...
Illustrative Mathematics
Illustrative Mathematics: G Srt, G Mg Seven Circles Iii
In this task, students are shown circle formations where an inner circle is surrounded by a set of circles and all circles are touching. In the first situation, all circles have the same diameter. In the second, the inner circle is...
Illustrative Mathematics
Illustrative Mathematics: G Srt Pythagorean Theorem
The purpose of this task is to prove the Pythagorean Theorem using similar triangles. Aligns with G-SRT.B.4.
Illustrative Mathematics
Illustrative Mathematics: G Srt, G Mg How Far Is the Horizon?
Some friends are at the beach looking out onto the ocean on a clear day and they wonder how far away the horizon is. A second problem asks how far the horizon would be from the top of a mountain. Students must also answer a question...
Illustrative Mathematics
Illustrative Mathematics: G Srt Similar Triangles
This task works toward establishing the AA criterion for similarity of triangles. Students are asked to provide a detailed sequence of transformations that moves one of the given triangles onto the other. Aligns with G-SRT.A.3.
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: G Srt Mt. Whitney to Death Valley
For this task, students are asked to make a mathematical model and determine if it is possible to see a point on the surface of the Earth that is 85 miles away, and well below sea level, from the top of a mountain. The curvature of the...
Illustrative Mathematics
Illustrative Mathematics: 6.sp4, 5c Puzzle Times
A performance task asking students to create a graph of provided information and then find the mean and the median of the data.