Illustrative Mathematics
Illustrative Mathematics: G Gpe, G Co, G Srt Unit Squares and Triangles
For this task, students are shown three unit squares and two line segments connecting two pairs of vertices. They are asked to find the area of a triangle formed by intersecting lines. They can solve it using coordinate geometry or...
Illustrative Mathematics
Illustrative Mathematics: G C Right Triangles Inscribed in Circles I
This task provides a good opportunity to use isosceles triangles and their properties to show an interesting and important result about triangles inscribed in a circle with one side of the triangle a diameter. The fact that these...
Illustrative Mathematics
Illustrative Mathematics: G C Two Wheels and a Belt
A certain machine is to contain two wheels, one of radius 3 centimeters and one of radius 5 centimeters, whose centers are attached to points 14 centimeters apart. The manufacturer of this machine needs to produce a belt that will fit...
Illustrative Mathematics
Illustrative Mathematics: G C Tangent to a Circle From a Point
This task builds on a previous one called ''Right triangles inscribed in circles I.'' Here young scholars are asked to construct a tangent line to a circle from a point outside of the circle. Aligns with G-C.A.4.
Illustrative Mathematics
Illustrative Mathematics: G C Right Triangles Inscribed in Circles Ii
In this task, learners analyze the characteristics of a right triangle that has two sides labeled with midpoints and show that the triangle is inscribed in a circle with a diameter the length of its hypotenuse. Aligns with G-C.A.2.
Illustrative Mathematics
Illustrative Mathematics: G C Locating Warehouse
You have been asked to place a warehouse so that it is an equal distance from three roads 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 why...
Illustrative Mathematics
Illustrative Mathematics: G C Orbiting Satellite
A satellite is orbiting the Earth at a given height and young scholars are asked to find the distance it travels to complete 70 percent of an orbit. This task provides a context for connecting an angle in radians to the arc length...
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 C Mutually Tangent Circles
Three circles are mutually tangent. Students are asked to find the total area of the circles plus the area inside where they meet. Students will need to know how to calculate the area of a circle, a sector of a circle, and an equilateral...
Illustrative Mathematics
Illustrative Mathematics: G C, G Srt Setting Up Sprinklers
In this task, learners 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
Students 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?
Learners 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
Young scholars 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
Young scholars 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. Young scholars will...
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.