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: S cp.a.3: Lucky Envelopes
This task builds on prior knowledge and understanding of conditional probability, and introduces the concept of independence of events. Multi-colored envelopes are required in this activity. Aligns with S-CP.A.3.
Illustrative Mathematics
Illustrative Mathematics: S cp.b.9: Random Walk Iv
This activity, which follows Random Walk III, is intended for instructional purposes only. The goal for students is to understand how to calculate and compare combinatorial symbols. Aligns with S-CP.B.9.
Illustrative Mathematics
Illustrative Mathematics: S cp.a.2/a.3/a.5 and S cp.b.7: Rain & Lightning
This task uses the same situation to explore different concepts of probability theory. Aligns with the S-CP.A.2.; S-CP.A.3; S-CP.A.5; and S-CP.B.7 standards.
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 C, G Co Tangent Lines and the Radius of a Circle
In this task, students are shown a circle with center O and point P on the circle. L is a line that is a tangent to the circle at P. They must show that line OP is perpendicular to line L. Aligns with G-C.A.2, G-CO.A, and G-CO.C.9.
Illustrative Mathematics
Illustrative Mathematics: F Tf, G Co, Trigonometric Identities and Rigid Motions
The purpose of this task is to apply translations and reflections to the graphs of the functions f(x)=cos x and g(x)=sin x in order to derive some trigonometric identities. There are also rotations 180 degrees about points on the x-axis...
Illustrative Mathematics
Illustrative Mathematics: G Co Inscribing an Equilateral Triangle in a Circle
Suppose we are given a circle of radius r. The goal of this task is to construct an equilateral triangle whose three vertices lie on the circle. Aligns with G-CO.D.13.
Illustrative Mathematics
Illustrative Mathematics: G Co Construction of Perpendicular Bisector
A and B are two distinct points in the plane and line AB is the segment joining them. The goal of this problem is to construct the perpendicular bisector of segment AB. Aligns with G-CO.D.12.
Illustrative Mathematics
Illustrative Mathematics: G Co Inscribing a Hexagon in a Circle
In this task, students inscribe a regular hexagon inside a circle and compare its area to that of the circle. Aligns with G-CO.D.13.
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 Dilations and Distances
The goal of this task is to study the impact of dilations on distances between points. Aligns with G-CO.A.2.
Illustrative Mathematics
Illustrative Mathematics: G Co Fixed Points of Rigid Motions
A rigid motion of the plane is a map of the plane to itself which preserves distances between points. The purpose of this task is to use fixed points as a tool for studying and classifying rigid motions of the plane, i.e., translations,...
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 students 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: G Co Building a Tile Pattern by Reflecting Hexagons
This task applies reflections to a regular hexagon to construct a pattern of six hexagons enclosing a seventh. The focus of the task is on using the properties of reflections to deduce this seven-hexagon pattern. Aligns with G-CO.B.6.
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 Classifying Triangles
The goal of this task is to help students synthesize their knowledge of triangles where only two of the vertices have been given. They will need to know that a triangle inscribed in a circle, with a diameter of the circle as one side, is...
Illustrative Mathematics
Illustrative Mathematics: G Co Points Equidistant From Two Points in the Plane
In this task, students are shown a line segment that is bisected at a right angle by a second line. They are asked to prove statements about this geometric construction. Includes a GeoGebra worksheet that can be used by the instructor to...
Illustrative Mathematics
Illustrative Mathematics: G Co Midpoints of Triangle Sides
The goal of this task is to use similarity transformations to relate two triangles. The triangles are obtained by taking midpoints of two sides of a given triangle. Aligns with HSG-CO.C.10.
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. Learners are asked to analyze...
Illustrative Mathematics
Illustrative Mathematics: G Co Origami Equilateral Triangle
The purpose of this task is to explore reflections in the context of paper folding. Each fold is associated with a line of reflection and understanding each step in the construction requires careful analysis of angles and of the...
Illustrative Mathematics
Illustrative Mathematics: G Co Midpoints of the Sides of a Paralellogram
Suppose that ABCD is a parallelogram and that M and N are the midpoints of lines AB and CD respectively. Students are asked to prove that MN=AD, and that the line MN is parallel to line AD. Aligns with G-CO.C.11.