Illustrative Mathematics
Illustrative Mathematics: G Gpe Explaining the Equation for a Circle
This problem examines equations defining different circles in the x-y plane. Students must use the Pythagorean Theorem to find equations whose solutions are points on the circle and explain why they work. Includes a GeoGebra worksheet...
Illustrative Mathematics
Illustrative Mathematics: G Gpe Equal Area Triangles on the Same Base Ii
This task has students apply their knowledge of parallel lines to solve a geometric problem on areas of triangles. The task is open-ended in that students can choose their method of completing the task. Aligns with G-GPE.B.5.
Illustrative Mathematics
Illustrative Mathematics: G Gpe Equal Area Triangles on the Same Base I
This task is a relatively easy application of the formula for the area of a triangle and the use of parallel lines. Aligns with G-GPE.B.5.
Illustrative Mathematics
Illustrative Mathematics: G Gpe Parallel Lines in the Coordinate Plane
The goal of this task is to prove the slope criterion for parallel lines. Aligns with HSG-GPE.B.5.
Illustrative Mathematics
Illustrative Mathematics: G Gpe When Are Two Lines Perpendicular?
The goal of this task is to examine when two lines in the plane are perpendicular in terms of their slopes. Aligns with HSG-GPE.B.5.
Illustrative Mathematics
Illustrative Mathematics: G Gpe Scaling a Triangle in the Coordinate Plane
The goal of this task is to apply dilations to a triangle in the coordinate plane. Students will need to find the coordinates of a point which cuts a given segment into one third and into two thirds. The two dilated triangles share a...
Illustrative Mathematics
Illustrative Mathematics: G Gpe Squares on a Coordinate Grid
The purpose of this task is to use the Pythagorean Theorem and knowledge about quadrilaterals in order to construct squares of different sizes on a coordinate grid. Aligns with G-GPE.B.7.
Illustrative Mathematics
Illustrative Mathematics: G Gpe Defining Parabolas Geometrically
The purpose of this task is to show that the points on a parabola can be characterized by being equidistant from a point (the focus) and a line (the directrix). Aligns with HSG-GPE.A.2.
Illustrative Mathematics
Illustrative Mathematics: G Gpe a Midpoint Miracle
In this task, students are asked to draw a quadrilateral so that no two sides are congruent, no two angles are congruent, and no two sides are parallel. The task gives students the opportunity to prove that if we join the midpoints of a...
Illustrative Mathematics
Illustrative Mathematics: G Gpe Triangle Perimeters
Students are shown two triangles touching points on a coordinate grid and are asked to answer questions about their perimeters. The purpose of this task is to apply the Pythagorean theorem to calculate distances and areas. Aligns with...
Illustrative Mathematics
Illustrative Mathematics: F Le, a Rei Population and Food Supply
In this task, students analyze the sizes of a country's population and of its food supply to determine when and if food shortages will occur. To solve it, they must construct and compare linear and exponential functions and find where...
Illustrative Mathematics
Illustrative Mathematics: F Le Taxi!
In this task, students explore the linear relationship between distance traveled and taxi fare cost. Aligns with A-REI.D.10 and F-LE.B.5.
Illustrative Mathematics
Illustrative Mathematics: N cn.a.2, N cn.b.5, and N cn.c.8 Complex Cube Roots
This task has students further their understanding of the algebra of the complex numbers. Aligns with N-CN.A.2, N-CN.B.5,a nd N-CN.C.8.
Illustrative Mathematics
Illustrative Mathematics: N q.a.1, a ced.a.1, and N q.a.2: Harvesting the Fields
This task is about farm-workers who are harvesting two fields. Students are presented with a scenario involving two teams of workers, two different sizes of fields, and work spread out over two days. They must calculate how many...
Illustrative Mathematics
Illustrative Mathematics: A Rei Two Squares Are Equal
This task asks students to solve a quadratic equation in as many different ways as they can. Aligns with A-REI.B.4 and A-REI.D.11.
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: 8.g, G Srt Points From Directions
For this problem, students must carefully read the description of a triangle and a fourth point that lies outside it and draw a picture to represent the problem. They must then use the Pythagorean Theorem to find side lengths. Aligns...
Illustrative Mathematics
Illustrative Mathematics: G Co Symmetries of a Quadrilateral I
Suppose ABCD is a quadrilateral for which there is exactly one rotation, through an angle larger than 0 degrees and less than 360 degrees, which maps it to itself. Further, no reflections map ABCD to itself. What shape is ABCD? Aligns...
Illustrative Mathematics
Illustrative Mathematics: G Co Symmetries of a Quadrilateral Ii
There is exactly one reflection and no rotation that sends the convex quadrilateral ABCD onto itself. What shape(s) could quadrilateral ABCD be? Explain. Aligns with G-CO.A.3.
Illustrative Mathematics
Illustrative Mathematics: G Co Symmetries of Rectangles
This task examines the rigid motions which map a rectangle onto itself. The emphasis here is on careful reasoning using the definitions of reflections and rotations. Aligns with G-CO.A.3.
Illustrative Mathematics
Illustrative Mathematics: G Co Why Does Sss Work?
In this task, students must show that two triangles are congruent given a set of steps which produce a rigid transformation of the plane. Includes an experimental GeoGebra worksheet that instructors can use to demonstrate the task....
Illustrative Mathematics
Illustrative Mathematics: G Co Why Does Sas Work?
In this task, students must explain the given reasoning for why triangle ABC is congruent to triangle DEF using the language of reflections. Aligns with G-CO.B.8.
Illustrative Mathematics
Illustrative Mathematics: g.co Bisecting an Angle
In this task, students practice bisecting an angle. Includes a GeoGebra worksheet that teachers can use to demonstrate the task. Aligns with G-CO.D.12.
Illustrative Mathematics
Illustrative Mathematics: g.c Inscribing a Circle in a Triangle Ii
This task focuses on a fact which comes out of the construction of the inscribed circle in a triangle: the angle bisectors of the three angles of triangle ABC all meet in a point. Aligns with G-C.A.3.