Illustrative Mathematics
Illustrative Mathematics: 6.ns Setting Goals
Sixth graders solve problems requiring decimal division in this task about setting financial goals. Aligns with 6.NS.B.3.
Illustrative Mathematics
Illustrative Mathematics: 6.ns Movie Tickets
For this task, 6th graders are asked to compare the buying power of $20 in 1987 and 2012 with respect to the cost of movie tickets. Aligns with 6.NS.B.3.
Illustrative Mathematics
Illustrative Mathematics: 6.ns How Many Are In. . . ?
In this task, 6th graders solve fraction division problems by drawing a picture and writing a number sentence. Aligns with 6.NS.A.1.
Illustrative Mathematics
Illustrative Mathematics: 6.ns Baking Cookies
Sixth graders are asked to do arithmetic with fractions in order to calculate the amount of ingredients they have for baking cookies and how many batches they can make. Aligns with 6.NS.A.1.
Illustrative Mathematics
Illustrative Mathematics: 6.ns Traffic Jam
Sixth graders can first model this fraction division problem with a drawing or manipulatives, then use division to solve it. Aligns with 6.NS.A.1.
Illustrative Mathematics
Illustrative Mathematics: 6.ns Cup of Rice
Sixth graders are asked to examine a drawing to find the solution to this fraction division problem. Aligns with 6.NS.A.
Illustrative Mathematics
Illustrative Mathematics: 6.ns Drinking Juice, Variation 3
For this task, 6th graders solve a fraction division problem by drawing a picture and/or using arithmetic. Aligns with 6.NS.A.1.
Illustrative Mathematics
Illustrative Mathematics: 6.ns Drinking Juice, Variation 2
In this task, 6th graders solve a fraction division problem by drawing a picture and/or using arithmetic. Aligns with 6.NS.A.1.
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: 6.ns Integers on the Number Line 2
Sixth graders examine negative numbers and their relationships in inequalities in this problem. Aligns with 6.NS.C.7.a.
Illustrative Mathematics
Illustrative Mathematics: 6.ns Mile High
Sixth graders work with positive and negative numbers in a real-world context in this problem about elevation as it relates to sea level. Aligns with 6.NS.C.5.
Illustrative Mathematics
Illustrative Mathematics: g.co Reflections and Equilateral Triangles Ii
This task examines some of the properties of reflections of the plane which preserve an equilateral triangle. The task gives students a chance to see the impact of these reflections on an explicit object and to see that the reflections...
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.6 Symmetries of a Circle
Suppose C is a circle with center O. Find all lines of symmetry of the circle and explain why the list is complete. Aligns with G-CO.A.
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.
Illustrative Mathematics
Illustrative Mathematics: g.c Inscribing a Circle in a Triangle I
The goal of this task is to show how to draw a circle which is tangent to all three sides of a given triangle: that is, the circle touches each side of the triangle in a single point. Aligns with G-C.A.3.
Illustrative Mathematics
Illustrative Mathematics: G Co Reflected Triangles
In this task, students must use a straightedge and compass to construct the line across which one triangle was reflected onto another. Aligns with G-CO.A.5 and G-CO.D.12.
Illustrative Mathematics
Illustrative Mathematics: G Srt Sine and Cosine of Complementary Angles
The goal of this task is to provide a geometric explanation for the relationship between the sine and cosine of acute angles. In addition, students will need to think about the sine and cosine as functions of an angle in order to reason...
Illustrative Mathematics
Illustrative Mathematics: Use Cavalieri's Principle to Compare Aquarium Volumes
The management of an ocean life museum will choose to include either Aquarium A or Aquarium B in a new exhibit. In doing this task, students discover the formula for the volume of a sphere. Aligns with G-GMD.A.2 and HSG-MG.A.1.