This is the first in a series of four tasks that gradually build in complexity. The purpose of this series of tasks is to build in a natural way from accessible, concrete problems involving volume to a more abstract understanding of volume. The purpose of this first task is to see the relationship between the side-lengths of a cube and its volume.

Use the idea of scaling to show that the ratio Area of Circle: (Radius of Circle)2 does not depend on the radius.
Use formulas for the area of squares and triangles to estimate the value of the real number c satisfying
Area(Circle of Radius r)=cr2.

When students successfully complete this task, they will have shown that there is more than one triangle with a 30-degree angle adjacent to a side of length 4 units and opposite to a side of length 3 units.

The goal of this task is twofold:

Use the idea of scaling to show that the ratio Area of Circle: (Radius of Circle)2 does not depend on the radius.
Use formulas for the area of squares and triangles to estimate the value of the real number c satisfying
Area(Circle of Radius r)=c

The purpose of this task is for students to find the area and perimeter of geometric figures whose boundaries are segments and fractions of circles and to combine that information to calculate the cost of a project.

The goal of this task is to provide an opportunity for students to apply a wide range of ideas from geometry and algebra in order to show that a given quadrilateral is a rectangle

The goal of this task is to give students experience applying and reasoning about reflections of geometric figures using their growing understanding of the properties of rigid motions.

The goal of this task is to give students an opportunity to experiment with reflections of triangles on a coordinate grid.

This task gives students a chance to explore several issues relating to rigid motions of the plane and triangle congruence

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use. Here are the first few lines of the commentary for this task: Isaiah is thinking of the number 9.52 in his head. Decide whether each of these has the same value as 9.52 and discuss your reasoning

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use. Here are the first few lines of the commentary for this task: Cari is the lead architect for the city’s new aquarium.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use. Here are the first few lines of the commentary for this task: Each shape below has a line of symmetry. Draw a line of symmetry for each shape. Not every shape has an line of symmetry.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: A small square is a square unit. What is the area of this rectangle? Explain. What fraction of the area of each rectangle is shaded blue?

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use. Here are the first few lines of the commentary for this task: Kipton has a digital scale. He puts a marshmallow on the scale and it reads 7.2 grams. How much would you expect 10 marshmallows to weigh? Why?

The purpose of this task is for students to compare two problems that draw on the same context but represent the two different interpretations of division, namely, the "How many groups?" interpretation and the "How many in each group?" interpretation.