This task aims to show learners that there is often more than one way to represent a quantity. This lesson also lays a foundation for students to understand the commutative property of multiplication.

This task will provide insight to teachers on students' level of understanding when reasoning about a problem. The task asks students to examine whether the sum of two numbers that are multiples of 6 produces another multiple of 6....

In this task, students investigate the volume of tennis balls and their cylindrical container, the empty space around the balls, different ways of slicing them, and what their visualizations will look like. Aligns with G-GMD.B.4 and...

This is a mathematical modeling task aimed at making a reasonable estimate for something which is too large to count accurately, the number of leaves on a tree, taking into account the tree size and the density of the leaves. Aligns with...

The purpose of this task is to have students think about the meaning of multiplying a number by a fraction, and use this burgeoning understanding of fraction multiplication to make sense of the commutative property of multiplication in...

The purpose of this task is to help students see that the definition of the logarithm as an exponent results in an inverse relationship between the exponential and logarithm functions with the same base. This prepares them to think about...

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....

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...

This is the first of a series of problems building to an understanding of an important property of polynomial functions, that a polynomial of degree d can have at most d roots. Aligns with A-APR.B.2.

In this task, students use the structure of an expression to find ways to rewrite it. They are asked to use the defining property of even and odd functions to manipulate expressions involving function notation and to see the structure in...

The goal of this task is to understand how congruence of triangles, defined in terms of rigid motions, relates to the corresponding sides and angles of triangles. Aligns with G-CO.B.7.

For this task, young scholars are asked to calculate the height above sea level of a lamp on top of a lighthouse that is visible to a boat, and to examine two other interpretations of the distance from the lighthouse to the boat. Aligns...

In this task, students are given an aluminum soda can and are simply asked how they could determine how thick the can is. Aligns with G-MG.A.1 and G-MG.A.2.

In this task, students must estimate the number of leaves on a large tree, taking into account various complex factors such as the area shaded by the tree, the area of irregularly shaped leaves, the uneven distribution of leaves, the...

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.