The purpose of this task is to help students see that 4x(9+2) is four times as big as (9+2). Though this task may seem very simple, it provides students and teachers with a very useful visual for interpreting an expression without...

The purpose of this task is to help students understand the commutative property of addition by using dominos as manipulatives. If the teacher does not already have dominoes, they are easily found online and can be printed onto colored...

Students will make 9 in as many ways as they can by adding two numbers between 0 and 9. This is a good introduction to the commutative property.

The goal of this task is to use properties of exponents for whole numbers in order to explain how expressions with fractional exponents are defined. Aligns with the N-RN.A.1 standard.

In this task, students are shown three unit squares and two line segments connecting two pairs of vertices. They are asked to find the area of a triangle formed by intersecting lines. They can solve it using coordinate geometry or...

Satellites communicate with a GPS device and establish the distance between them and their locations. The set of points at a fixed distance from a satellite form a sphere so when the GPS receives its distance from a given satellite, this...

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.

Beehives are made of walls, each of the same size, enclosing small hexagonal cells where honey and pollen are stored and bees are raised. This problem examines some of the mathematical advantages of the hexagonal tiling in a beehive....

The goal of this task is to examine sums and products of rational and irrational numbers. One important property of rational numbers is that their decimals always terminate or repeat: using a slightly different formulation, a rational...

The purpose of this task is to solve some expressions requiring fractional exponents in the modeling context of planetary motion. Aligns with N-RN.A.2.

The purpose of this task is for students to use the volume of a rectangular prism to see why you can multiply three numbers in any order you want and still get the same result. Aligns with 5.OA.A and 5.MD.C.5.

Sixth graders are presented with a completed multiplication equation and are asked to use it to find the answers to seven other equations. To do this, they must use their reasoning and estimation skills. Aligns with 6.NS.B.3.

Learners will use pictorial models to write as many equations for each picture as they can. Multiple variations and extension ideas are included in this lesson.

As a whole class, the teacher presents students with 3 numbers on cards, such as 5, 8, and 3. The teacher asks the students to find all the ways the numbers can be put together in addition or subtraction sentences. This lesson includes...

Picture a roll of toilet paper; assume that the paper in the roll is very tightly rolled. Assuming that the paper in the roll is very thin, find a relationship between the thickness of the paper, the inner and outer radii of the roll,...

In this task, students are given the dimensions of a soda can and are asked to estimate its thickness. They must first find the surface area and the volume of aluminum. Aligns with G-MG.A.1 and G-MG.A.2.

In this task, students investigate whether exponential functions will always be determined by two points. It complements the task "Do two points always determine a linear function?" Aligns with F-LE.A.2.