This simple-looking problem reveals much about how well students understand unit fractions as well as representing fractions on a number line.

In this activity students will learn the basic concept of Global Positioning Systems (GPS) using triangulation and measurement on a small scale in the classroom. Students discover how GPS and navigation integrate mathematic and scientific concepts to create a standard for locating people and objects. This activity helps students understand both the need for and methods of navigation.

The purpose of this task is to have students work on a sequence of area problems that shows the advantage of increasingly abstract strategies in preparation for developing general area formulas for parallelograms and triangles.

This task asks students to find and use two different common denominators to add the given fractions. The purpose of this question is to help students realize that they can use any common denominator to find a solution, not just the least common denominator.

This task asks students to use two different denominators to subtract fractions. The purpose of this is to help students realize that any common denominator will work, not just the least common denominator.

In this task students have the opportunity to construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

This real world problem is appropriate for mental mathematics and students should be encouraged to think through the solution mentally.

The purpose of this task is to give 4th grade students a problem involving an unknown quantity that has a clear visual representation. Students must understand that the four interior angles of a rectangle are all right angles and that right angles have a measure of 90_ and that angle measure is additive.

This tasks examines how to calculate the area of an equilateral triangle using high school geometry.

Teachers can feel overwhelmed when faced with students who are unmotivated to learn. The task becomes less daunting, though, when teachers realize that they can boost student motivation in five important ways: by (1) making positive changes to the learning environment, (2) fostering a sense of community in the classroom, (3) enhancing the interest of classroom activities, (4) responding to individual learning challenges, and (5) building in additional outcomes/pay-offs for learning. Here are some ideas:

This task helps students solidify their understanding of linear functions and push them to be more fluent in their reasoning about slope and y-intercepts. This task has also produced a reasonable starting place for discussing point-slope form of a linear equation.

This task "Uses facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure (7.G.5)" except that it requires students to know, in addition, something about parallel lines, which students will not see until 8th grade.

This task asks students to solve addition and subtraction equations with different structures so that they are able to see the connections between addition and subtraction more easily.

In this task students are asked to write an equation to solve a real-world problem. There are two natural approaches to this task. In the first approach, students have to notice that even though there is one variable, namely the number of firefighters, it is used in two different places. In the other approach, students can find the total cost per firefighter and then write the equation.

This task is the first in a series of three tasks that use inequalities in the same context at increasing complexity in 6th grade, 7th grade and in HS algebra. Students write and solve inequalities, and represent the solutions graphically.

This task is the second in a series of three tasks that use inequalities in the same context at increasing complexity in 6th grade, 7th grade and in HS algebra. Students write and solve inequalities, and represent the solutions graphically.

This task is the last in a series of three tasks that use inequalities in the same context at increasing complexity in 6th grade, 7th grade and in HS algebra. Students write and solve inequalities, and represent the solutions graphically. The progression of the content standards is 6.EE.8 to 7.EE.4 to A-REI.12.