This simple conceptual task focuses on what it means for a number to be a solution to an equation, rather than on the process of solving equations.

This task provides a context where it is appropriate for students to subtract fractions with a common denominator; it could be used for either assessment or instructional purposes.

This task allows students to reason about the relative costs per pound of the two fruits without actually knowing what the costs are. Students who find this difficult may add a scale to the graph and reason about the meanings of the ordered pairs. Comparing the two approaches in a class discussion can be a profitable way to help students make sense of slope.

This word problem requires students to use addition and subtraction and think about money.

The purpose of the task is to use the given prices of stuffed animals at the “pet shop” to solve problems using money. The students need to use their coins or bills to help them solve each problem.

This task was designed to support students to make sense of problems and persevere to solve them (MP1) and understand the relationship between addition and subtraction. Students will solve the take from, change unknown problem, and through a teacher-facilitated discussion, understand that the problem can be solved using addition or subtraction.

This task requires students to answer questions about the structure of an expression.

The purpose of this task is for students to select 2 numbers from a set of 3 that sum to 9. The task can be completed for sums equaling any number. Teachers may choose to ask students to write the simple equations they select.

This is a choral counting activity that can be easily adjusted as students learn higher numbers.

This task requires students to use functions to calculate how to best benefit from a pizza promotion.

Though this task primarily deals with comparing decimal numbers on a number line, it also requires students to draw upon what they know about the base ten system.

This task can be implemented in a variety of ways. For a class with previous exposure to properties of perpendicular bisectors, part (a) could be a quick exercise in geometric constructions, and an application of the result. Alternatively, this could be part of an introduction to perpendicular bisectors, culminating in a full proof that the three perpendicular bisectors are concurrent at the circumcenter of the triangle, an essentially complete proof of which is found in the solution below.

This is a simple exercise in creating equations from a situation with many variables. By giving three different scenarios, the problem requires students to keep going back to the definitions of the variables, thus emphasizing the importance of defining variables when you write an equation. In order to reinforce this aspect of the problem, the variables have not been given names that remind the student of what they stand for. The emphasis here is on setting up equations, not solving them.

The purpose of this task is to have students add mixed numbers with like denominators. This task illustrates the different kinds of solution approaches students might take to such a task.

This task is part of a series presenting important foundational geometric results and constructions which are fundamental for more elaborate arguments. They are presented without a real world context so as to see the important hypotheses and logical steps involved as clearly as possible.

This task is designed to get at a common student confusion between the independent and dependent variables. This confusion often arises in situations like (b), where students are asked to solve an equation involving a function, and confuse that operation with evaluating the function.

In this task students construct and compare linear and exponential functions and find where the two functions intersect. One purpose of this task is to demonstrate that exponential functions grow faster than linear functions even if the linear function has a higher initial value and even if we increase the slope of the line. This task could be used as an introduction to this idea.

The purpose of this task is to help students see that when you have a context that can be modeled with a ratio and associated unit rate, there is almost always another ratio with its associated unit rate (the only exception is when one of the quantities is zero), and to encourage students to flexibly choose either unit rate depending on the question at hand.

This task compares the usefulness of different forms of a quadratic expression. Students have to choose which form most easily provides information about the maximum value, the zeros and the vertical intercept of a quadratic expression in the context of a real world situation. Rather than just manipulating one form into the other, students can make sense out of the structure of the expressions.