The most engaging way to practice counting with students is to have them count meaningful things in their lives. Since five-year-olds are very focused on themselves this is easily done by allowing them to count themselves, their friends and objects within the classroom that relate to their daily lives.

This challenging problem and brainteaser gives first graders an opportunity to compose and decompose squares.

This is an instructional task related to deepening place-value concepts. The important piece of knowledge upon which students need to draw is that 10 tens is 1 hundred.

The objective of this lesson is to gain automaticity counting to 100 and to establish the importance of multiples of ten. The final goal of this lesson is for students to be able to count by tens and articulate the term for this.

This task involves solving equations with rational coefficients, and requires students to use the distributive law ("combine like terms"). The equation also provides opportunities for students to observe structure in the equation to find a quicker solution, as in the second solution presented.

This task presents a real world application of finite geometric series. The context can lead into several interesting follow-up questions and projects. Many drugs only become effective after the amount in the body builds up to a certain level. This can be modeled very well with geometric series.

This task presents a real world application of finite geometric series. The context can lead into several interesting follow-up questions and projects. Many drugs only become effective after the amount in the body builds up to a certain level. This can be modeled very well with geometric series.

Students practice crossing from one family to the next in counting forward with this concentration game.

This word problem requires students to create expressions to calculate gas milage for a vehicle.

In this task students are asked to write expressions about the relation to the price of oil and gas mileage.

This Illustrative Mathematics task presents a challenging exercise in both algebraic manipulations and seeing structure in algebraic expressions.

One common mistake students make when dividing fractions using visuals is the confusion between remainder and the fractional part of a mixed number answer.

The purpose of this task is to introduce or reinforce the concept of a function, especially in a context where the function is not given by an explicit algebraic representation. Further, the last part of the task emphasizes the significance of one variable being a function of another variable in an immediately relevant real-life context. Instructors might prepare themselves for variations on the problems that the students might wander into (e.g., whether one person could have two home phone numbers) and how such variants affect the correct responses.

The purpose of this task is to introduce or reinforce the concept of a function, especially in a context where the function is not given by an explicit algebraic representation. Further, the last part of the task emphasizes the significance of one variable being a function of another variable in an immediately relevant real-life context.

The purpose of this task is for students to encounter negative exponents in a natural way in the course of learning about exponential functions.

The purpose of this task is to help students explore the meaning of fraction division and to connect it to what they know about whole-number division.