In this problem students are comparing a very small quantity with a very large quantity using the metric system. The metric system is especially convenient when comparing measurements using scientific notations since different units within the system are related by powers of ten.
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This task requires students to work with very large and small values expressed both in scientific notation and in decimal notation (standard form). In addition, students need to convert units of mass.
This task provides a good entry point for students into representing quantities in contexts with variables and expressions and building equations that reflect the relationships presented in the context.
This task presents a real-world problem requiring the students to write linear equations to model different cell phone plans. Looking at the graphs of the lines in the context of the cell phone plans allows the students to connect the meaning of the intersection points of two lines with the simultaneous solution of two linear equations.
In this task students use different representations to analyze the relationship between two quantities and to solve a real world problem. The situation presented provides a good opportunity to make connections between the information provided by tables, graphs and equations.
This purpose of this task is to help students see two different ways to look at percentages both as a decrease and an increase of an original amount. In addition, students have to turn a verbal description of several operations into mathematical symbols.
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 problem asks the students to represent a sequence of operations using an expression and then to write and solve simple equations. The problem is posed as a game and allows the students to visualize mathematical operations. It would make sense to actually play a similar game in pairs first and then ask the students to record the operations to figure out each other's numbers.
The purpose of this task is to present students with a context that can naturally be represented with an inequality and to explore the relationship between the context and the mathematical representation of that context; thus, this is an intended as an instructional task.