Describing
series of calculations using operation strings, generalizing to find a formula,
and representing relationships found in tables.
Many problems in Expressions
and Formulas are presented in the
context of buying and selling. Students make change and determine grocery bills
that involve produce, meat, or cheese sold by the pound. They also find prices
in nongrocery contexts, such as calculating a plumber’s bill. To keep track of
the complicated sequences of calculations necessary to do these problems,
students are introduced to several new tools. As problems and calculations
become more complicated, students adapt their arrow language to include multiplication
and division. When dealing with all four arithmetic operations, students learn
about the order of operations and use another new tool—arithmetic trees—to help
them organize their work and prioritize their calculations. Finally, students
begin to generalize their calculations for specific problems using word
formulas. For example, in a problem about buying tomatoes, grapes, and green
beans at different unit prices, students consider the following formula:
amount of tomatoes x $1.50 +
amount of grapes x $1.70 +
amount of green
beans x $0.90 = total cost
Mathematical Content:
• using word variables and formulas
• performing a series of calculations
• expanding tables and charts
• discovering patterns and regularities
• applying the order of operations
• using inverse (or reverse) operations
• using smart calculations and grouping symbols