## Course I

In Course 1 instructional time should focus on four critical areas: (1) connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; (3) writing, interpreting, and using expressions and equations; and (4) developing understanding of statistical thinking.

Students should also build on their prior knowledge by reasoning about relationships among shapes to determine area (triangles and quadrilaterals), surface area (prisms & pyramids), and volume (prisms & pyramids).

- Students use reasoning about multiplication and division to solve ratio and rate problems about quantities. By viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative size of quantities, students connect their understanding of multiplication and division with ratios and rates.
- Students use the meaning of fractions, the meanings of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for dividing fractions make sense.
- Students understand the use of variables in mathematical expressions. They write expressions and equations that correspond to given situations, evaluate expressions, and use expressions and formulas to solve problems.
- Students begin to develop their ability to think statistically.

Students should also build on their prior knowledge by reasoning about relationships among shapes to determine area (triangles and quadrilaterals), surface area (prisms & pyramids), and volume (prisms & pyramids).