**Mathematics 7 (Grade 6/7) Course Expectations**In Mathematics 7, instructional time should focus on four critical areas: (1) developing understanding of and applying proportional relationships; (2) developing understanding of operations with rational numbers and working with expressions and linear equations; (3) solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume; and (4) drawing inferences about populations based on samples.

**1. The Number System (7.NS)**Students develop a unified understanding of number, recognizing fractions, decimals (that have a finite or a repeating decimal representation), and percents as different representations of rational numbers. Students extend addition, subtraction, multiplication, and division to all rational numbers, maintaining the properties of operations and the relationships between addition and subtraction, and multiplication and division. By applying these properties, and by viewing negative numbers in terms of everyday contexts (e.g., amounts owed or temperatures below zero), students explain and interpret the rules for adding, subtracting, multiplying, and dividing with negative numbers

**2. Ratios and Proportional Relationships (7.RP/7.G)**

Students extend their understanding of ratios and develop understanding of proportionality to solve single- and multi-step problems. Students use their understanding of ratios and proportionality to solve a wide variety of percent problems, including those involving discounts, interest, taxes, tips, and percent increase or decrease. Students solve problems about scale drawings by relating corresponding lengths between the objects or by using the fact that relationships of lengths within an object are preserved in similar objects. Students graph proportional relationships and understand the unit rate informally as a measure of the steepness of the related line, called the slope. They distinguish proportional relationships from other relationships. Students will apply their understanding of proportional relationships to similar figures. Students also solve problems involving scale drawings of geometric figures, including reproducing a scale drawing at a different scale.

**3. Expressions and Equations (7.EE)**

In this unit, students use the arithmetic of rational numbers as they formulate expressions and equations in one variable and use these equations to solve problems. Students will understand and use properties of operations to generate equivalent expressions. Students use and solve real-life mathematical problems using numerical and algebraic expressions and equations. Also, students will use variables to represent quantities in a real-world or mathematical problem to construct and solve simple equations and inequalities in one and two step. In gaining the understanding of solving the one and two-step equations and inequalities, students will reason about the quantity of their solutions. In preparation for work on congruence and similarity in Grade 8 they gain familiarity with the relationships between angles formed by intersecting lines and solve for unknowns in a figure.

**4. Geometry (7.G)**

Students continue their work with area from Mathematics 6, solving problems involving the area and circumference of a circle and surface area of three-dimensional objects. In preparation for work on congruence and similarity in Grade 8 they reason about relationships among informal geometric constructions. Students work with three-dimensional figures, relating them to two-dimensional figures by examining cross-sections. They solve real-world and mathematical problems involving area, surface area, and volume of two-and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes and right prisms.

**5. Statistics and Probability (7.SP)**

Students build on their previous work with single data distributions to compare two data distributions and address questions about differences between populations. They begin informal work with random sampling to generate data sets and learn about the importance of representative samples for drawing inferences.

In Mathematics 7, students move from concentrating on analysis of data to production of data, understanding that good answers to statistical questions depend upon a good plan for collecting data relevant to the questions of interest. Because statistically sound data production is based on random sampling, a probabilistic concept, students must develop some knowledge of probability before launching into sampling. Their introduction to probability is based on seeing probabilities of chance events as long-run relative frequencies of their occurrence, and many opportunities to develop the connection between theoretical probability models and empirical probability approximations. This connection forms the basis of statistical inference. With random sampling as the key to collecting good data, students begin to differentiate between the variability in a sample and the variability inherent in a statistic computed from a sample when samples are repeatedly selected from the same population. This understanding of variability allows them to make rational decisions, say, about how different a proportion of “successes” in a sample is likely to be from the proportion of “successes” in the population or whether medians of samples from two populations provide convincing evidence that the medians of the two populations also differ.