# Critical Areas

This is copied from ACOS 2010. I have edited the format to highlight important information. Information I have added is in italics.

In Grade 7, instructional time should focus on four critical areas. These areas are
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
4. drawing inferences about populations based on samples.

Important information regarding these four critical areas of instruction follows:

(1) Students extend their understanding of ratios and develop understanding of proportionality to solve single- and multi-step problems. They 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. Standards: 1, 2, 3, 6, 11

(2) 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. They 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, such as amounts owed or temperatures below zero, students explain and interpret the rules for adding, subtracting, multiplying, and dividing with negative numbers. Students use the arithmetic of rational numbers as they formulate expressions and equations in one variable and use these equations to solve problems. Standards: 4, 5, 6, 7, 8, 9, 10

(3) Students continue their work with area from Grade 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 two-dimensional figures using scale drawings and informal geometric constructions, and they gain familiarity with the relationships between angles formed by intersecting lines. 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. Standards: 11, 12, 13, 14, 15, 16

(4) 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. Standards: 17, 18, 19, 20

Not addressed in critical areas: 21, 22, 23, 24 (probability)