 Michael E. Smith Middle School
 State Standards
Bogacz, John
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 Problem of the Week #7
 State Standards

State Standards (Adapted from Big Ideas Math Website)
In Grade 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 threedimensional shapes to solve problems involving area, surface area, and volume; and (4) drawing inferences about populations based on samples.
 1. Students extend their understanding of ratios and develop understanding of proportionality to solve single and multistep 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.
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. 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. They use the arithmetic of rational numbers as they formulate expressions and equations in one variable and use these equations to solve problems.
3. Students continue their work with area from Grade 6, solving problems involving the area and circumference of a circle and surface area of threedimensional objects. In preparation for work on congruence and similarity in Grade 8 they reason about relationships among twodimensional figures using scale drawings and informal geometric constructions, and they gain familiarity with the relationships between angles formed by intersecting lines. Students work with threedimensional figures, relating them to twodimensional figures by examining crosssections. They solve realworld and mathematical problems involving area, surface area, and volume of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes and right prisms.
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.
Grade 7 Overview

Ratios and Proportional Relationships
 Analyze proportional relationships and use them to solve realworld and mathematical problems.

The Number System
 Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Expressions and Equations
 Use properties of operations to generate equivalent expressions.
 Solve reallife and mathematical problems using numerical and algebraic expressions and equations.

Geometry
 Draw, construct and describe geometrical figures and describe the relationships between them.
 Solve reallife and mathematical problems involving angle measure, area, surface area, and volume.

Statistics and Probability
 Use random sampling to draw inferences about a population.
 Draw informal comparative inferences about two populations.
 Investigate chance processes and develop, use, and evaluate probability models.

Mathematical Practices
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
 8. Look for and express regularity in repeated reasoning.