7: Grade 7

Grade 7

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Proportional relationships and rational number operations extend to multi-step real-world problems. Linear expressions and equations, including two-step inequalities, deepen algebraic reasoning. Geometry covers area, surface area, volume, circles, cross-sections, scale drawings, and rigid motion congruence; statistics introduces probability models, data distributions, and study design.

7.1Calculate unit rates of length, area, and other quantities measured in like or different units that include ratios or fractions.7.10Examine a sample of a population to generalize information about the population.7.11Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability.7.12Make informal comparative inferences about two populations using measures of center and variability and/or mean absolute deviation in context.7.13Use a number from 0 to 1 to represent the probability of a chance event occurring, explaining that larger numbers indicate greater likelihood of the event occurring, while a number near zero indicates an unlikely event.7.14Define and develop a probability model, including models that may or may not be uniform, where uniform models assign equal probability to all outcomes and non-uniform models involve events that are not equally likely.7.15Approximate the probability of an event using data generated by a simulation (experimental probability) and compare it to the theoretical probability.7.16Find probabilities of simple and compound events through experimentation or simulation and by analyzing the sample space, representing the probabilities as percents, decimals, or fractions.7.17Solve problems involving scale drawings of geometric figures, including computation of actual lengths and areas from a scale drawing and reproduction of a scale drawing at a different scale.7.18Construct geometric shapes (freehand, using a ruler and a protractor, and using technology), given a written description or measurement constraints with an emphasis on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.7.19Describe the two-dimensional figures created by slicing three-dimensional figures into plane sections.7.2Represent a relationship between two quantities and determine whether the two quantities are related proportionally.7.20Explain the relationships among circumference, diameter, area, and radius of a circle to demonstrate understanding of formulas for the area and circumference of a circle.7.21Use facts about supplementary, complementary, vertical, and adjacent angles in multi-step problems to write and solve simple equations for an unknown angle in a figure.7.22Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right rectangular prisms.7.3Solve multi-step percent problems in context using proportional reasoning, including simple interest, tax, gratuities, commissions, fees, markups and markdowns, percent increase, and percent decrease.7.4Apply and extend knowledge of operations of whole numbers, fractions, and decimals to add, subtract, multiply, and divide rational numbers including integers, signed fractions, and decimals.7.5Solve real-world and mathematical problems involving the four operations of rational numbers, including complex fractions. Apply properties of operations as strategies where applicable.7.6Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.7.7Generate expressions in equivalent forms based on context and explain how the quantities are related.7.8Solve multi-step real-world and mathematical problems involving rational numbers (integers, signed fractions and decimals), converting between forms as needed. Assess the reasonableness of answers using mental computation and estimation strategies.7.9Use variables to represent quantities in real-world or mathematical problems and construct algebraic expressions, equations, and inequalities to solve problems by reasoning about the quantities.
Example Problems
Julio pays $18 for pounds of coffee.

What is the cost per pound of coffee?
The Metro Cinema surveyed a random sample of 70 moviegoers about concession purchases.
Of the moviegoers surveyed, 49 said they buy popcorn. The cinema sells tickets to 2,100 patrons per week.
Based on the data, what is the most reasonable estimate for the number of weekly patrons who buy popcorn?
What is the mean of the following numbers?
You flip a fair coin.

What is ?
A bag contains 9 blue candies, 7 red candies and 5 green candies.
A candy is chosen from the bag at random.

Find the probability that the candy is: Not Orange
Goblins

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