Grade 7 | Mathematics

Action steps

1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate in miles per hour.

2. Recognize and represent proportional relationships between quantities.

3. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane.

4. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

5. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

6. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

Action steps

1. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

2. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions.

Action steps

1. Know the formulas for the area and circumference of a circle and use them to solve problems.

2. Give an informal derivation of the relationship between the circumference and area of a circle.

3. Solve 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 prisms.

Action steps

1. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

2. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.

3. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative.

4. Show that a number and its opposite have a sum of 0 (are additive inverses).

5. Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q).

6. Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

7. Apply properties of operations as strategies to add and subtract rational numbers.

8. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers.

9. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number.

10. Convert a rational number to a decimal using long division.

11. Know that the decimal form of a rational number terminates in 0s or eventually repeats.

Action steps

1. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers.

2. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

Action steps

1. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population.

2. Understand that random sampling tends to produce representative samples and support valid inferences.

3. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest.

4. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book.

5. Predict the winner of a school election based on randomly sampled survey data.

6. Gauge how far off the estimate or prediction might be.

Action steps

1. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities.

2. Measure the difference between the centers of two numerical data distributions by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team. Plot the separation between the two distributions.

3. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

Action steps

1. Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring.

2. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.

3. Develop a probability model and use it to find probabilities of events.

4. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

5. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.

6. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down.

7. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

8. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

9. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?