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Mathematics Grade 7

Common Core Standards

Mathematics: Grade 7

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 three-dimensional shapes to solve problems involving area, surface area, and volume; and (4) drawing inferences about populations based on samples.
Sophia and Common Core Standards
Our Many Ways to Learn method makes it easy to integrate the new standards into your teaching. By using multiple instructors and teaching styles for each tutorial, we make sure you're reaching your students, so they can reach their goals.
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7.RP - Ratios and Proportional Relationships

Analyze proportional relationships and use them to solve real-world and mathematical problems.

7.NS - The Number System

Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
Code
Standard
Concepts
7.NS.1c
Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). 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.
1
7.NS.1d
Apply properties of operations as strategies to add and subtract rational numbers.
2
7.NS.2a
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. Interpret products of rational numbers by describing real-world contexts.
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7.NS.2b
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. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real- world contexts.
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7.NS.2c
Apply properties of operations as strategies to multiply and divide rational numbers.
6
7.NS.2d
Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.
1
7.NS.3
Solve real-world and mathematical problems involving the four operations with rational numbers.
23

7.EE - Expressions and Equations

Use properties of operations to generate equivalent expressions.
Code
Standard
Concepts
7.EE.1
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
6
Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
Code
Standard
Concepts
7.EE.3
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.
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7.EE.4b
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. 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.
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7.G - Geometry

7.SP - Statistics and Probability

Draw informal comparative inferences about two populations.
Code
Standard
Concepts
Investigate chance processes and develop, use, and evaluate probability models.
Code
Standard
Concepts
7.SP.5
Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
4
7.SP.7a
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
7.SP.7b
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. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?
4
7.SP.8a
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.
8
7.SP.8b
Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.
3