MAFS.7.EE.1.2
Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that increase by 5% is the same as multiply by 1.05.

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**Content Complexity:**
Level 2: Basic Application of Skills & Concepts

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Use properties of operations to generate...__

MAFS.7.EE.2.3
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. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

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**Content Complexity:**
Level 2: Basic Application of Skills & Concepts

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Solve real-life and mathematical problems...__

Remarks/Examples:

**Fluency Expectations or Examples of Culminating Standards **

Students solve multistep problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. This work is the culmination of many progressions of learning in arithmetic, problem solving and mathematical practices.

**Examples of Opportunities for In-Depth Focus **

This is a major capstone standard for arithmetic and its applications.

MAFS.7.EE.2.4
Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?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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**Content Complexity:**
Level 2: Basic Application of Skills & Concepts

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Solve real-life and mathematical problems...__

Remarks/Examples:

**Fluency Expectations or Examples of Culminating Standards **

In solving word problems leading to one-variable equations of the form px + q = r and p(x + q) = r, students solve the equations fluently. This will require fluency with rational number arithmetic (7.NS.1.1–1.3), as well as fluency to some extent with applying properties operations to rewrite linear expressions with rational coefficients (7.EE.1.1).

**Examples of Opportunities for In-Depth Focus **

Work toward meeting this standard builds on the work that led to meeting 6.EE.2.7 and prepares students for the work that will lead to meeting 8.EE.3.7.

MAFS.7.G.1.1
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.

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**Content Complexity:**
Level 2: Basic Application of Skills & Concepts

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Draw, construct, and describe geometrical...__

MAFS.7.G.1.2
Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus 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.

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**Content Complexity:**
Level 2: Basic Application of Skills & Concepts

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Draw, construct, and describe geometrical...__

MAFS.7.G.2.4
Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

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**Content Complexity:**
Level 2: Basic Application of Skills & Concepts

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Solve real-life and mathematical problems...__

MAFS.7.G.2.6
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.

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**Content Complexity:**
Level 2: Basic Application of Skills & Concepts

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Solve real-life and mathematical problems...__

Remarks/Examples:

**Examples of Opportunities for In-Depth Focus
**

Work toward meeting this standard draws together grades 3–6 work with geometric measurement.

MAFS.7.NS.1.1
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. 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.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. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.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.Apply properties of operations as strategies to add and subtract rational numbers.

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**Content Complexity:**
Level 2: Basic Application of Skills & Concepts

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Apply and extend previous understandings of...__

Remarks/Examples:

**Fluency Expectations or Examples of Culminating Standards **

Adding, subtracting, multiplying, and dividing rational numbers is the culmination of numerical work with the four basic operations. The number system will continue to develop in grade 8, expanding to become the real numbers by the introduction of irrational numbers, and will develop further in high school, expanding to become the complex numbers with the introduction of imaginary numbers. Because there are no specific standards for rational number arithmetic in later grades and because so much other work in grade 7 depends on rational number arithmetic, fluency with rational number arithmetic should be the goal in grade 7.

MAFS.7.NS.1.2
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. 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.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.Apply properties of operations as strategies to multiply and divide rational numbers.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.

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**Content Complexity:**
Level 2: Basic Application of Skills & Concepts

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Apply and extend previous understandings of...__

Remarks/Examples:

**Fluency Expectations or Examples of Culminating Standards**

Adding, subtracting, multiplying, and dividing rational numbers is the culmination of numerical work with the four basic operations. The number system will continue to develop in grade 8, expanding to become the real numbers by the introduction of irrational numbers, and will develop further in high school, expanding to become the complex numbers with the introduction of imaginary numbers. Because there are no specific standards for rational number arithmetic in later grades and because so much other work in grade 7 depends on rational number arithmetic, fluency with rational number arithmetic should be the goal in grade 7.

MAFS.7.NS.1.3
Solve real-world and mathematical problems involving the four operations with rational numbers.

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**Content Complexity:**
Level 2: Basic Application of Skills & Concepts

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Apply and extend previous understandings of...__

Remarks/Examples:

**Examples of Opportunities for In-Depth Focus **

When students work toward meeting this standard (which is closely connected to 7.NS.1.1 and 7.NS.1.2), they consolidate their skill and understanding of addition, subtraction, multiplication and division of rational numbers.

MAFS.7.RP.1.1
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 as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

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**Content Complexity:**
Level 2: Basic Application of Skills & Concepts

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Analyze proportional relationships and use...__

MAFS.7.RP.1.2
Recognize and represent proportional relationships between quantities. 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 and observing whether the graph is a straight line through the origin.Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.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.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.

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**Content Complexity:**
Level 2: Basic Application of Skills & Concepts

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Analyze proportional relationships and use...__

Remarks/Examples:

**Examples of Opportunities for In-Depth Focus **

Students in grade 7 grow in their ability to recognize, represent, and analyze proportional relationships in various ways, including by using tables, graphs, and equations.

MAFS.7.RP.1.3
Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

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**Content Complexity:**
Level 2: Basic Application of Skills & Concepts

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Analyze proportional relationships and use...__

MAFS.7.SP.1.1
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. Understand that random sampling tends to produce representative samples and support valid inferences.

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**Content Complexity:**
Level 2: Basic Application of Skills & Concepts

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Use random sampling to draw inferences about...__

MAFS.7.SP.1.2
Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. 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; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

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**Content Complexity:**
Level 3: Strategic Thinking & Complex Reasoning

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Use random sampling to draw inferences about...__

MAFS.7.SP.2.3
Informally 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. 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, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.

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**Content Complexity:**
Level 2: Basic Application of Skills & Concepts

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Draw informal comparative inferences about...__

MAFS.7.SP.2.4
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.

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**Content Complexity:**
Level 2: Basic Application of Skills & Concepts

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Draw informal comparative inferences about...__

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