# Grade 7 Mathematics Standards (Georgia)

> Georgia Standards of Excellence: Mathematics, Grade 7. 7 standards.
> Source: https://georgiahomeroom.org/standards/math/grade-7
> Interactive explorer: https://georgiahomeroom.org/explorer?subject=math&grade=07

## Numerical Reasoning (NR)

Numerical Reasoning. Place value, fractions, decimals, integers — the spine of K-8 number sense.

### 7.NR.1: Rational Number Operations

Solve relevant, mathematical problems, including multi-step problems, involving the four operations with rational numbers and quantities in any form (integers, percentages, fractions, and decimal numbers).

- **7.NR.1.1**: Show that a number and its opposite have a sum of 0 (are additive inverses). Describe situations in which opposite quantities combine to make 0.
- **7.NR.1.2**: Show and explain $p + q$ as the number located a distance $|q|$ from $p$, in the positive or negative direction, depending on whether $q$ is positive or negative. Interpret sums of rational numbers by describing applicable situations.
- **7.NR.1.3**: Represent addition and subtraction with rational numbers on a horizontal or a vertical number line diagram to solve authentic problems.
- **7.NR.1.4**: Show and explain 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 contextual situations.
- **7.NR.1.5**: Apply properties of operations, including part-whole reasoning, as strategies to add and subtract rational numbers.
- **7.NR.1.6**: Make sense of multiplication of rational numbers using realistic applications.
- **7.NR.1.7**: Show and explain that integers can be divided, assuming the divisor is not zero, and every quotient of integers is a rational number.
- **7.NR.1.8**: Represent the multiplication and division of integers using a variety of strategies and interpret products and quotients of rational numbers by describing them based on the relevant situation.
- **7.NR.1.9**: Apply properties of operations as strategies to solve multiplication and division problems involving rational numbers represented in an applicable scenario.
- **7.NR.1.10**: Convert rational numbers between forms to include fractions, decimal numbers and percentages, using understanding of the part divided by the whole. Know that the decimal form of a rational number terminates in 0s or eventually repeats.
- **7.NR.1.11**: Solve multi-step, contextual problems involving rational numbers, converting between forms as appropriate, and assessing the reasonableness of answers using mental computation and estimation strategies.

## Patterning & Algebraic Reasoning (PAR)

Patterning & Algebraic Reasoning. Patterns build into expressions and equations across K-8.

### 7.PAR.2: Equivalent Algebraic Expressions

Use properties of operations, generate equivalent expressions and interpret the expressions to explain relevant contextual situations.

- **7.PAR.2.1**: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
- **7.PAR.2.2**: Rewrite an expression in different forms from a contextual problem to clarify the problem and show how the quantities in it are related.

### 7.PAR.3: Equations and Inequalities

Represent authentic situations using equations and inequalities with variables; solve equations and inequalities symbolically, using the properties of equality.

- **7.PAR.3.1**: Construct algebraic equations to solve practical problems leading to equations of the form $px + q = r$ and $p(x + q) = r$, where $p$, $q$, and $r$ are specific rational numbers. Interpret the solution based on the situation.
- **7.PAR.3.2**: Construct algebraic inequalities to solve problems, leading to inequalities of the form $px ± q \gt r$, $px ± q \lt r$, $px ± q \le r$, or $px ± q \ge r$, where $p$, $q$, and $r$ are specific rational numbers. Graph and interpret the solution based on the realistic situation that the inequalities represent.

### 7.PAR.4: Proportional Relationships

Recognize proportional relationships in relevant, mathematical problems; represent, solve, and explain these relationships with tables, graphs, and equations.

- **7.PAR.4.1**: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units presented in realistic problems.
- **7.PAR.4.2**: Determine the unit rate (constant of proportionality) in tables, graphs (1, r), equations, diagrams, and verbal descriptions of proportional relationships to solve realistic problems.
- **7.PAR.4.3**: Determine whether two quantities presented in authentic problems are in a proportional relationship.
- **7.PAR.4.4**: Identify, represent, and use proportional relationships.
- **7.PAR.4.5**: Use context to 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.
- **7.PAR.4.6**: Solve everyday 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.
- **7.PAR.4.7**: Use similar triangles to explain why the slope, m, is the same between any two distinct points on a nonvertical line in the coordinate plane.
- **7.PAR.4.8**: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
- **7.PAR.4.9**: Use proportional relationships to solve multi-step ratio and percent problems presented in applicable situations.
- **7.PAR.4.10**: Predict characteristics of a population by examining the characteristics of a representative sample. Recognize the potential limitations and scope of the sample to the population.
- **7.PAR.4.11**: Analyze sampling methods and conclude that random sampling produces and supports valid inferences.
- **7.PAR.4.12**: Use data from repeated random samples to evaluate how much a sample mean is expected to vary from a population mean. Simulate multiple samples of the same size.

## Geometric & Spatial Reasoning (GSR)

Geometric & Spatial Reasoning. Shapes, area, volume, and transformations from K through high school.

### 7.GSR.5: Angles, Circles & 3D Figures

Solve practical problems involving angle measurement, circles, area of circles, surface area of prisms and cylinders, and volume of cylinders and prisms composed of cubes and right prisms.

- **7.GSR.5.1**: Measure angles in whole nonstandard units.
- **7.GSR.5.2**: Measure angles in whole number degrees using a protractor.
- **7.GSR.5.3**: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve equations for an unknown angle in a figure.
- **7.GSR.5.4**: Explore and describe the relationship between pi, radius, diameter, circumference, and area of a circle to derive the formulas for the circumference and area of a circle.
- **7.GSR.5.5**: Given the formula for the area and circumference of a circle, solve problems that exist in everyday life.
- **7.GSR.5.6**: Solve realistic problems involving surface area of right prisms and cylinders.
- **7.GSR.5.7**: Describe the two-dimensional figures (cross sections) that result from slicing three-dimensional figures, as in the plane sections of right rectangular prisms, right rectangular pyramids, cones, cylinders, and spheres.
- **7.GSR.5.8**: Explore volume as a measurable attribute of cylinders and right prisms. Find the volume of these geometric figures using concrete problems.

## Mathematical Practices (MP)

Mathematical Practices. Cross-grade habits of mind: perseverance, precision, argument.

### 7.MP: Mathematical Practices Overview

Display perseverance and patience in problem-solving. Demonstrate skills and strategies needed to succeed in mathematics, including critical thinking, reasoning, and effective collaboration and expression. Seek help and apply feedback. Set and monitor goals.

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

## Probability Reasoning (PR)

Probability Reasoning. Grade 7 probability content.

### 7.PR.6: Simple Event Probability Models

Using mathematical reasoning, investigate chance processes and develop, evaluate, and use probability models to find probabilities of simple events presented in authentic situations.

- **7.PR.6.1**: Represent the probability of a chance event as a number between 0 and 1 that expresses the likelihood of the event occurring. Describe that a probability near 0 indicates an unlikely event, a probability around $\frac{1}{2}$ indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
- **7.PR.6.2**: Approximate the probability of a chance event by collecting data on an event and observing its long-run relative frequency will approach the theoretical probability.
- **7.PR.6.3**: Develop a probability model and use it to find probabilities of simple events. Compare experimental and theoretical probabilities of events. If the probabilities are not close, explain possible sources of the discrepancy.
- **7.PR.6.4**: Develop a uniform probability model by assigning equal probability to all outcomes and use the model to determine probabilities of events.
- **7.PR.6.5**: Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.
- **7.PR.6.6**: Use appropriate graphical displays and numerical summaries from data distributions with categorical or quantitative (numerical) variables as probability models to draw informal inferences about two samples or populations.