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NC.7.EE.Expressions and Equations
Expressions and Equations
Solve real-world and mathematical problems using numerical and algebraic expressions, equations, and inequalities. NC.7.EE.3. Solve multi-step real-world and mathematical problems posed with rational numbers in algebraic expressions. NC.7.EE.3.a. Apply properties of operations to calculate with positive and negative numbers in any form.
NC.7.EE.3.b. Convert between different forms of a number and equivalent forms of the expression as appropriate. Quiz, Flash Cards, Worksheet, Game & Study Guide Percentage
NC.7.EE.4. Use variables to represent quantities to solve real-world or mathematical problems. NC.7.EE.4.a. Construct equations to solve problems by reasoning about the quantities. NC.7.EE.4.a.1. Fluently solve multistep equations with the variable on one side, including those generated by word problems.
NC.7.EE.4.a.2. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. Quiz, Flash Cards, Worksheet, Game & Study Guide Formulas Quiz, Flash Cards, Worksheet, Game & Study Guide Functions Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
NC.7.EE.4.a.3. Interpret the solution in context.
NC.7.EE.4.b. Construct inequalities to solve problems by reasoning about the quantities. NC.7.EE.4.b.1. Fluently solve multi-step inequalities with the variable on one side, including those generated by word problems.
NC.7.EE.4.b.2. Compare an algebraic solution process for equations and an algebraic solution process for inequalities.
NC.7.EE.4.b.3. Graph the solution set of the inequality and interpret in context.
Draw, construct, and describe geometrical figures and describe the relationships between them. NC.7.G.1. Solve problems involving scale drawings of geometric figures by: NC.7.G.1.a. Building an understanding that angle measures remain the same and side lengths are proportional.
NC.7.G.1.b. Using a scale factor to compute actual lengths and areas from a scale drawing.
Solve real-world and mathematical problems involving angle measure, area, surface area, and volume. NC.7.G.4. Understand area and circumference of a circle. NC.7.G.4.a. Understand the relationships between the radius, diameter, circumference, and area. Quiz, Flash Cards, Worksheet, Game & Study Guide Area
NC.7.G.4.b. Apply the formulas for area and circumference of a circle to solve problems. Quiz, Flash Cards, Worksheet, Game & Study Guide Area Quiz, Flash Cards, Worksheet, Game & Study Guide Formulas
NC.7.G.5. 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.
NC.7.NS.The Number System
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. NC.7.NS.1. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers, using the properties of operations, and describing real-world contexts using sums and differences.
NC.7.NS.2. Apply and extend previous understandings of multiplication and division. NC.7.NS.2.a. Understand that a rational number is any number that can be written as a quotient of integers with a non-zero divisor.
NC.7.NS.2.b. Apply properties of operations as strategies, including the standard algorithms, to multiply and divide rational numbers and describe the product and quotient in real-world contexts.
NC.7.NS.2.c. Use division and previous understandings of fractions and decimals. NC.7.NS.2.c.1. Convert a fraction to a decimal using long division. Quiz, Flash Cards, Worksheet, Game & Study Guide Percentage
NC.7.NS.2.c.2. Understand that the decimal form of a rational number terminates in 0s or eventually repeats.
NC.7.NS.3. Solve real-world and mathematical problems involving numerical expressions with rational numbers using the four operations. Quiz, Flash Cards, Worksheet, Game & Study Guide Percentage
NC.7.RP.Ratio and Proportional Relationships
Ratio and Proportional Relationships
Analyze proportional relationships and use them to solve real-world and mathematical problems. NC.7.RP.1. Compute unit rates associated with ratios of fractions to solve real-world and mathematical problems.
NC.7.RP.2. Recognize and represent proportional relationships between quantities. NC.7.RP.2.a. Understand that a proportion is a relationship of equality between ratios. NC.7.RP.2.a.1. Represent proportional relationships using tables and graphs.
NC.7.RP.2.a.2. Recognize whether ratios are in a proportional relationship using tables and graphs.
NC.7.RP.2.a.3. Compare two different proportional relationships using tables, graphs, equations, and verbal descriptions.
NC.7.RP.2.b. Identify the unit rate (constant of proportionality) within two quantities in a proportional relationship using tables, graphs, equations, and verbal descriptions.
NC.7.RP.2.c. Create equations and graphs to represent proportional relationships.
NC.7.RP.3. Use scale factors and unit rates in proportional relationships to solve ratio and percent problems.
NC.7.SP.Statistics and Probability
Statistics and Probability
Use random sampling to draw inferences about a population. NC.7.SP.1. Understand that statistics can be used to gain information about a population by: NC.7.SP.1.a. Recognizing that generalizations about a population from a sample are valid only if the sample is representative of that population.
NC.7.SP.1.b. Using random sampling to produce representative samples to support valid inferences.
NC.7.SP.2. Generate multiple random samples (or simulated samples) of the same size to gauge the variation in estimates or predictions, and use this data to draw inferences about a population with an unknown characteristic of interest.
Make informal inferences to compare two populations. NC.7.SP.3. Recognize the role of variability when comparing two populations. NC.7.SP.3.a. Calculate the measure of variability of a data set and understand that it describes how the values of the data set vary with a single number. NC.7.SP.3.a.2. Understand that the range describes the spread of the entire data set. Quiz, Flash Cards, Worksheet, Game & Study Guide Statistics
Investigate chance processes and develop, use, and evaluate probability models. NC.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. Quiz, Flash Cards, Worksheet, Game & Study Guide Probability
NC.7.SP.6. Collect data to calculate the experimental probability of a chance event, observing its long-run relative frequency. Use this experimental probability to predict the approximate relative frequency.
NC.7.SP.7. Develop a probability model and use it to find probabilities of simple events. NC.7.SP.7.a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.
NC.7.SP.7.b. Develop a probability model (which may not be uniform) by repeatedly performing a chance process and observing frequencies in the data generated.
NC.7.SP.7.c. Compare theoretical and experimental probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.
NC.7.SP.8. Determine probabilities of compound events using organized lists, tables, tree diagrams, and simulation. NC.7.SP.8.a. 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.
NC.MP.Standards for Mathematical Practice
Standards for Mathematical Practice
MP.1. Make sense of problems and persevere in solving them.
MP.2. Reason abstractly and quantitatively.