This is the year math leans into proportional thinking. Students work with ratios, percents, and scale drawings, and they handle negative numbers in everyday situations like temperature drops and account balances. They also start solving multi-step equations with a variable and using probability to predict how often something will happen. By spring, students can set up an equation from a word problem, solve it, and explain what the answer means.
Students start the year adding, subtracting, multiplying, and dividing with negatives, fractions, and decimals all mixed together. They also learn why some fractions turn into repeating decimals when you divide.
Students use ratios and unit rates to solve everyday problems like tips, discounts, taxes, and recipes. They learn to spot when two quantities grow together at a steady rate and read that rate off a table or graph.
Students rewrite expressions to see them in simpler ways and solve multi-step equations with a variable like x. They also solve inequalities and graph the answer on a number line.
Students work with scale drawings, build triangles from given measurements, and find the area and circumference of circles. They also find missing angles in a figure and work out the area, surface area, and volume of shapes they can see around the house.
Students learn how a small sample can stand in for a larger group and how to compare two groups using averages and spread. They also figure out the chance of an event, run simple experiments, and predict how often something will happen.
Scale drawings shrink or stretch real shapes while keeping every angle the same. Students use the scale factor to find actual lengths and areas, then create their own scale drawings.
Given three angle or side measurements, students figure out whether those numbers can form exactly one triangle, many different triangles, or no triangle at all. Then they build the triangle to check.
Students learn how the radius, diameter, and circumference of a circle connect to each other, then use those relationships to calculate how far around a circle is and how much space it covers inside.
When two angles share a line or a corner, their measures follow rules. Students use those rules to write and solve equations that find a missing angle in a figure.
Students find the area, perimeter, volume, and surface area of shapes built from triangles, rectangles, and other polygons. That includes flat figures and 3-D objects like prisms and pyramids.
| Standard | Definition | Code |
|---|---|---|
| Solve problems involving scale drawings of geometric figures… | Scale drawings shrink or stretch real shapes while keeping every angle the same. Students use the scale factor to find actual lengths and areas, then create their own scale drawings. | NC.7.G.1 |
| Understand the characteristics of angles and side lengths that create a unique… | Given three angle or side measurements, students figure out whether those numbers can form exactly one triangle, many different triangles, or no triangle at all. Then they build the triangle to check. | NC.7.G.2 |
| Understand area and circumference of a circle.<ul><li>Understand the… | Students learn how the radius, diameter, and circumference of a circle connect to each other, then use those relationships to calculate how far around a circle is and how much space it covers inside. | NC.7.G.4 |
| Use facts about supplementary, complementary, vertical | When two angles share a line or a corner, their measures follow rules. Students use those rules to write and solve equations that find a missing angle in a figure. | NC.7.G.5 |
| Solve real-world and mathematical problems involving:<ul><li>Area and perimeter… | Students find the area, perimeter, volume, and surface area of shapes built from triangles, rectangles, and other polygons. That includes flat figures and 3-D objects like prisms and pyramids. | NC.7.G.6 |
Divide two fractions to find a rate, like miles per hour or price per ounce. Students use that rate to solve everyday problems involving speed, cost, or similar comparisons.
Two quantities share a proportional relationship when they grow or shrink at the same rate. Students identify that connection in tables, graphs, and equations, then use it to solve problems like finding the best price per item or how far a car travels at a steady speed.
Students learn to spot when two ratios stay equal as numbers grow, like miles per hour staying constant on a road trip. They show those relationships in tables and graphs, and compare two proportional situations side by side.
Students find the "per one" rate hiding inside a proportional relationship, whether it's shown as a table, a graph, an equation, or a written description. For example, if a car travels 150 miles in 3 hours, the unit rate is 50 miles per hour.
Students write equations and draw graphs that show proportional relationships, like how total cost changes as the number of items increases. Both forms show the same relationship in different ways.
Students read a graph showing a proportional relationship and explain what specific points mean in context. They identify why the line passes through (0, 0) and what the point (1, r) reveals about the unit rate.
Students use ratios and percentages to solve everyday problems, like figuring out a sale price, a tax amount, or how far a map distance translates to real miles. The math stays the same whether the numbers involve money, distance, or time.
| Standard | Definition | Code |
|---|---|---|
| Compute unit rates associated with ratios of fractions to solve real-world and… | Divide two fractions to find a rate, like miles per hour or price per ounce. Students use that rate to solve everyday problems involving speed, cost, or similar comparisons. | NC.7.RP.1 |
| Recognize and represent proportional relationships between quantities | Two quantities share a proportional relationship when they grow or shrink at the same rate. Students identify that connection in tables, graphs, and equations, then use it to solve problems like finding the best price per item or how far a car travels at a steady speed. | NC.7.RP.2 |
| Understand that a proportion is a relationship of equality between… | Students learn to spot when two ratios stay equal as numbers grow, like miles per hour staying constant on a road trip. They show those relationships in tables and graphs, and compare two proportional situations side by side. | NC.7.RP.2.a |
| Identify the unit rate | Students find the "per one" rate hiding inside a proportional relationship, whether it's shown as a table, a graph, an equation, or a written description. For example, if a car travels 150 miles in 3 hours, the unit rate is 50 miles per hour. | NC.7.RP.2.b |
| Create equations and graphs to represent proportional relationships | Students write equations and draw graphs that show proportional relationships, like how total cost changes as the number of items increases. Both forms show the same relationship in different ways. | NC.7.RP.2.c |
| Use a graphical representation of a proportional relationship in context… | Students read a graph showing a proportional relationship and explain what specific points mean in context. They identify why the line passes through (0, 0) and what the point (1, r) reveals about the unit rate. | NC.7.RP.2.d |
| Use scale factors and unit rates in proportional relationships to solve ratio… | Students use ratios and percentages to solve everyday problems, like figuring out a sale price, a tax amount, or how far a map distance translates to real miles. The math stays the same whether the numbers involve money, distance, or time. | NC.7.RP.3 |
Adding and subtracting with negative numbers, fractions, and decimals. Students work through problems like temperature drops, debt, and distance to make sense of what those operations actually mean.
Multiplying and dividing with negative numbers, fractions, and decimals. Students learn the rules for when answers turn negative and apply those rules to solve problems with any kind of number.
Any number that can be written as a fraction counts as a rational number. That includes whole numbers, negatives, and decimals that end or repeat, as long as the bottom of the fraction is not zero.
Multiplying and dividing positive and negative numbers, fractions, and decimals using reliable methods. Students explain what the answer means in a real situation, like figuring out a debt or a rate of speed.
Students practice turning fractions into decimals by dividing the top number by the bottom. They also learn that every fraction either ends cleanly as a decimal or settles into a repeating pattern, like 0.5 or 0.333...
Students practice adding, subtracting, multiplying, and dividing with fractions, decimals, and negative numbers to solve real problems, like splitting a bill or calculating a temperature drop.
| Standard | Definition | Code |
|---|---|---|
| Apply and extend previous understandings of addition and subtraction to add and… | Adding and subtracting with negative numbers, fractions, and decimals. Students work through problems like temperature drops, debt, and distance to make sense of what those operations actually mean. | NC.7.NS.1 |
| Apply and extend previous understandings of multiplication and division | Multiplying and dividing with negative numbers, fractions, and decimals. Students learn the rules for when answers turn negative and apply those rules to solve problems with any kind of number. | NC.7.NS.2 |
| Understand that a rational number is any number that can be written as a… | Any number that can be written as a fraction counts as a rational number. That includes whole numbers, negatives, and decimals that end or repeat, as long as the bottom of the fraction is not zero. | NC.7.NS.2.a |
| Apply properties of operations as strategies, including the standard… | Multiplying and dividing positive and negative numbers, fractions, and decimals using reliable methods. Students explain what the answer means in a real situation, like figuring out a debt or a rate of speed. | NC.7.NS.2.b |
| Use division and previous understandings of fractions and… | Students practice turning fractions into decimals by dividing the top number by the bottom. They also learn that every fraction either ends cleanly as a decimal or settles into a repeating pattern, like 0.5 or 0.333... | NC.7.NS.2.c |
| Solve real-world and mathematical problems involving numerical expressions with… | Students practice adding, subtracting, multiplying, and dividing with fractions, decimals, and negative numbers to solve real problems, like splitting a bill or calculating a temperature drop. | NC.7.NS.3 |
Students rewrite expressions by combining like terms, distributing a number across parentheses, and pulling out a shared factor. The goal is to write the same math in a simpler or more useful form.
Rewriting an expression in a different form, like turning 100 - 25 into 75% of 100, can show the same math relationship in a way that makes more sense for the situation. Students explain what each part of the new expression means in real life.
Students solve real-world problems that mix positive and negative numbers, fractions, and decimals. They rewrite numbers in whatever form makes the math easier, then work through multi-step calculations to find the answer.
Students set up and solve equations or inequalities to find an unknown value in a real-world situation, like figuring out how many hours of work it takes to reach a savings goal.
Students write equations to solve multi-step word problems, then work through each step to find the value of the unknown. They also check that the answer makes sense in the real situation.
Students write and solve inequalities (like x > 5) to answer real-world questions, then plot the answers on a number line. They also compare how solving an inequality differs from solving a regular equation.
| Standard | Definition | Code |
|---|---|---|
| Apply properties of operations as strategies to:<ul><li>Add, subtract | Students rewrite expressions by combining like terms, distributing a number across parentheses, and pulling out a shared factor. The goal is to write the same math in a simpler or more useful form. | NC.7.EE.1 |
| Understand that equivalent expressions can reveal real-world and mathematical… | Rewriting an expression in a different form, like turning 100 - 25 into 75% of 100, can show the same math relationship in a way that makes more sense for the situation. Students explain what each part of the new expression means in real life. | NC.7.EE.2 |
| Solve multi-step real-world and mathematical problems posed with rational… | Students solve real-world problems that mix positive and negative numbers, fractions, and decimals. They rewrite numbers in whatever form makes the math easier, then work through multi-step calculations to find the answer. | NC.7.EE.3 |
| Use variables to represent quantities to solve real-world or mathematical… | Students set up and solve equations or inequalities to find an unknown value in a real-world situation, like figuring out how many hours of work it takes to reach a savings goal. | NC.7.EE.4 |
| Construct equations to solve problems by reasoning about the… | Students write equations to solve multi-step word problems, then work through each step to find the value of the unknown. They also check that the answer makes sense in the real situation. | NC.7.EE.4.a |
| Construct inequalities to solve problems by reasoning about the… | Students write and solve inequalities (like x > 5) to answer real-world questions, then plot the answers on a number line. They also compare how solving an inequality differs from solving a regular equation. | NC.7.EE.4.b |
A survey or poll only tells you something true about a whole group if the people sampled actually represent that group. Students learn why random sampling matters and how to collect a sample that holds up.
Students collect several random samples of the same size, compare what each one shows, and use the differences between samples to make a reasonable guess about a larger group.
Students learn to compare two groups by looking at how spread out each group's data is, not just the averages. A wider spread means the data is less predictable, which matters when deciding if the two groups are really different.
Students learn three ways to describe how spread out a set of numbers is: the range (gap between the highest and lowest values), the interquartile range (spread of the middle half), and the mean absolute deviation (average distance each value sits from the middle).
Students look at two graphs side by side and judge how much the data overlaps or stays separate, using that visual gap to decide how different the two groups really are.
Students compare two groups using their averages and how spread out their numbers are. For example, they might use survey data to decide whether seventh graders or eighth graders tend to sleep more, and how consistent those patterns are.
Probability is a number from 0 to 1 that shows how likely something is to happen. A probability of 0 means it will never happen, and a probability of 1 means it will always happen. Numbers in between show how likely or unlikely an event is.
Flip a coin or roll a die many times, record the results, and use that data to figure out how often something is likely to happen. The more trials students run, the closer their results get to the true probability.
Students build a simple probability model, like a number cube or spinner, and use it to predict how likely a single outcome is to happen.
Students learn to assign equal chances to every possible outcome of a simple experiment, like rolling a number cube, then use those equal chances to figure out how likely a specific result is.
Students run an experiment many times, like flipping a coin or spinning a spinner, and use the results to build a model that predicts how often each outcome is likely to happen.
Students run an experiment, then compare what actually happened to what the math predicted would happen. If the results don't match, students explain why, such as too few trials or an uneven spinner.
Students figure out the chances of two or more things happening together, like flipping a coin and rolling a die at the same time. They use lists, tables, and branching diagrams to map out every possible outcome.
When two things happen together (like flipping a coin and rolling a die), students find the probability the same way they would for a single event: count the outcomes that match, then divide by the total number of possible outcomes.
Given a real situation like flipping two coins or rolling two number cubes, students find all possible results by reading a list, table, or tree diagram, then pick out which results match the event they are studying.
Students build a simple experiment, like flipping coins or rolling dice, to estimate how often two events happen together. They run the simulation and use the results to predict real-world probabilities.
| Standard | Definition | Code |
|---|---|---|
| Understand that statistics can be used to gain information about a population… | A survey or poll only tells you something true about a whole group if the people sampled actually represent that group. Students learn why random sampling matters and how to collect a sample that holds up. | NC.7.SP.1 |
| Generate multiple random samples | Students collect several random samples of the same size, compare what each one shows, and use the differences between samples to make a reasonable guess about a larger group. | NC.7.SP.2 |
| Recognize the role of variability when comparing two populations | Students learn to compare two groups by looking at how spread out each group's data is, not just the averages. A wider spread means the data is less predictable, which matters when deciding if the two groups are really different. | NC.7.SP.3 |
| Calculate the measure of variability of a data set and understand that it… | Students learn three ways to describe how spread out a set of numbers is: the range (gap between the highest and lowest values), the interquartile range (spread of the middle half), and the mean absolute deviation (average distance each value sits from the middle). | NC.7.SP.3.a |
| Informally assess the difference between two data sets by examining the overlap… | Students look at two graphs side by side and judge how much the data overlaps or stays separate, using that visual gap to decide how different the two groups really are. | NC.7.SP.3.b |
| Use measures of center and measures of variability for numerical data from… | Students compare two groups using their averages and how spread out their numbers are. For example, they might use survey data to decide whether seventh graders or eighth graders tend to sleep more, and how consistent those patterns are. | NC.7.SP.4 |
| Understand that the probability of a chance event is a number between 0 and 1… | Probability is a number from 0 to 1 that shows how likely something is to happen. A probability of 0 means it will never happen, and a probability of 1 means it will always happen. Numbers in between show how likely or unlikely an event is. | NC.7.SP.5 |
| Collect data to calculate the experimental probability of a chance event… | Flip a coin or roll a die many times, record the results, and use that data to figure out how often something is likely to happen. The more trials students run, the closer their results get to the true probability. | NC.7.SP.6 |
| Develop a probability model and use it to find probabilities of simple events | Students build a simple probability model, like a number cube or spinner, and use it to predict how likely a single outcome is to happen. | NC.7.SP.7 |
| Develop a uniform probability model by assigning equal probability to all… | Students learn to assign equal chances to every possible outcome of a simple experiment, like rolling a number cube, then use those equal chances to figure out how likely a specific result is. | NC.7.SP.7.a |
| Develop a probability model | Students run an experiment many times, like flipping a coin or spinning a spinner, and use the results to build a model that predicts how often each outcome is likely to happen. | NC.7.SP.7.b |
| Compare theoretical and experimental probabilities from a model to observed… | Students run an experiment, then compare what actually happened to what the math predicted would happen. If the results don't match, students explain why, such as too few trials or an uneven spinner. | NC.7.SP.7.c |
| Determine probabilities of compound events using organized lists, tables, tree… | Students figure out the chances of two or more things happening together, like flipping a coin and rolling a die at the same time. They use lists, tables, and branching diagrams to map out every possible outcome. | NC.7.SP.8 |
| Understand that, just as with simple events, the probability of a compound… | When two things happen together (like flipping a coin and rolling a die), students find the probability the same way they would for a single event: count the outcomes that match, then divide by the total number of possible outcomes. | NC.7.SP.8.a |
| For an event described in everyday language, identify the outcomes in the… | Given a real situation like flipping two coins or rolling two number cubes, students find all possible results by reading a list, table, or tree diagram, then pick out which results match the event they are studying. | NC.7.SP.8.b |
| Design and use a simulation to generate frequencies for compound events | Students build a simple experiment, like flipping coins or rolling dice, to estimate how often two events happen together. They run the simulation and use the results to predict real-world probabilities. | NC.7.SP.8.c |
End-of-grade mathematics assessment for grades 3 through 8, aligned to the North Carolina Standard Course of Study.
Alternate assessment for eligible students with significant cognitive disabilities, covering state-tested grades and subjects.
Students should work fluently with negative numbers, fractions, and decimals in the same problem. They should solve multi-step equations and inequalities, work with percents and proportions, and reason about circles, angles, area, and probability. Word problems get longer and lean more on setting up an equation.
Use real shopping moments. Ask what 20% off a $35 shirt comes to, or whether the bigger bag of rice is actually a better deal per pound. Tip calculations at restaurants and recipe scaling for more or fewer people both give honest practice in a few minutes.
A common path starts with operations on rational numbers, since signed numbers and fractions show up everywhere later. Then move into ratios, proportions, and percents, then expressions and equations, then geometry with circles and angles, and finish with statistics and probability. Probability often lands well at the end when students need a change of pace.
Subtracting a negative and multiplying two negatives are the usual sticking points. A number line and a simple money model (owing versus having) help more than rules. Short daily warmups with mixed signs build accuracy faster than a long unit followed by nothing.
Students can spot it in a table, on a graph as a straight line through the origin, and in an equation like y equals kx. They can say what the unit rate means in the situation, like dollars per hour or miles per gallon, and use it to answer a new question.
Read the problem together and ask what is happening before reaching for numbers. A quick sketch or a labeled bar often unlocks it. Try one problem a few nights a week instead of a long session, and let students explain their thinking out loud, even when the answer is wrong.
Operations with signed fractions, distributing a negative across parentheses, and solving equations when the variable appears with a negative coefficient. Many students also confuse area and circumference of a circle. Spiraled review problems across units catch these gaps before the next assessment.
Students learn that a sample only speaks for the group it was actually drawn from. Asking only the basketball team about favorite sports will not represent the whole school. Random selection and larger samples give predictions worth trusting.
Ready students can solve an equation like 3x minus 7 equals 20 without much fuss, find a percent of a number in their head for simple cases, and explain what a proportion means in a real situation. If those feel shaky in May, a few short summer sessions on those three skills go a long way.