This is the year math moves from following steps to reasoning with ratios and negative numbers. Students work with percents, proportions, and scale to solve real problems like tips, discounts, and maps. They add and subtract negative numbers, write and solve equations with a variable, and start drawing conclusions from data samples. By spring, students can figure out the better deal at a store and solve a two-step equation on paper.
Students start the year extending what they know about numbers to include negatives. They add, subtract, multiply, and divide with positive and negative values using examples like temperatures, elevations, and money owed.
Students use ratios and rates to solve everyday problems like tips, sales tax, discounts, and unit prices. They also work with scale drawings and figure out how a recipe or map changes when the numbers grow or shrink.
Students write and solve equations with letters standing in for unknown numbers. They rearrange expressions, combine like terms, and solve two-step problems that show up in real situations like phone plans or savings goals.
Students measure the area and circumference of circles and find the surface area and volume of boxes, prisms, and pyramids. They also work with angles formed when lines cross and build shapes from given side lengths.
Students close the year by drawing conclusions from samples, comparing two sets of data, and predicting how often events will happen. They run simple experiments and check whether the results match what they expected.
Students read a problem carefully, figure out what it's actually asking, and keep trying even when the first approach doesn't work. Getting stuck is part of the process.
Students take a real situation (a sale price, a recipe, a race) and strip it down to numbers and symbols to solve it, then translate the answer back into plain language that makes sense in context.
Students explain why their math answer makes sense and find the flaw when someone else's reasoning doesn't add up.
Students take a real situation (splitting a bill, planning a garden, estimating a trip) and write equations or draw diagrams to figure it out. Math becomes a tool for solving problems that actually come up outside school.
Students choose the right tool for the job, picking a calculator, a sketch, or a quick estimate depending on what the problem actually needs.
Students choose their words and units carefully when explaining math, and double-check calculations for accuracy. Saying "the area is 12 square inches" instead of just "12" is the kind of precision this standard builds.
Students spot patterns and hidden structure in numbers, shapes, and equations, then use those patterns as shortcuts to solve harder problems.
Students notice when the same steps keep showing up in a problem and use that pattern as a shortcut or rule. Instead of repeating the work each time, they ask why the pattern works and write it as a general method.
| Standard | Definition | Code |
|---|---|---|
| Make Sense of Problems | Students read a problem carefully, figure out what it's actually asking, and keep trying even when the first approach doesn't work. Getting stuck is part of the process. | NH-MATH.MP.7.1 |
| Reason Abstractly | Students take a real situation (a sale price, a recipe, a race) and strip it down to numbers and symbols to solve it, then translate the answer back into plain language that makes sense in context. | NH-MATH.MP.7.2 |
| Construct Arguments | Students explain why their math answer makes sense and find the flaw when someone else's reasoning doesn't add up. | NH-MATH.MP.7.3 |
| Model with Mathematics | Students take a real situation (splitting a bill, planning a garden, estimating a trip) and write equations or draw diagrams to figure it out. Math becomes a tool for solving problems that actually come up outside school. | NH-MATH.MP.7.4 |
| Use Tools Strategically | Students choose the right tool for the job, picking a calculator, a sketch, or a quick estimate depending on what the problem actually needs. | NH-MATH.MP.7.5 |
| Attend to Precision | Students choose their words and units carefully when explaining math, and double-check calculations for accuracy. Saying "the area is 12 square inches" instead of just "12" is the kind of precision this standard builds. | NH-MATH.MP.7.6 |
| Use Structure | Students spot patterns and hidden structure in numbers, shapes, and equations, then use those patterns as shortcuts to solve harder problems. | NH-MATH.MP.7.7 |
| Express Regularity | Students notice when the same steps keep showing up in a problem and use that pattern as a shortcut or rule. Instead of repeating the work each time, they ask why the pattern works and write it as a general method. | NH-MATH.MP.7.8 |
Students work with whole numbers, fractions, and negative numbers to solve grade-level problems. That means comparing values, placing them on a number line, and using them in calculations that match what seventh graders are expected to know.
Students use addition, subtraction, multiplication, and division to write expressions and solve word problems. The focus is on setting up the math correctly before calculating.
Students read and build tables, graphs, and basic statistical summaries to make sense of real data. The focus is on choosing the right display and explaining what the numbers actually mean.
Students sort, measure, and describe 2-D and 3-D shapes using angle measures, side lengths, and other geometric properties. The focus moves beyond naming shapes to explaining why they belong in a category or how their dimensions relate.
Students use ratios and proportions to solve everyday problems, like figuring out unit prices, scaling a recipe, or finding a percent discount. The math connects to real situations, not just worksheets.
| Standard | Definition | Code |
|---|---|---|
| Counting and Number | Students work with whole numbers, fractions, and negative numbers to solve grade-level problems. That means comparing values, placing them on a number line, and using them in calculations that match what seventh graders are expected to know. | NH-MATH.K8.7.1 |
| Operations and Algebraic Thinking | Students use addition, subtraction, multiplication, and division to write expressions and solve word problems. The focus is on setting up the math correctly before calculating. | NH-MATH.K8.7.2 |
| Measurement and Data | Students read and build tables, graphs, and basic statistical summaries to make sense of real data. The focus is on choosing the right display and explaining what the numbers actually mean. | NH-MATH.K8.7.3 |
| Geometry | Students sort, measure, and describe 2-D and 3-D shapes using angle measures, side lengths, and other geometric properties. The focus moves beyond naming shapes to explaining why they belong in a category or how their dimensions relate. | NH-MATH.K8.7.4 |
| Ratios and Proportional Relationships | Students use ratios and proportions to solve everyday problems, like figuring out unit prices, scaling a recipe, or finding a percent discount. The math connects to real situations, not just worksheets. | NH-MATH.K8.7.5 |
New Hampshire's spring summative math test for grades 3 through 8, aligned to New Hampshire's College and Career Ready Standards for Math.
Students should work confidently with positive and negative numbers, fractions, decimals, and percents. They should solve problems with ratios and proportions, write and solve simple equations, and reason about area, volume, and basic statistics from a data set.
Ask students to explain the problem out loud before solving it. If they get stuck, have them draw a picture or try smaller numbers first. Checking the answer against the question (does it make sense?) is often more useful than knowing the method yourself.
Cooking, shopping, and road trips are full of it. Doubling a recipe, comparing unit prices at the store, or figuring out miles per gallon all use the same reasoning students practice in class. Five minutes of real talk about these beats a worksheet.
Adding, subtracting, multiplying, and dividing with negatives is a major shift, and it trips up a lot of students. Temperatures, money owed, and elevation below sea level are good everyday examples. Expect some bumps in the fall and steadier work by spring.
Most teachers start with operations on rational numbers, then move into ratios and proportional reasoning, then expressions and equations, and finish with geometry and statistics. Ratios and rational number fluency pay off all year, so it helps to front-load them.
Operations with negative numbers and fraction-decimal-percent conversions are the two biggest sticking points. Solving multi-step equations with negatives also lags. Plan a short review block before any unit that builds on these.
Students can set up and solve a proportion from a word problem, work fluently with signed rationals, and solve two-step equations without a calculator. They can also pull a reasonable conclusion from a simple data set or sample.
Eighth grade leans hard on linear relationships and the coordinate plane. If students can solve proportion problems, graph a ratio as a line, and handle signed numbers without freezing up, they are in good shape.
Yes. Quick recall of multiplication and division facts makes fractions, ratios, and equations much easier. If facts are shaky, two or three minutes a night of flashcards or a fact app goes a long way.