Working with positive and negative numbers
Students start the year extending arithmetic to negative numbers. They add, subtract, multiply, and divide using number lines and real situations like temperature drops or money owed.
What does a student learn in
This is the year math moves from arithmetic to working with ratios, percents, and negative numbers in real situations. Students figure out tips, discounts, and sale prices, and they add and subtract with negatives on a number line. They start using letters to stand for unknown amounts and solve simple equations. By spring, they can find the better deal between two stores and explain why.
- Ratios and proportions
- Percents
- Negative numbers
- Equations
- Probability
- Area and volume
Year at a glance
How the year usually goes. Every school and district set their own curriculum, so treat this as a guide, not official pacing.
- 1
- 2
Ratios, rates, and percents
Students use ratios and rates to solve problems like unit pricing, tips, discounts, and scale drawings. Percent change and proportional relationships become a major focus.
- 3
Expressions and equations
Students write and solve equations with variables on both sides and work with expressions that include negatives and fractions. Word problems get translated into algebra.
- 4
Geometry and measurement
Students measure angles, find the area and circumference of circles, and calculate surface area and volume of solids. Scale drawings tie back to ratio work from earlier in the year.
- 5
Statistics and probability
Students wrap up the year by comparing data sets, drawing samples to make predictions about a larger group, and finding probabilities of simple and compound events.
Mastery Learning Standards
The required skills a student should display by the end of Grade 7.
Standards for Mathematical Practice
Standards for Mathematical Practice
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Make Sense of Problems
Students read a math problem all the way through before jumping in, figure out what the question is really asking, and keep trying when the first approach doesn't work.
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Reason Abstractly
Students take a real situation, like splitting a bill or measuring a room, and turn it into numbers and equations to solve it. Then they check whether the answer actually makes sense back in the real world.
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Construct Arguments
Students back up their math answers with reasons, then listen to classmates' thinking and point out where the logic holds or falls apart.
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Model with Mathematics
Students use math to make sense of real situations: drawing a diagram, writing an equation, or reading a graph to figure out what's actually happening. The model doesn't have to be perfect; it just has to be useful.
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Use Tools Strategically
Students choose the right tool for the problem, whether that means a calculator, a ruler, scratch paper, or a mental estimate. The goal is knowing when each tool helps and when it gets in the way.
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Attend to Precision
Students choose words, labels, and numbers carefully when solving and explaining math problems. A precise answer names the right unit (miles, not just "5") and uses the correct term (quotient, not just "answer").
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Use Structure
Students learn to spot patterns and hidden structures in math problems, like noticing that an expression can be rearranged or that a shape can be broken into simpler parts. That recognition helps them solve problems faster.
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Express Regularity
Students notice when the same steps keep showing up in different problems and use that pattern to find a shortcut or write a general rule.
| Standard | Definition | Code |
|---|---|---|
| Make Sense of Problems | Students read a math problem all the way through before jumping in, figure out what the question is really asking, and keep trying when the first approach doesn't work. | MA-MATH.MP.7.1 |
| Reason Abstractly | Students take a real situation, like splitting a bill or measuring a room, and turn it into numbers and equations to solve it. Then they check whether the answer actually makes sense back in the real world. | MA-MATH.MP.7.2 |
| Construct Arguments | Students back up their math answers with reasons, then listen to classmates' thinking and point out where the logic holds or falls apart. | MA-MATH.MP.7.3 |
| Model with Mathematics | Students use math to make sense of real situations: drawing a diagram, writing an equation, or reading a graph to figure out what's actually happening. The model doesn't have to be perfect; it just has to be useful. | MA-MATH.MP.7.4 |
| Use Tools Strategically | Students choose the right tool for the problem, whether that means a calculator, a ruler, scratch paper, or a mental estimate. The goal is knowing when each tool helps and when it gets in the way. | MA-MATH.MP.7.5 |
| Attend to Precision | Students choose words, labels, and numbers carefully when solving and explaining math problems. A precise answer names the right unit (miles, not just "5") and uses the correct term (quotient, not just "answer"). | MA-MATH.MP.7.6 |
| Use Structure | Students learn to spot patterns and hidden structures in math problems, like noticing that an expression can be rearranged or that a shape can be broken into simpler parts. That recognition helps them solve problems faster. | MA-MATH.MP.7.7 |
| Express Regularity | Students notice when the same steps keep showing up in different problems and use that pattern to find a shortcut or write a general rule. | MA-MATH.MP.7.8 |
K-8 Mathematics Content
K-8 Mathematics Content
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Counting and Number
Students work with whole numbers, fractions, and negative numbers to solve grade-level problems. They use what they know about how numbers are built and related to reason through calculations and comparisons.
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Operations and Algebraic Thinking
Students solve real problems using addition, subtraction, multiplication, and division, then write those situations as expressions or equations. The focus is on knowing which operation fits the problem and why.
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Measurement and Data
Students read and build tables, graphs, and basic statistics to make sense of real data. They use those tools to answer questions and spot patterns in what the numbers show.
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Geometry
Students sort and measure flat shapes like triangles and rectangles, then move into three-dimensional solids like prisms and pyramids. They use angle relationships and formulas to describe what makes each shape different.
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Ratios and Proportional Relationships
Students use ratios and rates to solve everyday problems, like figuring out unit prices, scaling a recipe, or finding a percentage. The math connects to situations students actually run into outside of school.
| Standard | Definition | Code |
|---|---|---|
| Counting and Number | Students work with whole numbers, fractions, and negative numbers to solve grade-level problems. They use what they know about how numbers are built and related to reason through calculations and comparisons. | MA-MATH.K8.7.1 |
| Operations and Algebraic Thinking | Students solve real problems using addition, subtraction, multiplication, and division, then write those situations as expressions or equations. The focus is on knowing which operation fits the problem and why. | MA-MATH.K8.7.2 |
| Measurement and Data | Students read and build tables, graphs, and basic statistics to make sense of real data. They use those tools to answer questions and spot patterns in what the numbers show. | MA-MATH.K8.7.3 |
| Geometry | Students sort and measure flat shapes like triangles and rectangles, then move into three-dimensional solids like prisms and pyramids. They use angle relationships and formulas to describe what makes each shape different. | MA-MATH.K8.7.4 |
| Ratios and Proportional Relationships | Students use ratios and rates to solve everyday problems, like figuring out unit prices, scaling a recipe, or finding a percentage. The math connects to situations students actually run into outside of school. | MA-MATH.K8.7.5 |
Assessments
The state tests students at this grade and subject take.
MCAS: Mathematics (Grades 3-8)
Massachusetts's spring summative math test for grades 3 through 8, aligned to the Massachusetts Curriculum Framework for Mathematics.
- When given:
- spring
- Frequency:
- annual
Common Questions
What math will students work on this year?
Students spend most of the year on ratios, percents, and rational numbers, including negatives. They also work with expressions and equations, basic probability, and shapes like circles and prisms. Word problems get longer and more layered than in earlier grades.
How can families help with math at home?
Cook, shop, and travel out loud together. Talk about tips at restaurants, sale prices, gas mileage, and recipe scaling. Ten minutes of real talk about percents, rates, or negative temperatures does more than a worksheet, because students hear the math used the way adults actually use it.
My student says they are bad at math. What should I do?
Treat it like a sport, not a talent. Sit next to them, ask what the problem is really asking, and let them explain their thinking out loud. Getting stuck is part of the work this year, and students who keep trying after a wrong answer make the most progress.
Do students need to memorize anything specific?
Quick recall of multiplication facts, common fraction and decimal equivalents, and percent benchmarks like 10, 25, and 50 percent makes everything else easier. Without that fluency, students get bogged down in arithmetic and lose the thread of the actual problem.
How should the year be sequenced?
Most plans open with rational number operations so signed numbers are solid, then move into ratios and proportional relationships, then expressions and equations that use both. Geometry and statistics fit well in the second half once students can handle the algebra inside area, circumference, and sampling problems.
Which skills usually need the most reteaching?
Subtracting negatives, dividing fractions, and setting up proportions from a word problem are the usual sticking points. Plan short spiral reviews into warm-ups through the spring rather than one big reteach unit, since these skills show up inside almost every later topic.
How much should students be writing in math class?
Students should explain their reasoning in a sentence or two on most tasks, not just show steps. Short written justifications make thinking visible, surface misconceptions early, and prepare students for the kind of argument and critique work that gets heavier in eighth grade.
How do I know students are ready for next year?
By June, students should solve multi-step percent and proportion problems, operate fluently with positive and negative rational numbers, and solve two-step equations with confidence. If those three are solid, the jump to linear functions and systems in the next grade is manageable.