Rational and irrational numbers
Students learn that some numbers, like the square root of 2 or pi, cannot be written as simple fractions. They place these numbers on a number line and estimate their size to compare them.
What does a student learn in
This is the year math shifts from arithmetic into real algebra. Students work with linear equations, slope, and the idea of a function, learning to see how one quantity changes in step with another. They also reason about exponents, square roots, and the Pythagorean theorem on the coordinate plane. By spring, students can graph a line, find its slope, and solve a word problem by writing and solving an equation.
- Linear equations
- Slope and graphs
- Functions
- Pythagorean theorem
- Exponents
- Scatter plots
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
Exponents and scientific notation
Students work with powers and the rules for multiplying and dividing them. They write very large and very small numbers in scientific notation, the shorthand used for things like distances in space or the size of a cell.
- 3
Linear equations and slope
Students solve equations with variables on both sides and graph straight lines. They learn what slope means as a rate of change, like miles per hour on a road trip or dollars earned per hour at a job.
- 4
Systems of equations
Students solve two equations at the same time to find where two lines cross. This shows up in real problems like comparing two phone plans or figuring out when two savings accounts will hold the same amount.
- 5
Functions and data patterns
Students start using functions, the idea that one input gives one output. They read graphs and tables to spot patterns, and they fit a straight line to scattered data points to make predictions.
- 6
Geometry and the Pythagorean theorem
Students use the Pythagorean theorem to find missing side lengths in right triangles, which is how builders check that a corner is square. They also study how shapes change under slides, flips, turns, and resizing.
Mastery Learning Standards
The required skills a student should display by the end of Grade 8.
Standards for Mathematical Practice
Standards for Mathematical Practice
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Make Sense of Problems
Students read a math problem carefully, figure out what it's actually asking, and keep trying even when the first approach doesn't work.
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Reason Abstractly
Students take a word problem apart, work with the numbers as symbols on paper, then check whether the answer still makes sense back in the real situation.
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Construct Arguments
Students explain their math thinking step by step and tell why an answer makes sense. They also listen to classmates' reasoning and point out where the logic holds up or falls short.
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Model with Mathematics
Students use math to make sense of real situations, like figuring out a budget, reading a graph, or estimating a distance. The math connects to something outside the classroom.
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Use Tools Strategically
Students choose the right tool for the problem, whether that means a calculator, a quick estimate in their head, or working it out by hand.
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Attend to Precision
Students choose words, labels, and units carefully when solving problems. A precise answer means saying "5 inches" or "3 square feet," not just writing a number.
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Use Structure
Students learn to spot patterns and underlying rules in math problems, like noticing that every even number is divisible by 2 or that a graph's shape reveals what an equation is doing. Recognizing structure helps students solve new problems faster.
-
Express Regularity
Students notice when a calculation or procedure keeps working the same way, then use that pattern to build a shortcut or general rule. The habit turns repeated practice into deeper understanding.
| Standard | Definition | Code |
|---|---|---|
| Make Sense of Problems | Students read a math problem carefully, figure out what it's actually asking, and keep trying even when the first approach doesn't work. | NH-MATH.MP.8.1 |
| Reason Abstractly | Students take a word problem apart, work with the numbers as symbols on paper, then check whether the answer still makes sense back in the real situation. | NH-MATH.MP.8.2 |
| Construct Arguments | Students explain their math thinking step by step and tell why an answer makes sense. They also listen to classmates' reasoning and point out where the logic holds up or falls short. | NH-MATH.MP.8.3 |
| Model with Mathematics | Students use math to make sense of real situations, like figuring out a budget, reading a graph, or estimating a distance. The math connects to something outside the classroom. | NH-MATH.MP.8.4 |
| Use Tools Strategically | Students choose the right tool for the problem, whether that means a calculator, a quick estimate in their head, or working it out by hand. | NH-MATH.MP.8.5 |
| Attend to Precision | Students choose words, labels, and units carefully when solving problems. A precise answer means saying "5 inches" or "3 square feet," not just writing a number. | NH-MATH.MP.8.6 |
| Use Structure | Students learn to spot patterns and underlying rules in math problems, like noticing that every even number is divisible by 2 or that a graph's shape reveals what an equation is doing. Recognizing structure helps students solve new problems faster. | NH-MATH.MP.8.7 |
| Express Regularity | Students notice when a calculation or procedure keeps working the same way, then use that pattern to build a shortcut or general rule. The habit turns repeated practice into deeper understanding. | NH-MATH.MP.8.8 |
K-8 Mathematics Content
K-8 Mathematics Content
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Counting and Number
Grade 8 students work with whole numbers, fractions, and negative numbers to solve problems. They use number-system reasoning to compare values, place numbers on a line, and make sense of relationships between different kinds of numbers.
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Operations and Algebraic Thinking
Eighth graders write and solve expressions using addition, subtraction, multiplication, and division to model real problems. They move fluently between words, equations, and diagrams to find a solution.
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Measurement and Data
Students read and build tables, graphs, and basic statistical summaries to make sense of real data. They use those tools to spot patterns and draw conclusions.
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Geometry
Students describe and measure flat shapes like triangles and rectangles, then move to solid shapes like cubes and cylinders. They sort shapes by their properties and calculate things like area, volume, and angle size.
-
Ratios and Proportional Relationships
Students use ratios and proportions to solve everyday problems, like finding the best price per unit or scaling a recipe up or down. The math connects numbers to real situations.
| Standard | Definition | Code |
|---|---|---|
| Counting and Number | Grade 8 students work with whole numbers, fractions, and negative numbers to solve problems. They use number-system reasoning to compare values, place numbers on a line, and make sense of relationships between different kinds of numbers. | NH-MATH.K8.8.1 |
| Operations and Algebraic Thinking | Eighth graders write and solve expressions using addition, subtraction, multiplication, and division to model real problems. They move fluently between words, equations, and diagrams to find a solution. | NH-MATH.K8.8.2 |
| Measurement and Data | Students read and build tables, graphs, and basic statistical summaries to make sense of real data. They use those tools to spot patterns and draw conclusions. | NH-MATH.K8.8.3 |
| Geometry | Students describe and measure flat shapes like triangles and rectangles, then move to solid shapes like cubes and cylinders. They sort shapes by their properties and calculate things like area, volume, and angle size. | NH-MATH.K8.8.4 |
| Ratios and Proportional Relationships | Students use ratios and proportions to solve everyday problems, like finding the best price per unit or scaling a recipe up or down. The math connects numbers to real situations. | NH-MATH.K8.8.5 |
Assessments
The state tests students at this grade and subject take.
NHSAS: Mathematics (Grades 3-8)
New Hampshire's spring summative math test for grades 3 through 8, aligned to New Hampshire's College and Career Ready Standards for Math.
- When given:
- spring
- Frequency:
- annual
NAEP (National Assessment of Educational Progress)
Federally administered sample-based assessment in reading, mathematics, science, and writing. NAEP results inform state-by-state comparisons rather than individual student or school accountability.
- When given:
- biennial in winter
- Frequency:
- every two years
Common Questions
What math will students work on this year?
Students move from arithmetic into early algebra. They solve equations with a variable on both sides, graph lines, work with slope, and start using exponents and square roots. They also study triangles, angles, and the Pythagorean theorem.
How can I help at home if my child gets stuck on a math problem?
Ask them to read the problem out loud and say what they already know. Then ask what they are trying to find. Most stuck moments come from skipping that first step, not from missing math skills.
Does my child still need to practice basic math facts?
Yes. Quick recall of times tables, fractions, decimals, and percents makes the harder work this year much easier. Five minutes of flashcards or mental math in the car still pays off.
What should I look for to know my child is on track by spring?
By spring, students should be able to solve a two-step equation, read a graph and describe its slope, and use the Pythagorean theorem to find a missing side of a right triangle. If those feel shaky, ask the teacher what to practice.
How should I sequence the year?
Most teachers start with rational numbers and exponents, move into expressions and linear equations, then graphing and systems, then functions, and finish with geometry and the Pythagorean theorem. Save data and scatter plots for a unit near the end when students can pull skills together.
Which topics usually need the most reteaching?
Slope as a rate of change, negative exponents, and solving equations with variables on both sides. Many students also struggle to tell the difference between a function and a relation. Plan extra practice and short warm-ups on these throughout the year.
What does mastery look like by the end of the year?
Students can model a real situation with a linear equation, solve it, and explain what the answer means in context. They can also justify their steps and spot errors in another student's work. That reasoning piece matters as much as the answer.
How do I know my child is ready for high school math?
Readiness shows up in three places: solving linear equations without a calculator, graphing a line from an equation, and explaining their thinking in a full sentence. If those are solid, algebra in high school will feel like a continuation, not a new subject.