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Learning Standards Standards

What does a student learn in ?

This is the year math shifts from whole numbers into ratios, rates, and negative numbers. Students compare prices per ounce, figure out the better deal, and start working with numbers below zero on a number line. They also begin using letters in place of numbers to write and solve simple equations. By spring, students can solve a problem like "if 3 apples cost $2, how much do 12 apples cost?" and explain their thinking.

  • Ratios and rates
  • Negative numbers
  • Equations with variables
  • Fraction division
  • Data and graphs
Source: New Hampshire New Hampshire College and Career Ready Standards
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. 1

    Ratios and rates

    Students start the year comparing amounts using ratios, like two cups of flour for every three eggs. They use this thinking to find unit prices, mix recipes, and figure out which deal at the store is actually better.

  2. 2

    Fractions, decimals, and percents

    Students divide fractions by fractions and work fluently with decimals. They also start using percents, so a sale sign or a tip at a restaurant becomes a math problem they can solve.

  3. 3

    Negative numbers and the number line

    Students extend the number line below zero. They place positive and negative numbers, compare temperatures and elevations, and plot points in all four sections of a coordinate grid.

  4. 4

    Expressions and equations

    Students move from arithmetic into early algebra. They write expressions with letters standing in for numbers, solve simple one-step equations, and describe how two quantities change together.

  5. 5

    Area, surface area, and volume

    Students find the area of triangles and other shapes by breaking them apart. They also measure the surface and volume of boxes and prisms, the kind of math used to wrap a gift or fill a fish tank.

  6. 6

    Statistics and data

    Students close the year by making sense of data sets. They build dot plots, histograms, and box plots, and they talk about the typical value and the spread, not just a single average.

Mastery Learning Standards
The required skills a student should display by the end of Grade 6.
Standards for Mathematical Practice

  • Make Sense of Problems

    NH-MATH.MP.6.1

    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.

  • Reason Abstractly

    NH-MATH.MP.6.2

    Students take a real situation, turn it into numbers and equations to solve it, then translate the answer back into what it means in real life.

  • Construct Arguments

    NH-MATH.MP.6.3

    Students explain why their math answer is correct and listen critically to a classmate's reasoning to spot where it holds up or falls apart.

  • Model with Mathematics

    NH-MATH.MP.6.4

    Students take a real-world situation, like splitting a restaurant bill or figuring out how many boxes fit in a truck, and use math to work it out. The math explains the real thing, not just a textbook problem.

  • Use Tools Strategically

    NH-MATH.MP.6.5

    Students choose the right tool for the math problem in front of them. That might mean reaching for a calculator, sketching on paper, or estimating in their head.

  • Attend to Precision

    NH-MATH.MP.6.6

    Students choose words, labels, and units carefully when solving problems. A measurement needs the right unit, a shape needs the right name, and an answer needs to show the work behind it.

  • Use Structure

    NH-MATH.MP.6.7

    Students spot patterns and hidden structure in numbers, shapes, and equations, then use what they notice to solve problems more efficiently. It is the habit of asking "why does this work?" instead of just following steps.

  • Express Regularity

    NH-MATH.MP.6.8

    Students notice when the same steps keep showing up in a problem and use that pattern as a shortcut or rule. Instead of solving from scratch each time, they ask why the pattern works and write it down as a general method.

K-8 Mathematics Content

  • Counting and Number

    NH-MATH.K8.6.1

    Sixth graders work with whole numbers, fractions, and negative numbers to solve problems. They use number-system patterns to compare values, place numbers on a line, and reason about how different types of numbers relate.

  • Operations and Algebraic Thinking

    NH-MATH.K8.6.2

    Sixth graders use addition, subtraction, multiplication, and division to write and solve expressions that model real problems. They translate a word problem into math notation and work through it step by step.

  • Measurement and Data

    NH-MATH.K8.6.3

    Students read and build tables, graphs, and basic statistical summaries to make sense of real data. They choose the right display for the information and explain what the numbers actually show.

  • Geometry

    NH-MATH.K8.6.4

    Students sort and measure flat shapes like triangles and rectangles alongside solid shapes like cubes and cylinders. They use what they know about angles, sides, and faces to describe what makes each shape different.

  • Ratios and Proportional Relationships

    NH-MATH.K8.6.5

    Students use ratios to solve everyday problems, like comparing prices, scaling a recipe, or figuring out speed. The math connects two quantities and asks what happens when one of them changes.

Assessments
The state tests students at this grade and subject take.
State Summative

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
Official source
Common Questions
  • What math will students work on this year?

    Students spend a lot of time on ratios, rates, and percents, like comparing prices per ounce or figuring out a tip. They also work with negative numbers, start using simple algebra with letters standing in for numbers, and build skills with fractions, decimals, and basic data and graphs.

  • 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 it is really asking in their own words. Then have them try a smaller version with easier numbers first. The goal is to get them talking through their thinking, not to hand them the answer.

  • What is a ratio and why is it such a big deal this year?

    A ratio compares two amounts, like 3 cups of flour for every 2 cups of sugar. Ratios show up in cooking, shopping, maps, and sports stats. Practicing with real examples at home, like unit prices at the store, makes the classroom work feel familiar.

  • Do students still need to know their times tables?

    Yes. Quick recall of multiplication and division facts makes ratios, fractions, and percents much less frustrating. Five minutes of flashcards or a quick fact game a few times a week is plenty.

  • How should I sequence the year?

    A common order is ratios and rates first, then fraction and decimal operations, then negative numbers and the coordinate plane, then expressions and one-step equations, and finally area, surface area, volume, and basic statistics. Ratios early gives students a model they can lean on all year.

  • Which topics usually need the most reteaching?

    Dividing fractions, working with negative numbers, and writing expressions from word problems tend to need the most revisits. Building in short spiral review once or twice a week keeps these from slipping away after the unit ends.

  • What does mastery look like by the end of the year?

    By June, students should solve ratio and percent problems in everyday contexts, add, subtract, multiply, and divide fractions and decimals, plot points in all four quadrants, and solve simple one-step equations. They should also be able to explain their reasoning, not just get an answer.

  • How do I know my child is ready for next year?

    Ask them to explain a percent problem out loud, like finding 15 percent of 40, or to compare two unit rates. If they can talk through the steps and catch their own mistakes, they are in good shape for seventh grade.