What math should students know by the end of the year?

By spring, students should add, subtract, multiply, and divide with larger whole numbers, work with decimals to the hundredths, and add and subtract fractions with unlike bottoms. They should also read graphs, find the volume of a box, and plot points on a grid.

How can families help with math at home in just a few minutes?

Cook together and double or halve a recipe. Ask students to estimate the grocery total before checkout, then compare. At dinner, ask how to split a bill four ways or how much pizza is left as a fraction.

What if a student gets stuck on a word problem?

Ask them to read it once for the story and once for the question. Then ask what they already know and what they need to find. Drawing a quick picture or writing the numbers in a simple sentence often unsticks the rest.

Do students still need to practice their times tables?

Yes. Fluent multiplication and division facts make this year much easier, because fractions, decimals, and long division all lean on them. Five minutes of flashcards or a quick car-ride quiz a few times a week is enough to keep facts sharp.

How should fractions and decimals be sequenced across the year?

Build fraction equivalence and addition with unlike bottoms before moving into multiplication and division of fractions. Decimals to the hundredths fit well alongside place value early in the year, so students can connect 0.25 and one quarter before operations get heavier.

Which skills usually need the most reteaching?

Adding and subtracting fractions with unlike bottoms, dividing with two-digit divisors, and interpreting remainders in word problems tend to need a second pass. Volume also trips students up when they confuse it with area.

What does mastery look like heading into next year?

Students should solve multi-step problems with whole numbers, decimals, and fractions, and explain their reasoning out loud or on paper. They should also use a coordinate grid, find volume by counting unit cubes or using length times width times height, and choose a sensible tool for the job.

Is it normal for students to count on their fingers or draw pictures?

Yes, and it is a good sign they are reasoning, not guessing. Pictures, number lines, and tally marks are real math tools at this age. Speed comes later, once the thinking is solid.

How much homework practice is reasonable at home?

Short and steady beats long and rare. Fifteen to twenty minutes of focused practice four nights a week, mixed with real-life math like money, cooking, or time, builds more than an hour-long Sunday session.

What does a student learn in ?

This is the year math stretches into decimals and fractions as serious tools, not just leftovers from whole numbers. Students add and subtract fractions with unlike bottoms, multiply and divide with decimals to the hundredths, and use exponents to think about place value. They also start reading and writing longer number expressions with parentheses. By spring, students can add one-half and one-third at the kitchen table and explain the answer.

Fractions
Decimals
Place value
Multi-step problems
Volume
Coordinate grids

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
Place value and decimals
Students extend place value to decimals out to the thousandths. They read, write, and compare decimal numbers, and round them to a chosen place.
2
Operations with whole numbers and decimals
Students multiply and divide multi-digit whole numbers and start adding, subtracting, multiplying, and dividing decimals. Word problems show up in money and measurement.
3
Adding and subtracting fractions
Students add and subtract fractions with different denominators, including mixed numbers. They check whether an answer makes sense by comparing it to a benchmark like one half.
4
Multiplying and dividing fractions
Students multiply fractions and divide whole numbers by unit fractions. They use these skills in recipes, measurement, and sharing problems.
5
Measurement, data, and volume
Students convert between units like inches and feet or grams and kilograms. They also find the volume of boxes by counting unit cubes and using length times width times height.
6
Graphing and shapes
Students plot points on a coordinate grid and use it to solve simple problems. They sort shapes like triangles and quadrilaterals by their properties.

Mastery Learning Standards

The required skills a student should display by the end of Grade 5.

Standards for Mathematical Practice

Make Sense of Problems

NH-MATH.MP.5.1

Students read a math problem carefully, figure out what it's actually asking, and keep trying even when the first approach doesn't work.
Reason Abstractly

NH-MATH.MP.5.2

Students take a real problem (like sharing 24 apples among 6 kids) and turn it into numbers and symbols to solve it, then translate the answer back into what it actually means in the real world.
Construct Arguments

NH-MATH.MP.5.3

Students explain why their math answer is correct and point out where a classmate's reasoning goes wrong. The focus is on backing up a solution with logic, not just getting the right number.
Model with Mathematics

NH-MATH.MP.5.4

Students use math to make sense of real situations, like splitting a bill, reading a chart, or figuring out how long a trip will take. The math connects to something that actually exists outside the classroom.
Use Tools Strategically

NH-MATH.MP.5.5

Students choose the right tool for the math problem in front of them. That might mean reaching for a calculator, sketching on paper, or making a quick estimate to check whether an answer makes sense.
Attend to Precision

NH-MATH.MP.5.6

Students choose words, labels, and units carefully when solving problems. That means writing "centimeters" instead of just a number, or saying "the sum" instead of "the answer."
Use Structure

NH-MATH.MP.5.7

Students notice patterns and hidden structure in numbers, shapes, and equations, then use what they spot to solve problems more efficiently. It is recognizing that a shortcut exists before reaching for a calculator.
Express Regularity

NH-MATH.MP.5.8

Students notice when a math process keeps working the same way and use that pattern as a shortcut or rule. Instead of solving each problem from scratch, they ask why it works and write it as a general method.

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.5.1
Reason Abstractly	Students take a real problem (like sharing 24 apples among 6 kids) and turn it into numbers and symbols to solve it, then translate the answer back into what it actually means in the real world.	NH-MATH.MP.5.2
Construct Arguments	Students explain why their math answer is correct and point out where a classmate's reasoning goes wrong. The focus is on backing up a solution with logic, not just getting the right number.	NH-MATH.MP.5.3
Model with Mathematics	Students use math to make sense of real situations, like splitting a bill, reading a chart, or figuring out how long a trip will take. The math connects to something that actually exists outside the classroom.	NH-MATH.MP.5.4
Use Tools Strategically	Students choose the right tool for the math problem in front of them. That might mean reaching for a calculator, sketching on paper, or making a quick estimate to check whether an answer makes sense.	NH-MATH.MP.5.5
Attend to Precision	Students choose words, labels, and units carefully when solving problems. That means writing "centimeters" instead of just a number, or saying "the sum" instead of "the answer."	NH-MATH.MP.5.6
Use Structure	Students notice patterns and hidden structure in numbers, shapes, and equations, then use what they spot to solve problems more efficiently. It is recognizing that a shortcut exists before reaching for a calculator.	NH-MATH.MP.5.7
Express Regularity	Students notice when a math process keeps working the same way and use that pattern as a shortcut or rule. Instead of solving each problem from scratch, they ask why it works and write it as a general method.	NH-MATH.MP.5.8

Standards for Mathematical Practice

Make Sense of Problems

NH-MATH.MP.5.1

Students read a math problem carefully, figure out what it's actually asking, and keep trying even when the first approach doesn't work.
Reason Abstractly

NH-MATH.MP.5.2

Students take a real problem (like sharing 24 apples among 6 kids) and turn it into numbers and symbols to solve it, then translate the answer back into what it actually means in the real world.
Construct Arguments

NH-MATH.MP.5.3

Students explain why their math answer is correct and point out where a classmate's reasoning goes wrong. The focus is on backing up a solution with logic, not just getting the right number.
Model with Mathematics

NH-MATH.MP.5.4

Students use math to make sense of real situations, like splitting a bill, reading a chart, or figuring out how long a trip will take. The math connects to something that actually exists outside the classroom.
Use Tools Strategically

NH-MATH.MP.5.5

Students choose the right tool for the math problem in front of them. That might mean reaching for a calculator, sketching on paper, or making a quick estimate to check whether an answer makes sense.
Attend to Precision

NH-MATH.MP.5.6

Students choose words, labels, and units carefully when solving problems. That means writing "centimeters" instead of just a number, or saying "the sum" instead of "the answer."
Use Structure

NH-MATH.MP.5.7

Students notice patterns and hidden structure in numbers, shapes, and equations, then use what they spot to solve problems more efficiently. It is recognizing that a shortcut exists before reaching for a calculator.
Express Regularity

NH-MATH.MP.5.8

Students notice when a math process keeps working the same way and use that pattern as a shortcut or rule. Instead of solving each problem from scratch, they ask why it works and write it as a general method.

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.5.1
Reason Abstractly	Students take a real problem (like sharing 24 apples among 6 kids) and turn it into numbers and symbols to solve it, then translate the answer back into what it actually means in the real world.	NH-MATH.MP.5.2
Construct Arguments	Students explain why their math answer is correct and point out where a classmate's reasoning goes wrong. The focus is on backing up a solution with logic, not just getting the right number.	NH-MATH.MP.5.3
Model with Mathematics	Students use math to make sense of real situations, like splitting a bill, reading a chart, or figuring out how long a trip will take. The math connects to something that actually exists outside the classroom.	NH-MATH.MP.5.4
Use Tools Strategically	Students choose the right tool for the math problem in front of them. That might mean reaching for a calculator, sketching on paper, or making a quick estimate to check whether an answer makes sense.	NH-MATH.MP.5.5
Attend to Precision	Students choose words, labels, and units carefully when solving problems. That means writing "centimeters" instead of just a number, or saying "the sum" instead of "the answer."	NH-MATH.MP.5.6
Use Structure	Students notice patterns and hidden structure in numbers, shapes, and equations, then use what they spot to solve problems more efficiently. It is recognizing that a shortcut exists before reaching for a calculator.	NH-MATH.MP.5.7
Express Regularity	Students notice when a math process keeps working the same way and use that pattern as a shortcut or rule. Instead of solving each problem from scratch, they ask why it works and write it as a general method.	NH-MATH.MP.5.8

K-8 Mathematics Content

Counting and Number

NH-MATH.K8.5.1

Students work with whole numbers, fractions, and negative numbers, using what they know about how our number system is built to solve grade-level problems.
Operations and Algebraic Thinking

NH-MATH.K8.5.2

Students write and solve math expressions using addition, subtraction, multiplication, and division. They learn to read a problem, set it up as an equation, and work through the steps to find the answer.
Measurement and Data

NH-MATH.K8.5.3

Students read and build tables and graphs to make sense of real data, like survey results or measurements. They also look at what the numbers say overall, such as the average or the spread of the data.
Geometry

NH-MATH.K8.5.4

Students sort and measure flat shapes (like triangles and rectangles) and solid shapes (like cubes and cones). They explain what makes each shape distinct, using side lengths, angles, and face counts.
Ratios and Proportional Relationships

NH-MATH.K8.5.5

Students use ratio reasoning to solve everyday problems at the grade 5 level, such as comparing quantities, finding equivalent ratios, or figuring out how much of something is needed when a recipe or mixture scales up or down.

Standard	Definition	Code
Counting and Number	Students work with whole numbers, fractions, and negative numbers, using what they know about how our number system is built to solve grade-level problems.	NH-MATH.K8.5.1
Operations and Algebraic Thinking	Students write and solve math expressions using addition, subtraction, multiplication, and division. They learn to read a problem, set it up as an equation, and work through the steps to find the answer.	NH-MATH.K8.5.2
Measurement and Data	Students read and build tables and graphs to make sense of real data, like survey results or measurements. They also look at what the numbers say overall, such as the average or the spread of the data.	NH-MATH.K8.5.3
Geometry	Students sort and measure flat shapes (like triangles and rectangles) and solid shapes (like cubes and cones). They explain what makes each shape distinct, using side lengths, angles, and face counts.	NH-MATH.K8.5.4
Ratios and Proportional Relationships	Students use ratio reasoning to solve everyday problems at the grade 5 level, such as comparing quantities, finding equivalent ratios, or figuring out how much of something is needed when a recipe or mixture scales up or down.	NH-MATH.K8.5.5

K-8 Mathematics Content

Counting and Number

NH-MATH.K8.5.1

Students work with whole numbers, fractions, and negative numbers, using what they know about how our number system is built to solve grade-level problems.
Operations and Algebraic Thinking

NH-MATH.K8.5.2

Students write and solve math expressions using addition, subtraction, multiplication, and division. They learn to read a problem, set it up as an equation, and work through the steps to find the answer.
Measurement and Data

NH-MATH.K8.5.3

Students read and build tables and graphs to make sense of real data, like survey results or measurements. They also look at what the numbers say overall, such as the average or the spread of the data.
Geometry

NH-MATH.K8.5.4

Students sort and measure flat shapes (like triangles and rectangles) and solid shapes (like cubes and cones). They explain what makes each shape distinct, using side lengths, angles, and face counts.
Ratios and Proportional Relationships

NH-MATH.K8.5.5

Students use ratio reasoning to solve everyday problems at the grade 5 level, such as comparing quantities, finding equivalent ratios, or figuring out how much of something is needed when a recipe or mixture scales up or down.

Standard	Definition	Code
Counting and Number	Students work with whole numbers, fractions, and negative numbers, using what they know about how our number system is built to solve grade-level problems.	NH-MATH.K8.5.1
Operations and Algebraic Thinking	Students write and solve math expressions using addition, subtraction, multiplication, and division. They learn to read a problem, set it up as an equation, and work through the steps to find the answer.	NH-MATH.K8.5.2
Measurement and Data	Students read and build tables and graphs to make sense of real data, like survey results or measurements. They also look at what the numbers say overall, such as the average or the spread of the data.	NH-MATH.K8.5.3
Geometry	Students sort and measure flat shapes (like triangles and rectangles) and solid shapes (like cubes and cones). They explain what makes each shape distinct, using side lengths, angles, and face counts.	NH-MATH.K8.5.4
Ratios and Proportional Relationships	Students use ratio reasoning to solve everyday problems at the grade 5 level, such as comparing quantities, finding equivalent ratios, or figuring out how much of something is needed when a recipe or mixture scales up or down.	NH-MATH.K8.5.5

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 should students know by the end of the year?
By spring, students should add, subtract, multiply, and divide with larger whole numbers, work with decimals to the hundredths, and add and subtract fractions with unlike bottoms. They should also read graphs, find the volume of a box, and plot points on a grid.
How can families help with math at home in just a few minutes?
Cook together and double or halve a recipe. Ask students to estimate the grocery total before checkout, then compare. At dinner, ask how to split a bill four ways or how much pizza is left as a fraction.
What if a student gets stuck on a word problem?
Ask them to read it once for the story and once for the question. Then ask what they already know and what they need to find. Drawing a quick picture or writing the numbers in a simple sentence often unsticks the rest.
Do students still need to practice their times tables?
Yes. Fluent multiplication and division facts make this year much easier, because fractions, decimals, and long division all lean on them. Five minutes of flashcards or a quick car-ride quiz a few times a week is enough to keep facts sharp.
How should fractions and decimals be sequenced across the year?
Build fraction equivalence and addition with unlike bottoms before moving into multiplication and division of fractions. Decimals to the hundredths fit well alongside place value early in the year, so students can connect 0.25 and one quarter before operations get heavier.
Which skills usually need the most reteaching?
Adding and subtracting fractions with unlike bottoms, dividing with two-digit divisors, and interpreting remainders in word problems tend to need a second pass. Volume also trips students up when they confuse it with area.
What does mastery look like heading into next year?
Students should solve multi-step problems with whole numbers, decimals, and fractions, and explain their reasoning out loud or on paper. They should also use a coordinate grid, find volume by counting unit cubes or using length times width times height, and choose a sensible tool for the job.
Is it normal for students to count on their fingers or draw pictures?
Yes, and it is a good sign they are reasoning, not guessing. Pictures, number lines, and tally marks are real math tools at this age. Speed comes later, once the thinking is solid.
How much homework practice is reasonable at home?
Short and steady beats long and rare. Fifteen to twenty minutes of focused practice four nights a week, mixed with real-life math like money, cooking, or time, builds more than an hour-long Sunday session.