This is the year math stretches past whole numbers and starts running on decimals and fractions. Students add and subtract fractions with unlike bottoms, multiply and divide fractions in real situations, and work with decimals out to the hundredths place. They also start writing simple expressions and plotting points on a grid. By spring, students can solve a multi-step word problem mixing fractions and decimals.
Students start the year working with very large and very small numbers. They learn how moving a digit one place to the left or right multiplies or divides it by ten, and they read and compare decimals to the thousandths.
Students multiply larger numbers by hand and divide with two-digit numbers. Word problems get longer, so students also practice deciding which operation the situation is actually asking for.
Students add and subtract fractions with different bottom numbers, like one half plus one third. They learn to rewrite the fractions so the pieces are the same size before combining them, and they check whether answers make sense.
Students multiply fractions and divide whole numbers by unit fractions, such as sharing three cups of flour into quarter-cup scoops. They also do arithmetic with decimals to the hundredths in money and measurement problems.
Students convert between units like inches and feet or grams and kilograms within the same system. They read line plots with fractional measurements and start finding the volume of boxes by counting unit cubes.
Students plot points on a grid using pairs of numbers and use the grid to solve simple real-world problems. They also sort shapes like rectangles, rhombuses, and squares by their properties.
Students read a math problem carefully, figure out what it's actually asking, and keep trying even when the first approach doesn't work.
Students take a word problem apart to work with the numbers, then put the story back together to make sure the answer actually makes sense in real life.
Students explain why their math answer is correct, using numbers or examples as proof. They also listen to a classmate's reasoning and push back if something doesn't add up.
Students use math to make sense of real situations, like figuring out how much something costs, splitting a bill, or planning a schedule. The math they choose fits the problem in front of them.
Students choose the right tool for the math problem in front of them, whether that means reaching for a calculator, sketching it out on paper, or making a quick estimate in their head.
Students choose words, labels, and numbers carefully so their math work says exactly what they mean. That means naming the right unit (inches, not just "numbers"), using math terms correctly, and checking that calculations are exact.
Students notice patterns and hidden structure in numbers, shapes, and problems, then use those patterns as shortcuts to solve something new. It's the habit of asking "wait, I've seen this before."
When the same steps keep appearing in a problem, students notice the pattern and use it as a shortcut. That habit saves time and builds toward general rules that work across many problems.
| 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. | VT-MATH.MP.5.1 |
| Reason Abstractly | Students take a word problem apart to work with the numbers, then put the story back together to make sure the answer actually makes sense in real life. | VT-MATH.MP.5.2 |
| Construct Arguments | Students explain why their math answer is correct, using numbers or examples as proof. They also listen to a classmate's reasoning and push back if something doesn't add up. | VT-MATH.MP.5.3 |
| Model with Mathematics | Students use math to make sense of real situations, like figuring out how much something costs, splitting a bill, or planning a schedule. The math they choose fits the problem in front of them. | VT-MATH.MP.5.4 |
| Use Tools Strategically | Students choose the right tool for the math problem in front of them, whether that means reaching for a calculator, sketching it out on paper, or making a quick estimate in their head. | VT-MATH.MP.5.5 |
| Attend to Precision | Students choose words, labels, and numbers carefully so their math work says exactly what they mean. That means naming the right unit (inches, not just "numbers"), using math terms correctly, and checking that calculations are exact. | VT-MATH.MP.5.6 |
| Use Structure | Students notice patterns and hidden structure in numbers, shapes, and problems, then use those patterns as shortcuts to solve something new. It's the habit of asking "wait, I've seen this before." | VT-MATH.MP.5.7 |
| Express Regularity | When the same steps keep appearing in a problem, students notice the pattern and use it as a shortcut. That habit saves time and builds toward general rules that work across many problems. | VT-MATH.MP.5.8 |
Students work with whole numbers, fractions, and basic negative numbers, using what they know about how numbers fit together to solve grade-level problems.
Students write number sentences and solve word problems using addition, subtraction, multiplication, and division. They also learn to read and write expressions like 3 x (4 + 2) without solving them.
Students read and build tables, graphs, and simple data summaries to answer real questions about the world. The focus is on what the numbers actually mean, not just how to plot them.
Students sort, describe, and measure flat and solid shapes, such as triangles, rectangles, and cubes. They use what they know about angles, sides, and faces to explain why a shape belongs to a certain group.
Students use ratio thinking to compare quantities and solve everyday problems, like figuring out how many cups of juice to mix with water for a larger batch. The math connects multiplication and division to real situations.
| Standard | Definition | Code |
|---|---|---|
| Counting and Number | Students work with whole numbers, fractions, and basic negative numbers, using what they know about how numbers fit together to solve grade-level problems. | VT-MATH.K8.5.1 |
| Operations and Algebraic Thinking | Students write number sentences and solve word problems using addition, subtraction, multiplication, and division. They also learn to read and write expressions like 3 x (4 + 2) without solving them. | VT-MATH.K8.5.2 |
| Measurement and Data | Students read and build tables, graphs, and simple data summaries to answer real questions about the world. The focus is on what the numbers actually mean, not just how to plot them. | VT-MATH.K8.5.3 |
| Geometry | Students sort, describe, and measure flat and solid shapes, such as triangles, rectangles, and cubes. They use what they know about angles, sides, and faces to explain why a shape belongs to a certain group. | VT-MATH.K8.5.4 |
| Ratios and Proportional Relationships | Students use ratio thinking to compare quantities and solve everyday problems, like figuring out how many cups of juice to mix with water for a larger batch. The math connects multiplication and division to real situations. | VT-MATH.K8.5.5 |
Vermont's spring summative math test for grades 3 through 9, aligned to Vermont's Common Core-based math standards.
Students should add, subtract, multiply, and divide larger whole numbers with confidence, work with decimals to the hundredths, and add and subtract fractions with different bottom numbers. They should also handle volume of boxes and plot points on a grid.
Ask students to read the problem out loud and explain what is happening before touching any numbers. Then ask what they already know and what they are trying to find. Drawing a quick picture or acting it out with coins or blocks often unsticks the thinking.
Spend the first months tightening place value and multi-digit operations, then move into decimals so students see them as another way to write fractions. Save fraction addition and subtraction with unlike bottom numbers for the middle of the year, once equivalent fractions feel solid.
Yes. Fluent recall of multiplication facts through 12 makes everything this year easier, from long division to finding common denominators. Five minutes a day of flashcards or a quick game in the car goes a long way.
Fraction addition with unlike denominators and dividing by a two-digit number tend to need a second pass. Decimal place value also slips when students stop connecting it to fractions of a whole, so keep that link visible on the board.
Use money and measuring cups. Ask students to add prices at the store, figure out change from a ten-dollar bill, or double a recipe that uses 0.25 of a cup. Saying decimals out loud as fractions, like twenty-five hundredths, builds the connection.
Students should solve multi-step problems with whole numbers, decimals, and fractions, explain their reasoning in writing, and use a coordinate grid without prompting. If they can also estimate before computing and catch their own errors, they are ready for ratios and rates next year.