Multiplication and division basics
Students learn what it means to multiply and divide with small numbers, using groups of objects, arrays, and skip counting. Times tables start to feel familiar by the end of this stretch.
What does a student learn in
This is the year math shifts from adding and subtracting into multiplying and dividing. Students learn their times tables and use them to solve real word problems, not just bare equations. Fractions show up as real numbers for the first time, with halves, thirds, and fourths placed on a number line. By spring, they can recall multiplication facts up to ten and explain why two fractions like 1/2 and 2/4 are the same amount.
- Multiplication
- Division
- Times tables
- Fractions
- Word problems
- Area and perimeter
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
Word problems and number patterns
Students use multiplication and division to solve real story problems, like sharing snacks or arranging chairs. They also spot patterns in the times tables and explain why they work.
- 3
Place value and bigger numbers
Students round numbers to the nearest ten or hundred and add and subtract within 1,000. Mental math gets faster, and written work gets neater.
- 4
Fractions on a number line
Fractions start here. Students see halves, thirds, and fourths as parts of a whole and as points on a number line, and they learn when two fractions are equal.
- 5
Measurement, time, and data
Students tell time to the minute, measure length and liquid volume, and read bar graphs and picture graphs. Word problems mix in money and minutes.
- 6
Shapes, area, and perimeter
Students sort shapes by their sides and angles, then find the area of a rectangle by counting squares or multiplying side lengths. Perimeter shows up in problems about fences and frames.
Mastery Learning Standards
The required skills a student should display by the end of Grade 3.
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 asking, and keep trying even when it gets hard. If one approach isn't working, they try a different one.
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Reason Abstractly
Students take a word problem and turn it into numbers and symbols to solve it, then translate the answer back into plain language. The math connects to something real.
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Construct Arguments
Students explain why their math answer is correct and listen to how classmates solved the same problem. They practice agreeing or respectfully disagreeing with another student's reasoning.
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Model with Mathematics
Students use math to make sense of real situations, like figuring out if there is enough money to buy lunch or how many chairs fit in a row. They draw pictures, write numbers, or build equations to solve problems that show up outside of class.
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Use Tools Strategically
Students choose the right tool for the job, whether that means a ruler, a calculator, pencil and paper, or a quick mental estimate. The point is picking what actually helps, not just grabbing the nearest thing.
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Attend to Precision
Students choose words, labels, and numbers carefully when explaining their math work. That means using the right unit (inches, not just "a number") and checking that calculations are exact before sharing an answer.
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Use Structure
Students learn to spot patterns and relationships in math, like noticing that shapes, equations, or number sequences follow a rule. Recognizing that structure helps students solve new problems faster.
-
Express Regularity
Students notice when the same steps keep showing up in a problem and use that pattern as a shortcut. Instead of starting from scratch each time, they ask why the pattern works and use it to solve new problems faster.
| Standard | Definition | Code |
|---|---|---|
| Make Sense of Problems | Students read a math problem carefully, figure out what it's asking, and keep trying even when it gets hard. If one approach isn't working, they try a different one. | DC-MATH.MP.3.1 |
| Reason Abstractly | Students take a word problem and turn it into numbers and symbols to solve it, then translate the answer back into plain language. The math connects to something real. | DC-MATH.MP.3.2 |
| Construct Arguments | Students explain why their math answer is correct and listen to how classmates solved the same problem. They practice agreeing or respectfully disagreeing with another student's reasoning. | DC-MATH.MP.3.3 |
| Model with Mathematics | Students use math to make sense of real situations, like figuring out if there is enough money to buy lunch or how many chairs fit in a row. They draw pictures, write numbers, or build equations to solve problems that show up outside of class. | DC-MATH.MP.3.4 |
| Use Tools Strategically | Students choose the right tool for the job, whether that means a ruler, a calculator, pencil and paper, or a quick mental estimate. The point is picking what actually helps, not just grabbing the nearest thing. | DC-MATH.MP.3.5 |
| Attend to Precision | Students choose words, labels, and numbers carefully when explaining their math work. That means using the right unit (inches, not just "a number") and checking that calculations are exact before sharing an answer. | DC-MATH.MP.3.6 |
| Use Structure | Students learn to spot patterns and relationships in math, like noticing that shapes, equations, or number sequences follow a rule. Recognizing that structure helps students solve new problems faster. | DC-MATH.MP.3.7 |
| Express Regularity | Students notice when the same steps keep showing up in a problem and use that pattern as a shortcut. Instead of starting from scratch each time, they ask why the pattern works and use it to solve new problems faster. | DC-MATH.MP.3.8 |
K-8 Mathematics Content
K-8 Mathematics Content
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Counting and Number
Third graders work with whole numbers, fractions, and basic number relationships. They count, compare, and reason about numbers to solve problems that fit the grade level.
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Operations and Algebraic Thinking
Third graders solve word problems using addition, subtraction, multiplication, and division. They learn when to use each operation and write number sentences that show their work.
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Measurement and Data
Students read and build bar graphs, picture graphs, and simple tables to answer questions about real data. They pull a specific number from a chart or figure out how much more one group has than another.
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Geometry
Students sort and describe flat and solid shapes by their sides, angles, and faces. They measure shapes and group them by what those features have in common.
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Ratios and Proportional Relationships
Ratio reasoning shows up in grade 3 as comparing groups, like "3 apples for every 2 oranges." Students use that kind of thinking to solve everyday problems involving equal groups and simple comparisons.
| Standard | Definition | Code |
|---|---|---|
| Counting and Number | Third graders work with whole numbers, fractions, and basic number relationships. They count, compare, and reason about numbers to solve problems that fit the grade level. | DC-MATH.K8.3.1 |
| Operations and Algebraic Thinking | Third graders solve word problems using addition, subtraction, multiplication, and division. They learn when to use each operation and write number sentences that show their work. | DC-MATH.K8.3.2 |
| Measurement and Data | Students read and build bar graphs, picture graphs, and simple tables to answer questions about real data. They pull a specific number from a chart or figure out how much more one group has than another. | DC-MATH.K8.3.3 |
| Geometry | Students sort and describe flat and solid shapes by their sides, angles, and faces. They measure shapes and group them by what those features have in common. | DC-MATH.K8.3.4 |
| Ratios and Proportional Relationships | Ratio reasoning shows up in grade 3 as comparing groups, like "3 apples for every 2 oranges." Students use that kind of thinking to solve everyday problems involving equal groups and simple comparisons. | DC-MATH.K8.3.5 |
Assessments
The state tests students at this grade and subject take.
DC CAPE: Mathematics (Grades 3-8)
DC's spring summative math test for grades 3 through 8, aligned to DC's Common Core-based math standards.
- When given:
- spring
- Frequency:
- annual
MSAA (Multi-State Alternate Assessment)
Alternate assessment for students with the most significant cognitive disabilities, given in grades 3-8 and high school in ELA, math, and science.
- When given:
- spring
- Frequency:
- annual
Common Questions
What math should my child know by the end of the year?
Students should know their times tables up to 10, divide small numbers, and solve word problems with all four operations. They should also understand simple fractions like halves, thirds, and fourths, and be able to find the area of a rectangle by counting squares.
How can I help with multiplication at home?
Practice short bursts of times tables during everyday moments, like setting the table or sorting laundry into equal piles. Ask questions like how many wheels are on four cars or how many socks are in three pairs. Five minutes a day beats a long weekend session.
What does mastery of fractions look like at this age?
Students should see a fraction as equal parts of a whole, place simple fractions on a number line, and tell when two fractions are equal in size. Folding paper, slicing fruit, and sharing snacks all help make this concrete.
How should multiplication and division be sequenced across the year?
Start with equal groups and arrays, then build the times tables through patterns and properties before moving to division as the inverse. Word problems and fact fluency should run alongside the whole sequence so students apply facts as soon as they learn them.
Which topics usually need the most reteaching?
Fractions on a number line and word problems with two steps tend to need the most return visits. Many students can compute but struggle to decide which operation a problem calls for, so spend planning time on problem types, not just procedures.
My child is stuck on a word problem. What should I do?
Ask students to read the problem out loud, then draw a picture or act it out with objects from the kitchen. The goal is to figure out what is happening before reaching for an operation. Getting the wrong answer with good reasoning is still progress.
How do I know students are ready for fourth grade math?
Look for quick recall of multiplication facts, confidence with simple fractions, and the ability to solve a two-step word problem and explain the steps. Measuring with a ruler, telling time to the minute, and reading a bar graph should also feel routine.
How much time should go to fluency versus problem solving?
Roughly a third of math time on fluency and the rest on reasoning and problem solving works well at this grade. Short daily fact practice protects time for richer tasks where students explain thinking and critique each other's solutions.