Multiplication and division basics
Students learn what multiplication and division mean by grouping objects and sharing them out. They start memorizing times tables up to ten and use them to solve simple word problems.
This is the year math shifts from adding and subtracting to thinking in groups. Students learn what multiplication and division actually mean, and they practice times tables until the facts come quickly. Fractions show up as real numbers students can place on a ruler, not just slices of pizza. By spring, they can solve a word problem like "six packs of eight juice boxes" without counting one by one.
Students learn what multiplication and division mean by grouping objects and sharing them out. They start memorizing times tables up to ten and use them to solve simple word problems.
Students work with numbers up to a thousand. They round to the nearest ten or hundred and add and subtract larger numbers using paper-and-pencil methods.
Students meet fractions as equal parts of a whole, like slices of a pizza. They place fractions on a number line and figure out when two fractions, such as one half and two fourths, are the same size.
Students tell time to the minute, measure liquids and weights, and read bar graphs and picture graphs. They use rulers marked in halves and quarters of an inch.
Students sort shapes by their sides and angles and learn that area is the space inside a shape. They find the area of rectangles by counting squares and measure the distance around a shape.
Students read a math problem carefully, figure out what it's asking, and keep trying even when the first approach doesn't work.
Students take a word problem and translate it into numbers and symbols to solve it, then explain what the answer means in real life. Math and meaning go in both directions.
Students explain how they got their answer and say whether a classmate's thinking makes sense. They back up their reasoning with numbers or examples from the problem.
Students use math to make sense of real situations, like figuring out how much something costs or how to split a snack equally. They show their thinking with drawings, numbers, or equations.
Students choose the right tool for the job, whether that means using a ruler, estimating in their head, or working it out on paper.
Students use the right math words, label their answers with the correct units (like inches or dollars), and check that their calculations are exact. Sloppy shortcuts or misused terms count as wrong.
Students learn to spot patterns and hidden rules in math, like noticing that a multiplication table has symmetry or that shapes can be broken into simpler pieces. Seeing the structure helps them solve new problems faster.
When the same steps keep showing up in a problem, students notice the pattern and use it as a shortcut. That habit saves time and builds number sense.
| Standard | Definition | Code |
|---|---|---|
| Make Sense of Problems | Students read a math problem carefully, figure out what it's asking, and keep trying even when the first approach doesn't work. | MD-MATH.MP.3.1 |
| Reason Abstractly | Students take a word problem and translate it into numbers and symbols to solve it, then explain what the answer means in real life. Math and meaning go in both directions. | MD-MATH.MP.3.2 |
| Construct Arguments | Students explain how they got their answer and say whether a classmate's thinking makes sense. They back up their reasoning with numbers or examples from the problem. | MD-MATH.MP.3.3 |
| Model with Mathematics | Students use math to make sense of real situations, like figuring out how much something costs or how to split a snack equally. They show their thinking with drawings, numbers, or equations. | MD-MATH.MP.3.4 |
| Use Tools Strategically | Students choose the right tool for the job, whether that means using a ruler, estimating in their head, or working it out on paper. | MD-MATH.MP.3.5 |
| Attend to Precision | Students use the right math words, label their answers with the correct units (like inches or dollars), and check that their calculations are exact. Sloppy shortcuts or misused terms count as wrong. | MD-MATH.MP.3.6 |
| Use Structure | Students learn to spot patterns and hidden rules in math, like noticing that a multiplication table has symmetry or that shapes can be broken into simpler pieces. Seeing the structure helps them solve new problems faster. | MD-MATH.MP.3.7 |
| Express Regularity | When the same steps keep showing up in a problem, students notice the pattern and use it as a shortcut. That habit saves time and builds number sense. | MD-MATH.MP.3.8 |
Students work with whole numbers, fractions, and basic number relationships that show up in third-grade math. They count, compare, and reason about numbers to make sense of everyday quantities.
Students practice solving word problems using addition, subtraction, multiplication, and division. They learn to choose the right operation for the situation and show their thinking clearly.
Students read and build bar graphs, picture graphs, and simple tables to answer questions about the data shown. They use the numbers in those displays to compare amounts and draw conclusions.
Students sort and describe flat and solid shapes by their sides, angles, and faces. They also measure shapes to find things like area and perimeter.
Students use ratio reasoning to solve everyday problems, like figuring out how many cookies to make if a recipe doubles. They compare quantities and use that relationship to find a missing number.
| Standard | Definition | Code |
|---|---|---|
| Counting and Number | Students work with whole numbers, fractions, and basic number relationships that show up in third-grade math. They count, compare, and reason about numbers to make sense of everyday quantities. | MD-MATH.K8.3.1 |
| Operations and Algebraic Thinking | Students practice solving word problems using addition, subtraction, multiplication, and division. They learn to choose the right operation for the situation and show their thinking clearly. | MD-MATH.K8.3.2 |
| Measurement and Data | Students read and build bar graphs, picture graphs, and simple tables to answer questions about the data shown. They use the numbers in those displays to compare amounts and draw conclusions. | MD-MATH.K8.3.3 |
| Geometry | Students sort and describe flat and solid shapes by their sides, angles, and faces. They also measure shapes to find things like area and perimeter. | MD-MATH.K8.3.4 |
| Ratios and Proportional Relationships | Students use ratio reasoning to solve everyday problems, like figuring out how many cookies to make if a recipe doubles. They compare quantities and use that relationship to find a missing number. | MD-MATH.K8.3.5 |
Maryland's spring summative math test for grades 3 through 8, aligned to the Maryland College and Career-Ready Standards for Mathematics.
The big focus is multiplication and division up to 100, and understanding fractions as equal parts of a whole. Students also work with area, perimeter, time, and reading bar graphs. By spring, most problems involve two steps and a written explanation.
Practice the times tables in short bursts, five minutes at dinner or in the car. Skip-count out loud by 3s, 4s, 6s, 7s, and 8s. Quick recall of these facts makes everything later in the year easier, from division to fractions.
Students should see a fraction like 3/4 as three equal parts out of four, place it on a number line, and tell which of two fractions is bigger when the pieces are the same size. Pizza slices, measuring cups, and folded paper all help.
Start with equal groups and arrays so the meaning is solid before the facts. Build the 2s, 5s, and 10s first, then 3s and 4s, then the harder facts using known ones. Save two-step word problems for after students can explain a one-step problem clearly.
Read the problem together and ask what is happening before asking for an answer. Have students draw a quick picture or act it out with coins or blocks. The drawing usually shows whether the problem needs adding, taking away, grouping, or sharing.
Division as the partner to multiplication is a common sticking point, especially when the unknown is the group size. Fractions on a number line and the difference between area and perimeter also tend to need a second pass later in the year.
Yes. Students should add and subtract within 1,000 fluently and use those skills inside larger problems. Ten minutes a week of mixed practice keeps the earlier work sharp while the new multiplication work takes center stage.
By June, students should recall most facts up to 10 times 10, solve a two-step word problem and explain the steps, compare simple fractions with a drawing, and find the area of a rectangle by multiplying. Comfort with all four operations is the strongest signal.