Multiplication and division basics
Students learn what it means to multiply and divide. They picture equal groups, draw arrays, and solve simple word problems within 100.
This is the year math leans hard on multiplication and division. Students learn their times tables by heart and use them to solve word problems, find the area of a rectangle, and split shapes into equal parts. Fractions show up as real numbers on a number line, not just slices of pizza. By spring, students can multiply any two single-digit numbers from memory and tell time to the nearest minute.
Students learn what it means to multiply and divide. They picture equal groups, draw arrays, and solve simple word problems within 100.
Students use patterns and the link between multiplication and division to learn their times tables. By the end of this stretch, students should know all one-digit products from memory.
Students round to the nearest ten or hundred and add and subtract within 1,000. They also multiply by numbers like 20, 50, or 80 using place value.
Students see fractions as real numbers, not just slices of pizza. They place fractions on a number line, find equal fractions like 1/2 and 2/4, and compare which is bigger.
Students tell time to the minute, measure liquids and weights in standard units, and read scaled bar and picture graphs. They also measure lengths to the half and quarter inch.
Students find the area of rectangles by tiling and by multiplying sides. They measure perimeter, sort quadrilaterals like squares and rhombuses, and split shapes into equal parts.
Multiplication and division are the focus here. Students learn to see multiplication as equal groups (3 groups of 4) and division as splitting a total into equal parts, then use that thinking to solve word problems.
Multiplication means putting equal groups together. Students read 5 x 7 as "5 groups of 7" and find the total, like 5 bags with 7 apples each.
Students learn what division actually means: splitting a group of objects into equal shares. If 56 crayons are split among 8 kids, how many does each kid get? Or, how many groups of 8 can you make?
Word problems ask students to figure out how many equal groups there are, how many are in each group, or how many total. Students solve by drawing pictures or writing equations with a box or letter standing in for the missing number.
Students find the missing number in a multiplication or division problem, like figuring out what goes in the blank in 6 x __ = 42. It's the skill behind checking whether an answer makes sense.
Multiplication and division are two sides of the same fact. Students learn that 3 x 4 and 12 / 4 are connected, and that changing the order of factors (like 3 x 4 or 4 x 3) gives the same product.
Shortcuts make multiplication faster. Students learn that changing the order of numbers or breaking a bigger number into smaller parts gives the same answer, so they can solve harder problems without starting from scratch.
Division is multiplication in reverse. Students solve a division problem by asking "what number times this equals that?" instead of splitting into groups.
Students practice multiplication and division with numbers up to 100, building toward quick, reliable recall. Think times tables and splitting groups evenly.
Students practice multiplying and dividing numbers up to 100 until the answers come quickly from memory. By the end of third grade, students know all the times tables through 9 x 9 without stopping to count.
Students use addition, subtraction, multiplication, and division to solve word problems, then spot and explain patterns they notice in the answers.
Students solve word problems that take two separate steps to finish, using any mix of adding, subtracting, multiplying, or dividing. They write an equation with a letter as the missing number, then check whether their answer makes sense by estimating.
Students look at number charts or tables to spot repeating patterns, then explain in words why those patterns happen. For example, they notice that adding two even numbers always gives an even result and explain why that makes sense.
| Standard | Definition | Code |
|---|---|---|
| Represent and solve problems involving multiplication and division | Multiplication and division are the focus here. Students learn to see multiplication as equal groups (3 groups of 4) and division as splitting a total into equal parts, then use that thinking to solve word problems. | 3.OA.A |
| Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number… | Multiplication means putting equal groups together. Students read 5 x 7 as "5 groups of 7" and find the total, like 5 bags with 7 apples each. | 3.OA.1 |
| Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as… | Students learn what division actually means: splitting a group of objects into equal shares. If 56 crayons are split among 8 kids, how many does each kid get? Or, how many groups of 8 can you make? | 3.OA.2 |
| Use multiplication and division within 100 to solve word problems in situations… | Word problems ask students to figure out how many equal groups there are, how many are in each group, or how many total. Students solve by drawing pictures or writing equations with a box or letter standing in for the missing number. | 3.OA.3 |
| Determine the unknown whole number in a multiplication or division equation… | Students find the missing number in a multiplication or division problem, like figuring out what goes in the blank in 6 x __ = 42. It's the skill behind checking whether an answer makes sense. | 3.OA.4 |
| Understand properties of multiplication and the relationship between… | Multiplication and division are two sides of the same fact. Students learn that 3 x 4 and 12 / 4 are connected, and that changing the order of factors (like 3 x 4 or 4 x 3) gives the same product. | 3.OA.B |
| Apply properties of operations as strategies to multiply and divide | Shortcuts make multiplication faster. Students learn that changing the order of numbers or breaking a bigger number into smaller parts gives the same answer, so they can solve harder problems without starting from scratch. | 3.OA.5 |
| Understand division as an unknown-factor problem | Division is multiplication in reverse. Students solve a division problem by asking "what number times this equals that?" instead of splitting into groups. | 3.OA.6 |
| Multiply and divide within 100 | Students practice multiplication and division with numbers up to 100, building toward quick, reliable recall. Think times tables and splitting groups evenly. | 3.OA.C |
| Fluently multiply and divide within 100, using strategies such as the… | Students practice multiplying and dividing numbers up to 100 until the answers come quickly from memory. By the end of third grade, students know all the times tables through 9 x 9 without stopping to count. | 3.OA.7 |
| Solve problems involving the four operations | Students use addition, subtraction, multiplication, and division to solve word problems, then spot and explain patterns they notice in the answers. | 3.OA.D |
| Solve two-step word problems using the four operations | Students solve word problems that take two separate steps to finish, using any mix of adding, subtracting, multiplying, or dividing. They write an equation with a letter as the missing number, then check whether their answer makes sense by estimating. | 3.OA.8 |
| Identify arithmetic patterns | Students look at number charts or tables to spot repeating patterns, then explain in words why those patterns happen. For example, they notice that adding two even numbers always gives an even result and explain why that makes sense. | 3.OA.9 |
Students use what they know about hundreds, tens, and ones to add, subtract, and multiply numbers with more than one digit.
Students learn to look at a number and decide whether it's closer to the nearest ten or hundred. A number like 47 rounds up to 50; a number like 43 rounds down to 40.
Students add and subtract numbers up to 1000 quickly and accurately. They use what they know about hundreds, tens, and ones to choose a strategy that works, not just follow steps by memory.
Students multiply a single number by a round number like 30, 60, or 80. They use what they know about tens to find the answer, so 4 x 70 becomes four groups of seven tens.
| Standard | Definition | Code |
|---|---|---|
| Use place value understanding and properties of operations to perform… | Students use what they know about hundreds, tens, and ones to add, subtract, and multiply numbers with more than one digit. | 3.NBT.A |
| Use place value understanding to round whole numbers to the nearest 10 or 100 | Students learn to look at a number and decide whether it's closer to the nearest ten or hundred. A number like 47 rounds up to 50; a number like 43 rounds down to 40. | 3.NBT.1 |
| Fluently add and subtract within 1000 using strategies and algorithms based on… | Students add and subtract numbers up to 1000 quickly and accurately. They use what they know about hundreds, tens, and ones to choose a strategy that works, not just follow steps by memory. | 3.NBT.2 |
| Multiply one-digit whole numbers by multiples of 10 in the range 10–90 | Students multiply a single number by a round number like 30, 60, or 80. They use what they know about tens to find the answer, so 4 x 70 becomes four groups of seven tens. | 3.NBT.3 |
Fractions are numbers, not just shaded shapes on a worksheet. Students learn to place fractions on a number line and compare them the way they compare whole numbers.
Students learn that fractions describe equal parts of a whole. If you cut a shape into 4 equal pieces, one piece is 1/4, and three pieces is 3/4.
Students place fractions on a number line, showing where a fraction like 1/2 or 3/4 falls between 0 and 1. The number line proves fractions are real numbers, not just pieces of a shape.
Students place a fraction like 1/4 on a number line by splitting the space between 0 and 1 into equal parts and marking where the first part ends. That mark is the fraction's location.
Students place a fraction on a number line by counting equal-sized jumps from zero. After enough jumps, the stopping point shows exactly where that fraction lives between two whole numbers.
Students learn that two different fractions can name the same amount, like 1/2 and 2/4, and practice deciding which of two fractions is larger by thinking about what each piece of the whole looks like.
Two fractions are equivalent when they take up the same amount of space or land on the same spot on a number line. Students learn to recognize when different-looking fractions, like 1/2 and 2/4, actually name the same value.
Students find two fractions that name the same amount, like showing that half a pizza equals two out of four equal slices. They use a drawing or diagram to explain why both fractions point to the same size piece.
Students practice writing a whole number, like 3, as a fraction (3/1) and recognize that some fractions, like 4/4, equal exactly 1. It connects the fraction notation they're learning to numbers they already know.
Students compare two fractions by thinking about the size of each piece or how many pieces there are. They use the symbols >, =, or < to show which fraction is bigger, smaller, or equal, and explain their thinking with a drawing or diagram.
| Standard | Definition | Code |
|---|---|---|
| Develop understanding of fractions as numbers | Fractions are numbers, not just shaded shapes on a worksheet. Students learn to place fractions on a number line and compare them the way they compare whole numbers. | 3.NF.A |
| Understand a fraction 1/b as the quantity formed by 1 part when a whole is… | Students learn that fractions describe equal parts of a whole. If you cut a shape into 4 equal pieces, one piece is 1/4, and three pieces is 3/4. | 3.NF.1 |
| Understand a fraction as a number on the number line | Students place fractions on a number line, showing where a fraction like 1/2 or 3/4 falls between 0 and 1. The number line proves fractions are real numbers, not just pieces of a shape. | 3.NF.2 |
| Represent a fraction 1/b on a number line diagram by defining the interval from… | Students place a fraction like 1/4 on a number line by splitting the space between 0 and 1 into equal parts and marking where the first part ends. That mark is the fraction's location. | 3.NF.2.a |
| Represent a fraction a/b on a number line diagram by marking off a lengths 1/b… | Students place a fraction on a number line by counting equal-sized jumps from zero. After enough jumps, the stopping point shows exactly where that fraction lives between two whole numbers. | 3.NF.2.b |
| Explain equivalence of fractions in special cases | Students learn that two different fractions can name the same amount, like 1/2 and 2/4, and practice deciding which of two fractions is larger by thinking about what each piece of the whole looks like. | 3.NF.3 |
| Understand two fractions as equivalent | Two fractions are equivalent when they take up the same amount of space or land on the same spot on a number line. Students learn to recognize when different-looking fractions, like 1/2 and 2/4, actually name the same value. | 3.NF.3.a |
| Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3) | Students find two fractions that name the same amount, like showing that half a pizza equals two out of four equal slices. They use a drawing or diagram to explain why both fractions point to the same size piece. | 3.NF.3.b |
| Express whole numbers as fractions | Students practice writing a whole number, like 3, as a fraction (3/1) and recognize that some fractions, like 4/4, equal exactly 1. It connects the fraction notation they're learning to numbers they already know. | 3.NF.3.c |
| Compare two fractions with the same numerator or the same denominator by… | Students compare two fractions by thinking about the size of each piece or how many pieces there are. They use the symbols >, =, or < to show which fraction is bigger, smaller, or equal, and explain their thinking with a drawing or diagram. | 3.NF.3.d |
Reading a bar graph or picture chart, students figure out what the data means and answer questions about it.
Students practice reading and building bar graphs where each block stands for more than one thing. Then they use those graphs to answer questions like "how many more" or "how many fewer" by comparing the bars.
Students measure real objects to the nearest half or quarter inch, then plot each measurement on a number line to show how the results are spread out.
Students read clocks, measure liquid in cups or liters, and weigh objects in grams or kilograms. They use those measurements to solve word problems and make reasonable estimates when an exact answer isn't needed.
Students read a clock to the nearest minute and figure out how many minutes have passed between two times. They solve problems like "the movie started at 2:14 and ended at 2:52, how long did it last?"
Students measure how heavy objects are and how much liquid containers hold, using grams, kilograms, and liters. Then they solve word problems with those measurements by adding, subtracting, multiplying, or dividing.
Students figure out how much space a flat shape covers, measured in square units. They connect that idea to multiplication, so finding the area of a rectangle becomes a times-table problem instead of counting squares one by one.
Area measures how much flat space a shape covers. Students learn to think of that space as filled with same-size squares and begin counting those squares to measure it.
A unit square is a square where each side measures 1 unit. Students use it as the basic building block for measuring area, the same way a ruler uses inches to measure length.
Covering a flat shape with same-size squares, without leaving gaps or stacking squares, tells students how much surface the shape takes up. That count of squares is the area.
Students count the square tiles that fit inside a shape to measure how much surface it covers. Those squares might be square inches, square centimeters, or any same-size square unit.
Students find the area of a rectangle by multiplying its side lengths, then connect that to addition by seeing each row of square units as a group. It ties together what they know about multiplication and shapes.
Students cover a rectangle with square tiles, count the total, then confirm that multiplying the two side lengths gives the same answer. It connects hands-on measuring to multiplication.
Students multiply the length and width of a rectangle to find its area, like figuring out how many square tiles cover a floor. They also work backward, using a rectangle's area to make sense of multiplication.
Students use rows and columns of square tiles to show why multiplying a side by two added lengths gives the same answer as multiplying each length separately and adding the results. It builds the logic behind how multiplication distributes across addition.
Students break an irregular shape into smaller rectangles, find the area of each piece, then add those areas together. This works for real-world shapes like floor plans or garden beds.
Students measure the distance around shapes like squares and rectangles and learn why that measurement is different from the space inside.
Students add up the side lengths of shapes to find the distance around them. They also work backward to find a missing side, and compare rectangles that have the same perimeter but different amounts of space inside.
| Standard | Definition | Code |
|---|---|---|
| Represent and interpret data | Reading a bar graph or picture chart, students figure out what the data means and answer questions about it. | 3.MD.A |
| Draw a scaled picture graph and a scaled bar graph to represent a data set with… | Students practice reading and building bar graphs where each block stands for more than one thing. Then they use those graphs to answer questions like "how many more" or "how many fewer" by comparing the bars. | 3.MD.3 |
| Generate measurement data by measuring lengths using rulers marked with halves… | Students measure real objects to the nearest half or quarter inch, then plot each measurement on a number line to show how the results are spread out. | 3.MD.4 |
| Solve problems involving measurement and estimation of intervals of time… | Students read clocks, measure liquid in cups or liters, and weigh objects in grams or kilograms. They use those measurements to solve word problems and make reasonable estimates when an exact answer isn't needed. | 3.MD.B |
| Tell and write time to the nearest minute and measure time intervals in minutes | Students read a clock to the nearest minute and figure out how many minutes have passed between two times. They solve problems like "the movie started at 2:14 and ended at 2:52, how long did it last?" | 3.MD.1 |
| Measure and estimate liquid volumes and masses of objects using standard units… | Students measure how heavy objects are and how much liquid containers hold, using grams, kilograms, and liters. Then they solve word problems with those measurements by adding, subtracting, multiplying, or dividing. | 3.MD.2 |
| Geometric measurement | Students figure out how much space a flat shape covers, measured in square units. They connect that idea to multiplication, so finding the area of a rectangle becomes a times-table problem instead of counting squares one by one. | 3.MD.C |
| Recognize area as an attribute of plane figures and understand concepts of area… | Area measures how much flat space a shape covers. Students learn to think of that space as filled with same-size squares and begin counting those squares to measure it. | 3.MD.5 |
| A square with side length 1 unit, called "a unit square," is said to have "one… | A unit square is a square where each side measures 1 unit. Students use it as the basic building block for measuring area, the same way a ruler uses inches to measure length. | 3.MD.5.a |
| A plane figure which can be covered without gaps or overlaps by n unit squares… | Covering a flat shape with same-size squares, without leaving gaps or stacking squares, tells students how much surface the shape takes up. That count of squares is the area. | 3.MD.5.b |
| Measure areas by counting unit squares | Students count the square tiles that fit inside a shape to measure how much surface it covers. Those squares might be square inches, square centimeters, or any same-size square unit. | 3.MD.6 |
| Relate area to the operations of multiplication and addition | Students find the area of a rectangle by multiplying its side lengths, then connect that to addition by seeing each row of square units as a group. It ties together what they know about multiplication and shapes. | 3.MD.7 |
| Find the area of a rectangle with whole-number side lengths by tiling it | Students cover a rectangle with square tiles, count the total, then confirm that multiplying the two side lengths gives the same answer. It connects hands-on measuring to multiplication. | 3.MD.7.a |
| Multiply side lengths to find areas of rectangles with whole-number side… | Students multiply the length and width of a rectangle to find its area, like figuring out how many square tiles cover a floor. They also work backward, using a rectangle's area to make sense of multiplication. | 3.MD.7.b |
| Use tiling to show in a concrete case that the area of a rectangle with… | Students use rows and columns of square tiles to show why multiplying a side by two added lengths gives the same answer as multiplying each length separately and adding the results. It builds the logic behind how multiplication distributes across addition. | 3.MD.7.c |
| Find areas of rectilinear figures by decomposing them into non-overlapping… | Students break an irregular shape into smaller rectangles, find the area of each piece, then add those areas together. This works for real-world shapes like floor plans or garden beds. | 3.MD.7.d |
| Geometric measurement | Students measure the distance around shapes like squares and rectangles and learn why that measurement is different from the space inside. | 3.MD.D |
| Solve real world and mathematical problems involving perimeters of polygons… | Students add up the side lengths of shapes to find the distance around them. They also work backward to find a missing side, and compare rectangles that have the same perimeter but different amounts of space inside. | 3.MD.8 |
Students sort and compare shapes by their sides, angles, and other features, grouping them by what they have in common.
Shapes like squares and rectangles all have four sides, which makes them part of the same bigger family. Students sort shapes into that family and draw four-sided shapes that don't fit the familiar names.
Students cut shapes like squares and circles into equal pieces, then name each piece as a fraction of the whole shape. A square split into 4 equal parts means each part is one-fourth.
| Standard | Definition | Code |
|---|---|---|
| Reason with shapes and their attributes | Students sort and compare shapes by their sides, angles, and other features, grouping them by what they have in common. | 3.G.A |
| Understand that shapes in different categories | Shapes like squares and rectangles all have four sides, which makes them part of the same bigger family. Students sort shapes into that family and draw four-sided shapes that don't fit the familiar names. | 3.G.1 |
| Partition shapes into parts with equal areas | Students cut shapes like squares and circles into equal pieces, then name each piece as a fraction of the whole shape. A square split into 4 equal parts means each part is one-fourth. | 3.G.2 |
This is the year students learn their times tables and start dividing. They also work with fractions as real numbers, measure time to the minute, and find the area of rectangles by multiplying the sides.
Five minutes of practice most days beats one long session. Pick one fact family at a time, like the fives or the threes, and practice in the car or at dinner. By the end of the year, students should know all the products of two one-digit numbers from memory.
Students learn that a fraction is a number, not just a piece of pizza. Help at home by cutting food into equal parts and naming them, or by marking halves and fourths on a ruler. Talk about which fraction is bigger and why.
Start with equal groups and arrays so students understand what multiplication means before drilling facts. Introduce the connection to division early, then build fluency through properties like the distributive property. Save two-step word problems for after students are comfortable with single-step ones.
Fractions on a number line and the difference between area and perimeter trip students up every year. Plan extra time for both, and use physical tiles and rulers before moving to drawings. Word problems with two steps also need steady practice from fall to spring.
Ask them to draw the problem before solving it. A quick sketch of groups, an array, or a bar model often shows whether to multiply, divide, add, or subtract. Then ask if the answer makes sense.
Students should know multiplication and division facts within 100 from memory, add and subtract within 1,000, compare simple fractions, tell time to the minute, and find the area and perimeter of rectangles. They should also solve two-step word problems and check whether their answer is reasonable.
They can answer a fact like 7 times 8 without counting, explain why 2/4 equals 1/2, and find the area of a rectangle by multiplying the sides. They can also read a clock to the minute and solve a word problem that takes two steps.
Often, especially for fractions and area. Tiles, number lines, and rulers give students something to reason about before they move to equations. Pull the tools back only when students can explain their thinking without them.