Place value to 100,000
Students start the year reading and writing larger numbers, up to one hundred thousand. They compare numbers, round them, and find 100, 1,000, or 10,000 more or less in their head.
This is the year arithmetic gets bigger and faster. Students read and round numbers up to 100,000, memorize their multiplication facts through ten, and start multiplying a two-digit number by a one-digit number. Fractions show up as real pieces of a whole, with halves, thirds, fourths, sixths, and eighths on number lines and in shapes. By spring, students can tell time to the nearest five minutes, find the perimeter and area of a rectangle, and solve word problems with all four operations.
Students start the year reading and writing larger numbers, up to one hundred thousand. They compare numbers, round them, and find 100, 1,000, or 10,000 more or less in their head.
Students add and subtract numbers up to five digits using paper-and-pencil methods. They estimate first to check that an answer makes sense, and solve word problems about everyday situations.
Students learn what multiplication means using groups, arrays, and skip counting. By the end of this stretch they know their times tables through ten and see how division undoes multiplication.
Students work with halves, thirds, fourths, sixths, and eighths using shapes, number lines, and sets of objects. They learn the words numerator and denominator and compare fractions of the same whole.
Students sort flat and solid shapes, name angles, and measure with rulers in inches and centimeters. They find the distance around a shape and learn why multiplying length by width gives the area of a rectangle.
Students tell time to the nearest five minutes and figure out how long something takes. They count coins and bills in real situations, and read bar graphs and pictographs to answer questions about data.
Reading and writing numbers up to 100,000, then comparing them using place value. Students explain why one number is larger or smaller by looking at the value of each digit's position.
Students read, write, and show numbers up to 100,000 in different ways: as digits, as words, and as pictures or diagrams. They also break a number apart to show what each digit is worth, like seeing 350 as 3 hundreds and 5 tens.
Students break a number like 45,302 into its ten thousands, thousands, hundreds, tens, and ones. They write it out in words, in standard form, and expanded form (40,000 + 5,000 + 300 + 2).
In their heads, without pencil or paper, students add or subtract 100, 1,000, or 10,000 from a number up to 99,999. The goal is recognizing which digit changes and which ones stay the same.
Students line up numbers as large as 100,000 and say which is greater, which is less, and which are equal. They write those comparisons using the symbols <, >, and =.
Students learn to round a number like 47,000 to the nearest thousand or ten-thousand by looking at which "neighbor" it sits closer to on a number line. It builds the estimation habit students use whenever an exact number isn't needed.
Students use addition, subtraction, multiplication, and division to solve problems they might actually encounter, like splitting a bill, sharing items equally, or figuring out a total cost.
Students show what multiplication means using pictures, objects, and patterns. They might draw equal rows of dots, hop by equal steps on a number line, or group counters to show that 3 groups of 4 equals 12.
Students practice multiplication facts until they can recall them quickly, using numbers 1 through 10. Think times tables: 6 x 7, 8 x 9, and every combination in between.
Adding and subtracting numbers up to five digits long, like 47,382 plus 6,519. Students work toward doing this accurately and confidently, using what they know about place value to keep track of each column.
Students decide when an exact number isn't needed and round to the nearest ten, hundred, thousand, or ten thousand to get a quick estimate of a sum or difference.
Students solve everyday word problems by adding or subtracting whole numbers, then check whether the answer makes sense given what the problem is actually asking.
Students learn that division means splitting a total into equal groups, then connect that idea back to multiplication. They practice with objects, drawings, and repeated subtraction to see how the two operations work together.
Students use what they know about multiplication to figure out a division problem, and vice versa. If 4 times 6 equals 24, they know 24 divided by 6 equals 4.
Students multiply a two-digit number by a one-digit number using whatever strategy makes sense to them, such as drawing an array, breaking the number apart by place value, or repeated addition.
Students match fractions to real situations, like splitting a pizza into equal slices or shading part of a shape, and explain why that fraction fits.
Students read and write fractions using numbers and words, learning that the bottom number (denominator) names how many equal parts a whole is split into, and the top number (numerator) counts how many of those parts are being used.
Students show fractions like one-half or one-fourth by dividing a shape into equal parts, grouping objects into equal sets, or marking equal sections on a number line or ruler.
Students break fractions apart and put them back together using the same whole. For example, they see that 3/4 is the same as three separate 1/4 pieces added together.
Students put fractions in order from smallest to largest using pictures, fraction bars, or a number line. All the fractions refer to pieces of the same whole shape or same total amount.
Students count a mix of coins or bills to find the total dollar and cent amount, then use that total to figure out how much something costs or how much change is owed.
Students count a mix of coins, add them up, and write the total using the cent symbol. They also practice making change or combining amounts in simple money situations.
Students add and subtract a mix of dollar bills to solve money problems, keeping totals at or under twenty dollars. No coins involved, just whole dollar amounts.
| Standard | Definition | Code |
|---|---|---|
| Compare and represent whole numbers up to 100,000 with an emphasis on place… | Reading and writing numbers up to 100,000, then comparing them using place value. Students explain why one number is larger or smaller by looking at the value of each digit's position. | 3.N.1 |
| Read, write, discuss | Students read, write, and show numbers up to 100,000 in different ways: as digits, as words, and as pictures or diagrams. They also break a number apart to show what each digit is worth, like seeing 350 as 3 hundreds and 5 tens. | 3.N.1.1 |
| Use place value to describe whole numbers between 1,000 and 100,000 in terms of… | Students break a number like 45,302 into its ten thousands, thousands, hundreds, tens, and ones. They write it out in words, in standard form, and expanded form (40,000 + 5,000 + 300 + 2). | 3.N.1.2 |
| Applying knowledge of place values, use mental strategies | In their heads, without pencil or paper, students add or subtract 100, 1,000, or 10,000 from a number up to 99,999. The goal is recognizing which digit changes and which ones stay the same. | 3.N.1.3 |
| Use place value to compare and order whole numbers, up to 100,000, using… | Students line up numbers as large as 100,000 and say which is greater, which is less, and which are equal. They write those comparisons using the symbols <, >, and =. | 3.N.1.4 |
| Use place value understanding to round numbers to the nearest thousand… | Students learn to round a number like 47,000 to the nearest thousand or ten-thousand by looking at which "neighbor" it sits closer to on a number line. It builds the estimation habit students use whenever an exact number isn't needed. | 3.N.1.5 |
| Solve real-world and mathematical problems using addition, subtraction… | Students use addition, subtraction, multiplication, and division to solve problems they might actually encounter, like splitting a bill, sharing items equally, or figuring out a total cost. | 3.N.2 |
| Represent multiplication facts by modeling a variety of approaches | Students show what multiplication means using pictures, objects, and patterns. They might draw equal rows of dots, hop by equal steps on a number line, or group counters to show that 3 groups of 4 equals 12. | 3.N.2.1 |
| Demonstrate fluency with multiplication facts using factors up to 10 | Students practice multiplication facts until they can recall them quickly, using numbers 1 through 10. Think times tables: 6 x 7, 8 x 9, and every combination in between. | 3.N.2.2 |
| Use strategies and algorithms based on knowledge of place value and equality to… | Adding and subtracting numbers up to five digits long, like 47,382 plus 6,519. Students work toward doing this accurately and confidently, using what they know about place value to keep track of each column. | 3.N.2.3 |
| Recognize when to round numbers and apply understanding to estimate sums and… | Students decide when an exact number isn't needed and round to the nearest ten, hundred, thousand, or ten thousand to get a quick estimate of a sum or difference. | 3.N.2.4 |
| Use addition and subtraction to solve problems involving whole numbers | Students solve everyday word problems by adding or subtracting whole numbers, then check whether the answer makes sense given what the problem is actually asking. | 3.N.2.5 |
| Represent division facts and divisibility by modeling a variety of approaches | Students learn that division means splitting a total into equal groups, then connect that idea back to multiplication. They practice with objects, drawings, and repeated subtraction to see how the two operations work together. | 3.N.2.6 |
| Apply the relationship between multiplication and division to represent and… | Students use what they know about multiplication to figure out a division problem, and vice versa. If 4 times 6 equals 24, they know 24 divided by 6 equals 4. | 3.N.2.7 |
| Use various strategies | Students multiply a two-digit number by a one-digit number using whatever strategy makes sense to them, such as drawing an array, breaking the number apart by place value, or repeated addition. | 3.N.2.8 |
| Use and justify fractional representations in real-world and mathematical… | Students match fractions to real situations, like splitting a pizza into equal slices or shading part of a shape, and explain why that fraction fits. | 3.N.3 |
| Read and write fractions with words and symbols using appropriate terminology | Students read and write fractions using numbers and words, learning that the bottom number (denominator) names how many equal parts a whole is split into, and the top number (numerator) counts how many of those parts are being used. | 3.N.3.1 |
| Model fractions using length, set | Students show fractions like one-half or one-fourth by dividing a shape into equal parts, grouping objects into equal sets, or marking equal sections on a number line or ruler. | 3.N.3.2 |
| Apply understanding of unit fractions and use this understanding to compose and… | Students break fractions apart and put them back together using the same whole. For example, they see that 3/4 is the same as three separate 1/4 pieces added together. | 3.N.3.3 |
| Use models and number lines to order and compare fractions that are related to… | Students put fractions in order from smallest to largest using pictures, fraction bars, or a number line. All the fractions refer to pieces of the same whole shape or same total amount. | 3.N.3.4 |
| Determine the value of a set of coins and determine the value of a set of bills… | Students count a mix of coins or bills to find the total dollar and cent amount, then use that total to figure out how much something costs or how much change is owed. | 3.N.4 |
| Use addition and subtraction to determine the value of a collection of coins up… | Students count a mix of coins, add them up, and write the total using the cent symbol. They also practice making change or combining amounts in simple money situations. | 3.N.4.1 |
| Add and subtract a collection of bills up to twenty dollars using whole dollars… | Students add and subtract a mix of dollar bills to solve money problems, keeping totals at or under twenty dollars. No coins involved, just whole dollar amounts. | 3.N.4.2 |
Students spot patterns in number sequences and shapes, then draw or extend them to show what comes next. This is the building block for understanding how math rules repeat and predict.
Students find the rule in a number pattern, such as "add 5 each time," then use that rule to predict what comes next or solve a problem. The pattern can grow by adding, shrinking by subtracting, or jump by multiplying.
Students look at a table of number pairs and figure out the one math rule connecting them, such as "always add 5" or "multiply by 3."
Students look at a shape pattern that grows or shrinks and figure out what comes next. They also draw or build the next step themselves.
Students write and solve multiplication equations that include a missing number, using everyday situations like equal groups of objects or items in rows to find the answer.
Students figure out a missing number in a simple equation like 4 x ? = 28, using what they know about addition, subtraction, and multiplication. They also write their own word problems to match a given number sentence.
Students learn that you can swap numbers in a multiplication or addition problem and still get the same answer, and that grouping them differently works too. These patterns help students solve problems faster without changing the result.
| Standard | Definition | Code |
|---|---|---|
| Describe and create representations of numerical and geometric patterns | Students spot patterns in number sequences and shapes, then draw or extend them to show what comes next. This is the building block for understanding how math rules repeat and predict. | 3.A.1 |
| Create, describe, and extend patterns involving addition, subtraction | Students find the rule in a number pattern, such as "add 5 each time," then use that rule to predict what comes next or solve a problem. The pattern can grow by adding, shrinking by subtracting, or jump by multiplying. | 3.A.1.1 |
| Describe the rule (limited to a single operation) for a pattern from an… | Students look at a table of number pairs and figure out the one math rule connecting them, such as "always add 5" or "multiply by 3." | 3.A.1.2 |
| Explore and develop visual representations of increasing and decreasing… | Students look at a shape pattern that grows or shrinks and figure out what comes next. They also draw or build the next step themselves. | 3.A.1.3 |
| Use number sentences involving multiplication and unknowns to represent and… | Students write and solve multiplication equations that include a missing number, using everyday situations like equal groups of objects or items in rows to find the answer. | 3.A.2 |
| Use number sense with the properties of addition, subtraction | Students figure out a missing number in a simple equation like 4 x ? = 28, using what they know about addition, subtraction, and multiplication. They also write their own word problems to match a given number sentence. | 3.A.2.1 |
| Identify, represent, and apply the number properties | Students learn that you can swap numbers in a multiplication or addition problem and still get the same answer, and that grouping them differently works too. These patterns help students solve problems faster without changing the result. | 3.A.2.2 |
Students sort and describe shapes by their sides, angles, and corners, then use those features to draw polygons or build 3-D figures like prisms and pyramids.
Students sort 3-D shapes like cubes, cones, and pyramids by what they notice about them: flat faces, curved surfaces, or the number of edges. It's the same skill as sorting blocks into groups.
Students look at a picture of a 3-D shape and build the same shape using small cubes. The goal is matching the structure cube by cube, counting layers and rows to get the shape right.
Students look at the corners of shapes and sort them by size: corners smaller than a right angle, exactly square, wider than a right angle, or fully flat. This skill builds the vocabulary students use to describe and compare shapes precisely.
Students measure real objects by choosing the right tool for the job, such as a ruler for length or a scale for weight. They learn which tool fits which question and read the result accurately.
Students add up the lengths of all sides of a shape to find its total distance around the outside. They practice with different shapes using whole-number measurements.
Students break a rectangle into small square tiles, count them in rows and columns, then see why multiplying the two side lengths gives the total number of tiles. It's the "why" behind the area formula, not just the answer.
Students pack a box or other 3-D shape with small cubes, counting carefully to find how many cubes fill it completely or halfway.
Students count small squares packed inside a flat shape to find out how much surface it covers. This is area, and it works the same way whether the shape is a rectangle on paper or a floor tile in the hallway.
Students pick the right tool (a ruler for small objects, a meter stick for larger ones) and measure how long something is to the nearest centimeter or meter.
Students pick the right tool for the job, then measure real objects to the nearest yard, foot, or half inch. A half inch is the smallest unit they work with here.
Students read an analog thermometer (the kind with a colored liquid line) and report the temperature in both Fahrenheit and Celsius, rounding to the nearest degree.
Students read a clock and name the time to the nearest five minutes, like 3:15 or 7:45. They use that skill to solve word problems about schedules and elapsed time.
Students read a clock face and write the time it shows, working to the nearest five minutes. They do this with both the old-style clock with hands and the digital display with numbers.
Students add and subtract time on a clock, working in five-minute jumps up to an hour. They use tools like a number line or a picture of a clock face to find answers to problems like "How many minutes between 2:15 and 2:45?"
| Standard | Definition | Code |
|---|---|---|
| Analyze and use geometric attributes to describe and create polygons and… | Students sort and describe shapes by their sides, angles, and corners, then use those features to draw polygons or build 3-D figures like prisms and pyramids. | 3.GM.1 |
| Sort three-dimensional shapes based on attributes | Students sort 3-D shapes like cubes, cones, and pyramids by what they notice about them: flat faces, curved surfaces, or the number of edges. It's the same skill as sorting blocks into groups. | 3.GM 1.1 |
| Build a three-dimensional figure using unit cubes when shown a picture of a… | Students look at a picture of a 3-D shape and build the same shape using small cubes. The goal is matching the structure cube by cube, counting layers and rows to get the shape right. | 3.GM.1.2 |
| Classify angles within a polygon as acute, right, obtuse | Students look at the corners of shapes and sort them by size: corners smaller than a right angle, exactly square, wider than a right angle, or fully flat. This skill builds the vocabulary students use to describe and compare shapes precisely. | 3.GM.1.3 |
| Understand measurable attributes of real-world and mathematical objects using… | Students measure real objects by choosing the right tool for the job, such as a ruler for length or a scale for weight. They learn which tool fits which question and read the result accurately. | 3.GM.2 |
| Find the perimeter of a polygon, given whole number lengths of the sides, using… | Students add up the lengths of all sides of a shape to find its total distance around the outside. They practice with different shapes using whole-number measurements. | 3.GM.2.1 |
| Analyze why length and width are multiplied to find the area of a rectangle by… | Students break a rectangle into small square tiles, count them in rows and columns, then see why multiplying the two side lengths gives the total number of tiles. It's the "why" behind the area formula, not just the answer. | 3.GM.2.2 |
| Count cubes systematically to identify the number of cubes needed to pack the… | Students pack a box or other 3-D shape with small cubes, counting carefully to find how many cubes fill it completely or halfway. | 3.GM.2.3 |
| Find the area of two-dimensional figures by counting the total number of… | Students count small squares packed inside a flat shape to find out how much surface it covers. This is area, and it works the same way whether the shape is a rectangle on paper or a floor tile in the hallway. | 3.GM.2.4 |
| Choose an appropriate measurement instrument and measure the length of objects… | Students pick the right tool (a ruler for small objects, a meter stick for larger ones) and measure how long something is to the nearest centimeter or meter. | 3.GM.2.5 |
| Choose an appropriate measurement instrument and measure the length of objects… | Students pick the right tool for the job, then measure real objects to the nearest yard, foot, or half inch. A half inch is the smallest unit they work with here. | 3.GM.2.6 |
| Use an analog thermometer to determine temperature to the nearest degree in… | Students read an analog thermometer (the kind with a colored liquid line) and report the temperature in both Fahrenheit and Celsius, rounding to the nearest degree. | 3.GM.2.7 |
| Solve problems by telling time to the nearest five-minute interval | Students read a clock and name the time to the nearest five minutes, like 3:15 or 7:45. They use that skill to solve word problems about schedules and elapsed time. | 3.GM.3 |
| Read and write time to the nearest five-minute interval | Students read a clock face and write the time it shows, working to the nearest five minutes. They do this with both the old-style clock with hands and the digital display with numbers. | 3.GM.3.1 |
| Determine the solutions to problems involving addition and subtraction of time… | Students add and subtract time on a clock, working in five-minute jumps up to an hour. They use tools like a number line or a picture of a clock face to find answers to problems like "How many minutes between 2:15 and 2:45?" | 3.GM.3.2 |
Students gather information, sort it into a chart or graph, and answer questions about what the data shows.
Students gather information, sort it into groups, and display it in a chart or graph where each mark or bar stands for more than one item.
Students read a bar graph or pictograph and use the numbers to solve a problem, sometimes in two steps. The graph's scale might count by twos, fives, or tens instead of ones.
| Standard | Definition | Code |
|---|---|---|
| Collect, organize, and analyze data | Students gather information, sort it into a chart or graph, and answer questions about what the data shows. | 3.D.1 |
| Collect and organize a data set with multiple categories using a frequency… | Students gather information, sort it into groups, and display it in a chart or graph where each mark or bar stands for more than one item. | 3.D.1.1 |
| Solve one- and two-step problems using categorical data represented with a… | Students read a bar graph or pictograph and use the numbers to solve a problem, sometimes in two steps. The graph's scale might count by twos, fives, or tens instead of ones. | 3.D.1.2 |
Students should multiply and divide within 100, add and subtract numbers up to 100,000, and read and compare those bigger numbers using place value. They should also work with fractions like halves, thirds, and fourths, tell time to the nearest five minutes, and find the area and perimeter of rectangles.
Practice facts up to ten times ten for a few minutes most days. Mix flashcards with real questions like how many shoes are in four pairs or how many cookies fit on three rows of six. The goal is quick, confident recall by spring.
Start with place value to 100,000 so students can read, compare, and round bigger numbers. Then build addition and subtraction strategies on that base before moving into multiplication facts and two-digit by one-digit multiplication. Division comes in alongside multiplication so students see the two as a pair.
Use food and paper. Fold a sandwich into halves, then fourths, and talk about how four fourths make a whole. Draw a number line from 0 to 1 and mark halves and fourths so fractions feel like points on a line, not just slices.
Multiplication fact fluency, comparing fractions with different denominators, and rounding to the nearest thousand or ten thousand tend to need the most return visits. Word problems that mix addition and subtraction across multiple steps also need steady practice all year.
Place value is the engine behind almost everything else this year. Once students see that 3,400 is 34 hundreds or 3 thousands and 4 hundreds, rounding, mental math, and standard addition and subtraction all get easier. Time spent here pays off later.
Keep an analog clock visible and ask what time it will be in 15 or 30 minutes. At the store, let students count out coins and bills and figure out the change. Five quick questions a week builds real comfort.
Ready students can recall multiplication facts up to ten, add and subtract five-digit numbers, and explain why a fraction like three fourths is bigger than one half. They can also find the area and perimeter of a rectangle and read a bar graph to answer a two-step question.