Eureka Math, Grade 4

In this Grade 4 Eureka Math lesson from Chapter 1, students learn to interpret a multiplication equation as a comparison by exploring how each place value unit is 10 times as much as the unit below it. Using place value disks and charts, students build understanding of statements like "1 ten is 10 times as much as 1 one" and extend this reasoning through hundreds and thousands. The lesson connects multiplicative comparison language to the base-ten structure of multi-digit whole numbers.

In this Grade 4 Eureka Math lesson from Chapter 1, students learn that each digit in a multi-digit number represents 10 times the value of the same digit one place to its right, building the place value chart up to 1 million. Through place value disks, multiplication sentences, and skip-counting practice, students explore how units like ones, tens, hundreds, and thousands relate by factors of 10. The lesson also introduces dividing to reverse the process, reinforcing the relationship between adjacent place value positions.

In this Grade 4 Eureka Math lesson, students learn to name numbers within 1 million by reading and building a place value chart that groups digits into ones, thousands, and millions periods. They practice identifying the value of digits in numbers like 1,468,357 and discover how commas mark the boundaries between base thousand units. The lesson also introduces the repeating ones-tens-hundreds pattern across place value periods, extending the concept beyond millions to billions and trillions to reinforce the structure of the base ten system.

In this Grade 4 Eureka Math lesson from Chapter 1, students learn to read and write multi-digit numbers using three representations: base ten numerals, number names (word form), and expanded form. The lesson covers numbers up to the hundred thousands place, with students practicing how to break apart digits by place value to write expressions such as 1,000 + 700 + 8 = 1,708. Fluency activities reinforce converting between unit form and standard form across base hundred, thousand, ten-thousand, and hundred-thousand units.

In this Grade 4 Eureka Math lesson from Chapter 2, students learn to compare multi-digit whole numbers up to the hundred thousands place by analyzing the value of each digit, starting with the largest unit. Students practice using the greater than (>), less than (<), and equal to (=) symbols to record comparison statements between numbers such as 43,021 and 45,302. The lesson builds on prior place value knowledge to help students understand why comparing digits must begin with the highest place value unit first.

In this Grade 4 Eureka Math lesson from Chapter 2, students practice finding 1 thousand, 10 thousand, and 100 thousand more and less than a given number using place value charts and number disks. Students build fluency with multi-digit numbers up to the hundred thousands place by identifying how specific units change when adding or subtracting these amounts. The lesson connects skip-counting, expanded form, and place value reasoning to deepen students' understanding of comparing multi-digit whole numbers.

In this Grade 4 Eureka Math lesson, students learn to round multi-digit numbers to the nearest thousand using a vertical number line, including identifying midpoints between consecutive thousands and placing numbers accurately on the line. The lesson builds rounding skills through fluency activities such as finding midpoints, skip-counting by place value, and applying number patterns with numbers up to the hundred thousands. Part of Chapter 3 on rounding multi-digit whole numbers, this lesson lays the conceptual foundation students need before rounding to larger place values.

In this Grade 4 Eureka Math lesson, students learn to round five- and six-digit numbers to the nearest ten thousand and hundred thousand using a vertical number line. They practice identifying endpoints and midpoints on the number line to determine which benchmark a number is closest to, then apply rounding to estimate sums and differences in addition and subtraction problems. The lesson builds place value understanding with multi-digit numbers up to the hundred thousands place.

Grade 4 students learn to round multi-digit whole numbers to any place value — including the nearest thousand, ten thousand, and hundred thousand — without relying on a number line. This Eureka Math lesson builds on place value understanding by identifying the two nearest benchmark numbers, finding the midpoint, and determining which benchmark the number is closer to. Students also apply rounding to real-world problems, such as comparing attendance figures by rounding to the nearest thousand.

In this Grade 4 Eureka Math lesson from Chapter 3, students use place value understanding to round multi-digit numbers to any place value, including the nearest thousand, ten thousand, and hundred thousand. Students practice applying rounding to real world scenarios, such as estimating stamp sales and predicting visitor counts, to determine the most appropriate unit of rounding for a given situation. The lesson builds fluency with multi-digit rounding while developing students' judgment about when different levels of estimation are most useful.

In this Grade 4 Eureka Math lesson from Chapter 4, students use place value understanding to fluently add multi-digit whole numbers using the standard addition algorithm. The lesson builds on rounding and base ten unit skills through fluency practice before guiding students to apply the algorithm to solve word problems with tape diagrams. A real-world calorie-tracking problem helps students connect estimation strategies, including rounding to the nearest thousand and ten thousand, to multi-digit addition.

In this Grade 4 Eureka Math lesson, students practice solving multi-step word problems using the standard addition algorithm modeled with tape diagrams, applying skills like multi-digit addition with regrouping across problems involving numbers in the thousands and hundred-thousands. Students learn to identify unknowns, set up tape diagrams to organize comparative and additive relationships, and then assess the reasonableness of their answers using rounding. The lesson is part of Chapter 4 on Multi-Digit Whole Number Addition and builds fluency with place value rounding alongside the standard algorithm.

In this Grade 4 Eureka Math lesson from Chapter 5, students learn to use place value understanding to regroup across columns — such as unbundling 1 hundred into 10 tens — to apply the standard subtraction algorithm with multi-digit whole numbers. Using place value disks, charts, and tape diagrams, students work through problems like 4,259 − 2,171 to practice identifying when regrouping is needed and recording the renamed values in the algorithm. The lesson also connects subtraction to real-world word problems, reinforcing how tape diagrams model the relationship between the whole and its parts.

In this Grade 4 Eureka Math lesson from Chapter 5, students practice using place value understanding to decompose larger units into smaller units up to three times in order to subtract multi-digit whole numbers using the standard subtraction algorithm. Students work through problems requiring regrouping across the ones, tens, hundreds, and thousands places, such as solving 22,397 minus 3,745 by unbundling thousands and ten thousands. The lesson also applies the algorithm to real-world word problems using tape diagrams to represent the whole, known part, and unknown part.

In this Grade 4 Eureka Math lesson from Chapter 5, students practice using place value understanding to decompose larger units into smaller ones multiple times across all places when applying the standard subtraction algorithm to multi-digit whole numbers. Students work through problems such as 253,421 minus 75,832, regrouping across up to five columns including ones, tens, hundreds, thousands, and ten thousands. They also use tape diagrams to model and solve subtraction word problems, reinforcing the connection between visual representations and the algorithm.

In this Grade 4 Eureka Math lesson from Chapter 5, students practice solving two-step word problems by applying the standard subtraction algorithm and modeling solutions with tape diagrams. They work with multi-digit numbers up to one million, learning to assess the reasonableness of their answers by rounding to the nearest ten thousand. Real-world contexts such as employee counts and website visitor data help students connect multi-digit subtraction to practical problem-solving situations.

Grade 4 students learn to solve additive compare word problems using tape diagrams in this Eureka Math lesson, focusing on "how much more" and "how many fewer" comparisons with multi-digit numbers. Students practice identifying whether the unknown is a missing part and determining when subtraction is needed, even when the language of a problem suggests addition. The lesson also reinforces checking solutions for reasonableness using estimation and rounding.

In this Grade 4 Eureka Math lesson from Chapter 6, students learn to solve multi-step word problems involving addition and subtraction by drawing and labeling tape diagrams. Students practice breaking complex problems into sequential steps, such as finding unknown quantities across multiple conditions, then assess the reasonableness of their answers using rounding and estimation. The lesson builds fluency with large numbers and unit conversions while reinforcing strategic problem-solving skills.

In this Grade 4 Eureka Math lesson, students learn to interpret tape diagrams and equations in order to create and solve their own multi-step word problems. Students practice writing story contexts that match given diagrams, then calculate solutions and evaluate the reasonableness of their answers. The lesson is part of Chapter 6, which focuses on addition and subtraction word problems.

In this Grade 4 Eureka Math lesson from Chapter 7, students learn to express metric length measurements in terms of a smaller unit, converting between kilometers, meters, and centimeters. Using number bonds and tape diagrams, students build fluency with unit conversions and apply that skill to solve addition and subtraction word problems involving mixed metric length units. The lesson connects metric measurement to place value concepts introduced in earlier Grade 4 modules.

Grade 4 students learn to express metric mass measurements in terms of smaller units, converting between kilograms and grams, as part of Eureka Math Chapter 7 on Metric Unit Conversions. The lesson builds on place value understanding to convert mixed units and apply those skills to solve addition and subtraction word problems involving metric mass. Students use number bonds, tape diagrams, and algorithms to model and solve real-world mass problems.

In this Grade 4 Eureka Math lesson from Chapter 7, students learn to convert metric capacity units (liters and milliliters) to a smaller unit and use that skill to solve addition and subtraction word problems involving metric capacity. Students draw tape diagrams and apply algorithms or simplifying strategies to model and solve multi-step problems with mixed units. The lesson builds directly on prior work with metric length and mass conversions, reinforcing how place value connects across all metric unit types.

In this Grade 4 Eureka Math lesson from Chapter 8, students learn to convert between metric units — including meters and centimeters, kilograms and grams, and liters and milliliters — by connecting these conversions to place value relationships. Students practice expressing measurements in different units, such as rewriting 1 m 20 cm as 120 cm or 1,500 g as 1 kg 500 g, building fluency through unit counting and mixed-unit addition. The lesson also applies these skills to a multi-step word problem involving subtraction of mixed metric units.

In this Grade 4 Eureka Math lesson from Chapter 8, students apply addition and subtraction to solve multi-step word problems involving metric units of length, mass, and capacity, including mixed units such as kilograms and grams or liters and milliliters. Students practice converting between metric units and use labeled diagrams and equations to model real-world problems like comparing weights of vegetables measured in mixed units. The lesson builds on prior work with metric conversions to develop fluency and problem-solving strategies with measurement contexts.

In this Grade 4 Eureka Math lesson from Chapter 9, students investigate and apply the formulas for area and perimeter of rectangles, learning to calculate perimeter by adding all four side lengths and area by multiplying length times width. Students practice finding unknown side lengths when given area or perimeter, and explore how the two measurements differ using grid paper models. This lesson builds fluency with multiplication facts and prepares students to solve real-world multiplicative comparison word problems.

In this Grade 4 Eureka Math lesson from Chapter 9, students solve multiplicative comparison word problems by applying the area formula (length × width) and the perimeter formula (2 × (length + width)) for rectangles and squares. Students use square-inch tiles and drawings to understand relationships such as "3 times as long as it is wide" and translate those comparisons into calculations. The lesson builds directly on students' prior knowledge of area and perimeter to connect multiplicative reasoning with real-world measurement contexts.

In this Grade 4 Eureka Math lesson from Chapter 9, students apply area and perimeter formulas to solve multi-step real-world word problems involving multiplicative comparisons. Using the RDW (Read, Draw, Write) approach, they work through scenarios such as comparing screen dimensions using the formula P = 2 × (l + w) and calculating remaining floor space by finding the difference between two rectangular areas. The lesson builds on prior work with unknown factors and prepares students to reason about how scaling dimensions affects both area and perimeter.

In this Grade 4 Eureka Math lesson, students learn to identify and represent patterns when multiplying by 10, 100, and 1,000 using place value disks and place value charts. They explore how multiplying shifts digits one place to the left for each factor of 10, connecting repeated multiplication (such as 3 × 10 × 10) to single expressions like 3 × 100. The lesson also reinforces group counting by multiples of 10 and 100 to build fluency with place value relationships.

In this Grade 4 Eureka Math lesson, students learn to multiply multiples of 10, 100, and 1,000 by single-digit numbers by recognizing place value patterns, such as understanding that 2 tens × 4 = 8 tens and 2 hundreds × 4 = 8 hundreds. Students use place value disks and unit form to connect basic multiplication facts to larger units, building fluency with problems like 8 × 20, 8 × 200, and 8 × 2,000. This lesson is part of Chapter 10 and develops the foundational understanding of how the number of zeros in a product relates to the place value of the factors.

In this Grade 4 Eureka Math lesson from Chapter 10, students learn to multiply two-digit multiples of 10 by two-digit multiples of 10, such as 30 × 20, using place value charts and the area model. Students practice decomposing expressions into unit form and applying the associative property to find products like 3 tens × 2 tens = 6 hundreds. Fluency activities reinforce multiplying by multiples of 10, 100, and 1,000 to build the foundational skills needed for the area model approach.

In this Grade 4 Eureka Math lesson, students use place value disks on a place value chart to model two-digit by one-digit multiplication, such as 2 × 23 and 4 × 34, while recording partial products vertically. Students practice regrouping ones into tens as they work through multiplication expressions and connect the visual disk model to the standard written method. The lesson builds on prior work with multiples of 10 and mental multiplication strategies from earlier in Chapter 11.

In this Grade 4 Eureka Math lesson, students extend their use of place value disks to solve three- and four-digit by one-digit multiplication problems, such as 2 × 324, by decomposing each factor into hundreds, tens, and ones. Students record partial products vertically and connect the disk representations to standard multiplication equations. This lesson builds directly on two-digit multiplication skills and reinforces expanded form and place value concepts.

In this Grade 4 Eureka Math lesson from Chapter 11, students learn to multiply three- and four-digit numbers by a single-digit number using the standard algorithm, including regrouping across the ones, tens, and hundreds places. The lesson connects place value chart representations and partial products to the standard algorithm, helping students understand why each step works. Fluency practice covers expanded form, mental multiplication, and disk models to build the foundational skills needed for multi-digit multiplication.

In this Grade 4 Eureka Math lesson from Chapter 11, students learn to multiply three- and four-digit numbers by a single-digit number using the standard algorithm. The lesson connects partial products to the standard algorithm through problems like 5 × 2,374 and 6 × 3,817, reinforcing place value understanding with unit language such as "6 times 7 ones is 42 ones." Students also apply the algorithm to real-world word problems involving multi-digit multiplication.

In this Grade 4 Eureka Math lesson, students learn to connect the area model and the partial products method to the standard algorithm for multiplying up to four-digit numbers by a single-digit number. Using visual rectangle models broken into hundreds, tens, and ones, students see how each partial product corresponds to a step in the standard algorithm. This lesson from Chapter 11 builds fluency across multiple representations of multiplication, helping students understand why the standard algorithm works.

Grade 4 students practice solving two-step word problems involving multiplicative comparison in this Eureka Math lesson from Chapter 12. Using the Read-Draw-Write approach, students work through real-world scenarios requiring them to find a product and then apply that result in a second calculation, such as multiplying a unit cost before scaling up or using a multiplicative comparison before adding or subtracting. The lesson builds on prior multi-digit multiplication skills to help students set up and solve multi-step problems with tape diagrams and equations.

Grade 4 students practice solving multi-step word problems using multiplication, addition, and subtraction in this Eureka Math lesson. Working through real-world scenarios, students apply skills such as multiplying multi-digit numbers by a single-digit number and combining operations across multiple steps to find a final answer. The lesson uses the RDW (Read, Draw, Write) problem-solving approach to help students model and solve problems involving money, weight, and other quantities.

In this Grade 4 Eureka Math lesson from Chapter 13, students learn to solve division word problems that produce remainders, interpreting both the quotient and the remainder in context. Using arrays and tape diagrams, students practice dividing two-digit numbers by one-digit numbers and determine whether the quotient represents the size of a group or the number of groups. The lesson builds on multiplication fluency to develop a foundational understanding of division with remainders.

In this Grade 4 Eureka Math lesson from Chapter 13, students learn to solve division problems with remainders using both the array model and the area model. They practice interpreting the quotient and remainder in real-world contexts, such as determining how many scrapbook pages are needed when photos are divided evenly with leftovers. The lesson builds fluency with expressions like 16 ÷ 3 = 5 R1 and connects division number sentences to visual representations on grid paper.

In this Grade 4 Eureka Math lesson from Chapter 13, students learn to solve two-digit dividend division problems where a remainder appears in the ones place by modeling the process with place value disks. Students practice distributing tens and ones into equal groups using long division notation, connecting the physical disk model to the written algorithm. The lesson builds on prior work with single-digit dividends and remainders to develop fluency with problems like 36 ÷ 3 and interpreting what remains after equal distribution.

In this Grade 4 Eureka Math lesson from Chapter 13, students learn to divide two-digit numbers by one-digit numbers by decomposing a remainder in the tens place into ones using place value disks and long division. Students practice recognizing when a ten cannot be evenly distributed and must be renamed as 10 ones before continuing the division process. The lesson builds fluency with the standard algorithm through problems such as 30 ÷ 2, connecting place value understanding to each step of long division.

In this Grade 4 Eureka Math lesson, students learn to find whole number quotients and remainders by dividing two-digit numbers by one-digit divisors using the standard long division algorithm. The lesson focuses on unbundling tens into ones when a remainder occurs in the tens place, and recording remainders correctly in both the tens and ones places. Students also practice checking their answers using the inverse relationship between multiplication and division.

In this Grade 4 Eureka Math lesson, students learn to explain remainders in division by using place value disks and place value charts to model problems such as 41 ÷ 3. They practice unbundling tens into ones when a remaining ten cannot be distributed equally, then continuing to divide the ones until a final remainder is reached. Students also write multiplication equations to check their division and connect the quotient, divisor, and remainder back to their place value models.

Grade 4 students learn to solve division problems without remainders using the area model, breaking apart a two-digit dividend into smaller parts that are easier to divide. In this Eureka Math lesson, students decompose dividends like 48 and 96 into tens and ones, use number bonds alongside partitioned rectangles to find unknown side lengths, and combine partial quotients to reach the full answer. The lesson builds on students' understanding of the distributive property and connects multiplication and division concepts introduced earlier in Chapter 13.

In this Grade 4 Eureka Math lesson from Chapter 13, students learn to solve division problems with remainders using the area model, working through examples like 37 ÷ 2 and 76 ÷ 3 by building rectangles part to whole according to place value. Students practice representing the quotient as the total length of a rectangle and identifying the leftover square units as the remainder. The lesson connects the area model to the distributive property and the standard division algorithm to reinforce conceptual understanding.

This Grade 4 Eureka Math lesson introduces students to finding factor pairs for numbers up to 100 using arrays and area models, then builds on that understanding to define prime and composite numbers. Students practice identifying all factor pairs of a given number by systematically connecting pairs such as 1 and 18, 2 and 9, and 3 and 6, learning to confirm when they have found every pair. The lesson is part of Chapter 14: Reasoning with Divisibility and connects multiplication fluency to foundational number theory concepts.

In this Grade 4 Eureka Math lesson, students learn to use division to test whether a number is a factor of a larger number by checking for a remainder, and apply the associative property to identify additional factors. Students practice finding factor pairs, distinguishing prime from composite numbers, and recognizing divisibility patterns with multi-digit numbers. This lesson is part of Chapter 14: Reasoning with Divisibility and builds foundational skills for understanding number relationships.

In this Grade 4 Eureka Math lesson from Chapter 14, students learn to identify multiples by skip-counting and determine whether a whole number is a multiple of another number. The lesson builds on prior work with factors and divisibility, helping students distinguish between factors and multiples using patterns in skip-counting. Students practice applying the associative property and use personal white boards to test and prove relationships between numbers.

In this Grade 4 Eureka Math lesson from Chapter 14, students explore the properties of prime and composite numbers up to 100 by using the Sieve of Eratosthenes to systematically cross out multiples and identify which numbers remain. Students practice distinguishing between factors and multiples, recognize that multiples are infinite while factors are finite, and determine whether numbers are prime or composite based on their factor pairs. By the end of the lesson, students can identify all prime and composite numbers to 100 and explain why certain numbers, like 1, fit neither category.

In this Grade 4 Eureka Math lesson from Chapter 15, students learn to divide multiples of 10, 100, and 1,000 by single-digit numbers using place value understanding and unit form. Students practice expressing division expressions such as 900 ÷ 3 as "9 hundreds ÷ 3" to apply basic facts across place value units, including decomposing mixed-unit dividends like 350 ÷ 5. Place value disk models and a thousands place value chart support students in building fluency with this foundational division strategy.

In this Grade 4 Eureka Math lesson, students learn to divide three-digit numbers by a one-digit divisor using both place value disks and the standard long division algorithm, with a focus on decomposing a remainder in the hundreds place into tens. Working through problems like 423 ÷ 3 and 783 ÷ 3, students practice regrouping hundreds into tens to continue dividing when a remainder cannot be distributed evenly. This lesson is part of Chapter 15 on Division of Thousands, Hundreds, Tens, and Ones and builds toward fluency with multi-digit division.

In this Grade 4 Eureka Math lesson from Chapter 15, students learn to represent and solve three-digit dividend division problems numerically using divisors of 2, 3, 4, and 5. The lesson focuses on the long division algorithm alongside place value charts and unit form reasoning, building fluency with problems such as 297 ÷ 4 and 846 ÷ 2. Students also practice multiplying and dividing by place value units to strengthen their understanding of hundreds, tens, and ones in division.

In this Grade 4 Eureka Math lesson, students practice dividing four-digit dividends by divisors of 2, 3, 4, and 5 using the standard long division algorithm, decomposing remainders up to three times across thousands, hundreds, tens, and ones place values. Students work through problems like 4,325 ÷ 3, learning to record each step numerically and use multiplication to check their answers. The lesson builds on students' understanding of place value units to support fluency with multi-digit division.

In this Grade 4 Eureka Math lesson from Chapter 15, students learn how to solve division problems that contain a zero in the dividend or a zero in the quotient, such as 804 ÷ 4. Using the long division algorithm, students practice recording each place value unit — including zero tens — to arrive at accurate quotients like 201. The lesson builds on prior work with remainders and place value to help students avoid common errors when zeros appear mid-calculation.

In this Grade 4 Eureka Math lesson from Chapter 15, students learn to interpret division word problems by identifying whether the unknown is the number of groups or the group size. Using tape diagrams and long division, students work through multi-digit division problems — such as dividing 1,868 milliliters equally into 4 containers — to distinguish between these two problem types. By the end of the lesson, students can both solve and write their own word problems that target each type of unknown.

In this Grade 4 Eureka Math lesson from Chapter 15, students learn to interpret and solve one-step division word problems using whole number quotients and remainders with larger divisors of 6, 7, 8, and 9. Using tape diagrams, students practice dividing multi-digit numbers and determining what the quotient and any remainder mean in real-world contexts. The lesson builds on prior division fluency to help fourth graders confidently work with divisors beyond the basic facts.

In this Grade 4 Eureka Math lesson from Chapter 15, students learn to connect the area model of division to the standard long division algorithm for three- and four-digit dividends. Using partitioned rectangles and number bonds, students break apart dividends like 672 and 1,344 by place value units before linking each step of the area model to its corresponding step in the long division process. This lesson builds conceptual understanding of why the long division algorithm works by grounding each step in a visual representation.

In this Grade 4 Eureka Math lesson, students learn to multiply two-digit multiples of 10 by two-digit numbers using a place value chart, building on their understanding of unit form and the associative property. Students explore how expressions like (4 × 10) × 22 and 40 × 22 represent the same product, reinforcing place value concepts such as tens multiplied by ones yielding hundreds. The lesson connects area models from prior topics to the place value chart as a new strategy for solving two-digit by two-digit multiplication problems.

In this Grade 4 Eureka Math lesson from Chapter 16, students learn to multiply two-digit multiples of 10 by two-digit numbers using the area model by decomposing factors into partial products. Students practice problems such as 30 × 25 by breaking the multiplication into smaller rectangular areas, recording expressions like 3 tens × 5 ones and 3 tens × 2 tens to find the total product. The lesson builds on prior work with one-digit by two-digit area models and place value charts to deepen students' understanding of multi-digit multiplication.

In this Grade 4 Eureka Math lesson, students learn to multiply two-digit by two-digit numbers by applying the distributive property to generate four partial products using an area model. Students break each factor into tens and ones, then find and sum the four smaller products — ones times ones, ones times tens, tens times ones, and tens times tens — to find the total. This lesson builds directly on prior work with multiples of 10 and prepares students for efficient two-digit multiplication strategies.

In this Grade 4 Eureka Math lesson, students learn how to transition from using four partial products to two partial products when solving two-digit by two-digit multiplication problems like 26 × 35. Using area models, students connect the partial product method to the standard multiplication algorithm by grouping and combining partial products. This lesson builds the conceptual foundation needed to apply the standard algorithm for two-digit by two-digit multiplication covered in Chapter 16.

Grade 4 students learn to transition from using four partial products to the more efficient standard algorithm for two-digit by two-digit multiplication, using examples like 22 × 42 and 29 × 62. The lesson connects area models and the distributive property to the vertical algorithm, helping students see how two partial products align with place value. This lesson is part of Chapter 16 in Eureka Math, Grade 4.

In this Grade 4 Eureka Math lesson from Chapter 21, students learn to decompose fractions as a sum of unit fractions by folding paper strips and drawing tape diagrams to represent the parts. The lesson builds understanding of fraction equivalence by writing addition sentences such as 1 = 1/3 + 1/3 + 1/3 and decomposing fractions like 5/6 into unit fractions. Students also explore how non-standard shapes like diagonal cuts can still represent equal fractional parts with the same area.

In this Grade 4 Eureka Math lesson from Chapter 21, students learn to decompose fractions as a sum of unit fractions using tape diagrams and number bonds. Working with fractions such as thirds, fourths, and eighths, students practice writing repeated addition sentences and breaking apart fractions like 3/4 and 7/8 into multiple equivalent expressions. The lesson builds fraction equivalence concepts by showing how the same fraction can be decomposed in different ways while maintaining the same value.

In this Grade 4 Eureka Math lesson from Chapter 21, students learn to decompose non-unit fractions and express them as a whole number times a unit fraction, such as writing 4/5 as 4 × 1/5. Using tape diagrams, students build understanding of fraction equivalence by visually representing how repeated unit fractions combine to form non-unit fractions. The lesson connects prior knowledge of multiplication and repeated addition to foundational concepts in fraction decomposition.

In this Grade 4 Eureka Math lesson from Chapter 21, students learn to decompose fractions into sums of smaller unit fractions using tape diagrams. Students practice expressing fractions like 2/3 and 3/4 as repeated addition sentences and multiplication expressions involving unit fractions. The lesson builds fraction equivalence skills by connecting visual tape diagram models to symbolic notation.

In this Grade 4 Eureka Math lesson from Chapter 21, students learn to decompose unit fractions using area models to demonstrate fraction equivalence, for example showing that one-half equals three-sixths or that two-thirds equals six-ninths. Students practice breaking apart unit fractions into smaller equal parts and writing the results as addition sentences and multiplication equations. The lesson builds directly on prior work with tape diagrams and prepares students to recognize and generate equivalent fractions using visual models.

In this Grade 4 Eureka Math lesson from Chapter 21, students learn to decompose fractions such as 3/4 and 2/3 into equivalent fractions like 6/8 and 8/12 by partitioning area models into smaller equal units. Students express these equivalences using addition and multiplication sentences with unit fractions, building a concrete understanding of why two fractions with different numerators and denominators can represent the same value. The lesson extends prior work with unit fractions to non-unit fractions across a variety of denominators including fourths, eighths, thirds, and twelfths.

In this Grade 4 Eureka Math lesson from Chapter 22, students learn how to use area models and multiplication to show that two fractions are equivalent. They explore how multiplying both the numerator and denominator by the same number produces an equivalent fraction, using visual models to see how fractional units change in size and quantity. The lesson builds on prior work with area models and prepares students for broader fraction equivalence concepts throughout the module.

In this Grade 4 Eureka Math lesson from Chapter 22, students learn how to use area models and multiplication to prove that two fractions are equivalent, such as showing that 2/3 equals 8/12 by multiplying both the numerator and denominator by the same number. The lesson builds understanding of fraction equivalence through visual models, number sentences, and counting exercises with equivalent fractions like thirds and sixths. Students practice applying this concept to both unit and non-unit fractions, connecting area model drawings to the multiplication rule for generating equivalent fractions.

In this Grade 4 Eureka Math lesson from Chapter 22, students learn how to simplify fractions and show equivalence by dividing both the numerator and denominator by the same number, a process called composing larger fractional units. Using area models, students visually group smaller units into larger ones to understand why fractions like 6/12 and 1/2 represent the same value. The lesson builds on prior work with multiplication-based equivalence and connects fraction concepts to real-world measurement contexts such as inches and feet.

In this Grade 4 Eureka Math lesson, students use area models and division to show that two fractions are equivalent, building on their understanding of numerators and denominators. They practice composing shaded units into larger units and applying division to both the numerator and denominator to simplify fractions such as 2/4 = 1/2 and 3/12 = 1/4. The lesson connects fraction equivalence to real-world contexts like money, helping students see why certain equivalent forms are more practical.

In this Grade 4 Eureka Math lesson from Chapter 22, students learn to explain fraction equivalence by using tape diagrams and number lines to visualize how fractions like one-half, two-fourths, and four-eighths represent the same value. Students connect these visual models to multiplication and division number sentences, such as multiplying or dividing both the numerator and denominator by the same number to generate equivalent fractions. The lesson builds fluency with composing and decomposing fractions across halves, fourths, eighths, fifths, and tenths.

In this Grade 4 Eureka Math lesson from Chapter 23: Fraction Comparison, students learn to compare two fractions by reasoning with benchmark values of 0, one-half, and 1 on a number line. Students practice identifying whether fractions like 6/4 or 2/8 fall below, near, or above these benchmarks to determine which fraction is greater. The lesson also extends comparison to fractions between 1 and 2, helping students build flexible thinking about fraction size and placement.

In this Grade 4 Eureka Math lesson from Chapter 23: Fraction Comparison, students learn how to compare two fractions by finding common units or a common number of units, using strategies such as area models and unit language. Students practice reasoning about fraction size by identifying whether denominators or numerators match, then applying benchmark fractions and number lines to order fractions with unrelated denominators. This lesson builds on prior work with equivalent fractions and prepares students to make precise comparisons using the greater than, less than, and equal to symbols.

Grade 4 students learn how to compare two fractions with unlike denominators by finding common units or a common number of units in this Eureka Math lesson. Using area models and equivalent fractions, students practice converting fractions like 3/4 and 4/5 to a shared denominator so they can accurately determine which is greater or lesser. This lesson builds on prior work with equivalent fractions and prepares students to compare fractions across a variety of real-world and mathematical contexts.

In this Grade 4 Eureka Math lesson from Chapter 24, students use visual models such as area models and number lines to add and subtract two fractions with the same units, building on their understanding of equivalent fractions and common denominators. Students practice counting by equivalent fractions, comparing fractions using area models, and applying fraction operations to real-world problems.

In this Grade 4 Eureka Math lesson from Chapter 24, students use visual models such as tape diagrams and number bonds to add and subtract two fractions with the same units, including subtracting a fraction from one whole. Students practice recognizing equivalent fractions, decomposing mixed numbers, and writing related addition and subtraction sentences using like-denominator fractions. The lesson builds toward fluency with fraction operations through hands-on drawing activities and guided concept development.

In this Grade 4 Eureka Math lesson (Chapter 24, Lesson 4), students apply addition and subtraction of fractions to solve real-world word problems using the Read-Draw-Write (RDW) process. Students practice working with like denominators, equivalent fractions, and mixed numbers in contextual situations such as measuring distances and everyday scenarios. Fluency with fraction operations is reinforced through counting by equivalent fractions and multi-step addition and subtraction exercises.

In this Grade 4 Eureka Math lesson from Chapter 24, students use visual models to add two fractions with related denominators, focusing on denominators 2, 3, 4, 5, 6, 8, 10, and 12 where one denominator is a factor of the other. Students build on their prior work with equivalent fractions to understand that units must be the same before adding, converting fractions to like units before finding sums. This lesson prepares students for adding decimals in later modules and for working with unrelated denominators in Grade 5.

In this Grade 4 Eureka Math lesson from Chapter 24, students use tape diagrams and number lines to add two fractions with related denominators, where one denominator is a factor of the other, using units of 2, 3, 4, 5, 6, 8, 10, and 12. Students practice converting fractions to like units by decomposing the larger unit, then apply number bonds to rename improper fraction sums as mixed numbers. This lesson builds directly on equivalent fraction skills from earlier in the module and prepares students for adding fractions with unlike denominators in Grade 5.

In this Grade 4 Eureka Math lesson from Chapter 25, students learn to add a fraction less than 1 to a whole number and subtract a fraction less than 1 from a whole number using decomposition strategies and visual models such as tape diagrams, number bonds, and number lines. Students practice expressing results as mixed numbers and build fluency with equivalent fractions, including tenths. This lesson lays the groundwork for understanding fractions greater than 1 within real-world and mathematical contexts.

In this Grade 4 Eureka Math lesson from Chapter 25, students learn to add and multiply unit fractions to build fractions greater than 1, using visual models such as number lines and number bonds to connect improper fractions and mixed numbers. The lesson develops fluency with equivalent fractions by counting by fractional units like sixths and fifths, and reinforces how whole numbers relate to fractions with the same denominator. Students also practice subtracting fractions from whole numbers, strengthening their understanding of fraction equivalence across values greater than 1.

In this Grade 4 Eureka Math lesson from Chapter 25, students learn to decompose and compose fractions greater than 1, expressing them as improper fractions, mixed numbers, and whole numbers. Through fluency practice and concept development activities, students work with equivalent fractions, number bonds, and number lines to convert between forms such as 7/2 and 3½. This lesson builds the fraction equivalence skills fourth graders need to fluently move between different representations of the same value.

In this Grade 4 Eureka Math lesson from Chapter 25, students learn to compare fractions greater than 1 by creating common numerators or common denominators. Using tape diagrams and area models, students apply equivalent fraction strategies to compare mixed numbers and improper fractions such as 3 3/8 and 3 3/4. The lesson builds directly on prior work converting between mixed numbers and fractions, reinforcing fraction equivalence in a comparison context.

In this Grade 4 Eureka Math lesson from the chapter on Extending Fraction Equivalence to Fractions Greater Than 1, students learn to create and interpret line plots using data expressed as fractions and mixed numbers. They practice converting mixed numbers to fractions and comparing fractions on a number line before applying those skills to plot real-world measurement data in eighths of a mile. Students then solve word problems by reading and analyzing the completed line plot.

In this Grade 4 Eureka Math lesson, students learn how to estimate sums and differences of mixed numbers by rounding fractions to the nearest benchmark whole number. Using number lines and number bonds, students practice identifying whether a fraction is closer to the whole number below or above it, then apply that rounding to find approximate totals and differences. The lesson is part of Chapter 26 on Addition and Subtraction of Fractions by Decomposition and builds on prior work with equivalent fractions and converting improper fractions to mixed numbers.

In this Grade 4 Eureka Math lesson from Chapter 26, students learn to add a mixed number and a fraction by applying unit form thinking and number line models. The lesson covers two key strategies: adding like units when the fractional parts sum to less than or equal to 1, and decomposing a fraction to complete a unit of 1 when the fractional parts sum to more than 1. Students build on their understanding of mixed numbers and equivalent fractions to solve problems involving unlike whole and fractional units.

In this Grade 4 Eureka Math lesson, students learn to add mixed numbers by combining like units — whole numbers with whole numbers and fractions with fractions — including cases where the fractional parts sum to more than one whole. Students practice decomposing mixed numbers and applying the arrow way and number line strategies to regroup and simplify sums. The lesson is part of Chapter 26, which focuses on addition and subtraction of fractions by decomposition.

In this Grade 4 Eureka Math lesson from Chapter 26, students learn how to subtract a fraction from a mixed number using multiple strategies, including counting back, decomposing the mixed number, and converting to a fraction greater than one. Students practice breaking apart the whole number portion to regroup and subtract like units, building on their understanding of equivalent fractions and mixed numbers. This lesson strengthens foundational fraction skills as part of the broader unit on addition and subtraction of fractions by decomposition.

In this Grade 4 Eureka Math lesson, students learn to subtract mixed numbers by decomposing a mixed number into a number bond when there are not enough fractional units to subtract. They practice renaming the minuend — for example, rewriting 9 and 1 fifth as 8 and 6 fifths — to complete subtraction problems involving both fractions and mixed numbers with like denominators. The lesson builds on prior work with regrouping in whole-number subtraction and uses number lines and number bonds as visual models to support understanding.

In this Grade 4 Eureka Math lesson from Chapter 27, students learn to represent the multiplication of a whole number times a fraction, such as n times a/b, as (n x a)/b by applying the associative property. Using visual models and real-world contexts, students explore how a fractional unit like "fourths" or "fifths" behaves just like any other unit in a multiplication expression. The lesson builds directly on students' prior work with equivalent fractions, mixed numbers, and fraction addition.

In this Grade 4 Eureka Math lesson, students learn to represent the multiplication of n times a/b as (n × a)/b by applying the associative property to fraction multiplication. Using visual models such as tape diagrams and number lines, students practice rewriting repeated addition of fractions as multiplication sentences and simplifying expressions like 5 × 5/6 = 25/6. This lesson from Chapter 27 builds fluency with multiplying whole numbers by fractions and converting improper fractions to mixed numbers.

In this Grade 4 Eureka Math lesson, students learn to find the product of a whole number and a mixed number by applying the distributive property, breaking the mixed number into its whole and fractional parts before multiplying each separately. Using tape diagrams, students work through expressions like 2 × 3⅕ = (2 × 3) + (2 × ⅕) to build conceptual understanding before solving. This lesson is part of Chapter 27 on repeated addition of fractions as multiplication.

In this Grade 4 Eureka Math lesson from Chapter 27, students learn to find the product of a whole number and a mixed number by applying the distributive property to decompose the mixed number into its whole and fractional parts. Students practice expressions such as 4 × 9¾ by breaking them into (4 × 9) + (4 × ¾) and combining the results into a single mixed number or whole number. Tape diagrams and number lines are used throughout to support understanding of the multiplication process.

In this Grade 4 Eureka Math lesson from Chapter 27, students learn to solve multiplicative comparison word problems involving fractions and mixed numbers, applying the distributive property to multiply a whole number by a mixed number. Using tape diagrams and equations, students work through multi-step problems that require comparing quantities expressed as fractions, such as finding how many times as far, tall, or long one measurement is compared to another. The lesson builds on prior fluency with multiplying whole numbers times fractions and mixed numbers to develop flexible problem-solving strategies.

In this Grade 4 Eureka Math lesson from Chapter 27, students solve word problems that require multiplying a whole number by a fraction, applying skills such as breaking apart mixed numbers and converting improper fractions. Students also construct and interpret line plots as a context for practicing fraction multiplication. The lesson builds on prior work with equivalent fractions and multiplying mixed numbers to deepen understanding of repeated addition of fractions.

In this Grade 4 Eureka Math lesson from Chapter 28, students discover and apply a pattern to calculate the sum of all fractional parts between 0 and 1 for both even and odd denominators, such as fourths, sixths, thirds, and fifths. Students use fraction cards to explore how pairing fractions that equal 1 simplifies finding these sums, then compare results across different denominators. The lesson also emphasizes sharing and critiquing peer strategies to deepen understanding of the pattern.

In this Grade 4 Eureka Math lesson from Chapter 29, students learn to decompose one whole into tenths using metric measurement, representing tenths in unit form, fraction form (1/10), and decimal form (0.1). Using hands-on tools like bags of rice measured in kilograms and meter strips, students build tape diagrams and number lines to connect the fraction and decimal notation for tenths. The lesson introduces the decimal point and establishes that one tenth, 1/10, and 0.1 are equivalent representations of the same value.

In this Grade 4 Eureka Math lesson from Chapter 29, students learn to represent tenths as fractions greater than 1 and as decimal numbers using metric measurement tools and area models. They practice converting between fraction form and decimal notation, including mixed numbers such as 1 3/10 and their decimal equivalents. The lesson builds on prior work with like-unit fraction addition and counting by tenths to connect measurement contexts with decimal representation.

In this Grade 4 Eureka Math lesson from Chapter 29, students learn to represent mixed numbers containing units of tens, ones, and tenths using three models: place value disks, the number line, and expanded form. Students practice converting between improper fractions, mixed numbers, and decimals, and explore how 10 tenths can be renamed as one whole. The lesson builds foundational understanding of decimal place value and prepares students for decimal fraction addition.

In this Grade 4 Eureka Math lesson from Chapter 30, students use a meter stick and paper strip to understand that one whole meter can be decomposed into 100 equal parts called hundredths, recognizing that 1 centimeter equals one hundredth of a meter. Students learn to represent hundredths as fractions and in decimal notation, for example writing 3/100 as 0.01 and 0.03. The lesson builds on prior work with tenths, connecting measurement units to fraction and decimal concepts.

In this Grade 4 Eureka Math lesson from Chapter 30, students learn to model the equivalence of tenths and hundredths using area models and place value disks, exploring how 10 hundredths equals 1 tenth. Through fluency practice and hands-on activities, students convert between fraction and decimal forms, such as recognizing that 1/10 and 10/100 represent the same value. This lesson builds foundational decimal place value understanding essential for comparing and computing with decimals.

In this Grade 4 Eureka Math lesson from Chapter 30, students learn to represent mixed numbers containing ones, tenths, and hundredths using area models and number lines in both fraction and decimal forms. The lesson builds on prior work with hundredths by connecting equivalent fractions such as tenths and hundredths to their decimal notation. Students practice converting between representations, reinforcing place value understanding for decimals to the hundredths place.

In this Grade 4 Eureka Math lesson from Chapter 30: Tenths and Hundredths, students learn to model mixed numbers using units of hundreds, tens, ones, tenths, and hundredths on a place value chart and in expanded form. Using place value disks, students represent numbers like 3.16 as 3 + 1 tenth + 6 hundredths, connecting fraction and decimal notation across multiple place value units. The lesson builds fluency with counting by hundredths and converting between fraction and decimal representations of mixed numbers.

In this Grade 4 Eureka Math lesson from the Tenths and Hundredths chapter, students use fraction equivalence to express decimal numbers in different units on the place value chart, converting between ones, tenths, and hundredths. Using area models and place value disks, students explore how a number like 2.4 can be expressed as 24 tenths or 240 hundredths, reinforcing that 0.4 equals 0.40. Students also practice writing decimals and mixed numbers in expanded decimal and expanded fraction form.

In this Grade 4 Eureka Math lesson from Chapter 31, students use place value charts and metric measurement tools to compare decimals, applying concepts like tenths, hundredths, and decimal fraction equivalence. Students practice renaming decimals as mixed numbers and fractions, then use real-world measurements of length, mass, and volume to answer comparison questions. The lesson builds on prior work with unit decomposition to develop fluency with decimal comparison using standard comparison symbols.

In this Grade 4 Eureka Math lesson from the Decimal Comparison chapter, students learn to compare decimal numbers using area models and number lines, then record those comparisons with the symbols <, >, and =. The lesson builds on decimal fraction equivalence and place value concepts as students analyze pairs of decimals such as 0.15 and 0.51 by shading hundredths grids and plotting values on a number line. Real-world contexts, like comparing volumes of water measured in tenths and hundredths of a liter, help students apply comparison reasoning to practical problems.

In this Grade 4 Eureka Math lesson from Chapter 31: Decimal Comparison, students learn to compare and order mixed numbers, fractions, and decimals by converting between forms such as expanded fraction form, expanded decimal form, and improper fractions. Students practice using greater than, less than, and equal signs to compare decimal numbers, then apply these skills to arrange values like hundredths, tenths, and mixed numbers on a number line from least to greatest. The lesson builds fluency with renaming decimals across equivalent forms to support accurate comparison of numbers in various representations.

In this Grade 4 Eureka Math lesson, students learn to add tenths and hundredths by applying fraction equivalence to convert unlike units into like units, for example renaming 3 tenths as 30 hundredths before adding. Students use area models and place value charts to build understanding of why tenths must be converted to hundredths before the fractions can be combined. This lesson from Chapter 32 connects prior knowledge of fraction equivalence and mixed number addition to working with decimal fractions.

In this Grade 4 Eureka Math lesson, students learn to add decimal numbers by converting them to fraction form, finding common denominators to add tenths and hundredths together. The lesson covers adding decimals less than 1 as well as mixed numbers, and students practice converting results back to decimal notation. This approach deepens understanding of the relationship between fractions and decimals as students work with expressions like 0.3 + 0.57 and 6.8 + 5.7.

In this Grade 4 Eureka Math lesson from Module 6 on Decimal Fractions, students practice solving word problems that require adding measurements expressed in decimal form, such as combining volumes in liters given in tenths and hundredths. Students apply the Read-Draw-Write process and convert decimals to fraction form to find sums, reinforcing part-whole relationships with decimal numbers. The lesson builds directly on prior work with decimal notation and adding tenths and hundredths in fraction and decimal form.

In this Grade 4 Eureka Math lesson from Chapter 33, students learn to express money amounts — including pennies, dimes, quarters, and combinations of coins — as decimal numbers using dollar notation. Students connect coin values to fractions of a dollar, such as recognizing that 1 dime equals one-tenth of a dollar and writing it as $0.10, and that 1 penny equals one-hundredth of a dollar written as $0.01. The lesson builds on prior knowledge of fractions with tenths and hundredths to help students fluently convert between cent amounts, fractional dollar notation, and decimal form.

In this Grade 4 Eureka Math lesson from Module 6: Decimal Fractions, students solve multi-step word problems involving money by adding and subtracting dollar and cent amounts expressed in unit form and decimal notation. Students apply strategies such as decomposing cents to make whole dollars and converting between cents and decimal form using the dollar symbol. The lesson builds on prior work with mixed unit addition and decimal fractions to develop fluency with real-world money calculations.

Grade 4 students in Eureka Math Chapter 34 learn how to build and use measurement conversion tables for customary units of length, weight, and capacity. Using hands-on tools like balance scales and rulers, students discover relationships such as 16 ounces in a pound and apply multiplication strategies to convert between units. The lesson also introduces the distinction between the customary system and the metric system of measurement.

In this Grade 4 Eureka Math lesson from Chapter 34, students build conversion tables for length, weight, and capacity units by using hands-on measurement tools such as gallon, quart, and pint containers. They discover conversion rules — for example, multiplying gallons by 4 to find quarts — and apply those rules to solve multi-step problems. The lesson reinforces key unit relationships including kilometers to meters, yards to feet, and liters to milliliters.

In this Grade 4 Eureka Math lesson from Chapter 34, students learn to create conversion tables for units of time, including minutes to seconds, hours to minutes, and days to hours. Students apply multiplication rules, such as multiplying by 60 or 24, to complete the tables and solve multi-step problems involving larger values like 16 minutes, 18 hours, and 36 hours. The lesson builds fluency with time unit relationships and reinforces the connection between conversion factors and repeated multiplication.

In this Grade 4 Eureka Math lesson, students learn to solve multiplicative comparison word problems by applying measurement conversion tables to relate units such as hours to minutes, meters to kilometers, and ounces to pounds. Using the Read-Draw-Write approach, students practice multi-step reasoning — for example, determining that a quantity twice as large must first be scaled and then converted — to find unknown measurements. This lesson builds on prior metric and customary unit conversions from earlier modules within Chapter 34.

In this Grade 4 Eureka Math lesson from the Measurement Conversion Tables chapter, students practice creating word problems from tape diagrams and converting between units such as feet to inches and gallons to quarts. Working in pairs, they use a share and critique form to evaluate peer strategies, identifying errors and discussing whether solutions are mathematically correct and contextually realistic. The lesson builds both measurement conversion fluency and mathematical reasoning through structured peer feedback.

In this Grade 4 Eureka Math lesson from Chapter 35, students learn to add and subtract mixed units of capacity, working with gallons, quarts, pints, and cups. They practice converting between units and renaming sums, for example expressing 5 quarts as 1 gallon 1 quart, using multiple solution strategies. Fluency with fraction addition and unit conversion supports students in solving real-world measurement problems involving mixed capacity units.

In this Grade 4 Eureka Math lesson from Chapter 35, students solve addition and subtraction problems involving mixed units of weight, converting between pounds and ounces and applying multiple strategies such as making a whole pound or decomposing sums. Students practice converting weight units (for example, expressing 1 pound 3 ounces as 19 ounces) and use those skills to solve multi-step word problems. The lesson builds directly on prior work with mixed units of length and fraction concepts to strengthen fluency with customary measurement.

In this Grade 4 Eureka Math lesson from Chapter 35: Problem Solving with Measurement, students learn to add and subtract mixed units of time, such as combining hours and minutes or minutes and seconds. They practice converting between time units like days, hours, and minutes, and apply multiple solution strategies to real-world word problems involving elapsed time. Fluency activities build understanding of twenty-fourths and sixtieths as a bridge to working with the 24-hour day and 60-minute hour.

In this Grade 4 Eureka Math lesson from Chapter 35, students practice solving multi-step measurement word problems involving customary units of capacity and length, such as converting between quarts, cups, gallons, feet, and inches. Students apply the RDW (Read-Draw-Write) problem-solving strategy to model, calculate, and interpret solutions across a series of word problems. The lesson builds on prior work with mixed numbers and unit conversions to strengthen fluency with compound measurement units.

In this Grade 4 Eureka Math lesson from Chapter 35, students practice solving multi-step measurement word problems involving mixed units of time and weight, such as hours and minutes or pounds and ounces. Using the Read-Draw-Write (RDW) approach, students draw tape diagrams and write equations to work through real-world scenarios that require adding and converting mixed measurement units across multiple steps. This lesson builds on prior work with fractions and unit conversion to strengthen students' problem-solving fluency with measurement.

In this Grade 4 Eureka Math lesson from Chapter 36, students practice solving multi-step word problems that require converting mixed number measurements — such as mixed hours to minutes or feet to inches — into a single unit. Using the RDW (Read, Draw, Write) approach and tape diagrams, students work through real-world scenarios involving length, weight, capacity, and time conversions. The lesson builds fluency with unit relationships across metric and customary systems, including centimeters to meters, ounces to pounds, and milliliters to liters.