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Welcome to the Fourth Grade Math homepage! In fourth grade, students continue to extend foundational understandings from early elementary to build new ideas that will carry them into middle school. By fourth grade, most students will have a firm understanding of the base ten number system and this year, they will be asked to generalize their understanding to larger multi-digit numbers. Students will use place value to compare and round multi-digit numbers as well as to become fluent with the addition and subtraction algorithms. Students will also extend their knowledge of operations and place value to perform multi-digit multiplication and division. Students continue to delve into fractions and a huge emphasis will be placed on using models and equations to compare and order fractions as well as find equivalent fractions and explore improper fractions and mixed numbers. Finally, students explore the connection between decimals, fractions, and place value which will lay the conceptual understanding of decimals which will carry them into fifth grade and beyond. Across all units of study, fourth graders will continue to be challenged to think critically, make real-world connections, and apply problem-solving skills.

Please review the CityTutor DC Lesson Overview and terms of use before using CTDC lessons.

To support alignment with common DC curricula, please review the 4th Grade Pacing Guide.

In this unit, fourth graders build on their work with numbers to 1,000. Students explore bundling and unbundling groups of 10s, 100s, 1,000s to generalize about place value and our number system. Later, students will extend their understanding of rounding numbers to the nearest 10 or 100 to multi-digit numbers and apply this skill as a strategy to estimate sums and differences. Finally, students will master the addition and subtraction algorithms in multi-digit numbers.

- Unit 1.1: Students will recognize a digit represents 10 times the value of what it represents in the place to its right
- Unit 1.2: Students will name numbers within 1 million
- Unit 1.3: Students will read and write multi-digit numbers
- Unit 1.4: Students will compare numbers using >, <, =
- Unit 1.5: Students will find 1, 10, and 100 thousand more and less than a given number
- Unit 1.6: Students will round multi-digit numbers to the hundreds place using number line
- Unit 1.7: Students will round multi-digit numbers to the thousands place using number line
- Unit 1.8: Students will use place value understanding to round multi-digit numbers to any place
- Unit 1.9: Students will use standard algorithm to add multi-digit numbers
- Unit 1.10: Students will use standard algorithm to subtract multi-digit numbers (decompose once)
- Unit 1.11: Students will use standard algorithm to subtract multi-digit numbers (decompose up to three times)
- Unit 1.12: Students will solve additive compare word problems
- Unit 1.13: Students will solve multi-step word problems

In this unit, fourth graders build fluency in multiplication facts up to 12×12 and learn diverse multiplication strategies, such as arrays and the distributive property. Progressing from single-digit multiplication, students master multi-digit multiplication using standard algorithms and visuals. They apply multiplication to real-world problem-solving, including finding area and solving word problems. Additionally, they understand the relationship between multiplication and division as they lay a solid foundation for future mathematical concepts.

- Unit 2.1: Interpret patterns when multiplying by 10, 100, and 1,000 (in arrays and numerically)
- Unit 2.2: Multiply multiples of 10, 100, and 1,000 by single digits and recognize patterns
- Unit 2.3: Multiply two-digit multiples of 10 by two digit multiples of 10
- Unit 2.4: Represent two-digit by one-digit multiplication with the area model, PV, partial product
- Unit 2.5: Represent three- and four-digit by one-digit multiplication with the area model, PV, partial product
- Unit 2.6: Multiply three- and four-digit numbers by one-digit numbers with the standard algorithm
- Unit 2.7: Connect the area model and the partial products method to the standard algorithm
- Unit 2.8: Multiply two-digit multiples of 10 by two-digit numbers using a place value chart
- Unit 2.9: Multiply two-digit multiples of 10 by two-digit numbers using the area model
- Unit 2.10: Multiply two-digit by two-digit numbers using four partial products
- Unit 2.11: Relate four partial products to the standard algorithm for two-digit by two-digit multiplication
- Unit 2.12: Solve two-step word problems, including multiplicative comparison

In this unit, students continue to build fluency in division facts and learn division strategies, including arrays and repeated subtraction. Students progress from single-digit division to dividing two and three-digit numbers with one and two-digit divisors, using standard algorithms and visuals. Real-world problem-solving is integral, with students tackling word problems that involve division to find equal groups or remainders.

- Unit 3.1: Solve division problems with a remainder using the array and array models
- Unit 3.2: Solve two-digit dividend division problems with a remainder in the ones place
- Unit 3.3: Solve division problems that require decomposing a remainder in the tens
- Unit 3.4: Find whole number quotients and remainders
- Unit 3.5: Solve division with/without remainders using the area model
- Unit 3.6: Find factor pairs for numbers to 100, use understanding to define prime and composite
- Unit 3.7: Use division and associative property to test for factors
- Unit 3.8: Determine if a whole number is a multiple of another number
- Unit 3.9: Explore properties of prime and composite numbers using multiples
- Unit 3.10: Divide multiples of 10, 100, and 1,000 by single-digit numbers
- Unit 3.11: Solve division problems with up to a three-digit dividend
- Unit 3.12: Solve three-digit dividend division with divisors of 2, 3, 4, and 5
- Unit 3.13: Solve four-digit dividend division with divisors of 2, 3, 4, and 5
- Unit 3.14: Interpret division word problems as either number of groups unknown or group size unknown

In this unit, fourth graders build on their work with fractions from third grade. Students will begin to explore how to add and subtract and convert fractions, even when the denominators differ. Mixed numbers, a mix of whole numbers and fractions, are also introduced, with students learning to fluently switch between them to help them solve problems. These lessons include practical applications to provide a strong foundation for working with fractions and mixed numbers in more complex math situations.

- Unit 4.1: Students will decompose fractions
- Unit 4.2: Students will decompose improper fractions
- Unit 4.3: Students will explore equivalent decompositions for fractions and improper fractions
- Unit 4.4: Students will show the equivalence of two fractions (model and multiplication)
- Unit 4.5: Students will show the equivalence of two fractions (model and division)
- Unit 4.6: Students will recognize and generate equivalent unit fractions with larger units
- Unit 4.7: Students will recognize and generate equivalent non-unit fractions with larger units
- Unit 4.8: Students will show equivalent fractions on number lines using both multiplication and division.
- Unit 4.9: Students will compare fractions with common denominators
- Unit 4.10: Students will compare fractions with common numerators
- Unit 4.11: Students will compare fractions using 1 as a benchmark.
- Unit 4.12: Students will compare fractions using 1/2 as a benchmark.
- Unit 4.13: Students will compare fractions using common denominators (one fraction has to change)
- Unit 4.14: Students will compare fractions using common denominators (both fractions have to change)
- Unit 4.15: Students will add a mixed number and a fraction
- Unit 4.16: Students will add mixed numbers
- Unit 4.17: Students will subtract a fraction from a mixed number
- Unit 4.18: Students will subtract a mixed number from a mixed number
- Unit 4.19: Students will add and subtract mixed numbers

In this unit, fourth graders focus on building foundational skills for working with decimals. Students learn that decimals are a means to represent parts of a whole and grasp the connection between decimals and fractions. They engage in activities to compare and order decimals, while also acquiring the ability to add and subtract decimals, both within the same place value and across different place values. Additionally, fourth graders explore the intricacies of decimal place value, honing their proficiency in recognizing the significance of digits like tenths and hundredths.

- Unit 5.1: Students will express metric length measurements with a smaller unit
- Unit 5.2: Students will relate metric units to place value units
- Unit 5.3: Use metric measurement to model the decomposition of one whole into tenths
- Unit 5.4: Use metric measurement and area models to represent tenths as fractions greater than 1 and decimal numbers
- Unit 5.5: Represent mixed numbers with units of tens, ones, and tenths
- Unit 5.6: Use meters to model the decomposition of one whole into hundredths, represent and count hundredths
- Unit 5.7: Model the equivalence of tenths and hundredths using an area model and place value
- Unit 5.8: Use an area model and number line to represent mixed numbers with units of ones, tenths, and hundredths in fraction and decimal forms
- Unit 5.9: Model mixed numbers with units of hundreds, tens, ones, tenths, and hundredths in expanded form and on the place value chart
- Unit 5.10: Use understanding of fraction equivalence to investigate decimal numbers on the place value chart expressed in different units
- Unit 5.11: Use the place value chart and metric measurement to compare decimals and answer comparison questions
- Unit 5.12: Use area models and the number line to compare decimal numbers, and record comparisons using, and =
- Unit 5.13: Compare and order mixed numbers in various forms
- Unit 5.14: Apply understanding of fraction equivalence to add tenths and hundredths
- Unit 5.15: Add decimal numbers by converting to fraction form
- Unit 5.16: Solve word problems involving the addition of measurements in decimal form

In partnership with the Office of the State Superintendent for Education (OSSE), CityTutor DC has developed a toolkit to help school leaders brainstorm and implement high-impact tutoring (HIT) in their schools.

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