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Welcome to the Third Grade Math homepage! In third grade, students build on and deepen their understanding of early elementary mathematical concepts. Third graders will extend their knowledge of addition and subtraction in one- and two-digit numbers to add and subtract three- and four-digit numbers with and without regrouping. The standards continue to emphasize the use of place value to explain why addition and subtraction strategies work. Additionally, students explore multiplication as the representation of equal groups and they will be pushed to use models, words, and equations to represent and explain multiplication. Similarly, students will extend what they know about subtraction to explore division as repeated subtraction. The lessons strongly emphasize solving two-step word problems across all four operations. Later, third graders will spend a large portion of time on the exploration of fractions. Students will use models, words, and fractional notation to explore and explain fractions. Finally, students will apply their understanding of fractions to compare fractions and find equivalent fractions. Across all units of study, third graders will 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 3rd Grade Pacing Guide.

In this unit, third graders explore multiplication and division through models and real world problems. Students move gradually from concrete drawings and “groups of” language to skip-counting and arrays to eventually using the distributive and associative property as strategies for multiplying and dividing larger factors. By the end of third grade, students will be able to multiply and divide within 100 as well as explain why strategies work based on properties of operations and the relationship between multiplication and division.

- Unit 1.1: Model equal groups and use groups of language
- Unit 1.2: Relate repeated addition to groups of language
- Unit 1.3: Understand groups of language as multiplication
- Unit 1.4: Relate multiplication to the array model
- Unit 1.5: Split numbers to multiply
- Unit 1.6: Model partitive division
- Unit 1.7: Model partitive division story problems
- Unit 1.8: Model quotative division
- Unit 1.9: Model quotative division story problems
- Unit 1.10: Represent division as repeated subtraction
- Unit 1.11: Solve division and multiplication story problems
- Unit 1.12: Explore how multiplication and division are connected
- Unit 1.13: Explore multiplication and division facts

In this unit, third graders build on their work with two-digit numbers from second grade. Students will extend their understanding of place value, including the ability to identify and represent the value of digits within numbers up to 1,000. They will learn to round numbers to the nearest 10 or 100 and apply this knowledge in solving real-world problems. Later on, students will use their knowledge of place value to add and subtract three-digit numbers with and without regrouping. Finally, students will apply their knowledge of place value to compare and order numbers based on their place value positions.

- Unit 2.1: Model three-digit numbers in word form, place value form, expanded form
- Unit 2.2: Compare three-digit numbers
- Unit 2.3: Add two-digit numbers
- Unit 2.4: Add three-digit numbers
- Unit 2.5: Subtract two-digit numbers
- Unit 2.6: Subtract three-digit numbers
- Unit 2.7: Subtract three-digit numbers with zeros
- Unit 2.8: Round numbers to 999 to the nearest hundred
- Unit 2.9: Round numbers to 99 to the nearest ten
- Unit 2.10: Round numbers to 999 to the nearest ten
- Unit 2.11: Estimate sums by rounding and apply estimation to solving word problems
- Unit 2.12: Estimate differences by rounding and apply estimation to solving word problems

In third grade, students begin to explore the concept of area, understanding it as the measurement of the space enclosed within a two-dimensional shape. They learn to calculate the area of rectangles and squares first by counting unit squares then by connecting side lengths to equal groups and skip counting and ultimately using multiplication. Additionally, third graders gain an awareness of how changing the dimensions of a shape affects its area, laying the foundation for more advanced geometry concepts.

- Unit 3.1: Explore the meaning of area using square tiles
- Unit 3.2: Measure the area of a rectangle using equal groups and skip counting
- Unit 3.3: Multiply the side lengths to find the area of rectangles
- Unit 3.4: Decompose and compose rectangles to compare areas
- Unit 3.5: Solve for the unknown side length of a rectangle when given one side length and the area
- Unit 3.6: Decompose rectangles using tiles
- Unit 3.7: Apply the distributive strategy to find the total area of a large rectangle by adding two products
- Unit 3.8: Decompose rectangles to show the distributive property
- Unit 3.9: Find the area of shapes made out of rectangles by decomposing the shape into smaller rectangles
- Unit 3.10: Find the area of rectilinear shapes made out of rectangles by decomposing the shape into smaller rectangles and finding the missing side lengths
- Unit 3.11: Solve word problems with area

In third grade, students build on their understanding from previous years in which they came to understand fractions as a way to name parts of a whole or a set. Until now students have not been exposed to fractional notation (i.e. writing a numerator over a denominator), instead they likely learned to name parts of a whole with words like halves, fourths, eighths. In this unit, they learn to write fractions and they understand the numerator as the number of pieces and the denominator as the size of the pieces. Students use these understandings to represent fractions on a number line and compare them based on their size. Third graders also gain the ability to add and subtract simple fractions with the same denominator, setting the stage for deeper explorations of fraction operations in subsequent grades.

- Unit 4.1: Partition a whole into equal parts and naming unit fractions with words (halves, fourths, and eighths)
- Unit 4.2: Partition a whole into equal parts and naming unit fractions with fractional notation
- Unit 4.3: Partition a whole into equal parts and naming unit fractions on a number line
- Unit 4.4: Explore non-unit fractions less than one whole on a number line
- Unit 4.5: Represent parts of one whole using number bonds
- Unit 4.6: Solve fraction story problems
- Unit 4.7: Compare unit fractions by reasoning about their size
- Unit 4.8: Compare unit fractions by using a number line
- Unit 4.9: Compare fractions with like numerators
- Unit 4.10: Compare fractions with like denominators
- Unit 4.11: Use models to find equivalent fractions
- Unit 4.12: Use number lines to find equivalent fractions

In third grade, students are introduced to quadrilaterals, which are four-sided polygons. They learn to differentiate between various types of quadrilaterals, such as squares, rectangles, parallelograms, and trapezoids, based on their defining characteristics like side lengths and angles. In this unit, third graders will also come back to the concept or area as they learn how to calculate perimeters of polygons.

- Unit 5.1: Describe shapes
- Unit 5.2: Describe quadrilaterals
- Unit 5.3: Describe parallelograms and trapezoids
- Unit 5.4: Describe rectangles
- Unit 5.5: Describe rhombuses
- Unit 5.6: Describe squares
- Unit 5.7: Compare and classify other polygons
- Unit 5.8: Measure side length in whole number units to determine the perimeter of polygons
- Unit 5.9: Determine the perimeter of polygons
- Unit 5.10: Differentiate between area and perimeter and calculate both for given rectangles

In third grade, students expand their time-telling skills by mastering both analog and digital clocks. They learn to tell time to the nearest minute on analog clocks and understand the relationship between the hour and minute hands. Additionally, third graders practice reading and interpreting digital time, honing their ability to apply these skills to real-world scenarios such as schedules and elapsed time calculations.

- Unit 6.1: Explore positive and negative numbers on a number line and understand opposites
- Unit 6.2: Find absolute value and order rational numbers
- Unit 6.3: Use absolute value and inequalities to compare and interpret rational numbers
- Unit 6.4: Find and plot pairs of rational numbers on a 4-quadrant coordinate plane
- Unit 6.5: Use coordinates to find distances and reflections on the coordinate plane
- Unit 6.6: Plot points on the coordinate plane to make polygons, and solve problems about vertical and horizontal distance between points

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