# Grade 3 - Math

## Math in 3rd Grade

Third Grade students study arithmetic, algebraic operations, and utilize 21st century skills as critical tools in solving problems of progressively greater complexity. Through engaging explorations and investigations, each student is challenged to achieve conceptual understanding while building mathematical confidence.

- Use place value understanding and properties of operations to perform multi-digit arithmetic
- Use place value understanding to round whole numbers to the nearest 10 or 100. Plot numbers, finding midpoint on a number line.
- Engage in NY number line lessons on a number line
- Identify and use counting patterns
- Compare and order numbers
- Read and write numbers to 10,000
- Understand, identify and write standard, expanded and word form numbers
- Conduct math sprints (Bill Davidson)
- Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
- Regroup 1s, 10s and 100s in addition and subtraction
- Regroup across zero in subtraction
- Add and subtract using base ten blocks (3 and 4 digits)
- Add and subtract by drawing base ten blocks on a place value mat (3 and 4 digits)
- Add and subtract mentally using number bonds
- Round to estimate sums and differences
- Front end estimation
- Use bar modeling strategies to solve problems
- Complete a “Buy Books for the Classroom Library” project as summative assessment
- Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.
- Use place value in multiplication
- Operations and Algebraic Thinking
- Represent and solve problems involving multiplication and division.
- Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each.
- Understand multiplication as equal groups, repeated addition and skip counting
- Learn and use the Commutative Property
- Complete multiplication on a number line
- Engage in NY lessons to represent groups, parts, wholes, and arrays
- Use counters and linking cubes to represent equations
- Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a
- Understand division as repeated subtraction
- Divide on a number line
- Engage in NY lessons to represent groups, parts, wholes, and arrays
- Use counters and linking cubes to represent equations
- Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
- Multiply ones, tens and hundreds mentally and with regrouping
- Use patterns to divide multiples of 10 and 100
- Divide to form equal groups
- Divide 1 or 2 digit numbers by 1 digit number
- Use base ten blocks to divide
- Utilize and practice with Engage NY
- Practice bar diagramming through Singapore Math problems of the day along with Math in Focus bar diagramming chapters
- Determine the unknown whole number in a multiplication or division equation relating three whole numbers.
- Use Engage NY unknown number lesson
- Practice Number bonds
- Understand properties of multiplication and the relationship between multiplication and division
- Apply properties of operations as strategies to multiply and divide including Commutative Property, Distributive Property, and Associative Property
- Understand division as an unknown-factor problem. Fact family exploration using counters
- Complete associated sprints (Bill Davidson)
- Multiply and divide within 100
- Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
- Practice daily multiplication facts and weekly timed tests
- Solve problems involving the four operations, and identify and explain patterns in arithmetic
- Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
- Practice Bar diagraming - Singapore Math problems of the day along with Math in Focus bar diagraming chapters
- Understand and practice number bonds
- Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.
- Fractions
- Develop understanding of fractions as numbers
- Understand fractions and identify unit and non-unit fractions
- Make a whole
- Identify the numerator and denominator
- Use models to identify fractions
- Fractions on a number line
- Compare and order unit fractions
- Equivalent fractions
- Add and subtract fractions
- Multiply and divide to find equivalent fractions
- Understand fraction of a set
- Practice fraction concepts in Engage NY supplement
- Create an Animal lifespan project as a culminating activity
- Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
- Understand a fraction as a number on the number line; represent fractions on a number line diagram.
- Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as a whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.
- Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.
- Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
- Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
- Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.
- Complete Fraction Flag art activity to reinforce concepts
- Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.
- Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
- Measurement and Data
- Solve problems involving measurement and estimation
- Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.
- Analog and digital clocks
- Minute, hour, quarter hour
- Add minutes to hours and hours to minutes
- Elapsed time
- Use Mini clocks manipulatives
- Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).
- Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.
- Meters and centimeters
- Kilometers and meters
- Kilograms and grams
- Liters and milliliters - volume
- Convert units of measurement
- Estimate and measure
- Make cross-curricular connections between science and measurement
- Engage in a liquid volume activity
- Represent and interpret data
- Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs.
- Create a tally chart
- Understand and interpret data from a picture graph
- Understand and interpret data from a Bar graph
- Understand and interpret data from Line plot
- Complete a survey project
- Create and utilize data from Digital graphs
- Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.
- Interpret data
- Make connections with science and measurement through projects
- Geometric measurement: understand concepts of area and relate area to multiplication and to addition
- Understand meaning of area
- Use square units to find the area of plane figures
- Compare areas of plane figures
- Use square inches, centimeters, meters and feet
- Estimate areas
- Recognize area as an attribute of plane figures and understand concepts of area measurement.
- A square with side length 1 unit, called "a unit square," is said to have "one square unit" of area, and can be used to measure area.
- A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.
- Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
- Relate area to the operations of multiplication and addition.
- Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
- Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.
- Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c.
- Use area models to represent the distributive property in mathematical reasoning.
- Recognize area as additive.
- Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.
- Recognize perimeter
- Understand meaning of perimeter
- Compare area to perimeter
- Find perimeter using addition
- Choose appropriate tools and units to measure perimeter
- Measure the surface of objects
- Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
- Design a school garden project as a culminating assessment
- Geometry
- Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals).
- Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
- Study Lines, corners, angles
- Identify open and closed figures
- Identify special polygons and quadrilaterals
- Classify polygons by the number of sides, vertices and angles
- Classify quadrilaterals by parallel sides, length of sides and angles
- Combine shapes to make new shapes
- Separate plane shaped to make more shapes
- Identify Slide, flip, and turn
- Understand congruence
- Complete a Quadrilateral project and presentation to culminate the unit
- Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.
- Study customary units of measurement
- Begin studying probability - complete a factory activity, experimenting with items in a bag activity
- Count money and calculate simple change to reinforce addition, subtraction, multiplication, and division skills

- Represent and solve problems involving multiplication and division.
- Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each.
- Understand multiplication as equal groups, repeated addition and skip counting
- Learn and use the Commutative Property
- Complete multiplication on a number line
- Engage in NY lessons to represent groups, parts, wholes, and arrays
- Use counters and linking cubes to represent equations
- Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a
- Understand division as repeated subtraction
- Divide on a number line
- Engage in NY lessons to represent groups, parts, wholes, and arrays
- Use counters and linking cubes to represent equations
- Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
- Multiply ones, tens and hundreds mentally and with regrouping
- Use patterns to divide multiples of 10 and 100
- Divide to form equal groups
- Divide 1 or 2 digit numbers by 1 digit number
- Use base ten blocks to divide
- Utilize and practice with Engage NY
- Practice bar diagramming through Singapore Math problems of the day along with Math in Focus bar diagramming chapters
- Determine the unknown whole number in a multiplication or division equation relating three whole numbers.
- Use Engage NY unknown number lesson
- Practice Number bonds
- Understand properties of multiplication and the relationship between multiplication and division
- Apply properties of operations as strategies to multiply and divide including Commutative Property, Distributive Property, and Associative Property
- Understand division as an unknown-factor problem. Fact family exploration using counters
- Complete associated sprints (Bill Davidson)
- Multiply and divide within 100
- Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
- Practice daily multiplication facts and weekly timed tests
- Solve problems involving the four operations, and identify and explain patterns in arithmetic
- Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
- Practice Bar diagraming - Singapore Math problems of the day along with Math in Focus bar diagraming chapters
- Understand and practice number bonds
- Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.

- Develop understanding of fractions as numbers
- Understand fractions and identify unit and non-unit fractions
- Make a whole
- Identify the numerator and denominator
- Use models to identify fractions
- Fractions on a number line
- Compare and order unit fractions
- Equivalent fractions
- Add and subtract fractions
- Multiply and divide to find equivalent fractions
- Understand fraction of a set
- Practice fraction concepts in Engage NY supplement
- Create an Animal lifespan project as a culminating activity
- Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
- Understand a fraction as a number on the number line; represent fractions on a number line diagram.
- Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as a whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.
- Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.
- Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
- Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
- Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.
- Complete Fraction Flag art activity to reinforce concepts
- Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.
- Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

- Solve problems involving measurement and estimation
- Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.
- Analog and digital clocks
- Minute, hour, quarter hour
- Add minutes to hours and hours to minutes
- Elapsed time
- Use Mini clocks manipulatives
- Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).
- Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.
- Meters and centimeters
- Kilometers and meters
- Kilograms and grams
- Liters and milliliters - volume
- Convert units of measurement
- Estimate and measure
- Make cross-curricular connections between science and measurement
- Engage in a liquid volume activity
- Represent and interpret data
- Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs.
- Create a tally chart
- Understand and interpret data from a picture graph
- Understand and interpret data from a Bar graph
- Understand and interpret data from Line plot
- Complete a survey project
- Create and utilize data from Digital graphs
- Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.
- Interpret data
- Make connections with science and measurement through projects
- Geometric measurement: understand concepts of area and relate area to multiplication and to addition
- Understand meaning of area
- Use square units to find the area of plane figures
- Compare areas of plane figures
- Use square inches, centimeters, meters and feet
- Estimate areas
- Recognize area as an attribute of plane figures and understand concepts of area measurement.
- A square with side length 1 unit, called "a unit square," is said to have "one square unit" of area, and can be used to measure area.
- A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.
- Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
- Relate area to the operations of multiplication and addition.
- Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
- Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.
- Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c.
- Use area models to represent the distributive property in mathematical reasoning.
- Recognize area as additive.
- Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.
- Recognize perimeter
- Understand meaning of perimeter
- Compare area to perimeter
- Find perimeter using addition
- Choose appropriate tools and units to measure perimeter
- Measure the surface of objects
- Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
- Design a school garden project as a culminating assessment

- Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals).
- Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
- Study Lines, corners, angles
- Identify open and closed figures
- Identify special polygons and quadrilaterals
- Classify polygons by the number of sides, vertices and angles
- Classify quadrilaterals by parallel sides, length of sides and angles
- Combine shapes to make new shapes
- Separate plane shaped to make more shapes
- Identify Slide, flip, and turn
- Understand congruence
- Complete a Quadrilateral project and presentation to culminate the unit
- Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.
- Study customary units of measurement
- Begin studying probability - complete a factory activity, experimenting with items in a bag activity
- Count money and calculate simple change to reinforce addition, subtraction, multiplication, and division skills