In This Unit of Study…

Third graders will demonstrate understanding of place value up to 10,000. They will exhibit this by using concrete manipulatives, pictorial models, and numbers (including standard numbers, words, and expanded form). Students will need to understand that the value of a digit depends on its place or position in the number (place value).

3,704: In this example, the 7 is in the hundreds place and represents 7 hundreds or 700. Students will also need to use accurate place value language to read, write, and say numbers: “Three thousand, seven hundred four.” Notice that the word and is not used to describe 3,704. The word and is used when students describe fractions and decimal fractions such as one and one-half.

Students will use their knowledge of place value and place value language to add, subtract, multiply, and divide. 

B.E.S.T. Benchmarks:

• MA.3.NSO.1.1 Read and write numbers from 0 to 10,000 using standard form, expanded form and word form
• MA.3.NSO.1.2 Compose and decompose four-digit numbers in multiple ways using thousands, hundreds, tens, and ones. Demonstrate each composition or decomposition using objects, drawings and expressions or equations.

Overarching Key Concepts:

• Read and write numbers to 10,000

In This Unit of Study…

Students will use and build upon their prior knowledge of plotting, comparing, and ordering numbers up to 1,000. The concept is similar to what they learned in kindergarten, first grade, and second grade; student simply must extend the concept to numbers up to 10,000. Students must first look at place value. Next, students must look at the value of the numbers within the place value.

B.E.S.T. Benchmarks:

• MA.3.NSO.1.3: Plot, order and compare whole numbers up to 10,000.

Overarching Key Concepts:

• Plot, compare, and order numbers to 10,000 using place value

In This Unit of Study…

Students use place value to round numbers to the nearest 10 or 100. Students approximate the value of a number by finding the closest number with no ones or tens and ones. Students learn that rounding is valuable when estimating, predicting, and justifying the reasonableness of solutions while problem solving.

B.E.S.T. Benchmarks:

• MA.3.NSO.1.4 Round whole numbers from 0 to 1,000 to the nearest 10 or 100.

Overarching Key Concepts:

• Round to the nearest 10 and 100 within 1,000

In This Unit of Study…

Third graders will solve addition and subtraction problems with procedural fluency. This includes word problems, multistep problems, and problems that require regrouping.

B.E.S.T. Benchmarks:

• MA.3.NSO.2.1  Add and subtract multi-digit whole numbers including using a standard algorithm with procedural fluency.
• MA.3.AR.1.2  Solve one- and two-step real-world problems involving any of four operations with whole numbers.

Overarching Key Concepts:

• Add within 10,000 by making connections between place value strategies and a standard algorithm
• Subtract within 10,000 by making connections between place value strategies and a standard algorithm

In This Unit of Study…

Students explore multiplication of two whole numbers, and they understand and interpret the product of whole numbers when given an equal number of groups with an equal number of objects in each group.  The meaning and properties of multiplication are at the center of instruction.  A variety of strategies, such as equal groups, arrays, area models, and equations, are used to determine the product. When exploring multiplication, they will learn that multiplication and division are related.  They can use a multiplication representation to solve a division problem.  Students must be able to describe and provide a context for any given multiplication problem.  Students also determine and explain whether an equation involving multiplication is true or false.

B.E.S.T. Benchmarks:

• MA.3.NSO.2.2  Explore multiplication of two whole numbers with products from 0 to 144, and related division facts.
• MA.3.AR.1.2  Solve one- and two-step real-world problems involving any of four operations with whole numbers. 
• MA.3.AR.3.2 Determine whether a whole number from 1 to 144 is a multiple of a given one-digit number. 

Overarching Key Concepts:

• Represent equal group multiplication using models
• Determine whether a whole number from 1 to 144 is a multiple of a given one-digit number
• Represent array and measurement multiplication using models
• Represent measurement and partitive division using equal group models
• Represent measurement and partitive division using array and linear models

In This Unit of Study…

Third graders will continue to develop an accurate method in which they multiply two whole numbers from 0 to 12 with procedural reliability. In addition, they will learn to apply the distributive property to multiply two-digit numbers by one-digit numbers. This will involve regrouping when the product of the ones column is greater than nine. Various strategies will be used to find the product of the factors. These methods include using and naming the commutative and associative properties of multiplication, as well as the distributive property.

B.E.S.T. Benchmarks:

• MA.3.NSO.2.4  Multiply two whole numbers from 0 to 12 and divide using related facts with procedural reliability
• MA.3.AR.1.1  Apply the distributive property to multiply a one-digit number and two-digit number. Apply properties of multiplication to find a product of one-digit whole numbers.

Overarching Key Concepts:

• Model and apply the Communitive Property of mutliplication
• Model and apply the Associative Property of multiplication

In This Unit of Study…

Students will explore another attribute of plane figures, area.  Area tells how much of a surface is covered, measured in square units.  The area of a figure is the number of same-sized square units that cover the figure without gaps or overlaps.  Students’ initial experiences with area are meant to help them visualize the concept as they explore finding areas by counting the number of square tiles that cover rectangular regions. Problems with real-world contexts help students understand applications of area in our lives, such as how much carpet or tile is needed to cover a floor.  Exploring area through problems allows students to practice their measurement skills as well as develop a deeper understanding of when and how area is used. As students investigate the areas of various rectangular figures, they gather and observe data that lead them to insights about the connection between multiplication and area.  Without being told formulas, students are able to determine shortcuts for finding area without counting every square and are able to explain and prove this insight.

B.E.S.T. Benchmarks:

• MA.3.GR.2.1 Explore area as an attribute of a two-dimensional figure by covering the figure with unit squares without gaps or overlaps. Find areas of rectangles by counting unit squares.
• MA.3.GR.2.2 Find the area of a rectangle with whole-number side lengths using a visual model and a multiplication formula.
• MA.3.GR.2.3 Solve mathematical and real-world problems involving the perimeter and area of rectangles with whole-number side lengths using a visual model and a formula.
• MA.3.GR.2.4 Solve mathematical and real-world problems involving the perimeter and area of composite figures composed of non-overlapping rectangles with whole-number side lengths.
• MA.3.NSO.2.4: Multiply two whole numbers from 0 to 12 and divide using related facts with procedural reliability. 
• MA.3.AR.1.1: Apply the distributive property to multiply a one-digit number and two-digit numbers. Apply properties of multiplication to find a product of one-digit whole numbers.  

Overarching Key Concepts:

• Explore area and measure it by couting squares
• Connect arrays and multiplication to find the area of a rectangle
• Model and apply the distributive property of multiplication to rectangles
• Apply the Distributive property to decompose and find the area of composite figures

In This Unit of Study…

Students will solve one-step multiplication and division problems by using the following variety of strategies:

1. Concrete objects
2. Pictorial models
• Arrays
• Area models>/li>
• Equal groupings
  Tape diagrams
3. Equations and algorithms

Additionally, students will use their comprehension of the relationship between multiplication and division to solve for missing numbers in multiplication or division equations.

B.E.S.T. Benchmarks:

• MA.3.NSO.2.4 Multiply two whole numbers from 0 to 12 and divide using related facts with procedural reliability. 
• MA.3.AR.2.1 Restate a division problem as a missing factor problem using the relationship between multiplication and division. 
• MA.3.AR.2.2 Determine and explain whether an equation involving multiplication or division is true or false. 
• MA.3.AR.2.3 Determine the unknown whole number in a multiplication or division equation, relating three whole numbers, with the unknown in any position. 

Overarching Key Concepts:

• Model and solve division problems using multiplication

In This Unit of Study…

Students will build upon their prior knowledge that fractions are equal parts of a whole, as well as their abilities to create and identify fractions of halves, thirds, and fourths. Students will extend their knowledge base to fractions with denominators of two (halves), three (thirds), four (fourths), five (fifths), six (sixths), eight (eighths), ten (tenths), and twelve (twelfths). Students should be able to represent and interpret unit fractions as part of a whole, part of a set, a point on a number line, or a visual model, as well as in fractional notation. Students will also represent and interpret fractions, including fractions greater than one, by composing and decomposing using unit fractions. In addition, students will read and write fractions by using standard form, numeral-word form, and word form.

B.E.S.T. Benchmarks:

• MA.3.FR.1.1 Represent and interpret unit fractions in the form 1/n as the quantity formed by one part when a whole is partitioned into n equal parts.
• MA.3.FR.1.2 Represent and interpret fractions, including fractions greater than one, in the form of m/n as the result of adding the unit fraction 1/? to itself ? times.
• MA.3.FR.1.3 Read and write fractions, including fractions greater than one, using standard form, numeral-word form and word form.

Overarching Key Concepts:

• Partition and iterate fractions using area models
• Represent and interpret fractions using linear and set models

In This Unit of Study…

Students build on their knowledge of fractions, number lines, and area models to identify equivalent fractions. Fractions are limited to fractions less than or equal to one with denominators of 2, 3, 4, 5, 6, 8, 10, and 12.

B.E.S.T. Benchmarks:

• MA.3.FR.2.2 Identify equivalent fractions and explain why they are equivalent.

Overarching Key Concepts:

• Identify equivalent fractions less than or equal to one whole.

In This Unit of Study…

Students plot, order, and compare two fractions or mixed numbers with the same numerator or the same denominator. They demonstrate an understanding that the larger the denominator is, the smaller the unit fraction. Instruction includes utilizing an appropriately scaled number line to reason about distances of each fraction from zero. Comparisons are made by using the symbols >, <, or =, accompanied with a justification of the comparison. Instruction includes making connections between using a ruler and plotting and ordering fractions on a number line, and denominators are limited to 2, 3, 4, 5, 6, 8, 10, and 12.

B.E.S.T. Benchmarks:

• MA.3.FR.2.1  Plot, order and compare fractional numbers with the same numerator or the same denominator.

Overarching Key Concepts:

• Plot, compare, and order fractions with the same denominator or numerator

In This Unit of Study…

Students will accurately multiply one-digit numbers by multiples of 10 up to 90 or a multiple of 100 up to 900 by utilizing place value strategies.  Students will also explain how multiplication by multiples of 10 and 100 is related to basic facts.

B.E.S.T. Benchmarks:

• MA.3.NSO.2.3 Multiply a one-digit whole number by a multiple of 10, up to 90, or a multiple of 100, up to 900, with procedural reliability. 
• MA.3.AR.1.1 Apply the distributive property to multiply a one-digit number and two-digit number. Apply properties of multiplication to find a product of one-digit whole numbers. 

Overarching Key Concepts:

• Multiply a one-digit whole number by multiples of 10 and 100
• Multiply a one-digit number by a two-digit number using the distributive property

In This Unit of Study…

Third graders use precise language to identify and draw quadrilaterals. Students distinguish a quadrilateral as a closed figure with four straight sides, and they notice the relationships between angles and between opposite sides within a quadrilateral. Within the category of quadrilaterals, students can classify and draw subcategories of shapes, such as parallelograms, rhombi, rectangles, squares, and trapezoids. Students use deductive reasoning   to justify their thinking about the categories into which shapes are sorted, while they gain a deeper understanding of “if . . .,  then . . .” relationships. For example, if a shape is a quadrilateral, then it must have four sides.

B.E.S.T. Benchmarks:

• MA.3.GR.1.1 Describe and draw points, lines, line segments, rays, intersecting lines, perpendicular lines and parallel lines. Identify these in two-dimensional figures. 
• MA.3.GR.1.2 Identify and quadrilaterals based on their defining attributes. Quadrilaterals include parallelograms, rhombi, rectangles, squares and trapezoids. 
• MA.3.GR.1.3 Draw line(s) of symmetry in a two-dimensional figure and identify line-symmetric two-dimensional figures. 

Overarching Key Concepts:

• Identify and draw attributes of two-dimensional figures
• Idenify and draw quadrilateral based on their defining attributes
• Identify and draw lines of symmetry in two-dimensional figures

In This Unit of Study…

Students will collect and represent data (whole number values) on a line plot. They will interpret the data on the line plot by solving one and two step word problems. 

B.E.S.T. Benchmarks:

• MA.3.M.1.1 Select and use appropriate tools to measure the length of an object, the volume of liquid within a beaker, and temperature. 
• MA.3.DP.1.1 Collect and represent numerical and categorical data with whole-number values using tables, scaled pictographs, scaled bar graphs or line plots. Use appropriate titles, labels, and units. 
• MA.3.DP.1.2 Interpret data with whole-number values represented with tables, scaled pictographs, circle graphs, scaled bar graphs or line plots by solving one- and two-step problems. 

Overarching Key Concepts:

• Represent and interpret data on line plots

In This Unit of Study…

Students will solve mathematical and real-world problems involving perimeter of rectangles with whole-number side lengths by using a visual model and a formula. As students begin to utilize formulas for the first time, they will discover and discuss the advantages and disadvantages to using them. They will transition from showing all lengths of a rectangle on a diagram to show just what is needed to serve as a reminder. Students will benefit from knowing or being fluently able to remind themselves of how to find the perimeter. With opportunities for repeated reasoning about how to calculate perimeter, students will understand that formulas are summaries of calculations. They will be tasked with finding the perimeter of rectangles when all side lengths are given, as well as finding the perimeter of composite figures composed of nonoverlapping rectangles. Students will also use knowledge from the previous third-grade FLM standards (MA.3.GR.2.1, MA.3.GR.2.2, MA.3.GR.2.3, MA.3.GR.2.4) regarding area to solve mathematical and real-world problems involving the area of rectangles and composite figures composed on nonoverlapping rectangles by using a visual model and a formula.

B.E.S.T. Benchmarks:

• MA.3.GR.2.3 Solve mathematical and real-world problems involving the perimeter and area of rectangles with whole-number side lengths using a visual model and a formula.
• MA.3.GR.2.4 Solve mathematical and real-world problems involving the perimeter and area of composite figures composed of non-overlapping rectangles with whole-number side lengths.

Overarching Key Concepts:

• Solve problems involving perimeter and how it relates to area

In This Unit of Study…

Students will solve one- and two-step problems with whole numbers by using any of the four operations. Addition and subtraction problems include numbers within 1,000, and multiplication is limited to factors within 12 and related division facts. Students will use a variety of strategies, including concrete objects, pictorial models such as arrays, area models, tape diagrams, equations, and algorithms.

B.E.S.T. Benchmarks:

• MA.3.AR.1.2 Solve one- and two-step real-world problems involving any of four operations with whole numbers.

Overarching Key Concepts:

• Solve two-step problems involving any of the four operations with whole numbers

In This Unit of Study…

Third-grade students will tell and write time to the nearest minute and distinguish between a.m. and p.m. This builds upon previous knowledge of understanding the concept of time in hours, half hours, and intervals of five minutes. Instruction with both analog and digital clocks is used to ensure that students have opportunities to develop their concept of telling time in both ways it is represented in their daily lives. Students are also expected to solve one- and two-step problems involving situations of elapsed time that do not cross between a.m. and p.m.

B.E.S.T. Benchmarks:

• MA.3.M.2.1 Using analog and digital clocks tell and write time to the nearest minute using a.m. and p.m. appropriately. 
• MA.3.M.2.2 Solve one- and two-step real-world problems involving elapsed time. 

Overarching Key Concepts:

• Tell and write time to the nearest minute
• Solve problems involving elapsed time

In This Unit of Study…

Students collect and represent numerical data by using tables, line plots, pictographs, and bar graphs. Students are expected to complete a representation or construct a new representation from a data set. They interpret displayed data on these types of graphs and on a circle graph. Students use data sets to solve one- or two-step problems involving addition and subtraction.

B.E.S.T. Benchmarks:

• MA.3.DP.1.1 Collect and represent numerical and categorical data with whole-number values using tables, scaled pictographs, scaled bar graphs or line plots. Use appropriate titles, labels, and units.
• MA.3.DP.1.2 Interpret data with whole-number values represented with tables, scaled pictographs, circle graphs, scaled bar graphs or line plots by solving one- and two-step problems.

Overarching Key Concepts:

• Create and read scaled pictographs and bar graphs
• Interpret data to solve one and two step problems