 Treadwell Elementary
 Math  3rd Grade

3.OA.A.1  Major Work of the Grade
Interpret the factors and products in whole number multiplication equations (e.g., 4 x 7 is 4 groups of 7 objects with a total of 28 objects or 4 strings measuring 7 inches each with a total of 28 inches.)

3.OA.A.2  Major Work of the Grade
Interpret the dividend, divisor, and quotient in whole number division equations (e.g., 28 ÷ 7 can be interpreted as 28 objects divided into 7 equal groups with 4 objects in each group or 28 objects divided so there are 7 objects in each of the 4 equal groups).

3.OA.A.3  Major Work of the Grade
Multiply and divide within 100 to solve contextual problems, with unknowns in all positions, in situations involving equal groups, arrays, and measurement quantities using strategies based on place value, the properties of operations, and the relationship between multiplication and division (e.g., contexts including computations such as 3 x ? = 24, 6 x 16 = ?, ? ÷ 8 = 3, or 96 ÷ 6 = ?) (See Table 2  Multiplication and Division Situations).

3.OA.A.4  Major Work of the Grade
Determine the unknown whole number in a multiplication or division equation relating three whole numbers within 100. For example, determine the unknown number that makes the equation true in each of the equations: 8 x ? = 48, 5 = ? ÷ 3, 6 x 6 =?

3.OA.B.5  Major Work of the Grade
Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) Examples: If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known (Commutative property of multiplication). 3 x 5 x 2 can be solved by (3 x 5) x 2 or 3 x (5 x 2) (Associative property of multiplication). One way to find 8 x 7 is by using 8 x (5 + 2) = (8 x 5) + (8 x 2). By knowing that 8 x 5 = 40 and 8 x 2 = 16, then 8 x 7 = 40 + 16 = 56 (Distributive property of multiplication over addition).

3.OA.B.6  Major Work of the Grade
Understand division as an unknownfactor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

3.OA.C.7  Major Work of the Grade
Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of 3rd grade, know from memory all products of two onedigit numbers and related division facts.

3.OA.D.8  Major Work of the Grade
Solve twostep contextual 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 (See Table 1  Addition and Subtraction Situations and Table 2  Multiplication and Division Situations).

3.OA.D.9  Major Work of the Grade
Identify arithmetic patterns (including patterns in the addition and multiplication tables) and explain them using properties of operations. For example, analyze patterns in the multiplication table and observe that 4 times a number is always even (because 4 x 6 = (2 x 2) x 6 = 2 x (2 x 6), which uses the associative property of multiplication) (See Table 3  Properties of Operations).

3.NBT.A.1
Round whole numbers to the nearest 10 or 100 using understanding of place value.

3.NBT.A.2
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.

3.NBT.A.3
Multiply onedigit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations.

3.NF.A.1  Major Work of the Grade
Understand a fraction, 1/b, as the quantity formed by 1 part when a whole is partitioned into b equal parts (unit fraction); understand a fraction a/b as the quantity formed by a parts of size 1/b. For example, 3/4 represents a quantity formed by 3 parts of size 1/4.

3.NF.A.2  Major Work of the Grade
Understand a fraction as a number on the number line. Represent fractions on a number line.
 Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint locates the number 1/b on the number line. For example, on a number line from 0 to 1, students can partition it into 4 equal parts and recognize that each part represents a length of 1/4 and the first part has an endpoint at 1/4 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. For example, 5/3 is the distance from 0 when there are 5 iterations of 1/3.
 Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint locates the number 1/b on the number line. For example, on a number line from 0 to 1, students can partition it into 4 equal parts and recognize that each part represents a length of 1/4 and the first part has an endpoint at 1/4 on the number line.

3.NF.A.3  Major Work of the Grade
Explain equivalence of fractions 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 ) and explain why the fractions are equivalent using a visual fraction model.
 Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers. For example, express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point on a number line diagram.
 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. Use the symbols >, =, or < to show the relationship and justify the conclusions.
 Understand two fractions as equivalent (equal) if they are the same size or the same point on a number line.

3.MD.A.1  Major Work of the Grade
Tell and write time to the nearest minute and measure time intervals in minutes. Solve contextual problems involving addition and subtraction of time intervals in minutes. For example, students may use a number line to determine the difference between the start time and the end time of lunch.

3.MD.A.2  Major Work of the Grade
Measure the mass of objects and liquid volume using standard units of grams (g), kilograms (kg), milliliters (ml), and liters (l). Estimate the mass of objects and liquid volume using benchmarks. For example, a large paper clip is about one gram, so a box of about 100 large clips is about 100 grams.

3.MD.B.3
Draw a scaled pictograph and a scaled bar graph to represent a data set with several categories. Solve one and twostep "how many more" and "how many less" problems using information presented in scaled graphs.

3.MD.B.4
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.

3.MD.C.5  Major Work of the Grade
Recognize that plane figures have an area and understand concepts of area measurement.
 Understand that 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.
 Understand that 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.
 Understand that 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.

3.MD.C.6  Major Work of the Grade
Measure areas by counting unit squares (square centimeters, square meters, square inches, square feet, and improvised units).

3.MD.C.7  Major Work of the Grade
Relate area of rectangles to the operations of multiplication and addition.
 Find the area of a rectangle with wholenumber 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 realworld and mathematical problems and represent wholenumber products as rectangular areas in mathematical reasoning.
 Use tiling to show in a concrete case that the area of a rectangle with wholenumber side lengths a and b + c is the sum of a x b and a x c. Use area models to represent the distributive property in mathematical reasoning. For example, in a rectangle with dimensions 4 by 6, students can decompose the rectangle into 4 x 3 and 4 x 3 to find the total area of 4 x 6. (See Table 3  Properties of Operations)
 Recognize area as additive. Find areas of rectilinear figures by decomposing them into nonoverlapping rectangles and adding the areas of the nonoverlapping parts, applying this technique to solve realworld problems.
 Find the area of a rectangle with wholenumber side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengths.

3.MD.D.8
Solve realworld 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.

3.G.A.1
Understand that shapes in different categories may share attributes and that the shared attributes can define a larger category. Recognize rhombuses, rectangles, and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategories.

3.G.A.2
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.

3.G.A.3
Determine if a figure is a polygon.