Maryland College and Career-Ready Standards 3rd Grade Math Skills

MD.MA.3.OA. Operations and Algebraic Thinking (OA)

3.OA.A. Represent and solve problems involving multiplication and division.

3.OA.A.1. Major Standard: Interpret products of whole numbers, e.g., interpret 5x7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5x7.

3.OA.A.1.3. Ability to use concrete objects, pictures, and arrays to represent the product as the total number of objects.

3.OA.A.1.6. Knowledge that the example in Standard 3.0A.A.1 can also represent the total number of objects with 5 items in each of 7 groups (Commutative Property).

3.OA.A.2. Major Standard: 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 number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56÷8.

3.OA.A.2.2. Ability to use concrete objects to represent the total number and represent how these objects could be shared equally.

3.OA.A.2.3. Knowledge that the quotient can either represent the amount in each group or the number of groups with which a total is shared.

3.OA.A.3. Major Standard: 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.

3.OA.A.3.1. Ability to determine when to use multiplication or division to solve a given word problem situation.

3.OA.A.3.2. Ability to represent a problem using drawings and equations without or with a symbol for the unknown number.

3.OA.A.3.3. Ability to solve different types of multiplication and division word problems (CCSS, Page 89, Table 2).

3.OA.B. Understand properties of multiplication and the relationship between multiplication and division.

3.OA.B.5. Major Standard: Apply properties of operations as strategies to multiply and divide: If 6x4 = 24 is known, then 4x6 = 24 is also known (Commutative property of multiplication); 3x5x2 can be found by 3x5 = 15, then 15x2 = 30, or by 5x2 = 10, then 3x10 = 30 (Associative property of multiplication); Knowing that 8x5 = 40 and 8x2 = 16, one can find 8x7 as 8x(5+2) = (8x5)+(8x2) which leads to 40+16 = 56 (Distributive property).

3.OA.B.5.1. Ability to break apart and manipulate the numbers (decomposing and composing numbers).

3.OA.B.5.2. Knowledge of the properties of multiplication include Zero, Identity, Commutative, Associative and Distributive properties (CCSS, Page 90, Table 3).

3.OA.B.5.4. Ability to understand and apply the Properties of Operations as opposed to simply naming them.

3.OA.B.5.5. Ability to apply of the Properties of Operations as strategies for increased efficiency.

3.OA.C. Multiply and divide within 100.

3.OA.C.7. Major Standard: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8x5 = 40, one knows 40÷5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

3.OA.C.7.1. Knowledge of multiplication and division strategies and properties to achieve efficient recall of facts.

3.OA.C.7.2. Ability to use multiple strategies to enhance understanding.

3.OA.C.7.3. Ability to model the various properties using concrete materials.

3.OA.D. Solve problems involving the four operations, and identify and explain patterns in arithmetic.

3.OA.D.8. Major Standard: 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.

3.OA.D.8.1. Knowledge of strategies for word problems as established for addition and subtraction (2.OA.A.1).

3.OA.D.8.2. Ability to solve word problems that use whole numbers and yield whole-number solutions.

3.OA.D.8.6. Ability to use various strategies applied in one-step word problems to solve multi-step word problems.

3.OA.D.8.8. Knowledge of and ability to apply estimation strategies, including rounding and front-end estimation, to make sense of the solution(s).

3.OA.D.8.9. Ability to apply knowledge of place value to estimation.

3.OA.D.9. Major Standard: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends.

3.OA.D.9.1. Ability to apply knowledge of skip counting (1.OA C.5 and 2.NBT.B.2) and explain “why” the pattern works the way it does as it relates to the properties of operations.

3.OA.D.9.2. Ability to investigate, discover, and extend number patterns and explain why they work.

3.OA.D.9.3. Knowledge that subtraction and division are not commutative.

3.OA.D.9.4. Knowledge of multiplication and division properties (CCSS, Page 90, Tables 3 & 4).

3.OA.D.9.5. Ability to apply knowledge of Properties of operations to explain patterns and why they remain consistent.

MD.MA.3.NBT. Number and Operations in Base Ten (NBT)

3.NBT.A. Use place value understanding and properties of operation to perform multi-digit arithmetic.

3.NBT.A.1. Additional Standard: Use place value understanding to round whole numbers to the nearest 10 or 100.

3.NBT.A.1.1. Knowledge of place value through 1,000 (2.NBT.A.1) to provide the foundation for rounding whole numbers.

3.NBT.A.1.2. Knowledge that place value refers to what a digit is worth in a number.

3.NBT.A.1.3. Knowledge that each place in a number is worth 10 times more than the place to the right of it (The tens column is worth 10 ones, the hundreds column is worth 10 tens).

3.NBT.A.1.4. Ability to use a variety of strategies when rounding (e.g., number line, proximity, and hundreds chart).

3.NBT.A.1.5. Ability to round a three-digit number to the nearest 10 or 100.

3.NBT.A.2. Additional Standard: 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.2.1. Knowledge of and ability to apply strategies of decomposing and composing numbers, partial sums, counting up, and counting back by ones, tens, and hundreds.

3.NBT.A.3. Additional Standard: Multiply one-digit whole numbers by multiples of 10 in the range of 1090 (e.g., 9x80, 5x60) using strategies based on place value and properties of operations.

3.NBT.A.3.1. Ability to apply knowledge of place value (e.g., 9x80 is 9 times 8 tens = 72 tens).

3.NBT.A.3.2. Ability to apply the Properties of Operations (CCSS, Page 90, Tables 3 & 4).

MD.MA.3.NF. Number and Operations – Fractions (NF)

3.NF.A. Develop the understanding of fractions as numbers.

3.NF.A.1. Major Standard: 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.

3.NF.A.1.1. Knowledge of the relationship between the number of equal shares and the size of the share (1.G.A.3).

3.NF.A.1.2. Knowledge of the relationship between the number of equal shares and the size of the share (1.G.A.3).

3.NF.A.1.3. Knowledge that unit fractions represent 1 of the total number of parts, for example, the fraction is formed by 1 part of a whole which is divided into 4 equal parts.

3.NF.A.1.5. Knowledge of the terms numerator (the number of parts being counted) and denominator (the total number of equal parts in the whole).

3.NF.A.1.7. Ability to identify and create fractions of a region and of a set, including the use of concrete materials.

3.NF.A.1.8. Knowledge of the size or quantity of the original whole when working with fractional parts.

3.NF.A.2. Major Standard: Understand a fraction as a number on the number line; represent fractions on a number line diagram.

3.NF.A.2.1. Ability to apply knowledge of whole numbers on a number line to the understanding of fractions on a number line.

3.NF.A.2.2. Ability to apply knowledge of unit fractions to represent and compute fractions on a number line.

3.NF.A.2.3. Ability to use linear models (e.g., equivalency table and manipulatives such as fraction strips, fraction towers, Cuisenaire rods) for fraction placement on a number line.

3.NF.A.2.4. Knowledge of the relationship between the use of a ruler in measurement to the use of a ruler as a number line.

3.NF.A.2.5. Knowledge that a number line does NOT have to start at zero.

3.NF.A.2.6. Ability to identify fractions on a number line with tick marks as well as on number lines without tick marks.

3.NF.A.3. Major Standard: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

3.NF.A.3.1. Ability to use concrete manipulatives and visual models to explain reasoning about fractions.

3.NF.A.3.2. Knowledge that equivalent fractions are ways of describing the same amount by using different-sized fractional parts. (e.g., 1/2 is the same as 2/4 or 3/6 or 4/8).

3.NF.A.3.3. Ability to use a variety of models when investigating equivalent fractions (e.g., number line, Cuisenaire rods, fraction towers, fraction circles, equivalence table, fraction strips).

3.NF.A.3.4. Ability to relate equivalency to fractions of a region or fractions of a set.

3.NF.A.3.5. Ability to use benchmarks of 0, 1/2, and 1 comparing fractions.

3.NF.A.3.6. Knowledge of and experience with fractional number sense to lay foundation for manipulating, comparing, finding equivalent fractions, etc.

3.NF.A.3a. Major Standard: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size – Represent two fractions as equivalent (equal) if they are the same size, or the same point on the number line.

3.NF.A.3a.1. Ability to describe the same amount by using different-sized fractional parts (e.g., 1/2 is the same as 2/4 or 3/6 or 4/8).

3.NF.A.3a.2. Ability to use number lines as well as fractions of a set or fractions of a region to model equivalent fractions.

3.NF.A.3a.3. Ability to use a variety of models to investigate relationships of equivalency.

3.NF.A.3b. Major Standard: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size – 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.

3.NF.A.3b.1. Ability to describe the same amount by using different-sized fractional parts (e.g., 1/2 is the same as 2/4 or 3/6 or 4/8).

3.NF.A.3b.2. Ability to use fraction models (e.g., fraction towers, fraction strips) to justify understanding of equivalent fractions.

3.NF.A.3c. Major Standard: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size – Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.

3.NF.A.3c.1. Knowledge of the denominator as the number of parts that a whole is divided into in order to explain why a denominator of 1 indicates whole number.

3.NF.A.3d. Major Standard: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size – 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.

3.NF.A.3d.1. Ability to use benchmarks of 0, 1/2 and 1 to explain relative value of fractions.

3.NF.A.3d.2. Knowledge that as the denominator increases the size of the part decreases.

3.NF.A.3d.3. Knowledge that when comparing fractions the whole must be the same size.

3.NF.A.3d.4. Ability to use a variety of models when comparing fractions (e.g., number line, and manipulatives such as Cuisenaire rods, fraction towers, fraction strips).

MD.MA.3.MD. Measurement and Data (MD)

3.MD.A. Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

3.MD.A.1. Major Standard: 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.

3.MD.A.1.1. Ability to tell time to the nearest 5-minute interval (2.MD.C.7).

3.MD.A.1.2. Ability to tell time to the nearest minute in a.m. and p.m.

3.MD.A.1.3. Ability to measure time intervals in minutes.

3.MD.A.1.5. Ability to initially add minutes in order to find the end time followed by working backwards to find start time.

3.MD.A.1.6. Ability to find the elapsed time of an event.

3.MD.A.1.8. Ability to find start time, end time, or elapsed time.

3.MD.A.2. Major Standard: 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.

3.MD.A.2.2. Ability to use the tools to measure mass and volume.

3.MD.A.2.3. Ability to explain the differences between mass and volume.

3.MD.B. Represent and interpret data.

3.MD.B.3. Supporting Standard: 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 may less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.

3.MD.B.3.2. Ability to apply experience with constructing and analyzing simple, single-unit scaled bar and picture graphs (pictograph) with no more than 4 categories (2.MD.D.10).

3.MD.B.3.5. Knowledge of and ability to connect understanding of locating points on a number line with locating points between intervals on a given axis (e.g., if given a scale counting by 5s students would need to be able to estimate the location of 13 between intervals of 10 and 15).

3.MD.C. Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

3.MD.C.5. Major Standard: Recognize area as an attribute of plane figures and understand concept of area measurement.

3.MD.C.5.2. Knowledge that area is the measure of total square units inside a region or how many square units it takes to cover a region.

3.MD.C.5a. Major Standard: Recognize area as an attribute of plane figures and understand concept 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.

3.MD.C.5a.1. Ability to use square units of measure (inch tile) to measure figures and identify length, perimeter, or area to give the total measure.

3.MD.C.5b. Major Standard: Recognize area as an attribute of plane figures and understand concept of area measurement – 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.

3.MD.C.5b.1. Ability to use square units of measure to cover a variety of plane figures without gaps or overlaps to provide the total area of the figure.

3.MD.C.6. Major Standard: Measure areas by counting unit squares (square cm, square m, square in., square ft., and improvised units).

3.MD.C.6.1. Ability to use manipulatives and visual models to calculate area.

3.MD.C.7a. Major Standard: 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.

3.MD.C.7a.1. Ability to justify the understanding of area by comparing tiling and counting with repeated addition/multiplication.

3.MD.C.7b. Major Standard: Relate area to the operations of multiplication and addition – 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.

3.MD.C.7b.1. Ability to apply the formula for area of a rectangle to solve word problems.

3.MD.C.7b.3. Use understanding of area to identify false reasoning and explain how to correctly find the area of rectangles.

3.MD.C.7d. Major Standard: Major Standard: Relate area to the operations of multiplication and addition – 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.

3.MD.C.7d.2. Knowledge that rectilinear figures refer to any polygon with all right angles.

3.MD.D. Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

3.MD.D.8. Additional Standard: 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.

3.MD.D.8.1. Knowledge that the perimeter is the distance around a region.

3.MD.D.8.2. Ability to use manipulatives and visual models to find the perimeter of a polygon.

3.MD.D.8.3. Ability to apply a variety of strategies to find the perimeter of a polygon.

3.MD.D.8.5. Use understanding of perimeter to identify false reasoning and explain how to correctly find the perimeter of plane figures.

3.MD.D.8.6. Knowledge that this is a geometry application of unit fractions (3.NF.A.1) and ability to make use of unit fraction understanding.

3.MD.D.8.7. Ability to use concrete materials to divide shapes into equal areas (e.g., pattern blocks, color tiles, geoboards).

MD.MA.3.G. Geometry (G)

3.G.A. Reason with shapes and their attributes.

3.G.A.1. Supporting Standard: 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.

3.G.A.1.1. Ability to compare and sort polygons based on their attributes, extending beyond the number of sides (2.G.A.1).

3.G.A.1.2. Ability to explain why two polygons are alike or why they are different based on their attributes.

3.G.A.2. Supporting Standard: 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.2.1. Knowledge that this is a geometry application of unit fractions (3.NF.A.1) and ability to make use of unit fraction understanding.

3.G.A.2.2. Ability to use concrete materials to divide shapes into equal areas (e.g., pattern blocks, color tiles, geoboards).