Massachusetts State Standards for Mathematics: Grade 3

MA.3.N. Number Sense and Operations: Students engage in problem solving, communicating, reasoning, connecting, and representing.

3.N.1. Exhibit an understanding of the values of the digits in the base ten number system by reading, modeling, writing, comparing, and ordering whole numbers through 9,999.

3.N.2. Represent, order, and compare numbers through 9,999. Represent numbers using expanded notation, e.g., 853 = 8 x 100 + 5 x 10 + 3, and written out in words, e.g., eight hundred fifty-three.

3.N.3. Identify and represent fractions between 0 and 1 with denominators through 10 as parts of unit wholes and parts of groups.

3.N.4. Locate on the number line and compare fractions (between 0 and 1) with denominators 2, 3, and 4, e.g., 2/3; and the mixed numbers 1 1/4, 1 1/2, and 1 3/4.

3.N.5. Recognize classes (odd numbers, even numbers, and multiples of numbers through 10) to which a number may belong, and identify the numbers in those classes, e.g., the class of multiples of 7 between 1 and 29 consists of 7, 14, 21, 28.

3.N.6. Select, use, and explain various meanings and models of multiplication (through 10 x10). Relate a multiplication problem to a corresponding division problem, e.g., draw a model to represent 5 x 6 and 30 / 6.

3.N.7. Use the commutative (order) and identity properties of addition and multiplication on whole numbers in computations and problem situations, e.g., 3 + 4 + 7 = 3 + 7 + 4 = 10 + 4.

3.N.8. Select and use appropriate operations (addition, subtraction, multiplication, and division) to solve problems, including those involving money. This standard is intentionally the same as standard 4.N.1.0.

3.N.9. Know multiplication facts through 10 x 10 and related division facts, e.g., 9 x 8 = 72 and 72 / 9 = 8. Use these facts to solve related problems, e.g., 3 x 5 is related to 3 x 50.

3.N.10. Add and subtract (up to four-digit numbers) and multiply (up to two-digit numbers by a one-digit number) accurately and efficiently.

3.N.11. Round whole numbers through 1,000 to the nearest 10, 100, and 1,000.

3.N.12. 2 Understand and use the strategies of rounding and regrouping to estimate quantities, measures, and the results of whole-number computations (addition, subtraction, and multiplication) up to two-digit whole numbers and amounts of money to $100, and to judge the reasonableness of the answer.

3.N.13. Use concrete objects and visual models to add and subtract (only when the answer is greater than or equal to zero) common fractions (halves, thirds, fourths, sixths, and eighths) with like denominators.

MA.3.P. Patterns, Relations, and Algebra: Students engage in problem solving, communicating, reasoning, connecting, and representing.

3.P.1. Create, describe, extend, and explain symbolic (geometric) patterns and addition and subtraction patterns, e.g., 2, 6,10, ?; and 50, 45, 40...

3.P.2. Determine which symbol (<, >, or =) is appropriate for a given number sentence, e.g., 7 x 8 __ 49 + 6.

3.P.3. Determine the value of a variable (through 10) in simple equations involving addition, subtraction, or multiplication.

3.P.4. Write number sentences using +, -, x, /, <, = , and/or > to represent mathematical relationships in everyday situations.

MA.3.G. Geometry: Students engage in problem solving, communicating, reasoning, connecting, and representing.

3.G.1. Compare and analyze attributes and other features (e.g., number of sides, corners, diagonals, and lines of symmetry) of two-dimensional geometric shapes.

3.G.2. Describe, model, draw, compare, and classify two-dimensional shapes, e.g., circles, triangles, and quadrilaterals. Identify and describe simple three-dimensional shapes, e.g., cubes, spheres, and pyramids.

3.G.3. Identify angles as right angles, less than a right angle, and greater than a right angle.

3.G.4. Identify and draw parallel lines, perpendicular lines, and other intersecting lines.

3.G.5. Using ordered pairs of whole numbers and/or letters, locate, and identify points on a grid.

3.G.6. Identify and draw lines of symmetry in two-dimensional shapes.

3.G.7. Predict and explain the results of taking apart and combining two-dimensional shapes.

MA.3.M. Measurement: Students engage in problem solving, communicating, reasoning, connecting, and representing.

3.M.1. Demonstrate an understanding of the attributes length, area, and weight, and select the appropriate type of unit for measuring each attribute using both the U.S. Customary (English) and metric systems.

3.M.2. Carry out simple unit conversions within a system of measurement, e.g., hours to minutes, cents to dollars, yards to feet or inches, etc. This standard is intentionally the same as standard 4.M.2..

3.M.3. Identify time to the minute on analog and digital clocks using a.m. and p.m. Compute elapsed time less than one hour using a clock (e.g., minutes since?) and using a calendar (e.g., days since ?).

3.M.4. Estimate and find area and perimeter of a rectangle using diagrams and grids, or by measuring.

3.M.5. Identify and use appropriate metric and U.S. Customary (English) units and tools (e.g., ruler, scale, thermometer, clock) to estimate, measure, and solve problems involving length, area, weight, temperature, and time.

MA.3.D. Data Analysis, Statistics, and Probability: Students engage in problem solving, communicating, reasoning, connecting, and representing.

3.D.1. Collect and organize data using observations, measurements, surveys, or experiments, and identify appropriate ways to display the data. This standard is intentionally the same as standard 4.D.1.

3.D.2. Match representations of a data set in the form of tables, line plots, pictographs, tallies, or bar graphs with the actual data set.

3.D.3. Construct and draw conclusions from representations of data sets in the form of tables, line plots, pictographs, tallies, and bar graphs.

3.D.4. List and count the number of possible combinations of objects from two sets, e.g., how many different outfits can one make from a set of two sweaters, and a set of three skirts?

MA.CC.3.OA. Operations and Algebraic Thinking

3.OA.1. Interpret products of whole numbers, e.g., interpret 5 * 7 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 5 * 7.

3.OA.2. 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.3. 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.4. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 * ? = 48, 5 = __ / 3, 6 * 6 = ?.

3.OA.5. Apply properties of operations as strategies to multiply and divide. Examples: If 6 * 4 = 24 is known, then 4 * 6 = 24 is also known. (Commutative property of multiplication.) 3 * 5 * 2 can be found by 3 * 5 = 15, then 15 * 2 = 30, or by 5 * 2 = 10, then 3 * 10 = 30. (Associative property of multiplication.) Knowing that 8 * 5 = 40 and 8 * 2 = 16, one can find 8 * 7 as 8 * (5 + 2) = (8 * 5) + (8 * 2) = 40 + 16 = 56. (Distributive property.)

3.OA.6. Understand division as an unknown-factor problem. For example, find 32 8 by finding the number that makes 32 when multiplied by 8.

3.OA.7. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 * 5 = 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.8. 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.9. 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.

MA.CC.3.NBT. Number and Operations in Base Ten

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

3.NBT.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.3. 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.

MA.CC.3.NF. Number and Operations-Fractions

3.NF.1. 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.2. Understand a fraction as a number on the number line; represent fractions on a number line diagram.

3.NF.2.a. 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 of the part based at 0 locates the number 1/b on the number line.

3.NF.2.b. 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.

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

3.NF.3.a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

3.NF.3.b. 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.3.c. 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.3.d. 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.

MA.CC.3.MD. Measurement and Data

3.MD.1. 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.2. 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.3. 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. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.

3.MD.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.5. Recognize area as an attribute of plane figures and understand concepts of area measurement.

3.MD.5.a. 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.5.b. 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.6. Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).

3.MD.7. Relate area to the operations of multiplication and addition.

3.MD.7.a. 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.7.b. 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.7.c. 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.

3.MD.7.d. 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.8. 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.

MA.CC.3.G. Geometry