Massachusetts State Standards for Mathematics: Grade 2

MA.2.N. Number Sense and Operations: Students engage in problem solving, communicating, reasoning, connecting, and representing.

2.N.1. Name and write (in numerals) whole numbers to 1000, identify the place values of the digits, and order the numbers.

2.N.2. Identify and distinguish among multiple uses of numbers, including cardinal (to tell how many) and ordinal (to tell which one in an ordered list), and numbers as labels and as measurements.

2.N.3. Identify and represent common fractions (1/2, 1/3, 1/4) as parts of wholes, parts of groups, and numbers on the number line.

2.N.4. Compare whole numbers using terms and symbols, e.g., less than, equal to, greater than (<, =, >).

2.N.5. Identify odd and even numbers and determine whether a set of objects has an odd or even number of elements.

2.N.6. Identify the value of all U.S. coins, and $1, $5, $10, and $20 bills. Find the value of a collection of coins and dollar bills and different ways to represent an amount of money up to $5. Use appropriate notation, e.g., 69 cents, $1.35.

2.N.7. Demonstrate an understanding of various meanings of addition and subtraction, e.g., addition as combination (plus, combined with, more); subtraction as comparison (how much less, how much more), equalizing (how many more are needed to make these equal), and separation (how much remaining).

2.N.8. Understand and use the inverse relationship between addition and subtraction (e.g., 8 + 6 = 14 is equivalent to 14 - 6 = 8 and is also equivalent to 14 - 8 = 6) to solve problems and check solutions.

2.N.9. Know addition facts (addends to ten) and related subtraction facts, and use them to solve problems.

2.N.10. Demonstrate the ability to add and subtract three-digit numbers accurately and efficiently.

2.N.11. Demonstrate in the classroom an understanding of and the ability to use the conventional algorithms for addition (two 3-digit numbers and three 2-digit numbers) and subtraction (two 3-digit numbers).

2.N.12. Estimate, calculate, and solve problems involving addition and subtraction of two-digit numbers. Describe differences between estimates and actual calculations.

MA.2.P. Patterns, Relations, and Algebra: Students engage in problem solving, communicating, reasoning, connecting, and representing.

2.P.1. Identify, reproduce, describe, extend, and create simple rhythmic, shape, size, number, color, and letter repeating patterns.

2.P.2. Identify different patterns on the hundreds chart.

2.P.3. Describe and create addition and subtraction number patterns, e.g., 1, 4, 7, 10; or 25, 23, 21).

2.P.4. Skip count by twos, fives, and tens up to at least 50, starting at any number.

2.P.5. Construct and solve open sentences that have variables, e.g., n + 7 = 10.

2.P.6. Write number sentences using +, -, <, =, and/or > to represent mathematical relationships in everyday situations.

2.P.7. Describe functions related to trading, including coin trades and measurement trades, e.g., five pennies make one nickel or four cups make one quart.

MA.2.G. Geometry: Students engage in problem solving, communicating, reasoning, connecting, and representing.

2.G.1. Describe attributes and parts of two- and three-dimensional shapes, e.g., length of sides, and number of corners, edges, faces, and sides.

2.G.2. Identify, describe, draw, and compare two-dimensional shapes, including both polygonal (up to six sides) and curved figures such as circles.

2.G.3. Recognize congruent shapes.

2.G.4. Identify shapes that have been rotated (turned), reflected (flipped), (slid), and enlarged. Describe direction of translations, e.g., left, right, up, down.

2.G.5. Identify symmetry in two-dimensional shapes.

2.G.6. Predict the results of putting shapes together and taking them apart.

2.G.7. Relate geometric ideas to numbers, e.g., seeing rows in an array as a model of repeated addition.

MA.2.M. Measurement: Students engage in problem solving, communicating, reasoning, connecting, and representing.

2.M.1. Identify parts of the day (e.g., morning, afternoon, evening), days of the week, and months of the year. Identify dates using a calendar.

2.M.2. Tell time at quarter-hour intervals on analog and digital clocks using a.m. and p.m.

2.M.3. Compare the length, weight, area, and volume of two or more objects by using direct comparison.

2.M.4. Measure and compare common objects using metric and English units of length measurement, e.g., centimeter, inch.

2.M.5. Select and correctly use the appropriate measurement tools, e.g., ruler, balance scale, thermometer.

2.M.6. Make and use estimates of measurement, including time, volume, weight, and area.

MA.2.D. Data Analysis, Statistics, and Probability: Students engage in problem solving, communicating, reasoning, connecting, and representing.

2.D.1. Use interviews, surveys, and observations to gather data about themselves and their surroundings.

2.D.2. Organize, classify, represent, and interpret data using tallies, charts, tables, bar graphs, pictographs, and Venn diagrams; interpret the representations.

2.D.3. Formulate inferences (draw conclusions) and make educated guesses (conjectures) about a situation based on information gained from data.

2.D.4. Decide which outcomes of experiments are most likely.

MA.CC.2.OA. Operations and Algebraic Thinking

2.OA.1. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

2.OA.2. Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.

2.OA.MA.2a. By the end of Grade 2, know from memory related subtraction facts of sums of two one-digit numbers.

2.OA.3. Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.

2.OA.4. Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

MA.CC.2.NBT. Number and Operations in Base Ten

2.NBT.1. Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:

2.NBT.1.a. 100 can be thought of as a bundle of ten tens-called a ''hundred.''

2.NBT.1.b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).

2.NBT.2. Count within 1000; skip-count by 5s, 10s, and 100s.

2.NBT.3. Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.

2.NBT.4. Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

2.NBT.5. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

2.NBT.6. Add up to four two-digit numbers using strategies based on place value and properties of operations.

2.NBT.7. Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

2.NBT.8. Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900.

2.NBT.9. Explain why addition and subtraction strategies work, using place value and the properties of operations.

MA.CC.2.MD. Measurement and Data

2.MD.1. Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.

2.MD.2. Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.

2.MD.3. Estimate lengths using units of inches, feet, centimeters, and meters.

2.MD.4. Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.

2.MD.5. Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.

2.MD.6. Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram.

2.MD.7. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.

2.MD.MA.7a. Know the relationships of time, including seconds in a minute, minutes in an hour, hours in a day, days in a week, a month, and a year; and weeks in a month and a year.

2.MD.8. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and cents symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?

2.MD.9. Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.

2.MD.10. Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems, using information presented in a bar graph.

MA.CC.2.G. Geometry