# Massachusetts State Standards for Mathematics: Grade 1

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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.1.OA. Operations and Algebraic Thinking

1.OA.1. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

1.OA.2. Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

1.OA.3. Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)

1.OA.4. Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8.

1.OA.5. Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

1.OA.6. Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use mental strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

1.OA.7. Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.

1.OA.8. Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = __ - 3, 6 + 6 = __.

1.OA.MA.9. Write and solve number sentences from problem situations that express relationships involving addition and subtraction within 20.

MA.CC.1.NBT. Number and Operations in Base Ten

1.NBT.1. Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.

1.NBT.2. Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:

1.NBT.2.a. 10 can be thought of as a bundle of ten ones-called a ''ten.''

1.NBT.2.b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.

1.NBT.2.c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

1.NBT.3. Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

1.NBT.4. Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, 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 and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

1.NBT.5. Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.

1.NBT.6. Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), 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 and explain the reasoning used.

MA.CC.1.MD. Measurement and Data

1.MD.1. Order three objects by length; compare the lengths of two objects indirectly by using a third object.

1.MD.2. Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.

1.MD.3. Tell and write time in hours and half-hours using analog and digital clocks.

1.MD.4. Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

1.MD.MA.5. Identify the values of all U.S. coins; know their comparative values, e.g., a dime is of greater value than a nickel. Find equivalent values, e.g., a nickel is equivalent to 5 pennies. Use appropriate notation (e.g., 69 cents). Use the value of coins in the solution of problems.

MA.CC.1.G. Geometry

1.G.1. Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes that possess defining attributes.

1.G.2. Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.

1.G.3. Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.