Grade 2 Math Colorado standards Standards

Geometry

Measurement & Data

Operations & Algebraic Thinking

Number & Operations in Base Ten

Standards for Mathematical Practice

Reason with shapes and their attributes.

Geometry: Reason with shapes and their attributes.

Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. (Sizes are compared directly or visually, not compared by measuring.) Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

Recognize and create circles, squares, rectangles, and triangles having specified attributes, such as a given number of angles or a given number of faces. Example: draw and name a shape that has three angles and three sides.

Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.

Partition a rectangle into up to 5 rows and up to 5 columns of same-size squares and count to find the total number of them.

Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

Partition circles and rectangles into two or four equal shares, describe the shares using the words halves and quarters, and describe the whole as two halves.

Measure and estimate lengths in standard units.

Measurement & Data: Measure and estimate lengths in standard units.

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

Identify appropriate tools for measuring length, such as rules, yardsticks, meter sticks, and measuring tapes.

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.

Measure the length of an object using a tool marked with whole-number standard units, such as a ruler marked only for whole inches.

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

Estimate lengths using non-standard units. Examples: “I think the student is about 5 books tall.” “I’m guessing the desk is 3 pieces of paper wide.”

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

Compare the lengths of two objects indirectly by using a third object.

Relate addition and subtraction to length.

Measurement & Data: Relate addition and subtraction to length.

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.

Use addition and subtraction within 20 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers).

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.

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 20 on a number line diagram.

Work with time and money.

Measurement & Data: Work with time and money.

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

Tell time on analog and digital clocks to the nearest hour.

Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately.

Identify and sort coins (quarters, dimes, nickels, and pennies) and understand that money has value.

Represent and interpret data.

Measurement & Data: Represent and interpret data.

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.

Create a picture graph to represent a data set with two categories.

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.

Generate measurement data by measuring lengths of several objects to the nearest whole unit.

Match the measurement data to a given line plot, where the horizontal scale is marked off in whole-number units.

Understand place value.

Number & Operations in Base Ten: Understand place value.

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:

Understand that the two digits of a two-digit number represent amounts of tens and ones; e.g., 37 equals 3 tens and 7 ones.

100 can be thought of as a bundle of ten tens — called a "hundred."

Understand the following as special cases: 10 can be thought of as a bundle or ten ones, called and ten, and the numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, and nine tens.

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).

Decompose numbers less than 20 in more than one way.

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

Count within 50.

Skip count by fives and tens.

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

Understand and represent numbers to 50 with objects, written representations, and/or numerals.

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

Compare two two-digit numbers less than or equal to 50 based on the meanings of the tens and ones digits.

Use place value understanding and properties of operations to add and subtract.

Number & Operations in Base Ten: Use place value understanding and properties of operations to add and subtract.

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

Add and subtract within 20 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

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

Add up to three two-digit numbers using strategies based on place value and properties of operations.

Limit sums to 50 or less.

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.

Add and subtract within 50, 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 two-digit numbers, one adds or subtracts tens and tens, ones and ones, and sometimes it is necessary to compose or decompose tens.

Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.

Mentally add 1 or 10 to a given number 1-50, and mentally subtract 1 or 10 from a given number 1-50.

Explain why addition and subtraction strategies work, using place value and the properties of operations. (Explanations may be supported by drawings or objects.)

Demonstrate an understanding of the meanings of symbols in addition and subtraction situations, including the “+” sign (i.e., combine, plus, add), “-“ sign (i.e., separate, subtract, take away), and “=” sign (equal).

Represent and solve problems involving addition and subtraction.

Operations & Algebraic Thinking: Represent and solve problems involving addition and subtraction.

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.

Use addition and subtraction within 20 to solve one-and two-step word problems involving situations or adding to, taking from, putting together, taking apart, and comparing by using objects, drawings, or other written methods.

Add and subtract within 20.

Operations & Algebraic Thinking: Add and subtract within 20.

Fluently add and subtract within 20 using mental strategies. (See 1.OA.C.6 for a list of strategies.) By end of Grade 2, know from memory all sums of two one-digit numbers.

Add and subtract within 10 using mental strategies.

Work with equal groups of objects to gain foundations for multiplication.

Operations & Algebraic Thinking: Work with equal groups of objects to gain foundations for multiplication.

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.

Determine whether a group of objects (up to 10) has an odd or even number of members, e.g., by pairing objects or counting them by 2s.

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.

Use addition to find the total number of objects arranged within equal groups up to a total of 10.

Algebra and Functions

Data, Statistics, and Probability

Geometry

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.

Number and Quantity