All West Virginia teachers are responsible for classroom instruction that integrates content standards and mathematical habits of mind. Students in the second grade will focus on four critical areas: (1) extending understanding of base-ten notation; (2) building fluency with addition and subtraction; (3) using standard units of measure; and (4) describing and analyzing shapes. Mathematical habits of mind, which should be integrated in these content areas, include: making sense of problems and persevering in solving them, reasoning abstractly and quantitatively; constructing viable arguments and critiquing the reasoning of others; modeling with mathematics; using appropriate tools strategically; attending to precision, looking for and making use of structure; and looking for and expressing regularity in repeated reasoning.

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### Operations and Algebraic Thinking

#### Standards

M.2.1

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).

#### Alignment

M.1.1

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).

M.1.2

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).

M.2.1

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).

#### Standards

M.2.2

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

#### Alignment

M.1.5

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

M.1.6

Add and subtract within 20, demonstrating fluency for addition and subtraction within 10 and use 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).

M.2.2

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

#### Standards

M.2.3

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.

M.2.4

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.

#### Resources

• What is an Array

#### Alignment

M.2.3

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.

M.2.4

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.

### Number and Operations in Base Ten

#### Standards

M.2.5

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:

• 100 can be thought of as a bundle of ten tens – called a “hundred.”
• Numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight or nine hundred, and 0 tens and 0 ones.

M.2.6

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

M.2.7

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

M.2.8

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

#### Resources

• Making Math Fun with Place Value Games

#### Alignment

M.1.10

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

• 10 can be thought of as a bundle of ten ones — called a “ten.” (e.g., A group of ten pennies is equivalent to a dime.)
• The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight or nine ones.
• 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).

M.1.11

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

M.2.5

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:

• 100 can be thought of as a bundle of ten tens – called a “hundred.”
• Numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight or nine hundred, and 0 tens and 0 ones.

M.2.6

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

M.2.7

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

M.2.8

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

#### Standards

M.2.9

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

M.2.10

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

M.2.11

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.

M.2.12

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

M.2.13

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

#### Resources

• Shirts full of Buttons

#### Alignment

M.1.12

• 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.

M.1.13

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

M.1.14

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.

M.2.9

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

M.2.10

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

M.2.11

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.

M.2.12

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

M.2.13

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

### Measurement and Data

#### Standards

M.2.14

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

M.2.15

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.

M.2.16

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

M.2.17

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

#### Alignment

M.2.14

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

M.2.15

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.

M.2.16

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

M.2.17

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

#### Standards

M.2.18

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.

M.2.19

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.

#### Alignment

M.2.18

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.

M.2.19

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.

#### Standards

M.2.20

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

M.2.21

Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using \$ and ¢ symbols appropriately (e.g., If you have 2 dimes and 3 pennies, how many cents do you have?).

#### Alignment

M.2.20

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

M.2.21

Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using \$ and ¢ symbols appropriately (e.g., If you have 2 dimes and 3 pennies, how many cents do you have?).

#### Standards

M.2.22

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.

M.2.23

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.

#### Resources

• High Horse
• Shirts full of Buttons

#### Alignment

M.1.18

Organize, represent, 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.

M.2.22

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.

M.2.23

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.

M.3.18

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 (e.g., draw a bar graph in which each square in the bar graph might represent 5 pets).

M.3.19

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.

### Geometry

#### Standards

M.2.24

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.

M.2.25

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

M.2.26

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., describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

#### Alignment

M.1.19

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

M.1.20

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.

M.1.21

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 and understand for these examples that decomposing into more equal shares creates smaller shares.

M.2.24

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.

M.2.25

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

M.2.26

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., describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.