# Grade 2 — Common Core State Standards

## Mathematics Standards

### Operations and Algebraic Thinking (2.OA)

#### Represent and solve problems involving addition and subtraction.

**2.OA.A.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.

Existing Resources:

- Addition and Subtraction Table Kit – 5-82699-00
- Consumable Hundreds Chart – 5-82710-00
- Consumable Number Lines, Large Print Set – 1-03012-00; Braille/Tactile Set – 1-03013-00
- Cranmer Abacus – 1-03150-00
- Expanded Beginner’s Abacus Kit – 1-03181-00
- EZeeCOUNT Abacus – 1-03185-00
- Hundreds Board and Manipulatives – 1-03105-00
- Large Abacus – 1-03170-00
- Math Drill Cards in Braille and Large Print, Number & Math Signs – 1-03551-00
- Nemeth Code Reference Sheet, Print – 7-87500-00; Braille – 5-87400-00
- Number Line Device – 1-03480-01
- Tactile Tokens – 61-421-090

#### Add and subtract within 20.

**2.OA.B.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.

Existing Resources:

- Cranmer Abacus – 1-03150-00
- Desktop Stick-On Number Lines – 1-03481-00
- Expanded Beginner’s Abacus Kit – 1-03181-00
- EZeeCOUNT Abacus – 1-03185-00
- Large Abacus – 1-03170-00
- Math Flash, CD-ROM – D19910-01; Digital Download – D-19910-ED
- Math Drill Cards in Braille and Large Print, Addition – 1-03552-00
- Math Drill Cards in Braille and Large Print, Subtraction – 1-03552-00
- Quick Pick Math, Addition – 1-03570-00
- Quick Pick Math, Subtraction – 1-03571-00
- Math Robot™ for the iPhone – Works with your Apple® iPad® or iPad mini® running iOS 7® or later. Available on Quota at APH and at the App Store at itunes.apple.com/app/math-robot/id704570512

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

**2.OA.C.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.

Existing Resources:

- Math Drill Cards in Braille and Large Print, Number & Math Signs – 1-03551-00
- Nemeth Code Reference Sheet, Print – 7-87500-00; Braille – 5-87400-00
- Tactile Tokens – 61-421-090
- Tactile Algebra Tiles – 1-08410-00

**2.OA.C.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.

Existing Resources:

- EZeeCount Abacus – 1-03185-00
- DRAFTSMAN Tactile Drawing Board – 1-08857-00
- Graph Paper (assorted Low Relief and Bold-line available) with any Feel ‘n Peel Stickers
- Tactile Tokens – 61-421-090
- Tactile Algebra Tiles – 1-08410-00

### Number and Operations in Base Ten (2.NBT)

#### Understand place value.

**2.NBT.A.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.A.1a 100 can be thought of as a bundle of ten tens — called a “hundred.”
- 2.NBT.A.1b 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 tens and 0 ones).

Existing Resources:

- Cranmer Abacus – 1-03150-00
- Expanded Beginner’s Abacus Kit – 1-03181-00
- EZeeCOUNT Abacus – 1-03185-00
- Large Abacus – 1-03170-00
- FOCUS in Mathematics, Print Kit – 1-08280-01; Braille Kit – 1-08281-01

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

Existing Resources:

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

Existing Resources:

- Brannan Cubarithm Slate – 1-00320-00
- Cubarithm Plastic Cubes – 1-00330-00
- FOCUS in Mathematics, Print Kit – 1-08280-01; Braille Kit – 1-08281-01
- Nemeth Code Reference Sheet, Print – 7-87500-00; Braille – 5-87400-00
- Quick Check: Index of Literary Braille Signs, Print – 7-35960-01; Braille – 5-35960-01

**2.NBT.A.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.

Existing Resources:

- FOCUS in Mathematics, Print Kit – 1-08280-01; Braille Kit – 1-08281-01
- Nemeth Code Reference Sheet, Print – 7-87500-00; Braille – 5-87400-00

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

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

Existing Resources:

- Addition and Subtraction Table Kit – 5-82699-00
- Brannan Cubarithm Slate – 1-00320-00
- Consumable Hundreds Chart – 5-82710-00
- Cranmer Abacus – 1-03150-00
- Cubarithm Plastic Cubes – 1-00330-00
- Expanded Beginner’s Abacus Kit – 1-03181-00
- EZeeCOUNT Abacus – 1-03185-00
- FOCUS in Mathematics, Print Kit – 1-08280-01; Braille Kit – 1-08281-01
- Hundreds Board and Manipulatives – 1-03105-00
- Large Abacus – 1-03170-00
- Math Flash, CD-ROM – D19910-01; Digital Download – D-19910-ED
- Math Robot™ for the iPhone – Works with your Apple® iPad® or iPad mini® running iOS 7® or later. Available on Quota at APH and at the App Store at itunes.apple.com/app/math-robot/id704570512

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

Existing Resources:

- Brannan Cubarithm Slate – 1-00320-00
- Cranmer Abacus – 1-03150-00
- Cubarithm Plastic Cubes – 1-00330-00
- Expanded Beginner’s Abacus Kit – 1-03181-00
- EZeeCOUNT Abacus – 1-03185-00
- FOCUS in Mathematics, Print Kit – 1-08280-01; Braille Kit – 1-08281-01
- Large Abacus – 1-03170-00
- Nemeth Code Reference Sheet, Print – 7-87500-00; Braille – 5-87400-00

**2.NBT.B.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.

Existing Resources:

- Brannan Cubarithm Slate – 1-00320-00
- Cranmer Abacus – 1-03150-00
- Cubarithm Plastic Cubes – 1-00330-00
- EZeeCOUNT Abacus – 1-03185-00
- FOCUS in Mathematics, Print Kit – 1-08280-01; Braille Kit – 1-08281-01
- Large Abacus – 1-03170-00
- Nemeth Code Reference Sheet, Print – 7-87500-00; Braille – 5-87400-00

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

Existing Resources:

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

Existing Resources:

- Addition and Subtraction Table Kit – 5-82699-00
- Cranmer Abacus – 1-03150-00
- Expanded Beginner’s Abacus Kit – 1-03181-00
- EZeeCOUNT Abacus – 1-03185-00
- FOCUS in Mathematics, Print Kit – 1-08280-01; Braille Kit – 1-08281-01
- Large Abacus – 1-03170-00

### Measurement and Data (2.MD)

#### Measure and estimate lengths in standard units.

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

Existing Resources:

- Braille/Large Print Yardstick – 1-03002-00
- English Measurement Ruler – 1-03070-00
- Flexible Rulers (Braille/Large Print), 18-Inch – 1-03050-00; 30-Centimeter – 1-03031-00
- Large Print/Braille Toss-Away Ruler, Large Print/Braille – 1-03010-00; Large Print Only – 1-03011-00
- MathBuilders, Unit 5: Measurement and Estimation, Large Print Kit – 7-03562-00; Braille Kit – 5-03562-00
- Meterstick (Braille) – 1-03000-00
- Metric-English Measurement Ruler – 1-03100-00
- Transparent CCTV Ruler Kit, Yellow – 1-03008-00; Clear – 1-030089-00

**2.MD.A.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.

Existing Resources:

- Braille/Large Print Yardstick – 1-03002-00
- English Measurement Ruler – 1-03070-00
- Flexible Rulers (Braille/Large Print), 18-Inch – 1-03050-00; 30-Centimeter – 1-03031-00
- Large Print/Braille Toss-Away Ruler, Large Print/Braille – 1-03010-00; Large Print Only – 1-03011-00
- MathBuilders, Unit 5: Measurement and Estimation, Large Print Kit – 7-03562-00; Braille Kit – 5-03562-00
- Meterstick (Braille) – 1-03000-00
- Metric-English Measurement Ruler – 1-03100-00
- Transparent CCTV Ruler Kit, Yellow – 1-03008-00; Clear – 1-030089-00

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

Existing Resources:

- Braille/Large Print Yardstick – 1-03002-00
- English Measurement Ruler – 1-03070-00
- Flexible Rulers (Braille/Large Print), 18-Inch – 1-03050-00; 30-Centimeter – 1-03031-00
- Large Print/Braille Toss-Away Ruler, Large Print/Braille – 1-03010-00; Large Print Only – 1-03011-00
- MathBuilders, Unit 5: Measurement and Estimation, Large Print Kit – 7-03562-00; Braille Kit – 5-03562-00
- Meterstick (Braille) – 1-03000-00
- Metric-English Measurement Ruler – 1-03100-00

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

Existing Resources:

- Braille/Large Print Yardstick – 1-03002-00
- English Measurement Ruler – 1-03070-00
- Flexible Rulers (Braille/Large Print), 18-Inch – 1-03050-00; 30-Centimeter – 1-03031-00
- Large Print/Braille Toss-Away Ruler, Large Print/Braille – 1-03010-00; Large Print Only – 1-03011-00
- Meterstick (Braille) – 1-03000-00
- Metric-English Measurement Ruler – 1-03100-00
- Transparent CCTV Ruler Kit, Yellow – 1-03008-00; Clear – 1-030089-00

#### Relate addition and subtraction to length.

**2.MD.B.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.

Existing Resources:

- Addition and Subtraction Table Kit – 5-82699-00
- Nemeth Code Reference Sheet, Print – 7-87500-00; Braille – 5-87400-00

**2.MD.B.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.

Existing Resources:

- Consumable Number Lines, Large Print Set – 1-03012-00; Braille/Tactile Set – 1-03013-00
- Desktop Stick-On Number Lines, Large Print/Braille – 1-03481-00
- Number Line Device – 1-03480-01

#### Work with time and money.

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

Existing Resources:

- Analog Clock Model – 1-03125-00
- Clock Face Sheets in Braille – 1-03111-00

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

Existing Resources:

- Nemeth Code Reference Sheet, Print – 7-87500-00; Braille – 5-87400-00

#### Represent and interpret data.

**2.MD.D.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.

Existing Resources:

- Braille/Large Print Yardstick – 1-03002-00
- English Measurement Ruler – 1-03070-00
- Flexible Rulers (Braille/Large Print), 18-Inch – 1-03050-00; 30-Centimeter – 1-03031-00
- Graph Paper (assorted Low Relief and Bold-line available) with any Feel ‘n Peel Stickers
- Large Print/Braille Toss-Away Ruler, Large Print/Braille – 1-03010-00; Large Print Only – 1-03011-00
- MathBuilders, Unit 8: Data Collection, Graphing, and Probability/Statistics, Large Print Kit – 7-03565-00; Braille Kit – 5-03565-00
- Meterstick (Braille) – 1-03000-00
- Metric-English Measurement Ruler – 1-03100-00

**2.MD.D.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.

Existing Resources:

- Graph Paper (assorted Low Relief and Bold-line available) with any Feel ‘n Peel Stickers
- MathBuilders, Unit 8: Data Collection, Graphing, and Probability/Statistics, Large Print Kit – 7-03565-00; Braille Kit – 5-03565-00

### Geometry (2.G)

#### Reason with shapes and their attributes.

**2.G.A.1** Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

Existing Resources:

- DRAFTSMAN Tactile Drawing Board – 1-08857-00
- FOCUS in Mathematics, Print Kit – 1-08280-01; Braille Kit – 1-08281-01
- Geometro, GS22 Medium Set – 1-03023-00
- Graphic Art Tape – 1-08878-00
- MathBuilders, Unit 6: Geometry, Large Print Kit – 7-03563-00; Braille Kit – 5-03563-00
- Picture Maker: Wheatley Tactile Diagramming Kit – 1-08838-00

**2.G.A.2** Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.

Existing Resources:

- Plexiglas Blocks (1-08663-00) with a tactile graphic of a rectangle
- Tiles from MathBuilders, Unit 8: Data Collections, Graphing, and Probability/Statistics (Large Print Kit – 7-03565-00; Braille Kit – 5-03565-00) with a tactile graphic of a rectangle
- Unit cubes from FOCUS in Mathematics (Print Kit – 1-08280-01; Braille Kit – 1-08281-0) with a tactile graphic of a rectangle

**2.G.A.3** 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.

Existing Resources:

- Geometro GS 10 Cylinder and Cone – 1-03030-00
- DRAFTSMAN Tactile Drawing Board – 1-08857-00
- FOCUS in Mathematics, Print Kit – 1-08280-01; Braille Kit – 1-08281-01
- Graphic Art Tape (1-08878-00) with tactile graphic
- MathBuilders, Unit 6: Geometry, Large Print Kit – 7-03563-00; Braille Kit – 5-03563-00
- MathBuilders, Unit 7: Fractions, Mixed Numbers, and Decimals, Large Print Kit – 7-03564-00; Braille Kit – 5-03564-00

## English Language Arts Standards

**Note:** APH product recommendations for the English Language Arts CCSS will be published in the future.