# Grade 3 — Common Core State Standards

## Mathematics Standards

- Operations and Algebraic Thinking
- Number and Operations in Base Ten
- Number and Operations—Fractions
- Measurement and Data
- Geometry

### Operations and Algebraic Thinking (3.OA)

#### Represent and solve problems involving multiplication and division.

**3.OA.A.1** Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. *For example, describe a context in which a total number of objects can be expressed as 5 × 7.*

Existing Resources:

- EZeeCount Abacus – 1-03185-00
- Brannan Cubarithm Slate – 1-00320-00
- Cubarithm Plastic Cubes – 1-00330-00
- 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
- Textured Sorting Circles and Shapes – 1-08834-00

**3.OA.A.2** Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. *For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.*

Existing Resources:

- Brannan Cubarithm Slate – 1-00320-00
- Cubarithm Plastic Cubes – 1-00330-00
- Graph Paper (assorted Low Relief and Bold-line available) with any Feel ‘n Peel Stickers
- Tactile Tokens – 61-421-090
- Textured Sorting Circles and Shapes – 1-08834-00

**3.OA.A.3** Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

Existing Resources:

- Graph Paper (assorted Low Relief and Bold-line available) with any Feel ‘n Peel Stickers
- 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 Algebra Tiles – 1-08410-00

**3.OA.A.4** Determine the unknown whole number in a multiplication or division equation relating three whole numbers. *For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = ? ÷ 3, 6 × 6 = ?.*

Existing Resources:

- Multiplication/Division Table – 5-82700-01
- Nemeth Code Reference Sheet, Print – 7-87500-00; Braille – 5-87400-00

#### Understand properties of multiplication and the relationship between multiplication and division.

**3.OA.B.5** Apply properties of operations as strategies to multiply and divide. *Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3× 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)*

Existing Resources:

- Math Drill Cards in Braille and Large Print, Number & Math Signs – 1-03551-00
- Multiplication/Division Table – 5-82700-01

**3.OA.B.6** Understand division as an unknown-factor problem. *For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.*

Existing Resources:

#### Multiply and divide within 100.

**3.OA.C.7** Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

Existing Resources:

- Math Drill Cards in Braille and Large Print, Division – 1-03555-00
- Math Drill Cards in Braille and Large Print, Multiplication – 1-03554-00
- Math Flash, CD-ROM – D19910-01; Digital Download – D-19910-ED
- Multiplication/Division Table – 5-82700-01
- Quick Pick Math, Division – 1-03573-00
- Quick Pick Math, Multiplication – 1-03572-00
- 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

#### Solve problems involving the four operations, and identify and explain patterns in arithmetic.

**3.OA.D.8** Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Existing Resources:

**3.OA.D.9** Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. *For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.*

Existing Resources:

### Number and Operations in Base Ten (3.NBT)

#### Use place value understanding and properties of operations to perform multi-digit arithmetic.

**3.NBT.A.1** Use place value understanding to round whole numbers to the nearest 10 or 100.

Existing Resources:

- Consumable Hundreds Chart – 5-82710-00
- Hundreds Board and Manipulatives – 1-03105-00
- Number Line Device – 1-03480-01

**3.NBT.A.2** Fluently add and subtract within 1000 using strategies and algorithms 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
- Cranmer Abacus – 1-03150-00
- EZeeCOUNT Abacus – 1-03185-00
- Brannan Cubarithm Slate – 1-00320-00
- Cubarithm Plastic Cubes – 1-00330-00
- 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

**3.NBT.A.3** Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.

Existing Resources:

- Brannan Cubarithm Slate – 1-00320-00
- Cubarithm Plastic Cubes – 1-00330-00
- Multiplication/Division Table – 5-82700-01

### Number and Operations—Fractions (3.NF)

#### Develop understanding of fractions as numbers.

**3.NF.A.1** Understand a fraction 1/*b* as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction *a*/*b* as the quantity formed by a parts of size 1/*b*.

Existing Resources:

- Fractional Parts of Wholes Set – 1-03290-00
- MathBuilders, Unit 7: Fractions, Mixed Numbers, and Decimals, Large Print Kit – 7-03564-00; Braille Kit – 5-03564-00
- Nemeth Code Reference Sheet, Print – 7-87500-00; Braille – 5-87400-00

**3.NF.A.2** Understand a fraction as a number on the number line; represent fractions on a number line diagram.

- 3.NF.A.2a Represent a fraction 1/
*b*on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into*b*equal parts. Recognize that each part has size 1/*b*and that the endpoint of the part based at 0 locates the number 1/*b*on the number line. - 3.NF.A.2b Represent a fraction
*a*/*b*on a number line diagram by marking off a lengths 1/*b*from 0. Recognize that the resulting interval has size*a*/*b*and that its endpoint locates the number*a*/*b*on the number line.

Existing Resources:

- Consumable Number Lines, Large Print Set – 1-03012-00; Braille/Tactile Set – 1-03013-00
- MathBuilders, Unit 7: Fractions, Mixed Numbers, and Decimals, Large Print Kit – 7-03564-00; Braille Kit – 5-03564-00
- Nemeth Code Reference Sheet, Print – 7-87500-00; Braille – 5-87400-00
- Number Line Device – 1-03480-01

**3.NF.A.3** Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

- 3.NF.A.3a Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
- 3.NF.A.3b Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.
- 3.NF.A.3c Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.
*Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.* - 3.NF.A.3d Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Existing Resources:

- Consumable Number Lines, Large Print Set – 1-03012-00; Braille/Tactile Set – 1-03013-00
- MathBuilders, Unit 7: Fractions, Mixed Numbers, and Decimals, Large Print Kit – 7-03564-00; Braille Kit – 5-03564-00
- Nemeth Code Reference Sheet, Print – 7-87500-00; Braille – 5-87400-00
- Number Line Device – 1-03480-01

### Measurement and Data (3.MD)

#### Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

**3.MD.A.1** Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.

Existing Resources:

- Analog Clock Model – 1-03125-00
- Clock Face Sheets in Braille – 1-03111-00
- Consumable Number Lines – Large Print Set – 1-03012-00; Braille/Tactile Set – 1-03013-00
- MathBuilders, Unit 5: Measurement and Estimation, Large Print Kit – 7-03562-00; Braille Kit – 5-03562-00
- Number Line Device – 1-03480-01

**3.MD.A.2** Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.

Existing Resources:

#### Represent and interpret data.

**3.MD.B.3** 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. *For example, draw a bar graph in which each square in the bar graph might represent 5 pets.*

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

**3.MD.B.4** 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.

Existing Resources:

- 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
- Metric-English Measurement Ruler – 1-03100-00
- Transparent CCTV Ruler Kit, Yellow – 1-03008-00; Clear – 1-030089-00

#### Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

**3.MD.C.5** Recognize area as an attribute of plane figures and understand concepts of area measurement.

- 3.MD.C.5a A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area.
- 3.MD.C.5b A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.

Existing Resources:

- MathBuilders, Unit 6: Geometry, Large Print Kit – 7-03563-00; Braille Kit – 5-03563-00
- 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

**3.MD.C.6** Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).

Existing Resources:

- Plexiglas Blocks (1-08663-00) with a tactile graphic of a square or 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 square or a rectangle
- Unit cubes from FOCUS in Mathematics (Print Kit – 1-08280-01; Braille Kit – 1-08281-0) with a tactile graphic of a square or a rectangle

**3.MD.C.7** Relate area to the operations of multiplication and addition.

- 3.MD.C.7a Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
- 3.MD.C.7b Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.
- 3.MD.C.7c Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths
*a*and*b*+*c*is the sum of*a*×*b*and*a*×*c*. Use area models to represent the distributive property in mathematical reasoning. - 3.MD.C.7d Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.

Existing Resources:

- Graph Sheets (assorted Low Relief and Bold-line available)
- Light Box Materials: Level II (Colored 1 in. Cube Set and Foam Grid Pattern) – 1-08680-00
- MathBuilders, Unit 6: Geometry, Large Print Kit – 7-03563-00; Braille Kit – 5-03563-00
- Multiplication/Division Table – 5-82700-01
- Plexiglas Blocks (1-08663-00) with a tactile graphic of a rectangle
- Tactile Tangrams: Print Grid Sheets – 61-249-016
- 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

#### Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

**3.MD.D.8** Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeter.

Existing Resources:

### Geometry (3.G)

#### Reason with shapes and their attributes.

**3.G.A.1** Understand that shapes in different categories (e.g., rhombuses rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

Existing Resources:

- DRAFTSMAN Tactile Drawing Board – 1-08857-00
- MathBuilders, Unit 6: Geometry, Large Print Kit – 7-03563-00; Braille Kit – 5-03563-00
- Picture Maker: Wheatley Tactile Diagramming Kit – 1-08838-00

**3.G.A.2** Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. *For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.*

Existing Resources:

- DRAFTSMAN Tactile Drawing Board – 1-08857-00
- Geometro, GS16 Mini Set – 1-03022-00 with Graphic Art Tape – 1-08878-00
- Graphic Art Tape – 1-08878-00 with a tactile graphic
- MathBuilders, Unit 6: Geometry, Large Print Kit – 7-03563-00; Braille Kit – 5-03563-00

## English Language Arts Standards

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