# Alabama Learning Standards for Mathematics — Grade 5

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#### 5-G1

Use a pair of perpendicular number lines, called axes, to define a coordinate system with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

#### 5-G2

Represent real-world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

#### 5-G3

Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.

#### 5-G4

Classify two-dimensional figures in a hierarchy based on properties.

#### 5-MD1

Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multistep, real-world problems.

#### 5-MD2

Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots.

#### 5-MD3

Recognize volume as an attribute of solid figures, and understand concepts of volume measurement.

#### 5-MD3a

A cube with side length 1 unit, called a 'unit cube,' is said to have 'one cubic unit' of volume, and can be used to measure volume.

#### 5-MD3b

A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.

#### 5-MD4

Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

#### 5-MD5

Relate volume to the operations of multiplication and addition, and solve real-world and mathematical problems involving volume.

#### 5-MD5a

Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.

#### 5-MD5b

Apply the formulas V = l x w x h and V = B x h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real-world and mathematical problems.

#### 5-MD5c

Recognize volume as additive. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms by adding the volumes of the nonoverlapping parts, applying this technique to solve real-world problems.

#### 5-NBT1

Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

#### 5-NBT2

Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

#### 5-NBT3

Read, write, and compare decimals to thousandths.

#### 5-NBT3a

Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000).

#### 5-NBT3b

Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

#### 5-NBT4

Use place value understanding to round decimals to any place

#### 5-NBT5

Fluently multiply multi-digit whole numbers using the standard algorithm.

#### 5-NBT6

Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

#### 5-NBT7

Add, subtract, multiply, and divide decimals to hundredths, 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.

#### 5-NF1

Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.

#### 5-NF2

Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally, and assess the reasonableness of answers.

#### 5-NF3

Interpret a fraction as division of the numerator by the denominator (a/b = a b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

#### 5-NF4

Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

#### 5-NF4a

Interpret the product (a/b) x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q b.

#### 5-NF4b

Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

#### 5-NF5

Interpret multiplication as scaling (resizing), by:

#### 5-NF5a

Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

#### 5-NF5b

Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case), explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number, and relating the principle of fraction equivalence a/b = (n x a)/(n x b) to the effect of multiplying by 1.

#### 5-NF6

Solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

#### 5-NF7

Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (Students able to multiply fractions in general can develop strategies to divide fractions in general by reasoning about the relationship between multiplication and division. However, division of a fraction by a fraction is not a requirement at this grade.)

#### 5-NF7a

Interpret division of a unit fraction by a nonzero whole number, and compute such quotients.

#### 5-NF7b

Interpret division of a whole number by a unit fraction, and compute such quotients.

#### 5-NF7c

Solve real-world problems involving division of unit fractions by nonzero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem.

#### 5-OA1

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

#### 5-OA2

Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.

#### 5-OA3

Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane.