Grade 5 Arizona Math Standards

Understand and describe a coordinate system as perpendicular number lines, called axes, that intersect at the origin (0, 0). Identify a given point in the first quadrant of the coordinate plane using an ordered pair of numbers, called coordinates. Understand that the first number (x) indicates the distance traveled on the horizontal axis, and the second number (y) indicates the distance traveled on the vertical axis

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

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

Classify two-dimensional figures in a hierarchy based on properties

Convert among different-sized standard measurement units within a given measurement system, and use these conversions in solving multi-step, real-world problems

Make a line plot to display a data set of measurements in fractions of a unit (1/8, 1/2, 3/4). Use operations on fractions for this grade to solve problems involving information presented in line plots

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

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

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

Apply concepts of place value, multiplication, and division to understand 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

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

Read, write, and compare decimals to thousandths

Use place value understanding to round decimals to any place

Fluently multiply multi-digit whole numbers using a standard algorithm

Apply and extend understanding of division to find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors

Add, subtract, multiply, and divide decimals to hundredths, connecting objects or drawings to strategies based on place value, properties of operations, and/or the relationship between operations. Relate the strategy to a written form

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 (e.g., 2/3 + 5/4 = 8/12 + 15/12 = 23/12)

Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators by using a variety of representations, equations, and visual models to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers (e.g. recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2)

Interpret a fraction as the number that results from dividing the whole number numerator by the whole number denominator (a/b =a÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers

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

Interpret multiplication as scaling (resizing), by:

Solve problems in real-world contexts involving multiplication of fractions, including mixed numbers, by using a variety of representations including equations and models

Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions

Use parentheses and brackets in numerical expressions, and evaluate expressions with these symbols (Order of Operations)

Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them (e.g., express the calculation "add 8 and 7, then multiply by 2" as 2 x (8 + 7). Recognize that 3 x (18,932 + 921) is three times as large as 18,932 + 921, without having to calculate the indicated sum or product)

Generate two numerical patterns using two given rules (e.g., generate terms in the resulting sequences). Identify and explain the 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 (e.g., given the rule "add 3" and the starting number 0, and given the rule "add 6" and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence)