Standard 1: Understands and Applies Concepts of Numbers and Operations

Mathematics Curriculum

Diocese of Sioux City

Grade 7

Standard 1

Standard 1: Understands and applies concepts of numbers and operations.

Benchmark 1:Describes the properties of numbers and number systems

Critical Objectives:

7.1.1.1.Uses the appropriate form of a rational number (fraction, decimal, percent) in computations (ITBS)***

7.1.1.2.Understands fractions, decimals, and percents can be expressed in various ways

7.1.1.3.Knows which rational number is most appropriate based on the context of the problem

7.1.1.4.Knows percents can be greater than 100 and less than 1

7.1.1.5.Converts fractions, decimals, and percents to equivalent forms

(ITBS)

7.1.1.6.Identifies the appropriate rational number to use in a problem situation (ITBS)

7.1.1.7.Represents decimals in words (ITBS)

7.1.1.8.Understands the use of negative and positive numbers in computations (ITBS)*

7.1.1.9.Knows absolute value of a number is its distance from zero on a number line

7.1.1.10.Knows negative numbers are the opposite of positive numbers

7.1.1.11.Knows applications for negative numbers

7.1.1.12.Finds the absolute value of given numbers

7.1.1.13.Simplifies expressions involving integers (ITBS)

7.1.1.14.Compares fractions, decimals, and percents (ITBS)**

7.1.1.15.Uses ratios and proportions to represent quantitative relationships (ITBS)*

7.1.1.16.Knows a ratio is a comparison of two numbers

7.1.1.17.Knows a/b, a to b, and a:b are all ways to express a ratio

7.1.1.18.Knows a percentage is a ratio of a number to 100

7.1.1.19.Knows a proportion is a comparison of two ratios

7.1.1.20.Writes a ratio in a variety of ways (ITBS)

7.1.1.21.Sets up a proportion correctly

7.1.1.22.Writes numbers using scientific notation

7.1.1.23.Uses exponential notation

7.1.1.24.Expresses numbers using exponents (ITBS)*

7.1.1.25.Knows an exponent tells how many times a base is used as a factor

7.1.1.26.Writes exponents in expanded notation

7.1.1.27.Simplifies expressions containing exponents

7.1.1.28.Understands number theory (ITBS)*

7.1.1.29.Predicts the results of operations on odd and even numbers (ITBS)

7.1.1.30.Explains the difference between prime and composite numbers

7.1.1.31.Completes prime factorization expressing the answer with exponents

Standard 1: Understands and applies concepts of numbers and operations.

Benchmark 2: Understands the properties of operations

Critical Objectives:

7.1.2.1.Uses the properties of operations to simplify computations (ITBS)*

7.1.2.2.Knows the inverse operations undo each other

7.1.2.3.Knows the identity properties of addition and multiplication

7.1.2.4.Knows the distributive, associative, and commutative properties of addition and multiplication

7.1.2.5.Knows squaring and square root are inverse operations

7.1.2.6.Knows a perfect square is the product of a whole number multiplied by itself

7.1.2.7.Simplifies equations using properties of operations (ITBS)

7.1.2.8.Explains the meaning of adding, subtracting, multiplying, and dividing integers

7.1.2.9.Uses inverse properties and relationships to solve problems

7.1.2.10.Finds the square root of perfect of squares

7.1.2.11.Uses order of operations, including grouping symbols, to simplify computations (ITBS)*

7.1.2.12.Knows the order of operations

7.1.2.13.Simplifies equations using order of operations

7.1.2.14.Applies the order of operations to perform computations (ITBS)

Standard 1: Understands and applies concepts of numbers and operations.

Benchmark 3:Computes fluently and makes reasonable estimates

Critical Objectives:

7.1.3.1.Uses appropriate methods to compute with fractions (ITBS)*

7.1.3.2.Knows adding and subtracting fractions requires expressions terms with a common denominator

7.1.3.3.Knows finding a common denominator uses the same process for finding a least common multiple

7.1.3.4.Finds the greatest common factor and least common multiple

7.1.3.5.Explains the difference between factor and multiple

7.1.3.6.Knows the rules for adding, subtracting, multiplying, and dividing fractions

7.1.3.7.Knows a fraction must be reduced to lowest terms

7.1.3.8.Adds, subtracts, multiplies, and divides fractions (ITBS)

7.1.3.9.Uses appropriate methods to compute with decimals (ITBS)*

7.1.3.10.Knows to add or subtract decimals the decimal points must line up vertically

7.1.3.11.Knows the rules for adding, subtracting, multiplying, and dividing decimals

7.1.3.12.Knows rules for computing with %.

7.1.3.13.Adds, subtracts, multiplies, and divides decimals

7.1.3.14.Finds % of a number (ITBS)

7.1.3.15.Adds, subtracts, multiples, and divides percents

7.1.3.16.Applies fractions, decimals, and percents to problem solving

7.1.3.17.Uses appropriate methods to compute with integers (ITBS)*

7.1.3.18.Locates integers on the number line

7.1.3.19.Knows the absolute value of a number is its distance from zero on a number line

7.1.3.20.Knows negative numbers are the opposite of positive numbers

7.1.3.21.Knows the rules for adding, subtracting, multiplying and dividing integers

7.1.3.22.Adds, subtracts, multiplies, and divides integers (ITBS)

7.1.3.23.Compares and orders integers

7.1.3.24.Computes expressions with absolute value symbols (ITBS)

7.1.3.25.Uses appropriate methods to solve proportions (ITBS)*

7.1.3.26.Knows a/b, a to b, and a:b are all ways to represent a ratio

7.1.3.27.Knows a proportion is a comparison of two ratios

7.1.3.28.Develops and uses proportions for problem solving

7.1.3.29.Knows the cross-multiplication method

7.1.3.30.Converts from one form of a ratio to another (ITBS)

7.1.3.31.Solves for unknown numbers in a proportion

7.1.3.32.Uses scale to find distances (ITBS)

7.1.3.33.Uses estimation strategies for computing rational numbers (ITBS)***

7.1.3.34.Knows when an estimate or an exact answer is more appropriate

7.1.3.35.Knows how to judge the reasonableness of an answer

7.1.3.36.Knows rounding rules

7.1.3.37.Checks answers using estimation strategies (ITBS)

7.1.3.38.Uses standard rounding to estimate (ITBS)

7.1.3.39.Uses order of magnitude to estimate (ITBS)

7.1.3.40.Uses number sense to estimate (ITBS)

7.1.3.41.Solves expressions using the rules of order of operations

7.1.3.42.Solves equations using inverse operations

Diocese of Sioux City-1-2006