Download Standard 1 - Briar Cliff University

Mathematics Curriculum
Diocese of Sioux City
Grade 8
Standard 1
Standard 1: Understands and applies concepts of numbers and operations.
Benchmark 1: Describes the properties of numbers and number systems
Vocabulary
Critical Objectives:
8.1.1.1. Represents and uses rational numbers in a variety of forms
Rational number
Fraction
8.1.1.2. Compares, orders, and graphs rational numbers
Decimal
8.1.1.3. Uses the appropriate form of a rational number (fraction,
Percent
decimal, percent) in computations (ITBS)**
Equivalent formats
8.1.1.4. Understands fractions, decimals, and percents can be expressed
Negative number
in various ways
Positive number
Absolute value
8.1.1.5. Knows which rational number is most appropriate based on the
Ratio
context of the problem
Proportion
8.1.1.6. Knows percents can be greater than 100 and less than 1
Exponent
8.1.1.7. Identifies the appropriate rational number to use in a problem
Base
situation (ITBS)
Expanded
Notation
8.1.1.8. Places expressions on a number line (ITBS)
Powers
8.1.1.9. Understands the use of negative and positive numbers in
computations
(ITBS)*
8.1.1.10. Knows absolute value of a number is its distance from zero on a number line
8.1.1.11. Knows negative numbers are the opposite of positive numbers
8.1.1.12. Knows applications for negative numbers
8.1.1.13. Finds the absolute value of given numbers (ITBS)
8.1.1.14. Simplifies expressions involving integers (ITBS)
8.1.1.15. Represents a change in a word problem with an integer (ITBS)
8.1.1.16. Compares fractions, decimals, and percents (ITBS)*
8.1.1.17. Understands fractions, decimals, and percents can be expressed in various ways
8.1.1.18. Knows percents can be greater than 100 or less than 1
8.1.1.19. Converts fractions, decimals, and percents to equivalent forms (ITBS)
8.1.1.20. Uses ratios and proportions to represent quantitative relationships (ITBS)*
8.1.1.21. Knows a ratio is a comparison of two numbers
8.1.1.22. Knows a/b, a to b, and a:b are all ways to express a ratio
8.1.1.23. Knows a percentage is a ratio of a number to 100
8.1.1.24. Knows a proportion is a comparison of two ratios
8.1.1.25. Writes a ratio in a variety of ways (ITBS)
8.1.1.26. Sets up a proportion correctly
8.1.1.27. Expresses numbers using exponents (ITBS)*
8.1.1.28. Knows an exponent tells how many times a base is used as a factor
8.1.1.29. Writes exponents in expanded notation
8.1.1.30. Simplifies expressions containing exponents (ITBS)
8.1.1.31. Understands number theory (ITBS)*
8.1.1.32. Finds a multiple of a number (ITBS)
Diocese of Sioux City
-1-
2006
Mathematics Curriculum
Diocese of Sioux City
Grade 8
Standard 1
Standard 1: Understands and applies concepts of numbers and operations.
Benchmark 2: Understands the properties of operations
Vocabulary
Critical Objectives:
8.1.2.1. Uses the properties of operations to simplify computations
Identity property
Inverse property
(ITBS)*
Distributive property
8.1.2.2. Knows the inverse operations undo each other
Associative property
8.1.2.3. Knows the identity properties of addition and multiplication
Commutative property
8.1.2.4. Knows the distributive, associative, and commutative properties
Squaring
of addition and multiplication
Square root
Perfect square
8.1.2.5. Knows squaring and square root are inverse operations
Order of operations
8.1.2.6. Knows a perfect square is the product of a whole number
Grouping
multiplied by itself
8.1.2.7. Simplifies equations using properties of operations (ITBS)
8.1.2.8. Explains the meaning of adding, subtracting, multiplying, and dividing integers
8.1.2.9. Uses inverse properties and relationships to solve problems
8.1.2.10. Finds the square root of perfect squares
8.1.2.11. Approximates the square root of non-perfect squares
8.1.2.12. Uses order of operations, including grouping symbols, to simplify computations
(ITBS)*
8.1.2.13. Knows the order of operations
8.1.2.14. Simplifies equations using order of operations
8.1.2.15. Applies the order of operations to perform computations (ITBS)
Diocese of Sioux City
-2-
2006
Mathematics Curriculum
Diocese of Sioux City
Grade 8
Standard 1
Standard 1: Understands and applies concepts of numbers and operations.
Benchmark 3: Computes fluently and makes reasonable estimates
Vocabulary
Critical Objectives:
8.1.3.1. Uses appropriate methods to compute with fractions (ITBS)*
Numerator
Denominator
8.1.3.2. Knows adding and subtracting fractions requires expression
Common denominator
terms with a common denominator
Least common multiple
8.1.3.3. Knows finding a common denominator uses the same process for
Reciprocal
finding a least common multiple
Lowest terms
8.1.3.4. Knows the rules for adding, subtracting, multiplying, and
Decimal
Decimal places
dividing fractions
Integer
8.1.3.5. Knows a fraction must be reduced to lowest terms
Negative number
8.1.3.6. Adds, subtracts, multiplies, and divides fractions (ITBS)
Positive number
8.1.3.7. Uses appropriate methods to compute with decimals and
Absolute value
percents (ITBS)*
Ratio
Proportion
8.1.3.8. Knows to add or subtract decimals the decimal points must line
Cross-multiplication
up vertically
Estimation
8.1.3.9. Knows the rules for adding, subtracting, multiplying, and
Exact answer
dividing decimals
Mental computation
8.1.3.10. Knows the rules for finding the percent of a number
Rounding
8.1.3.11. Adds, subtracts, multiplies, and divides decimals
8.1.3.12. Finds a percent of a number (ITBS)
8.1.3.13. Solves real-life problems involving percent (discount, interest, mark-up)
8.1.3.14. Uses appropriate methods to compute with integers (ITBS)*
8.1.3.15. Knows the absolute value of a number is its distance from zero on a number line
8.1.3.16. Knows negative numbers are the opposite of positive numbers
8.1.3.17. Knows the rules for adding, subtracting, multiplying, and dividing integers
8.1.3.18. Adds, subtracts, multiplies, and divides integers
8.1.3.19. Understands proportional relationships
8.1.3.20. Uses appropriate methods to solve proportions (ITBS)*
8.1.3.21. Knows a/b, a to b, and a:b are all ways to represent a ratio
8.1.3.22. Knows a proportion is a comparison of two ratios
8.1.3.23. Knows the cross-multiplication method
8.1.3.24. Converts from one form of a ratio to another (ITBS)
8.1.3.25. Solves for unknown numbers in a proportion
8.1.3.26. Uses estimation strategies for computing rational numbers (ITBS)***
8.1.3.27. Knows when an estimate or an exact answer is more appropriate
8.1.3.28. Knows how to judge the reasonable of an answer
8.1.3.29. Knows rounding rules
8.1.3.30. Checks answers using estimation strategies (ITBS)
8.1.3.31. Uses standard rounding to estimate (ITBS)
8.1.3.32. Uses order of magnitude to estimate (ITBS)
8.1.3.33. Uses number sense (ITBS)
Diocese of Sioux City
-3-
2006