Quality Core Curriculum
addressed within the InterMath Integers Unit
SIXTH GRADE
Strand: Problem Solving
1 Topic: Problem Solving Strategies, Reasoning, Estimation Strategies, Mental Computation
Standard: Solves problems, reasons, and estimates throughout mathematics
Selects and uses problemsolving strategies such as reading the problem, drawing a picture or diagram, using trial and error, making a table or chart, looking for patterns, making a simpler problem and then generalizing, working backwards, etc.
Selects and uses appropriate tools (such as mental computation, calculators, manipulative materials, paper and pencil, computer) in solving problems.
Uses appropriate estimation strategies (such as frontend, breaking numbers apart, compatible numbers, guess and check, clustering, rounding, compensation) to check the reasonableness of results.
Solves nonroutine problems for which the answer is not obvious.
Relates concepts and skills to practical applications.
2 Topic: Communication, Reasoning
Standard: Describe orally and in writing, using the appropriate mathematical vocabulary, mathematical concepts and procedures, such as solving a word problem or computing.
3 Topic: Technology, Calculator Skills, Computer Skills, Problem Solving, Reasoning
Standard: Uses scientific calculator and computer skills to solve problems, to discover patterns and sequences, to investigate situations and draw conclusions.
4 Topic: Technology, Computer Skills, Charts, Tables, Graphs
Standard: Uses computer software and applications to research, investigate, and analyze data and to represent this information using charts, tables, graphs, or other presentation forms.
46 Topic: Problem Solving Strategies
Standard: Selects and uses appropriate problemsolving strategies, determines operations to use and whether problems contain extraneous or insufficient information.
47 Topic: Problem Solving
Standard: Solves problems using one or two operations.
Strand: Patterns & Relationships; Algebra
5 Topic: Expressions, Equations (Number Sentences)
Standard: Uses a variable to represent an unknown amount in a mathematical expression or equation (number sentence), and evaluates simple algebraic expressions (e.g., Given a + 4. If a = 2, then 2 + 4 = 6).
7 Topic: Equations (Number Sentences)
Standard: Finds the value of or solves for the variable in a simple Number Concept equation such as a + 6 = 10.
8 Topic: Problem Solving, Equations
Standard: Writes and solves a simple onestep equation (number sentence) for a given word problem.
Strand: Whole Number Computation; Estimation; Whole Number Operations
9 Topic: Whole Numbers, Decimals, Fractions, Mixed Numbers, Remainders
Standard: Uses addition, subtraction, multiplication, and division (interpreting remainders in context of problem) in computation and problem solving with whole numbers, decimals, fractions, and mixed numbers with like and unlike denominators.
40 Topic: Divisibility
Standard: Identifies and uses prime factors in practical applications, writes the prime factorization for a composite number, finds the multiples of a given number, and finds the greatest common factor and least common multiple of a set of numbers.
42 Topic: Properties of Real Numbers
Standard: Recognizes and uses the commutative and associative properties of addition and multiplication, the distributive property, identities, inverses (including reciprocals), and properties of zero.
Strand: Patterns & Relationships; Algebra
43 Topic: Sequences, Patterns
Standard: Recognizes, describes, and generalizes patterns and sequences.
Seventh Grade
Strand: Problem Solving
1 Topic: Problem Solving Strategies, Reasoning, Estimation Strategies, Mental Computation
Standard: Solves problems, reasons, and estimates throughout mathematics.
Selects and uses problemsolving strategies such as reading the problem, drawing a picture or diagram, using trial and error, making a table or chart, looking for patterns, making a simpler problem and then generalizing, working backwards, etc.
Selects and uses appropriate tools (such as mental computation, calculators, manipulative materials, paper and pencil, computer) in solving problems.
Uses appropriate estimation strategies (such as frontend, breaking numbers apart, compatible numbers, guess and check, clustering, rounding, compensation) to check the reasonableness of results.
Solves nonroutine problems for which the answer is not obvious.
Relates concepts and skills to practical applications.
2 Topic: Communication, Reasoning
Standard: Describes orally and in writing, using the appropriate mathematical vocabulary, mathematical concepts and procedures, such as solving a word problem or computing.
3 Topic: Technology, Calculator Skills, Computer Skills, Problem Solving, Reasoning
Standard: Uses scientific calculator and computer skills to solve problems, to discover patterns and sequences, to investigate situations and draw conclusions.
4 Topic: Technology, Computer Skills, Charts, Tables, Graphs
Standard: Uses computer software and applications to research, investigate, and analyze data and to represent this information using charts, tables, graphs, or other presentation forms.
40 Topic: Problem Solving Strategies
Standard: Selects and uses appropriate problemsolving strategies to solve single and multiplestep problems.
Strand: Patterns & Relationships; Algebra
5 Topic: Expressions, Equations, Inequalities
Standard: Identifies the use of a variable as a placeholder in an algebraic expression or equation.
6 Topic: Expressions
Standard: Evaluates algebraic expressions (e.g., Given 3a + 4. If a = 2, then 3(2) + 4 = 10).
7 Topic: Equations, Inequalities
Standard: Writes and solves onestep algebraic equations and inequalities using addition, subtraction, multiplication, and division (e.g., a + 11 = 15; b  2 = 21; m/2 = 15; 5x = 40).
11 Topic: Expressions, Equations
Standard: Translates English phrases and sentences into mathematical expressions, equations, and inequalities.
12 Topic: Variables
Standard: Determines how changes in one variable can affect another variable (e.g., Given b = 2a. If a = 2, then b = 4. If a = 3, then b = 6).
13 Topic: Problem Solving, Equations
Standard: Writes and solves an equation for a given word problem.
Strand: Whole Number Computation; Estimation; Whole Number Operations
14 Topic: Whole Numbers, Fractions, Decimals, Computation, Problem Solving
Standard: Uses addition, subtraction, multiplication, and division (interpreting remainders in context of problem) in computation and problem solving with whole numbers, fractions, and decimals.
15 Topic: Integers
Standard: Computes with integers using models, manipulatives, and/or rules.
Strand: Number Sense & Numeration; Fractions & Decimals
33 Topic: Number Theory
Standard: Identifies factors, multiples, primes, and composites.
35 Topic: Positive Integers
Standard: Identifies greatest common factor and least common multiple.
36 Topic: Divisibility
Standard: Uses divisibility rules for 2, 3, 5, 6, 9, and 10.
Strand: Statistics & Integers
44 Topic: Measures of Central Tendency and Spread
Standard: Uses mean, median, and mode to describe central tendencies of a data set, and uses range to describe spread of the data.
Eighth Grade
Strand: Problem Solving
1 Topic: Problem Solving Strategies, Reasoning, Estimation Strategies, Mental Computation
Standard: Solves problems, reasons, and estimates throughout mathematics.
Selects and uses problemsolving strategies such as reading the problem, drawing a picture or diagram, using trial and error, making a table or chart, looking for patterns, making a simpler problem and then generalizing, working backwards, etc.
Selects and uses appropriate tools (such as mental computation, calculators, manipulative materials, paper and pencil, computer) in solving problems.
Uses appropriate estimation strategies (such as frontend, breaking numbers apart, compatible numbers, guess and check, clustering, rounding, compensation) to check the reasonableness of results.
Solves nonroutine problems for which the answer is not obvious.
Relates concepts and skills to practical applications.
2 Topic: Communication, Reasoning
Standard: Describe orally and in writing, using the appropriate mathematical vocabulary, mathematical concepts and procedures, such as solving a word problem or computing.
3 Topic: Technology, Calculator Skills, Computer Skills, Problem Solving, Reasoning
Standard: Uses scientific calculator and computer skills to solve problems, to discover patterns and sequences, to investigate situations and draw conclusions.
4 Topic: Technology, Computer Skills, Charts, Tables, Graphs
Standard: Uses computer software and applications to research, investigate, and analyze data using charts, tables, graphs, or other presentation forms.
43 Topic: Problem Solving Strategies
Standard: Selects and uses appropriate problemsolving strategies to solve single and multiplestep problems.
Strand: Patterns & Relationships; Algebra
5 Topic: Expressions, Equations, Inequalities
Standard: Identifies the use of a variable as a placeholder in algebraic expressions, equations, and inequalities.
6 Topic: Expressions
Standard: Uses signs or symbols to represent words, phrases, numbers, or quantities.
7 Topic: Equations, Expressions, Inequalities
Standard: Translates English phrases and sentences into mathematical/algebraic expressions, equations, and inequalities.
8 Topic: Number Sentences
Standard: Determines the number that makes a given number sentence true using the properties of equations.
10 Topic: Expressions
Standard: Evaluates algebraic expressions using substitution.
11 Topic: Equations, Inequalities, Formulas
Standard: Solves single and multistep algebraic equations (including formulas) and inequalities using addition, subtraction, multiplication, and division.
15 Topic: Relations, Functions
Standard: Examines relations (functions) to determine how changes in one variable can effect another variable (e.g., Given b = 2a. If a = 2, then b = 4. If a = 3, then b = 6).
16 Topic: Problem Solving, Equations, Inequalities
Standard: Writes and solves an equation or simple inequality for a given word problem.
Strand: Whole Number Computation; Estimation; Whole Number Operations
18 Topic: Integers, Fractions, Decimals
Standard: Adds, subtracts, multiplies, and divides integers and other rational numbers.
Strand: Number Sense & Numeration; Fractions & Decimals
34 Topic: Exponents
Standard: Evaluates powers using exponents and bases correctly, and finds square roots.
36 Topic: Properties of Real Numbers
Standard: Identifies and uses properties of the real number system including associative, commutative, distributive, inverses, identities, and properties of zero and one.
40 Topic: Divisibility, Factorization
Standard: Identifies and applies divisibility, factors, prime factors, greatest common factor, and lowest common multiple.
Strand: Statistics & Integers
47 Topic: Measures of Central Tendency and Spread
Standard: Uses mean, median, mode, and range to describe tendencies of a data set and make predictions.
