Quality Core Curriculum
addressed within the InterMath Circles 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.
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; Geometry
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 geometric 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 geometric equation such as a + 6 = 10.
Strand: Patterns & Relationships; Geometry
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.
40 Topic: Problem Solving Strategies
Standard: Selects and uses appropriate problemsolving strategies to solve single and multiplestep problems.
Strand: Patterns & Relationships; Geometry
5 Topic: Expressions, Equations, Inequalities
Standard: Identifies the use of a variable as a placeholder in an geometric expression or equation.
6 Topic: Expressions
Standard: Evaluates geometric expressions (e.g., Given 3a + 4. If a = 2, then 3(2) + 4 = 10).
7 Topic: Equations, Inequalities
Standard: Writes and solves onestep geometric equations and inequalities using addition, subtraction, multiplication, and division (e.g., a + 11 = 15; b  2 = 21; m/2 = 15; 5x = 40).
8 Topic: Inequalities, Graphing
Standard: Graphs inequalities on a number line.
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).
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.
43 Topic: Problem Solving Strategies
Standard: Selects and uses appropriate problemsolving strategies to solve single and multiplestep problems.
Strand: Patterns & Relationships; Geometry
5 Topic: Expressions, Equations, Inequalities
Standard: Identifies the use of a variable as a placeholder in geometric 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/geometric 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 geometric expressions using substitution.
11 Topic: Equations, Inequalities, Formulas
Standard: Solves single and multistep geometric equations (including formulas) and inequalities using addition, subtraction, multiplication, and division.
14 Topic: Inequalities, Graphing
Standard: Graphs simple and compound inequalities on a number line.
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).
Strand: Geometry & Spatial Sense; Measurement
24 Topic: Geometric Properties, Geometric Figures
Standard: Uses geometric figures, properties, and relations to solve problems.
Strand: Number Sense & Numeration; Fractions & Decimals
37 Topic: Equations, Expressions, Properties of Real Numbers
Standard: Recognizes, describes, and applies the distributive property of multiplication over addition in situations such as combining like terms of linear expressions, and solving equations of the form ax + b = cx + d.
