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 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 problem-solving 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 front-end, breaking numbers apart, compatible numbers, guess and check, clustering, rounding, compensation) to check the reasonableness of results. -Solves non-routine 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 problem-solving 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 problem-solving 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 front-end, 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 problem-solving strategies to solve single- and multiple-step 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 one-step 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 problem-solving 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 front-end, 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 problem-solving strategies to solve single- and multiple-step 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 multi-step 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.