Gifted and Talented Math
Mr. Schwab, Mr. Weiskind, and Mrs. Harvey
Quarter 3: Expressions and Equations
Through this unit, students understand…
· the use of variables in mathematical expressions.
· how to write expressions and equations that correspond to given situations.
· how to evaluate expressions.
· how to use expressions and formulas to solve problems.
· that expressions in different forms can be equivalent.
· how to use the properties of operations to rewrite expressions in equivalent forms.
· that the solutions of an equation are the values of the variables that make the equation true.
· and apply properties of operations and work with rational numbers (integers and positive / negative fractions and decimals) to write equivalent expressions.
· the reason for rewriting an expression in terms of a contextual situation. For example, students understand that a 20% discount is the same as finding 80% of the cost, c (0.80c).
Vocabulary: (Words your child will need to understand)
• Variable: A letter or other symbol used to represent an unspecified number or value.
• Algebraic Expression: An expression consisting of one or more numbers and variables along with one or more arithmetic operations. Ex: 2x + 3
• Rational Number: A number that can be expressed as a ratio of two integers
• Like Terms: Parts of an algebraic expression with the same variable or that are constant. Ex: in the expression 2x + 3 + x + 7, 2x and x are like terms & 3 and 7 are like terms. The simplified expression would therefore be 3x + 10.
Coefficient: The factor in a term with a variable.
• Greatest Common Factor (GCF): The largest factor of two or more numbers.
• Constant: A term in an expression or equation that does not contain a variable.
• Distributive Property: a x (b+c)=(axb) + (axc) and a x(b-c) = (axb) – (axc), where a, b, and c stand for real numbers.
Through this unit, students understand…
· the use of variables in mathematical expressions.
· how to write expressions and equations that correspond to given situations.
· how to evaluate expressions.
· how to use expressions and formulas to solve problems.
· that expressions in different forms can be equivalent.
· how to use the properties of operations to rewrite expressions in equivalent forms.
· that the solutions of an equation are the values of the variables that make the equation true.
· and apply properties of operations and work with rational numbers (integers and positive / negative fractions and decimals) to write equivalent expressions.
· the reason for rewriting an expression in terms of a contextual situation. For example, students understand that a 20% discount is the same as finding 80% of the cost, c (0.80c).
- and solve contextual problems and mathematical problems using rational numbers. Students convert between fractions, decimals, and percents as needed to solve the problem. Students use estimation to justify the reasonableness of answers.
Vocabulary: (Words your child will need to understand)
• Variable: A letter or other symbol used to represent an unspecified number or value.
• Algebraic Expression: An expression consisting of one or more numbers and variables along with one or more arithmetic operations. Ex: 2x + 3
• Rational Number: A number that can be expressed as a ratio of two integers
• Like Terms: Parts of an algebraic expression with the same variable or that are constant. Ex: in the expression 2x + 3 + x + 7, 2x and x are like terms & 3 and 7 are like terms. The simplified expression would therefore be 3x + 10.
Coefficient: The factor in a term with a variable.
• Greatest Common Factor (GCF): The largest factor of two or more numbers.
• Constant: A term in an expression or equation that does not contain a variable.
• Distributive Property: a x (b+c)=(axb) + (axc) and a x(b-c) = (axb) – (axc), where a, b, and c stand for real numbers.