| Lesson Area | Lesson Set | Description |
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Exploring Integers
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Graphing Integers on a Number Line
| Start by exploring graphs of integers on a number line. Explore both positive and negative integers progressively from between -5 and +5 to between -20 and +20.
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Basic Addition (+)
| Start with positive operands only and operands no greater than 10. When comfortable, move directly into both positive and negative operands between -10 and 10.
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Expressions with Addition
| Move beyond addition of two numbers into addition of 3 to 5 numbers between +/-10.
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Basic Subtraction (-)
| Start with positive operands only and operands no greater than 10. When comfortable, move directly into both positive and negative operands (between -10 and 10) and expressions with 3 terms.
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More Graphing of Integer Values
| Now move from graphs of integers on a number line, interpolating poisitions on scales based on +/-20 to +/-100.
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Combining Subtraction & Addition
| Start with positive operands only and operands no greater than 10. When comfortable, move directly into both positive and negative operands (between -20 and 20) and expressions of three terms.
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More Subtraction & Addition
| Get more practice as you work with operands up to +/-100.
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Expressions with Addition & Subtraction
| Work with both positive and negative operands in small and large expressions.
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Basic Multiplication (*)
| Start with positive operands only and operands no greater than 10. When comfortable, move to positive operands up to 20.
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More Multiplication
| Return to operands no greater than 10. Move quickly into positive and negative operands up to +/-20.
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Combining Addition & Multiplication
| Start with positive operands only and operands no greater than 10. When comfortable, move directly into both positive and negative operands (between -10 and 10.)
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Combining Addition, Subtraction & Multiplication
| Start with positive operands only and operands no greater than 10. When comfortable, move directly into both positive and negative operands (between -10 and 10.)
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Expressions with Addition, Subtraction & Multiplication
| Work with both positive and negative operands in small and large expressions.
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Basic Division (/)
| Start with positive operands only and operands no greater than 10. When comfortable, move to positive operands up to 20.
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More Division
| Return to operands no greater than 10. Move quickly into positive and negative operands up to +/-20.
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Combining Multiplication & Division
| Start with positive operands only and operands no greater than 10. When comfortable, move directly into both positive and negative operands (between -20 and 20.)
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Combining Addition, Multiplication & Division
| Start with positive operands only and operands no greater than 10. When comfortable, move directly into both positive and negative operands (between -20 and 20.)
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Combining All Operations
| Work directly with both positive and negative operands (+/20).
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Expressions with All Operations
| Start with combining all operations with 3 terms and move into 5 terms.
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Expressions with ( )'s
| More expression practice this time including use of parentheses.
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Basic Exponents (^)
| Use positive and negative exponents with operands between -10 and 10.
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Expressions with Exponents
| Use exponents along with other operators in integer math.
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Variable Subsitutions
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Solving Simple Expressions with Subsitution
| Start by subsituting values into simple variable expressions utilizing integers.
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Solving Complex Expressions with Subsitution
| Now solve more complex expressions with a variable. Subsitute the value for the variable and then solve the expression.
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Exploring Graphs
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More Graphing Integers on a Number Line
| Start by exploring graphs of integers on a number line. Explore both positive and negative integers between -50 and 50.
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Graphing Points on a Plane
| Next explore the graphs of integer-valued points on a two-dimensional plane. Explore both positive and negative integers between -100 and 100.
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Basic Graphing of Lines
| Learn how to determine the equation behind various lines either through the origin or vertical.
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More on Graphing Lines
| Learn how to determine the equation behind various lines on planes (range +/-20).
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Graphing Simple Parabolas
| Learn how to determine the equation behind various lines on planes (range +/-20).
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Exploring Decimals
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Basic Addition (+)
| Start with positive operands only and operands no greater than 10. When comfortable, move directly into both positive and negative operands between -10 and 10.
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Expressions with Addition
| Move beyond addition of two numbers into addition of 3 to 5 numbers between +/-10.
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Basic Subtraction (-)
| Start with positive operands only and operands no greater than 10. When comfortable, move directly into both positive and negative operands (between -10 and 10) and expressions with 3 terms.
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Combining Subtraction & Addition
| Start with positive operands only and operands no greater than 10. When comfortable, move directly into both positive and negative operands (between -20 and 20) and expressions of three terms.
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More Subtraction & Addition
| Get more practice as you work with operands up to +/-100.
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Expressions with Addition & Subtraction
| Work with both positive and negative operands in small and large expressions.
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Basic Multiplication (*)
| Start with positive operands only and operands no greater than 10. When comfortable, move to positive operands up to 20.
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More Multiplication
| Return to operands no greater than 10. Move quickly into positive and negative operands up to +/-20.
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Combining Addition & Multiplication
| Start with positive operands only and operands no greater than 10. When comfortable, move directly into both positive and negative operands (between -10 and 10.)
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Expressions with Addition, Subtraction & Multiplication
| Work with both positive and negative operands in small and large expressions.
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Basic Division (/)
| Start with positive operands only and operands no greater than 10. When comfortable, move to positive operands up to 20.
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More Division
| Return to operands no greater than 10. Move quickly into positive and negative operands up to +/-20.
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Combining Multiplication & Division
| Start with positive operands only and operands no greater than 10. When comfortable, move directly into both positive and negative operands (between -20 and 20.)
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Combining All Operations
| Work directly with both positive and negative operands (+/20).
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Expressions with ( )'s
| More expression practice this time including use of parentheses.
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Exploring Graphical Solutions
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Solving Equations of the Form 0=BX+C
| Be introduced to the graphs of points representing solutions to equations. Work on solving the equations in conjunction with the graphically guided tour. (This is more open-ended and thought provoking then previous lessons. Results for these are not tracked.)
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Solving Equations of the Form 0=AX^2+ BX+C
| Now solve quadratics. Be introduced to the graphs of points representing real solutions to equations, when available.
Compare your results using the quadratic formula in conjunction with this graphically guided tour. (This is more open-ended and thought provoking then previous lessons. Results for these are not tracked.)
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