Description:Algebra I Unit 1 By the end of eighth grade students have learned to solve linear equations in one variable and have applied graphical and algebraic methods to analyze and solve systems of linear equations in two variables. This unit builds on these earlier experiences by asking students to analyze and explain the process of solving an equation. Students develop fluency writing, interpreting, and translating between various forms of linear equations and inequalities, and using them to solve problems. They master the solution of linear equations and apply related solution techniques and the laws of exponents to the creation and solution of simple exponential equations. All of this work is grounded on understanding quantities and on relationships between them.

Last Updated:Aug-21-2012

• Mathematics

• Grades 6-8 / Ages 11-13
• Grades 9-10 / Ages 14-16

• middle
• 6th
• 7th
• 8th
• tween
• high
• 9th
• 10th
• secondary
• freshman
• sophomore
• teen

• Curriculum: Unit

Description:In earlier grades, students define, evaluate, and compare functions, and use them to model relationships between quantities. In this unit, students will learn function notation and develop the concepts of domain and range. They move beyond viewing functions as processes that take inputs and yield outputs and start viewing functions as objects in their own right. They explore many examples of functions, including sequences; they interpret functions given graphically, numerically, symbolically, and verbally, translate between representations, and understand the limitations of various representations. They work with functions given by graphs and tables, keeping in mind that, depending upon the context, these representations are likely to be approximate and incomplete. Their work includes functions that can be described or approximated by formulas as well as those that cannot. When functions describe relationships between quantities arising from a context, students reason with the units in which those quantities are measured. Students explore systems of equations and inequalities, and they find and interpret their solutions. Students build on and informally extend their understanding of integer exponents to consider exponential functions. They compare and contrast linear and exponential functions, distinguishing between additive and multiplicative change. They interpret arithmetic sequences as linear functions and geometric sequences as exponential functions.

Last Updated:Jul-24-2012

• Mathematics
• Mathematics > Algebra

• Grades 6-8 / Ages 11-13
• Grades 9-10 / Ages 14-16

• middle
• 6th
• 7th
• 8th
• tween
• high
• 9th
• 10th
• secondary
• freshman
• sophomore
• teen

• Curriculum: Unit

Description:Experience with descriptive statistics began as early as Grade 6. Students were expected to display numerical data and summarize it using measures of center and variability. By the end of middle school they were creating scatter plots and recognizing linear trends in data. This unit builds upon that prior experience, providing students with more formal means of assessing how a model fits data. Students use regression techniques to describe approximately linear relationships between quantities. They use graphical representations and knowledge of the context to make judgments about the appropriateness of linear models. With linear models, they look at residuals to analyze the goodness of fit.

Last Updated:Aug-21-2012

• Mathematics

• Grades 6-8 / Ages 11-13
• Grades 9-10 / Ages 14-16

• middle
• 6th
• 7th
• 8th
• tween
• high
• 9th
• 10th
• secondary
• freshman
• sophomore
• teen

• Curriculum: Unit

Description:In this unit, students will learn to build on their knowledge from Unit 2, where they extended the laws of exponents to rational exponents. Students apply this new understanding of number and strengthen their ability to see structure in and create quadratic and exponential expressions. They create and solve equations, inequalities, and systems of equations involving quadratic expressions. The five lessons (4.1-4.5) provide the instruction and practice that supports the culminating activity in the final unit project.

Last Updated:Aug-21-2012

• Mathematics

• Grades 6-8 / Ages 11-13
• Grades 9-10 / Ages 14-16

• middle
• 6th
• 7th
• 8th
• tween
• high
• 9th
• 10th
• secondary
• freshman
• sophomore
• teen

• Activity: Assignment/Homework
• Activity: Problem Set
• ...

Description:between rational and irrational numbers. They consider quadratic function, comparing the key characteristics of quadratic functions to those of linear and exponential functions. They select from among these functions to model phenomena. Students learn to anticipate the graph of a quadratic function by interpreting various forms of quadratic expressions. In particular, they identify the real solutions of a quadratic equation as the zeros of a related quadratic function. Students learn that when quadratic equations do not have real solutions the number system must be extended so that a solution exists, analogous to the way in which extending the whole numbers to the negative numbers allows X+1=0 to have a solution. Formal work with complex numbers comes in Algebra II. Students expand their experience with functions to include more specialized functions—absolute value, step, and those that are piecewise defined. The eight lessons (5.1-5.8) provide the instruction and practice that supports the culminating activity in the final unit project. The lessons in this unit focus on working with quadratic relationships.

Last Updated:Aug-16-2012

• Mathematics

• Grades 6-8 / Ages 11-13
• Grades 9-10 / Ages 14-16

• middle
• 6th
• 7th
• 8th
• tween
• high
• 9th
• 10th
• secondary
• freshman
• sophomore
• teen

• Activity: Exercise
• Activity: Problem Set
• ...