Micro School
Common Core Math TK8
Secure your spot in the online Common Core Math course, a micro school environment tailored to meet the needs of students from TK (transitional kindergarten) through 8th grade.
The virtual and interactive math course is based on state standards, being in sync with your child's school curriculum so they can get the support to catch up and/or get ahead. Live lessons are taught via Zoom for each grade level, and collaboration is fostered by realtime instruction and small class sizes. Students are guided through math concepts using the online learning platform, IXL, and learn concepts in a way that is organized and encourages them to solve realworld problems.

$30/week

Custom weekly registration available to work with your schedule.


Materials: IXL account (included)

Inclass instruction is based on Common Core Math Standards. Associated IXL skills are used as an aid in teaching lesson plans.

Course Assessment Measures: In addition to inclass assignments, weekly "Diagnostic" problems pin point student levels of understanding so the instructor can recommend tailored practice problems.

Note: The weekly schedule for each grade is tentative and subject to change upon the progress of the class. For example, if students in a class are proficient in the course's first topic, the instructor may spend a day or week less on said topic to continue moving forward in the schedule. On the other hand, an extra day may be spent to solidify certain concepts. With recommended skills offered to each student along the way, students recieve individualized instruction to learn at their own pace.
Use the following table of contents to quickly jump to a certain grade level's course description.
Common Core Kindergarten Math
Mon, Tue, Thu
11:00 AM  12:00 PM
Pacific Time
Course Description:
This is a virtual and interactive mathematics course for Kindergartenlevel students. Following Common Core Standards, instructional time focuses on representing and comparing whole numbers, and describing shapes and space, using the IXL learning platform to introduce and practice concepts.
Course Objectives:
This course teaches students:

Number names and the count sequence

Counting to tell the number of objects

Comparing numbers

Understanding addition as putting together and adding to, and subtraction as taking apart and taking from

Working with numbers 1119 to gain foundations for place value

Describing and comparing measurable attributes

Classifying objects and counting the numbers of objects in each category

Identifying and describing shapes

To analyze, compare, create, and compose shapes
Student Learning Outcomes:
Students will be able to:

Use numbers, including written numerals, to represent quantities and to solve quantitative problems.

Choose, combine, and apply effective strategies for answering quantitative questions.

Describe their physical world using geometric ideas (e.g., shape, orientation, spatial relations) and vocabulary.

Identify, name, and describe basic twodimensional shapes, such as squares, triangles, circles, rectangles, and hexagons, presented in a variety of ways (e.g., with different sizes and orientations), as well as threedimensional shapes such as cubes, cones, cylinders, and spheres.

Use basic shapes and spatial reasoning to model objects in their environment and to construct more complex shapes.
Schedule:
Week 1 4: Counting & Cardinality
Week 5  9: Operations and Algebraic Thinking
Week 10  11: Number & Operations in Base Ten
Week 12  15: Measurement & Data
Week 16  20: Geometry
Common Core 1st Grade Math
Mon, Tue, Thu
1:30  2:30 PM
Pacific Time
Course Description:
This is a virtual and interactive mathematics course for First Gradelevel students. Following Common Core Standards, instructional time focuses on: (1) developing understanding of addition, subtraction, and strategies for addition and subtraction within 20; (2) developing understanding of whole number relationships and place value, including grouping in tens and ones; (3) developing understanding of linear measurement and measuring lengths as iterating length units; and (4) reasoning about attributes of, and composing and decomposing geometric shapes. The IXL learning platform will be used to introduce and practice concepts.
Course Objectives:
This course teaches students to:

Represent and solve problems involving addition and subtraction.

Understand and apply properties of operations and the relationship between addition and subtraction.

Add and subtract within 20.

Work with addition and subtraction equations.

Extend the counting sequence.

Understand place value.

Use place value understanding and properties of operations to add and subtract.

Measure lengths indirectly and by iterating length units.

Tell and write time.

Represent and interpret data.

Reason with shapes and their attributes.
Student Learning Outomes:
Students will be able to:

Develop strategies for adding and subtracting whole numbers based on their prior work with small numbers.

Use a variety of models, (e.g., cubes connected to form lengths), to model addto, takefrom, put together, takeapart, and compare situations to develop meaning for the operations of addition and subtraction, and to develop strategies to solve arithmetic problems with these operations.

Understand connections between counting and addition and subtraction (e.g., adding two is the same as counting on two).

Use properties of addition to add whole numbers and to create and use increasingly sophisticated strategies based on these properties (e.g., “making tens”) to solve addition and subtraction problems within 20.

Build their understanding of the relationship between addition and subtraction by comparing a variety of solution strategies.

Develop, discuss, and use efficient, accurate, and generalizable methods to add within 100 and subtract multiples of 10.

Compare whole numbers (at least to 100) to develop understanding of and solve problems involving their relative sizes.

Understand the order of the counting numbers and their relative magnitudes, through activities that build number sense.

Develop an understanding of the meaning and processes of measurement, including underlying concepts such as iterating (the mental activity of building up the length of an object with equalsized units) and the transitivity principle for indirect measurement.

Compose and decompose plane or solid figures (e.g., put two triangles together to make a quadrilateral) and build understanding of partwhole relationships as well as the properties of the original and composite shapes.

Combine shapes and recognize them from different perspectives and orientations, describe their geometric attributes, and determine how they are alike and different.
Schedule:
Week 1 6: Operations and Algebraic Thinking
Week 7  11: Number & Operations in Base Ten
Week 12  15: Measurement & Data
Week 16  20: Geometry
Common Core 2nd Grade Math
Mon, Tue, Thu
2:30  3:30 pm
Pacific Time
Course Description:
This is a virtual and interactive mathematics course for Second Gradelevel students. Following Common Core Standards, instructional time focuses on: (1) extending understanding of baseten notation; (2) building fluency with addition and subtraction; (3) using standard units of measure; and (4) describing and analyzing shapes. The IXL learning platform will be used to introduce and practice concepts.
Course Objectives:
This course teaches students to:

Represent and solve problems involving addition and subtraction.

Add and subtract within 20.

Work with equal groups of objects to gain foundations for multiplication.

Understand place value.

Understand place value.

Use place value understanding and properties of operations to add and subtract.

Measure and estimate lengths in standard units.

Relate addition and subtraction to length.

Represent and interpret data.

Reason with shapes and their attributes.
Student Learning Outomes:
Students will be able to:

Extend their understanding of the baseten system. This includes ideas of counting in fives, tens, and multiples of hundreds, tens, and ones, as well as number relationships involving these units, including comparing.

Understand multidigit numbers (up to 1000) written in baseten notation, recognizing that the digits in each place represent amounts of thousands, hundreds, tens, or ones (e.g., 853 is 8 hundreds + 5 tens + 3 ones).

Use their understanding of addition to develop fluency with addition and subtraction within 100.

Solve problems within 1000 by applying their understanding of models for addition and subtraction, and they develop, discuss, and use efficient, accurate, and generalizable methods to compute sums and differences of whole numbers in baseten notation, using their understanding of place value and the properties of operations.

Select and accurately apply methods that are appropriate for the context and the numbers involved to mentally calculate sums and differences for numbers with only tens or only hundreds.

Recognize the need for standard units of measure (centimeter and inch) and they use rulers and other measurement tools with the understanding that linear measure involves an iteration of unit.

Recognize that the smaller the unit, the more iterations they need to cover a given length.

Describe and analyze shapes by examining their sides and angles.

Investigate, describe, and reason about decomposing and combining shapes to make other shapes.

Develop a foundation for understanding area, volume, congruence, similarity, and symmetry through building, drawing, and analyzing two and threedimensional shapes
Schedule:
Week 1 4: Operations and Algebraic Thinking
Week 5  11: Number & Operations in Base Ten
Week 12  18: Measurement & Data
Week 19  20: Geometry
Common Core 3rd Grade Math
Mon, Tue, Thu
3:30  4:30 PM
Pacific Time
Course Description:
This is a virtual and interactive mathematics course for Third Gradelevel students. Following Common Core Standards, instructional time focuses on: (1) developing understanding of multiplication and division and strategies for multiplication and division within 100; (2) developing understanding of fractions, especially unit fractions (fractions with numerator 1); (3) developing understanding of the structure of rectangular arrays and of area; and (4) describing and analyzing twodimensional shapes. The IXL learning platform will be used to introduce and practice concepts.
Course Objectives:
This course teaches students to:

Represent and solve problems involving multiplication and division.

Understand properties of multiplication and the relationship between multiplication and division.

Multiply and divide within 100.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Use place value understanding and properties of operations to perform multidigit arithmetic.

Develop understanding of fractions as numbers.

Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

Represent and interpret data.

Understand concepts of area and relate area to multiplication and to addition.

Recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

Reason with shapes and their attributes.
Student Learning Outomes:
Students will be able to:

Develop an understanding of the meanings of multiplication and division of
whole numbers through activities and problems involving equalsized groups, arrays, and area models.

Use properties of operations to calculate products of whole numbers, using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving singledigit factors.

Learn the relationship between multiplication and division, by comparing a variety of solution strategies.

Develop an understanding of fractions, beginning with unit fractions.

View fractions in general as being built out of unit fractions, and they use fractions along with visual fraction models to represent parts of a whole.

Understand that the size of a fractional part is relative to the size of the whole.

Use fractions to represent numbers equal to, less than, and greater than one.

Solve problems that involve comparing fractions by using visual fraction models and strategies based on noticing equal numerators or denominators.

Recognize area as an attribute of twodimensional regions.

Measure the area of a shape by finding the total number of samesize units of area required to cover the shape without gaps or overlaps, a square with sides of unit length being the standard unit for measuring area.

Understand that rectangular arrays can be decomposed into identical rows or into identical columns.

Connect area to multiplication, and justify using multiplication to determine the area of a rectangle by decomposing rectangles into rectangular arrays of squares.

Describe, analyze, and compare properties of twodimensional shapes.

Compare and classify shapes by their sides and angles, and connect these with definitions of shapes.

Relate their fraction work to geometry by expressing the area of part of shape as a unit fraction of the whole.
Schedule:
Week 1 9: Operations and Algebraic Thinking
Week 10  11: Number & Operations in Base Ten
Week 12  15: Number & Operations  Fractions
Week 16  19: Measurement & Data
Week 20: Geometry
Common Core 4th Grade Math
Mon, Tue, Thu
4:30  5:30 PM
Pacific Time
Course Description:
This is a virtual and interactive mathematics course for Fourth Gradelevel students. Following Common Core Standards, instructional time focuses on: (1) developing understanding and fluency with multidigit multiplication, and developing understanding of dividing to find quotients involving multidigit dividends; (2) developing understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; and (3) understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry. The IXL learning platform will be used to introduce and practice concepts.
Course Objectives:
This course teaches students to:

Use the four operations with whole numbers to solve problems.

Gain familiarity with factors and multiples.

Generate and analyze patterns.

Generalize place value understanding for multidigit whole numbers.

Use place value understanding and properties of operations to perform multidigit arithmetic.

Extend understanding of fraction equivalence and ordering.

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

Understand decimal notation for fractions, and compare decimal fractions.

Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

Represent and interpret data.

Geometric measurement: understand concepts of angle and measure angles.

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
Student Learning Outomes:
Students will be able to:

Generalize their understanding of place value to 1,000,000, understanding the relative sizes of numbers in each place.

Apply their understanding of models for multiplication (equalsized groups, arrays, area models), place value, and properties of operations, in particular the distributive property, as they develop, discuss, and use efficient, accurate, and generalizable methods to compute products of multidigit whole numbers.

Develop fluency with efficient procedures for multiplying whole numbers; understand and explain why the procedures work based on place value and properties of operations; and use them to solve problems.

Apply their understanding of models for division, place value, properties of operations, and the relationship of division to multiplication as they develop, discuss, and use efficient, accurate, and generalizable procedures to find quotients involving multidigit dividends.

Select and accurately apply appropriate methods to estimate and mentally calculate quotients, and interpret remainders based upon the context.

Develop understanding of fraction equivalence and operations with fractions.

Recognize that two different fractions can be equal (e.g., 15/9 = 5/3), and they develop methods for generating and recognizing equivalent fractions.

Compose fractions from unit fractions, decompose fractions into unit fractions, and use the meaning of fractions and the meaning of multiplication to multiply a fraction by a whole number.

Describe, analyze, compare, and classify twodimensional shapes.

Deepen their understanding of properties of twodimensional objects and the use of them to solve problems involving symmetry through building, drawing, and analyzing twodimensional shapes.
Schedule:
Week 1 2: Operations and Algebraic Thinking
Week 3  8: Number & Operations in Base Ten
Week 9  14: Number & Operations  Fractions
Week 15  17: Measurement & Data
Week 18  20: Geometry
Common Core 5th Grade Math
Mon, Tue, Thu
1:30  2:30 PM
Pacific Time
Course Description:
This is a virtual and interactive mathematics course for Fifth Gradelevel students. Following Common Core Standards, instructional time focuses on: (1) developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions); (2) extending division to 2digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations; and (3) developing understanding of volume. The IXL learning platform will be used to introduce and practice concepts.
Course Objectives:
This course teaches students to:

Write and interpret numerical expressions.

Analyze patterns and relationships.

Understand the place value system.

Perform operations with multidigit whole numbers and with decimals to hundredths.

Use equivalent fractions as a strategy to add and subtract fractions.

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Convert like measurement units within a given measurement system.

Represent and interpret data.

Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

Graph points on the coordinate plane to solve realworld and mathematical problems.

Classify twodimensional figures into categories based on their properties
Student Learning Outomes:
Students will be able to:

Apply their understanding of fractions and fraction models to represent the addition and subtraction of fractions with unlike denominators as equivalent calculations with like denominators.

Develop fluency in calculating sums and differences of fractions, and make reasonable estimates of them.

Use the meaning of fractions, of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for multiplying and dividing fractions make sense. (Note: this is limited to the case of dividing unit fractions by whole numbers and whole numbers by unit fractions.)

Develop understanding of why division procedures work based on the meaning of baseten numerals and properties of operations.

Finalize fluency with multidigit addition, subtraction, multiplication, and division.

Apply their understandings of models for decimals, decimal notation, and properties of operations to add and subtract decimals to hundredths. They develop fluency in these computations, and make reasonable estimates of their results.

Use the relationship between decimals and fractions, as well as the relationship between finite decimals and whole numbers (i.e., a finite decimal multiplied by an appropriate power of 10 is a whole number), to understand and explain why the procedures for multiplying and dividing
finite decimals make sense.

Compute products and quotients of decimals to hundredths efficiently and accurately.

Recognize volume as an attribute of threedimensional space. They understand that volume can be measured by finding the total number of samesize units of volume required to fill the space without gaps or overlaps.

Understand that a 1unit by 1unit by 1unit cube is the standard unit for measuring volume.

Select appropriate units, strategies, and tools for solving problems that involve estimating and measuring volume.

Decompose threedimensional shapes and find volumes of right rectangular prisms by viewing them as decomposed into layers of arrays of cubes.

Measure necessary attributes of shapes in order to determine volumes to solve real world and mathematical problems.
Schedule:
Week 1: Operations and Algebraic Thinking
Week 2  6: Number & Operations in Base Ten
Week 7  11: Number & Operations  Fractions
Week 13  16: Measurement & Data
Week 17  20: Geometry
Common Core 6th Grade Math
Mon, Tue, Thu
2:30  3:30 PM
Pacific Time
Course Description:
This is a virtual and interactive mathematics course for Sixth Gradelevel students. Following Common Core Standards, instructional time focuses on: (1) connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; (3) writing, interpreting, and using expressions and equations; and (4) developing understanding of statistical thinking. The IXL learning platform will be used to introduce and practice concepts.
Course Objectives:
This course teaches students to:

Understand ratio concepts and use ratio reasoning to solve problems.

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

Multiply and divide multidigit numbers and find common factors and multiples.

Apply and extend previous understandings of numbers to the system of rational numbers.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Reason about and solve onevariable equations and inequalities.

Represent and analyze quantitative relationships between dependent and independent variables.

Solve realworld and mathematical problems involving area, surface area, and volume.

Develop understanding of statistical variability.

Summarize and describe distributions.
Student Learning Outomes:
Students will be able to:

Use reasoning about multiplication and division to solve ratio and rate problems about quantities.

Connect their understanding of multiplication and division with ratios and rates by viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative size of quantities.

Connect ratios and fractions.

Use the meaning of fractions, the meanings of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for dividing fractions make sense.

Extend their previous understandings of number and the ordering of numbers to the full system of rational numbers.

Reason about the order and absolute value of rational numbers and about the location of points in all four quadrants of the coordinate plane.

Understand the use of variables in mathematical expressions.

Write expressions and equations that correspond to given situations, evaluate expressions, and use expressions and formulas to solve problems.

Understand that expressions in different forms can be equivalent, and they use the properties of operations to rewrite expressions in equivalent forms.

Know that the solutions of an equation are the values of the variables that make the equation true.

Use properties of operations and the idea of maintaining the equality of both sides of an equation to solve simple onestep equations.

Construct and analyze tables, such as tables of quantities that are in equivalent ratios, and they use equations (such as 3x = y) to describe relationships between quantities.

Develop their ability to think statistically. Students recognize that a data distribution may not have a definite center and that different ways to measure center yield different values.

Recognize that a measure of variability (interquartile range or mean absolute deviation) can also be useful for summarizing data because two very different sets of data can have the same mean and median yet be distinguished by their variability.

Describe and summarize numerical data sets, identifying clusters, peaks, gaps, and symmetry, considering the context in which the data were collected.

Reason about relationships among shapes to determine area, surface area, and volume. They find areas of right triangles, other triangles, and special quadrilaterals by decomposing these shapes, rearranging or removing pieces, and relating the shapes to rectangles. Using these methods, students discuss, develop, and justify formulas for areas of triangles and parallelograms.

Find areas of polygons and surface areas of prisms and pyramids by decomposing them into pieces whose area they can determine.

Reason about right rectangular prisms with fractional side lengths to extend formulas for the volume of a right rectangular prism to fractional side lengths.

Draw polygons in the coordinate plane.
Schedule:
Week 1  2: Ratios and Proportional Relationships
Week 3  8: The Number System
Week 9  14: Expressions and Equations
Week 15  17: Geometry
Week 18  20: Statistics & Probability
Common Core 7th Grade Math
Mon, Tue, Thu
3:30  4:30 PM
Pacific Time
Course Description:
This is a virtual and interactive mathematics course for Seventh Gradelevel students. Following Common Core Standards, instructional time focuses on: (1) developing understanding of and applying proportional relationships; (2) developing understanding of operations with rational numbers and working with expressions and linear equations; (3) solving problems involving scale drawings and informal geometric constructions, and working with two and threedimensional shapes to solve problems involving area, surface area, and volume; and (4) drawing inferences about populations based on samples.The IXL learning platform will be used to introduce and practice concepts.
Course Objectives:
This course teaches students to:

Analyze proportional relationships and use them to solve realworld and
mathematical problems. 
Apply and extend previous understandings of operations with fractions to
add, subtract, multiply, and divide rational numbers. 
Use properties of operations to generate equivalent expressions.

Solve reallife and mathematical problems using numerical and algebraic
expressions and equations. 
Draw, construct and describe geometrical figures and describe the
relationships between them. 
Solve reallife and mathematical problems involving angle measure, area,
surface area, and volume. 
Use random sampling to draw inferences about a population.

Draw informal comparative inferences about two populations.

Investigate chance processes and develop, use, and evaluate probability
models.
Student Learning Outomes:
Students will be able to:

Extend their understanding of ratios and develop understanding of proportionality to solve single and multistep problems. Students use their understanding of ratios and proportionality to solve a wide variety of percent problems, including those involving discounts, interest, taxes, tips, and percent increase or decrease.

Solve problems about scale drawings by relating corresponding lengths between the objects or by using the fact that relationships of lengths within an object are preserved in similar objects.

Graph proportional relationships and understand the unit rate informally as a measure of the steepness of the related line, called the slope. They distinguish proportional relationships from other relationships.

Develop a unified understanding of number, recognizing fractions, decimals (that have a finite or a repeating decimal representation), and percents as different representations of rational numbers.

Extend addition, subtraction, multiplication, and division to all rational numbers, maintaining the properties of operations and the relationships between addition and subtraction, and multiplication and division. By applying these properties, and by viewing negative numbers in terms of everyday contexts (e.g., amounts owed or temperatures below zero), students explain and interpret the rules for adding, subtracting, multiplying, and dividing with negative numbers.

Use the arithmetic of rational numbers as they formulate expressions and equations in one variable and use these equations to solve problems.

Solve problems involving the area and circumference of a circle and surface area of threedimensional objects.

Reason about relationships among twodimensional figures using scale drawings and informal geometric constructions, and they gain familiarity with the relationships between angles formed by intersecting lines.

Work with threedimensional figures, relating them to twodimensional figures by examining crosssections.

Solve realworld and mathematical problems involving area, surface area, and volume of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes and right prisms.

Compare two data distributions and address questions about differences between populations. They begin informal work with random sampling to generate data sets and learn about the importance of representative samples for drawing inferences.
Schedule:
Week 1  4: Ratios and Proportional Relationships
Week 5 11: The Number System
Week 12  15: Expressions and Equations
Week 16  18: Geometry
Week 19  20: Statistics & Probability
Common Core 8th Grade Math
Mon, Tue, Thu
4:30  5:30 PM
Pacific Time
Course Description:
This is a virtual and interactive mathematics course for Eighth Gradelevel students. Following Common Core Standards, instructional time focuses on: (1) formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations; (2) grasping the concept of a function and using functions to describe quantitative relationships; (3) analyzing two and threedimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem.The IXL learning platform will be used to introduce and practice concepts.
Course Objectives:
This course teaches students to:

Know that there are numbers that are not rational, and approximate them by rational numbers.

Work with radicals and integer exponents.

Understand the connections between proportional relationships, lines, and
linear equations. 
Analyze and solve linear equations and pairs of simultaneous linear
equations. 
Define, evaluate, and compare functions.

Use functions to model relationships between quantities.

Understand congruence and similarity using physical models, transparencies, or geometry software.

Understand and apply the Pythagorean Theorem.

Solve realworld and mathematical problems involving volume of cylinders,
cones and spheres. 
Investigate patterns of association in bivariate data.
Student Learning Outomes:
Students will be able to:

Use linear equations and systems of linear equations to represent, analyze and solve a variety of problems.

Recognize equations for proportions (y/x = m or y = mx) as special linear equations (y = mx + b), understanding that the constant of proportionality (m) is the slope, and the graphs are lines through the origin.

Understand that the slope (m) of a line is a constant rate of change, so that if the input or xcoordinate changes by an amount A, the output or ycoordinate changes by the amount m·A.

Use a linear equation to describe the association between two quantities in bivariate data (such as arm span vs. height for students in a classroom).

Strategically choose and efficiently implement procedures to solve linear equations in one variable, understanding that when they use the properties of equality and the concept of logical equivalence, they maintain the solutions of the original equation.

Solve systems of two linear equations in two variables and relate the systems to pairs of lines in the plane; these intersect, are parallel, or are the same line.

Use linear equations, systems of linear equations, linear functions, and their understanding of slope of a line to analyze situations and solve problems.

Students grasp the concept of a function as a rule that assigns to each input exactly one output. They understand that functions describe situations where one quantity determines another.

Translate among representations and partial representations of functions, and they describe how aspects of the function are reflected in the different representations.

Use ideas about distance and angles, how they behave under translations, rotations, reflections, and dilations, and ideas about congruence and similarity to describe and analyze twodimensional figures and to solve problems.

Show that the sum of the angles in a triangle is the angle formed by a straight line, and that various configurations of lines give rise to similar triangles because of the angles created when a transversal cuts parallel lines.

Understand the statement of the Pythagorean Theorem and its converse, and can explain why the Pythagorean Theorem holds. They apply the Pythagorean Theorem to find distances between points on the coordinate plane, to find lengths, and to analyze polygons.

Complete their work on volume by solving problems involving cones, cylinders, and spheres.
Schedule:
Week 1: The Number System
Week 2  8: Expressions & Equations
Week 9  12: Functions
Week 13  19: Geometry
Week 20: Statistics & Probability