8th+Grade+Honors+Algebra+1


 * ~  ||~ Half Quarter ||~ Content/concepts/skills ||~ Common Core Standards ||~ Chapter ||~ Assessment ||~ Resources/Materials ||~ **Essential Questions** ||
 * || 1st A || Order of operations; properties of operations; logical thinking; +-x/ rationals; roots; using formulas || * Interpret the structure of expressions
 * Interpret expressions that represent a quantity in terms of its context
 * Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line
 * Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers
 * Solve real-world and mathematical problems involving the four operations with rational numbers
 * Know that numbers that are not rational are called irrational. Understand that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number
 * Evaluate square roots of small perfect squares and cube roots of small perfect cubes || 1, 2 || 1 test, 2 quizzes, 1 project, daily homework, classwork investigations || TI-83 graphing calculators; 2-color counters; fraction bars || What do we remember about how to combine rational numbers? What would it take for a number not to be rational? What is meant by a "logical" argument? Why is it so important to understand what variables are and the various ways we use them? ||
 * || 1st B || Graphs, charts, tables; central tendency & variation; box & whiskers; proportions & percent; simple probability, Counting principle, permutations; solving linear equations and formulas || * Represent data with plots on the real number line
 * Use statistics appropriate to the shape of the distribution to compare center (mean, median) and spread (interquartile range, standard deviation) of two or more different data sets
 * Interpret linear models
 * Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters
 * Rearrange formulas to highlight a quantity of interest, using the same reasoning || 13,14, 5 || same; quarter exam || TI graphing calculators; data collection materials for labs; boxes & klinkers || What information can we get when data is portrayed in different ways? How can we find a ratio equivalent to another ratio? Is percent a ratio? Is there a shortcut for counting the number of ways to order things? How can complicated linear equations be solved? How can missing values in formulas be found? ||
 * || 2nd A || Writing & graphing linear equations || * Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales
 * Define, evaluate, and compare functions
 * || 5 || same || TI graphing calculators; geoboards || What is meant by the "slope" of a line & how is this used to write an equation for the line? How can we recognize a linear equation? What features allow us to easily graph it? ||
 * || 2nd B || Recursive functions; sequences; parallel & perpendicular lines; inequalities || * Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters
 * Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers || 5, 6 || same; quarter exam || TI graphing calculators; geoboards || What are the distinguishing features of arithmetic sequences? How are they related to linear functions? How can slope be used to create parallel or perpendicular lines? What if we replace the equal sign in an equation with an inequality symbol? How can we indicate a half-plane & what is its relation to an inequality? ||
 * || 3rd A || Systems; rules of exponents; operations with polynomials || * Analyze and solve pairs of simultaneous linear equations
 * Solve systems of linear equations exactly and approximately, focusing on pairs of linear equations in two variables
 * Prove that, given a system of equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions || 7, 8 || same || TI graphing calculators; Algebra tiles || What is the solution when two or more equations must be simultaneously true? How can this solution be found? What shortcuts can allow us to easily combine or simplify expressions containing exponents? ||
 * || 3rd B || Factoring polynomials || * Factor a quadratic expression to real the zeros of the function it defines
 * Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines
 * Use the structure of an expression to identify ways to rewrite it || 9 || same; quarter exam || TI graphing calculators; Algebra tiles || How can we determine whether a polynomial is actually a product of two simpler polynomials? ||
 * || 4th A || Solving & graphing quadratic equations; geometric sequences || * Graph linear and quadratic functions and show intercepts, maxima and minima
 * Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values and symmetry of the graph
 * Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms || 10 || same || TI graphing calculators || What can we find out about 2nd degree equations? How are they different from 1st degree equations? What are the distinguishing features of a geometric sequence? ||
 * || 4th B || Operations with radicals; Pythagorean theorem; distance formula; equations with x in the denominator || * Rewrite expressions involving radicals and rational exponents using the properties of exponents
 * Apply the Pythagorean theorem to find the distance between two points in a coordinate system || 11, 12 || same; quarter exam || TI graphing calculators; geoboards || What shortcuts can allow us to easily combine or simplify expressions containing radicals? What surprising relationship allows us to find the length of the 3rd side of a right triangle if we know the lengths of the other two sides? How can we use the Pythagorean Theorem to find the distance between any two points on the coordinate plane? How does having the variable in a denominator complicate the way we solve the equation? ||
 * |||| Textbook: Glencoe "Algebra 1." 2005 Edition ||  ||   ||   ||   ||   ||
 * |||| Textbook: Glencoe "Algebra 1." 2005 Edition ||  ||   ||   ||   ||   ||