Integrated Beginning Algebra 1, Curricular Guide Trademarked Skyline Education, Inc., June 2011 Cannot be reproduced without permission Integrated Beginning Algebra 1 This course explores beginning Algebraic concepts including: real numbers, solving equations and inequalities, proportionality, functions, and rate of change. Students will use problem- solving strategies to prepare solutions to authentic situations involving algebra, geometry, and probability through algorithmic thinking, logic, and problem-solving skills. This course meets one of the four math requirements for university admission and Arizona State Graduations requirements.
An Introduction to Curriculum Mapping and Standards Log Objectives are mapped according to when they should be introduced and when they should be assessed throughout the month (K-4), block (5-8), or course (7-12). A record of when all objectives are introduced and assessed is to be kept through the course map and log, using the month, day, and year introduced. Objectives only have to be reviewed if assessment is not 80% students at 80% mastery. **In some cases, it is not necessary to teach the standards if 80% students are at 80% mastery when pretested. However, if less than 80% students achieve 80% mastery, it is necessary to give instruction and a posttest.** The curriculum is standards-based, and it is the Skyline philosophy to use “Backwards Design” when lesson planning. Backwards Design starts with standards, and from there, an assessment is created in alignment with the standards; next, the instruction for that assessment and those standards is created. Also, all standards addressed for instruction and assessment should be visibly posted in the classroom, along with student-friendly wording of the objectives. Assessments for mastery are to be summative, or cumulative in nature. Formative assessments are generally quick-assessments where the teacher can gauge whether or not student-learning is acquired. Curriculum binders are set up to have a master of each grade or content level, as well as a teacher’s copy, which is to serve as a working document. Teachers may write in the teacher’s binder to log standards, suggest remapping, adjust timing, and so on. The curriculum mapping may be modified or adjusted as necessary for individual students and classes, as well as available resources, within reason. Major changes are to be submitted to the school’s Professional Learning Community, Administration, and the Board.
A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
HS.G-SRT.1b
The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
HS.A-SSE.1B
Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)
n as the product of P
and a factor not depending on P.
HS.F-BF.1b
Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.
ETHS-S6C1-03;ETHS-S6C2-03
HS.F-BF.1c
Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function o
ETHS-S6C1-03;ETHS-S6C2-03
HS.M.BS
Modeling Standards are spread through the rest of the standards. Anything that requires composing a organized form of data, graphic, or formula is modeling.
HS.A-CED.1
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
HS.A-CED.4
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.
Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
HS.A-REI.2
Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
HS.F-IF.2
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
9-10.RST.4
HS.F-IF.3
Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.
HS.F-LE.1c
Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
11-12.RST.4
HS.F-BF.2
Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
HS.A-SSE.1A
Interpret parts of an expression, such as terms, factors, and coefficients. 9-10.RST.4
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Practices Applied in all Math Classes Mathematical Practices (MP)
1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
Suggested Coursework and Pacing Beginning Algebra is a Freshman level course, and has no Honors curriculum. The course is planned as an 8 week course with padded time for
