|Secondary Math 1 Honors Curriculum Map (Quarter 1)|
|Time Frame||Utah State Core Standard||Expected Student Outcome (Objective)||Essential Academic Vocabulary||Assessments (Formative & Summative)||Instructional Learning Activities|
|taught throughout||N.Q.1||I can select and use appropriate units of measurement. |
Given a graph, I can draw conclusions and make inferences.
I can choose appropriate scales to create linear and exponential graphs.
I can determine, from the labels on a graph, what the units of the rate change are.
|Scale, units of measurement||Explore a variety of examples of measurements used in graphs.|
Construct graphs using a variety of data sets.
|N.Q.2||I can choose appropriate measures and units for problem situations.|
I can create a relationship among different units.
|Unit rates, modeling, quantity, unit conversion, propertion, ratio||Integrate this objective into problem solving throughout the curriculum.|
Place an emphasis on relationships between two different units.
|N.Q.3||I can determine whether whole numbers, fractions, or decimals are most appropriate.|
I can determine the appropriate power of ten to reasonably measure a quantity.
I can determine the resulting accuracy in calculations.
I can determine what level of rounding should be used in a problem situation.
|Precision, accuracy||Discuss misconceptions in resulting calculations involving measurement.|
|A.SSE.1 a, b||Given an expression, I can identify the terms, bases, exponents, coefficients, and factors.|
I can determine the real world context of the variables in an expression.
I can identify the individual factors of a given term within as expression.
I can explain the context of different parts of a formula.
|Exponents, factors, terms, bases, coefficients, expression||Given a word problem and a formula have students examine the structure and explain the context of different parts of the formula.|
Design a game around identifying terms, bases, exponents, coefficients, and factors.
Create formulas based on context.
|2 days||A.REI.1||I can understand, apply, and explain the results of using inverse operations.|
I can justify the steps in solving equations by applying and explaining the properties of equality, inverse, and identity.
I can use the names of the properties and common sense explanations to explain the steps in solving an equation.
|Constant, coefficient, properties of operations and properties of equalities, like terms, variable, evaluate, justify, viable.||Linear #1||Have students share different ways of solving equations that lead to the same answer.|
Find and analyze mistakes in student work samples.
Partner problems: One student solves, the other writes reasons why steps work.
Introduce a two-colume proof as a way of organizing justifications.
|10 days||A.REI.3||I can write equations in equivalent forms to solve problems.|
I can analyze and solve literal equations for a specified variable.
I can understand and apply the properties of inequalities.
I can verify that a given number is a solution to the equation or inequality.
I can interpret the solution of an inequality in real terms.
I can solve simple exponential equations using the law of exponents.
|Properties of Inequalities.||Exponentials & Comparisons #1, 2|
Linear #2, 3, 4
|Solve specified variables, using connon formulas used in science, economics, or other disciplines.|
Examine and prove why dividing or multiplying by a negative reverses the inequality sign.
Use applications from a varieity of disciplines to motivate solving linear equations and inequalities.
|A.REI.3||(New for 2016-2017)|
I can solve compound one variable inequalities.
I can solve absolute value one variable inequalities.
|absolute value, compound inequality, AND, OR|
|4 days||A.CED.1||I can create one-variable linear equations and inequalities form contextual situation.|
I can create one-variable exponential equations and inequalities from contextual situations.
I can solve and interpret the solution to multi-step linear equations and inequalities in context.
I can use properties of exponents to solve and interpret the solution to exponential equations and inequalities in context.
|Greater than, less than, at most, at least, =, <, >, no morethan, no less than.||Exponentials & Comparisons #3, 4|
ACT: Pre-Algebra; linear equations in one varable, Intermediate Algebra; modeling
|Convert contextual information into mathematical notation.|
Use story contexts to create linear and exponential equations and inequalities.
|A.CED.4||I can extend to concepts used in solving numerical equations to rearranging formulas for a particular variable.||Constant, variable, formula, literal equation||Linear #5||Use formulas from a varitiy of disciplines such as physics, chemistry, or sports to explore the advantages of different formats of the same formula.|
|7 days||A.CED.2||I can write and graph an equation to represent a linear relationship.|
I can write and graph an equation to represent as exponential relationship.
I can model a data set using an equation.
I can choose the best form of an equation to model linear and exponential functions.
|Variable, dependent variable, independent variable, domain, range, scale||Exponentials & Comparisons #6|
ACT:Intermediate Algebra; modeling
|Use story contexts to create linear and exponential graphs.|
Use technology to explore a variety of linear and exponential graphs.
Use data sets to generate linear and exponential graphs and equations.
|A.REI.10||I can identify solutions and non-solutions of linear and exponential equations.|
I can graph points that satisfy liner and exponential equations.
I can understand that a continuous or a line contains an infinite number of solutions.
|Ordered pair, coordinate plane, solution, non-solution, sets||Exponentials & Comparisons #5|
|A.CED.3||I can determine whether a point is a solution to an equation or inequality.|
I can determine whether a solution has meaning in a real-world context.
I can write and graph equations and inequalities representing constraints in contextual situations.
|Constraint, greater the, >, less then, <, greater then or equal to, less then or equal to, inequality, viable|
|14 days||A.REI.11||I can approximate solutions to systems of two equations using graphing technology.|
I can approximate solutions to systems of two equations using tables a values.
I can explain why the x-coordinates of the points where the graphs of the equations y = f(x) and = g(x) intersect are the solutions of the equation f(x) = g(x).
|Function, intersection, approximate, linear, exponential, f(x), g(x).|
|A.REI.6||I can solve a system of equations exactly (with algebra) and approximately (with graphs).|
I can test a solution to the system in both original equations.
I can analyze a system of equations using slope to predict one, infinitely many or no solutions.
|System of equations, consistent and inconsistent systems, dependent and independent systems, solution set|
|A.REI.5||I can explain the use of the multiplication property of equality to solve a system of equations.|
I can explain why the sum of two equations is justifiable in the solving of a system of equations.
I can relate the process of linear combinations with the process of substitution for solving a system of linear equations.
|Elimination by multiplication and addition, substitution|
|N.VM.13+||I can represent a system of linear equations using matrices.|
I can solve a system of two equations with two unknowns by hand using matrices.
I can use technology to solve a system of three or more equations using matrices.
|matrices, row-echelon form, inverse, identity, determinant, dependent, inconsistent, sigular matrix||ACT: Intermediate Alg. matrices||Use row-echelon form to solve systems of equations.|
Use matrix equations to solve systems.
Use contextual situations with multiple variables to explore the power of matrices.
Explore dependent and inconsistent systems of equations.
|5 days||N.VM.6 +||I can organize data in a matrix.|
I can identify and name matrix properties accurately.
I can interpret data in a matrix.
I can recognize and use matrix notation.
|row, column, dimension, square matrix, row matrix, column matrix||ACT: Intermediate Alg. matrices||Use matrices to represent a logic problem.|
Relate matrices to tables and spreadsheets.
Find examples in the media of data that can be represented in a matrix.
|N.VM.7 +||I understand that scalar multiplication does not change the order of elements in a matrix.|
I can multiply a matrix by a scalar.
|scalar||ACT: Intermediate Alg. matrices||Interpret scalar multiplication in real-world contexts.|
Multiply using a variety of scalars.
Use scalar multiplication with a matrix representing a polygon to create a dilation.
Generalize scalar multiplication to include variables.
|N.VM.8 +||I can recognize the necessary conditions for matrix operations|
I can add and subtract matrices by hand and using technology.
I can multiply matrices by hand and using technology.
Explain the meaning of the result of matrix operations in context.
|row, column, matrix||ACT: Intermediate Alg. matrices||Connect matrix operations to a context.|
Use matrix operations to preform geometric transformations.
|N.VM.9 +||I understand that multiplication of matrices in not commutative.|
I understand that the associative and distributive properties hold for matrix multiplication.
|associative, commutative, distributive, square matrix||ACT: Intermediate Alg. matrices||Explore the result of a variety of matrix operations on square matrices using technology.|
|N.VM.10 +||I can recognize and create matrices that are identity matrices.|
I can determine additive and multiplicative identities and inverses of a matrix when they exist.
I can find the determinant of a matrix using technology.
I can use the determinant to determine of a square matrix has an inverse.
|identity, inverse, determinant, square matrix, non-zero, variable matrix, singular matrix||ACT: Intermediate Alg. matrices||Explore transformations by trying different values in a transformation matrix and observing the resultant vector.|
Apply transsformations of matrices to cryptology.
|4 days||A.REI.12||I can graph the solution to linear inequalities in two variables.|
I can graph the solution to systems of linear inequalities in two variables.
I can identify the solutions as a region of the plane.
|Inequality, solution, half-plane, solution region.||ACT: Coordinate Geometry; graphing inequalities|