District Blueprint - Secondary Math 1
A steering committee of representatives from most schools in Alpine School District creating the following blueprint as a recommended sequence for the content in the new Utah Core. These resources will help you transition from the old core to the new core standards.
The following is a brief outline of the District Blueprint for Secondary Math 1.
To download the full blueprint (including examples) click here.
To download the full blueprint (including examples) click here.
Modeling, Overarching (This unit does not exist on its own but should be included throughout the year as other units are taught.)
N.Q.2 I can identify appropriate units for modeling different contextual situations.
For example: It’s normally not appropriate to measure the height of a person in mm.
A.SSE.1.b I can determine the real world context of the variables in an expression.
For example: For I understand what P and represent and how each affects the total amount.
N.Q.1.a I can use unit analysis to help set up and solve contextual situations involving different units.
For example: If my answer needs to be in feet and I have a rate of feet per second, I know I need to multiply by seconds to get the number of feet.
For example: Which is the best unit rate: bottles per dollar or dollars per bottle?
N.Q.3 I can chose a level of accuracy appropriate to limitations on measurement when reporting quantities.
For example: When finding the volume of a sphere, if the radius is given in cm, then the answer does not need to given to the nearest hundredth of a mm.
For example: Do not round the answer until the end!!!!
For example: Round appropriately based on context of the problem.
Note: This standard should be taught throughout the year.
N.Q.1.b I can interpret and use the scales and units in a graph.
For example: In the graph of the position of a car over time, where the scale on the y-axis is 15 miles, and the scale on the x-axis is 1 hour, I can find the velocity of the car in mph.
Note: This standard should be taught throughout the year.
For example: It’s normally not appropriate to measure the height of a person in mm.
A.SSE.1.b I can determine the real world context of the variables in an expression.
For example: For I understand what P and represent and how each affects the total amount.
N.Q.1.a I can use unit analysis to help set up and solve contextual situations involving different units.
For example: If my answer needs to be in feet and I have a rate of feet per second, I know I need to multiply by seconds to get the number of feet.
For example: Which is the best unit rate: bottles per dollar or dollars per bottle?
N.Q.3 I can chose a level of accuracy appropriate to limitations on measurement when reporting quantities.
For example: When finding the volume of a sphere, if the radius is given in cm, then the answer does not need to given to the nearest hundredth of a mm.
For example: Do not round the answer until the end!!!!
For example: Round appropriately based on context of the problem.
Note: This standard should be taught throughout the year.
N.Q.1.b I can interpret and use the scales and units in a graph.
For example: In the graph of the position of a car over time, where the scale on the y-axis is 15 miles, and the scale on the x-axis is 1 hour, I can find the velocity of the car in mph.
Note: This standard should be taught throughout the year.
Modeling. This is how we compare linear and exponential functions. (This unit does not exist on its own but should be included throughout the year as other units are taught.)
F.BF.2.c I can model situations using arithmetic and geometric sequences
S.ID.6.a I can fit a function to the data and use the function fitted to solve problems in the context of the data.
S.ID.6 I can make a scatter plot with and without technology and determine if the relationship is linear, exponential or neither.
S.ID.6.b.1 I can calculate the residuals. (Residuals are the vertical distances between each data point and a point on the regression function)
S.ID.6.b.2 I can make a residual plot with and without technology.
S.ID.6b.3 I can analyze a residual plot to assess the fit of the regression. (Good or bad fit)
S.ID.8 I can compute (using technology) and interpret the correlation coefficient.
S.ID.9 I can distinguish between correlation and causation.
F.LE.5 I can interpret the parameters of linear and exponential functions within a contextual situation.
For example: Plant growth can be modeled with a function: y = 2x + 4. Explain the contextual meaning of 2 and 4 in terms of the plant.
A.CED.1 I can create linear and exponential equations and linear inequalities and use them to solve contextual situations.
S.ID.6.a I can fit a function to the data and use the function fitted to solve problems in the context of the data.
S.ID.6 I can make a scatter plot with and without technology and determine if the relationship is linear, exponential or neither.
S.ID.6.b.1 I can calculate the residuals. (Residuals are the vertical distances between each data point and a point on the regression function)
S.ID.6.b.2 I can make a residual plot with and without technology.
S.ID.6b.3 I can analyze a residual plot to assess the fit of the regression. (Good or bad fit)
S.ID.8 I can compute (using technology) and interpret the correlation coefficient.
S.ID.9 I can distinguish between correlation and causation.
F.LE.5 I can interpret the parameters of linear and exponential functions within a contextual situation.
For example: Plant growth can be modeled with a function: y = 2x + 4. Explain the contextual meaning of 2 and 4 in terms of the plant.
A.CED.1 I can create linear and exponential equations and linear inequalities and use them to solve contextual situations.
Graphing Linear and Exponential Functions (This unit does not exist on its own but should be included throughout the year as other units are taught.)
A.CED.2.b I can graph a linear and exponential equation on the same coordinate axes with labels and scales.
F.IF.4.a Given a linear or exponential function , I can identify the following from a graph or a table:
§ x- and y- intercepts
§ Increasing and decreasing intervals
§ Positive and negative intervals
§ Maximum and minimum values (is this relevant to linear and exponential functions)
§ Symmetry
§ End behavior
F.IF.4.b I can sketch graphs of linear and exponential functions given the key features listed above.
F.IF7e I can graph exponential functions and show the following key features of the graph (simple cases by hand and complex cases using technology):
§ Intercepts
§ End behavior
F.IF.4.a Given a linear or exponential function , I can identify the following from a graph or a table:
§ x- and y- intercepts
§ Increasing and decreasing intervals
§ Positive and negative intervals
§ Maximum and minimum values (is this relevant to linear and exponential functions)
§ Symmetry
§ End behavior
F.IF.4.b I can sketch graphs of linear and exponential functions given the key features listed above.
F.IF7e I can graph exponential functions and show the following key features of the graph (simple cases by hand and complex cases using technology):
§ Intercepts
§ End behavior
1- Algebra Skills Unit
A.SSE.1.a I know the vocabulary (expression, terms, factors, and coefficients) and can identify them in linear and exponential expressions.
A.REI.1 I can solve linear equations and justify each step in the solution using Algebraic properties.
A.REI.3.a I can solve linear equations and inequalities in one variable.
A.REI.3.b I can solve a literal equation for a given variable including equations with coefficients represented by letters.
For example: Ax + By = c: solve for B
A.CED.4 I can isolate a variable in a formula.
A.REI.1 I can solve linear equations and justify each step in the solution using Algebraic properties.
A.REI.3.a I can solve linear equations and inequalities in one variable.
A.REI.3.b I can solve a literal equation for a given variable including equations with coefficients represented by letters.
For example: Ax + By = c: solve for B
A.CED.4 I can isolate a variable in a formula.
2- Geometry Constructions Unit
G.CO.1 I can precisely define an angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
G.CO.12a I can copy and construct a segment and an angle and explain why the procedure is accurate.
G.CO.12b I can bisect a segment and an angle and explain why the procedure is accurate.
G.CO.13 I can construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle and explain why the procedure results in the desired object.
G.CO.7 I can show that two triangles are congruent if and only if corresponding pairs of sides and angles are congruent.
G.CO.8 I can identify the minimum conditions (ASA, SAS, AAS, SSS, or exceptions to SSA)
G.CO.12c I can construct perpendicular lines, including the perpendicular bisector of a line segment; and construct a line parallel to a given line through a point not on a line and explain why the procedure results in the desired object.
G.CO.12a I can copy and construct a segment and an angle and explain why the procedure is accurate.
G.CO.12b I can bisect a segment and an angle and explain why the procedure is accurate.
G.CO.13 I can construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle and explain why the procedure results in the desired object.
G.CO.7 I can show that two triangles are congruent if and only if corresponding pairs of sides and angles are congruent.
G.CO.8 I can identify the minimum conditions (ASA, SAS, AAS, SSS, or exceptions to SSA)
G.CO.12c I can construct perpendicular lines, including the perpendicular bisector of a line segment; and construct a line parallel to a given line through a point not on a line and explain why the procedure results in the desired object.
3- Coordinate Geometry and Proofs of Quadrilaterals in Coordinate Plane Unit
G.GPE.7 I can use tools of coordinate geometry (distance formula) to compute perimeters of any polygon and areas of right triangles.
G.GPE.5a I can determine if two lines are parallel, perpendicular or neither.
G.GPE.4 I can use the midpoint formula, slope, and the Pythagorean Theorem (distance formula) with coordinates to prove the following (but not limited to):
§ If both pairs of opposite sides of a quadrilateral are congruent then the quadrilateral is a parallelogram.
§ Both pairs of opposite sides of a quadrilateral are parallel then the quadrilateral is a parallelogram.
§ If one pair of opposite sides of a quadrilateral is parallel and congruent then the quadrilateral is a parallelogram.
§ If the diagonals of a quadrilateral bisect each other then the quadrilateral is a parallelogram.
§ If all four sides of a quadrilateral are parallel and congruent, then the quadrilateral is a rhombus.
§ If all four angles of a quadrilateral are parallel and congruent, then the quadrilateral is a square.
If the opposite sides of a quadrilateral are both parallel and the consecutive sides are perpendicular, the quadrilateral is a rectangle.
G.GPE.5a I can determine if two lines are parallel, perpendicular or neither.
G.GPE.4 I can use the midpoint formula, slope, and the Pythagorean Theorem (distance formula) with coordinates to prove the following (but not limited to):
§ If both pairs of opposite sides of a quadrilateral are congruent then the quadrilateral is a parallelogram.
§ Both pairs of opposite sides of a quadrilateral are parallel then the quadrilateral is a parallelogram.
§ If one pair of opposite sides of a quadrilateral is parallel and congruent then the quadrilateral is a parallelogram.
§ If the diagonals of a quadrilateral bisect each other then the quadrilateral is a parallelogram.
§ If all four sides of a quadrilateral are parallel and congruent, then the quadrilateral is a rhombus.
§ If all four angles of a quadrilateral are parallel and congruent, then the quadrilateral is a square.
If the opposite sides of a quadrilateral are both parallel and the consecutive sides are perpendicular, the quadrilateral is a rectangle.
4- Functions Unit
F.IF.1.d I can explain what it means to be a function.
F.IF.1.c I can identify whether a relation is a function by looking at a table of values or by looking at the graph.
F.IF.1.a I can explain the relationship between x and , that notation means “the y-value of the function f at x”.
F.IF.1.b I can identify the domain (input, x-value) and range (output, y-value, ) of a function from an equation, table, or graph.
F.IF.5 I can determine an appropriate domain for the given context of a function.
F.IF.2.a I can evaluate functions in notation for values in the domain.
F.IF.1.b I can identify the domain (input, x-value) and range (output, y-value, ) of a function from an equation, table, or graph.
F.IF.5 I can determine an appropriate domain for the given context of a function.
F.IF.2.a I can evaluate functions in notation for values in the domain.
F.BF.1.b I can combine standard function types using arithmetic operations.
F.IF.2.b I can interpret statements that use function notation in terms of a context. For example, given the amount of money in a savings account is , I can explain what represents.
A.REI.10.a I can identify the coordinates of a linear and exponential function from a graph as solutions to an equation/function.
A.REI.10.b I can graph points that satisfy a linear or exponential function and explain the meaning of each coordinate in relation to the function, using function notation.
A.REI.10.c I can explain why a continuous curve (including lines) contains an infinite number of solutions.
F.IF.1.c I can identify whether a relation is a function by looking at a table of values or by looking at the graph.
F.IF.1.a I can explain the relationship between x and , that notation means “the y-value of the function f at x”.
F.IF.1.b I can identify the domain (input, x-value) and range (output, y-value, ) of a function from an equation, table, or graph.
F.IF.5 I can determine an appropriate domain for the given context of a function.
F.IF.2.a I can evaluate functions in notation for values in the domain.
F.IF.1.b I can identify the domain (input, x-value) and range (output, y-value, ) of a function from an equation, table, or graph.
F.IF.5 I can determine an appropriate domain for the given context of a function.
F.IF.2.a I can evaluate functions in notation for values in the domain.
F.BF.1.b I can combine standard function types using arithmetic operations.
F.IF.2.b I can interpret statements that use function notation in terms of a context. For example, given the amount of money in a savings account is , I can explain what represents.
A.REI.10.a I can identify the coordinates of a linear and exponential function from a graph as solutions to an equation/function.
A.REI.10.b I can graph points that satisfy a linear or exponential function and explain the meaning of each coordinate in relation to the function, using function notation.
A.REI.10.c I can explain why a continuous curve (including lines) contains an infinite number of solutions.
5- Review of Linear Functions Unit
F.LE.1.b I can recognize contextual situations with a common difference between terms.
F.IF.3.c I can recognize the relationship between arithmetic sequences and linear functions.
F.BF.2.a I understand that a linear relationship can be represented as an arithmetic sequence.
F.LE.2.a I can construct a linear function given either: 1) an arithmetic sequence, 2) a graph, 3) a description or 4) input/output pairs.
S.ID.7 Given a linear model, I can interpret the slope and the y-intercept in the context of the data.
F.IF.7.a I can graph linear functions and identify slope and intercepts (simple cases by hand and complex cases using technology).
A.REI.12.a I can graph the solution to linear inequalities in two variables and explain the meaning of the shaded regions (solutions) and non-shaded regions (not solutions).
S.ID.6.c I can use technology to create a linear regression for the data set.
G.GPE.5b I can write an equation of a line through a point that is parallel or perpendicular to a given line.
F.IF.3.c I can recognize the relationship between arithmetic sequences and linear functions.
F.BF.2.a I understand that a linear relationship can be represented as an arithmetic sequence.
F.LE.2.a I can construct a linear function given either: 1) an arithmetic sequence, 2) a graph, 3) a description or 4) input/output pairs.
S.ID.7 Given a linear model, I can interpret the slope and the y-intercept in the context of the data.
F.IF.7.a I can graph linear functions and identify slope and intercepts (simple cases by hand and complex cases using technology).
A.REI.12.a I can graph the solution to linear inequalities in two variables and explain the meaning of the shaded regions (solutions) and non-shaded regions (not solutions).
S.ID.6.c I can use technology to create a linear regression for the data set.
G.GPE.5b I can write an equation of a line through a point that is parallel or perpendicular to a given line.
6- Linear or Exponential Unit
F.IF.6.a I can calculate and interpret the average rate of change of a function between two values.
F.IF.6.b I can calculate and interpret the average rate of change of a function from a graph or table and explain what it means in terms of the function.
F.IF.6.c I can estimate the (instantaneous) rate of change at a point from a graph.
F.LE.1.a I understand and can prove that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals.
F.LE.3 I can explain and show why a quantity increasing exponentially will eventually exceed a quantity increasing linearly.
A.CED.2.a I can create two variable linear and exponential equations and use them to compare two quantities.
For example: Given two populations that follow linear or exponential growth models, I can find when the populations will be the same, and which population is bigger in 20 years.
F.IF.9 I can compare properties of two functions represented in different ways.
For example: Given a table of one function and a graph of another, find the best way to determine which function grows faster or has a greater y intercept.
F.LE.1.c I can recognize contextual situations with a common ratio between terms.
F.BF.2.b I understand that an exponential relationship can be represented as a geometric sequence.
F.IF.3.d I can recognize the relationship between geometric sequences and exponential functions.
F.IF.3.b I can recognize and find values of recursive sequences.
For example: The Fibonacci sequence is defined recursively by f(0) = f(1) =1, f(n+1)=f(n) +f(n-1) for n1.
F.LE.1.c I can recognize contextual situations with a common ratio between terms.
F.BF.2.b I understand that an exponential relationship can be represented as a geometric sequence.
F.IF.3.d I can recognize the relationship between geometric sequences and exponential functions.
F.IF.3.b I can recognize and find values of recursive sequences.
For example: The Fibonacci sequence is defined recursively by f(0) = f(1) =1, f(n+1)=f(n) +f(n-1) for n1.
F.BF.1.a I can write an explicit expression (function rule) or recursive process that describes a linear or exponential relationship between two quantities.
F.BF.2.d I can write an explicit rule given a recursive definition and vice versa.
F.LE.2.b I can construct an exponential function given either: 1) a geometric sequence, 2) a graph, 3) a description or 4) input/output pairs.
F.IF.6.b I can calculate and interpret the average rate of change of a function from a graph or table and explain what it means in terms of the function.
F.IF.6.c I can estimate the (instantaneous) rate of change at a point from a graph.
F.LE.1.a I understand and can prove that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals.
F.LE.3 I can explain and show why a quantity increasing exponentially will eventually exceed a quantity increasing linearly.
A.CED.2.a I can create two variable linear and exponential equations and use them to compare two quantities.
For example: Given two populations that follow linear or exponential growth models, I can find when the populations will be the same, and which population is bigger in 20 years.
F.IF.9 I can compare properties of two functions represented in different ways.
For example: Given a table of one function and a graph of another, find the best way to determine which function grows faster or has a greater y intercept.
F.LE.1.c I can recognize contextual situations with a common ratio between terms.
F.BF.2.b I understand that an exponential relationship can be represented as a geometric sequence.
F.IF.3.d I can recognize the relationship between geometric sequences and exponential functions.
F.IF.3.b I can recognize and find values of recursive sequences.
For example: The Fibonacci sequence is defined recursively by f(0) = f(1) =1, f(n+1)=f(n) +f(n-1) for n1.
F.LE.1.c I can recognize contextual situations with a common ratio between terms.
F.BF.2.b I understand that an exponential relationship can be represented as a geometric sequence.
F.IF.3.d I can recognize the relationship between geometric sequences and exponential functions.
F.IF.3.b I can recognize and find values of recursive sequences.
For example: The Fibonacci sequence is defined recursively by f(0) = f(1) =1, f(n+1)=f(n) +f(n-1) for n1.
F.BF.1.a I can write an explicit expression (function rule) or recursive process that describes a linear or exponential relationship between two quantities.
F.BF.2.d I can write an explicit rule given a recursive definition and vice versa.
F.LE.2.b I can construct an exponential function given either: 1) a geometric sequence, 2) a graph, 3) a description or 4) input/output pairs.
7- Transformations Unit
G.CO.2.a I can identify different transformations (translation, rotation, dilation, reflection) on an object.
G.CO.2.c I can distinguish between rigid and non-rigid transformations.
G.CO.6a I can identify the types of transformations that result in a rigid motion on a figure.
G.CO.6b I can predict the effect of transformations to determine if two figures are congruent.
G.CO.5.b I can describe the series of transformations from an image to a pre-image.
G.CO.2.b I can perform a series of transformations on an object.
G.CO.5.a I can perform a series of transformations on a figure (using graph paper, tracing paper, technology, etc).
G.CO.3.b I can recognize rotational and reflectional symmetry.
G.CO.3.a I can describe the rotations and reflections of a rectangle, parallelogram, trapezoid or regular polygon that carry it onto itself.
G.CO.4 I can define transformations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
F.BF.3.a I can identify and explain the following transformations on a linear or exponential function (with or without technology).
For example:
(Vertical translation)
(Horizontal translation)
(Vertical stretch/compression, vertical reflection)
(Horizontal stretch/compression, horizontal reflection)
F.BF.3.b I can determine the value of k (see above) given the graph.
G.CO.2.c I can distinguish between rigid and non-rigid transformations.
G.CO.6a I can identify the types of transformations that result in a rigid motion on a figure.
G.CO.6b I can predict the effect of transformations to determine if two figures are congruent.
G.CO.5.b I can describe the series of transformations from an image to a pre-image.
G.CO.2.b I can perform a series of transformations on an object.
G.CO.5.a I can perform a series of transformations on a figure (using graph paper, tracing paper, technology, etc).
G.CO.3.b I can recognize rotational and reflectional symmetry.
G.CO.3.a I can describe the rotations and reflections of a rectangle, parallelogram, trapezoid or regular polygon that carry it onto itself.
G.CO.4 I can define transformations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
F.BF.3.a I can identify and explain the following transformations on a linear or exponential function (with or without technology).
For example:
(Vertical translation)
(Horizontal translation)
(Vertical stretch/compression, vertical reflection)
(Horizontal stretch/compression, horizontal reflection)
F.BF.3.b I can determine the value of k (see above) given the graph.
8- Systems of Equations Unit
A.REI.11.c I can explain why the x-coordinate at the point of intersection of two functions is the solution to .
A.REI.11.a I can approximate solutions to a system of equations by graphing (with and without technology) to approximate the intersection of the curves.
A.REI.11.b I can approximate solutions to a system of equations using tables (with and without technology).
A.REI.6 I can solve systems of linear equations in two variables using the following methods:
1) Substitution
2) Linear combination/Elimination
3) Graphing
A.REI.5 I can explain why using a linear combination produces another equation that has the same solution as the original system of equations.
A.REI.12.b I can graph the solution to systems of linear inequalities in two variables and explain the meaning of the shaded regions (solutions) and non-shaded regions (not solutions).
A.CED.3 Write and graph equations and inequalities representing constraints in contextual situations.
For example: If I have $300 to spend, and hot dogs cost $2 per pound and hamburger costs $4 per pound, Determine what possible amounts of hamburger and hot dogs I can buy.
For example: Linear programming
A.REI.11.a I can approximate solutions to a system of equations by graphing (with and without technology) to approximate the intersection of the curves.
A.REI.11.b I can approximate solutions to a system of equations using tables (with and without technology).
A.REI.6 I can solve systems of linear equations in two variables using the following methods:
1) Substitution
2) Linear combination/Elimination
3) Graphing
A.REI.5 I can explain why using a linear combination produces another equation that has the same solution as the original system of equations.
A.REI.12.b I can graph the solution to systems of linear inequalities in two variables and explain the meaning of the shaded regions (solutions) and non-shaded regions (not solutions).
A.CED.3 Write and graph equations and inequalities representing constraints in contextual situations.
For example: If I have $300 to spend, and hot dogs cost $2 per pound and hamburger costs $4 per pound, Determine what possible amounts of hamburger and hot dogs I can buy.
For example: Linear programming
9 -Distributions and Two-way Tables Unit
S.ID.1 I can create or interpret dot plots, histograms and box plots to represent data sets.
S.ID.2.a I can compare distribution graphs using comparisons of center (median, mean) and spread (interquartile range, standard deviation).
S.ID.2.b I can describe corresponding shapes of graphs given information about center and spread for data sets.
S.ID.3 I can describe the changes in shape, center and spread that are caused by outliers.
S.ID.5.a I can create a two-way frequency table from categorical data.
S.ID.5.b Given a 2-way table, I can count the following frequencies
- Joint frequency
- Marginal frequency
- Conditional relative frequency
S.ID.2.a I can compare distribution graphs using comparisons of center (median, mean) and spread (interquartile range, standard deviation).
S.ID.2.b I can describe corresponding shapes of graphs given information about center and spread for data sets.
S.ID.3 I can describe the changes in shape, center and spread that are caused by outliers.
S.ID.5.a I can create a two-way frequency table from categorical data.
S.ID.5.b Given a 2-way table, I can count the following frequencies
- Joint frequency
- Marginal frequency
- Conditional relative frequency