## 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.## 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.

## 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

## 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:**A

*x*+ B

*y*= 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.

## 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.

## 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.

## 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.

## 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.

## 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.

## 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

## 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