This is the first trimester of Integrated Math 1. This course is comprised of three units.

**Unit 1: Relationships and Reasoning with Equations**

**Unit 1: Relationships and Reasoning with Equations**

*Timeline: Approximately 5 weeks*

*Big Ideas:*

- There are universal practices in graphing points and lines. Those graphs help represent real data and functions.
- Solving equations and inequalities helps determine unknown variables and the functions themselves.
- The different parts of expressions, equations and inequalities can represent certain values in the context of a situation and help determine a solution process.
- Relationships between quantities can be represented symbolically, numerically, graphically, and verbally in the exploration of real world situations.
- Rules of arithmetic and algebra can be used together with notions of equivalence to transform equations and inequalities.
- Equivalent forms of an expression can be found, dependent on how the expression is used

*Essential Questions:*

- How do you graph points and values from a table?
- How do you determine scale for the axes of a graph?
- How does input/output relate to x/y and graphing?
- How do you solve one and two step equations and inequalities?
- How are equations and inequalities used to solve real world problems?
- When is it advantageous to represent relationships between quantities symbolically? numerically? graphically?
- Why are procedures and properties necessary when manipulating numeric or algebraic expressions?
- How can the structure of expressions/equations/inequalities help determine a solution strategy?
- For a linear expression that represents a real-world context, what do the coefficient and the constant represent?
- How does changing (either) the coefficient/constant in a given equation affect the other terms?
- Why do some word problems require linear equations, while other word problems require linear inequalities?
- How do you know if your solution to an equation or inequality makes sense for a given context?
- Why is it important to consider constraints when writing an equation for a context (word problem)?
- Why might you want to rearrange a given formula to highlight a specific variable or quantity? (For example, consider the distance equation D = rt. Why might you want to solve for r?)

*Power Standards:*

**A.SSE.1**Interpret expressions that represent a quantity in terms of its context. ★

**a)**Interpret parts of an expression, such as terms, factors, and coefficients.

**b)**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.**A.REI.1**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.**A.REI.3**Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.**A.CED.1**Create equations and inequalities in one variable including ones with absolute value and use them to solve problems. Include equations arising from linear and~~quadratic~~functions,~~and~~~~si~~mple rational and exponential functions.**A.CED.3**Represent constraints by equations or inequalities,~~a~~~~nd by systems of equations and/or inequalities~~, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

**Unit 2: Connecting Algebra and Geometry Through Coordinates**

**Unit 2: Connecting Algebra and Geometry Through Coordinates**

*Timeline: Approximately 3 weeks*

*Big Ideas:*

- Geometric figures can be represented in the coordinate plane.
- Algebraic properties (including those related to the distance between points in the coordinate plane) may be used to prove geometric relationships.
- The algebraic relationship between the slopes of parallel lines and the slopes of perpendicular lines.
- The distance formula may be used to determine measurements related to geometric objects represented in the coordinate plane (e.g., the perimeter or area of a polygon).
- The distance formula may be used to determine measurements related to geometric objects represented in the coordinate plane (e.g., the perimeter or area of a polygon).
- Algebraic formulas can be used to find measures of distance on the coordinate plane.
- The coordinate plane allows precise communication about graphical representations.
- The coordinate plane permits use of algebraic methods to obtain geometric results.

*Essential Questions:*

- How are basic geometric figures constructed in order to maintain their properties using a variety of tools?
- What is the relationship between the slopes of parallel lines and of perpendicular lines?
- Given a polygon represented in the coordinate plane, what is its perimeter and area?
- How can geometric relationships be proven through the application of algebraic properties to geometric figures represented in the coordinate plane?
- Why are the slopes of parallel lines equal?
- Why do the slopes of perpendicular lines have a product of –1?
- Why is it useful to know the Pythagorean Theorem, if you can’t remember the distance formula?
- If we are given the equation of a line parallel or perpendicular to a line we are trying to find, what do we know and what do we not know?
- What information would you need in order to prove/disprove that a triangle is a right isosceles triangle (given its coordinates on a coordinate plane)?
- How can the distance between two points be determined?
- How are the slopes of lines used to determine if the lines are parallel, perpendicular, or neither?
- How do we write the equation of a line that goes through a given point and is parallel or perpendicular to another line?
- How can slope and the distance formula be used to determine properties of polygons and circles?
- How can slope and the distance formula be used to classify polygons?
- How do I apply what I have learned about coordinate geometry to a real–world situation?

*Power Standards:*

**G.GPE.4**Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle;~~prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2)~~.**G.GPE.5**Prove the slope criteria for parallel and perpendicular lines; use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).**G.GPE.7**Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.**★**

**Unit 3: Descriptive Statistics**

**Unit 3: Descriptive Statistics**

*Timeline: Approximately 3.5 weeks*

*Big Ideas:*

- Statistical patterns of change can be represented using data tables, graphs, and problem conditions.
- Data can be represented and interpreted in a variety of formats.
- Extreme data points (outliers) can skew interpretations of a set of data.
- Synthesizing information from multiple sets of data results in evidence-based interpretation.
- Center and spread of a data set may be compared in multiple ways.
- Data in a two –way frequency table can be summarized using relative frequencies in the context of the data.
- Making predictions for values within or near the data set is more reliable than for values far beyond the data set
- Linear models can be created, used, and interpreted for real-life situations.

*Essential Questions:*

- How is useful data collected, reported, and analyzed?
- How can data be varied?
- How do various representations of data lead to different interpretations of the data?
- When and how can extreme data points impact interpretation of data?
- Why are multiple sets of data used?
- How are center and spread of data sets described and compared?
- How is a data set represented in a two-way frequency table summarized?
- How do you determine which model is best to represent a given data set?
- How do outliers affect the center, shape, and spread of a data set?
- Which graphical representations display each of the following: mean, median, interquartile range, and standard deviation?
- How can you determine if the data is skewed?
- How can data be represented in order to promote a certain agenda?
- What real world situations can be modeled by a linear relationship?
- How can technology help to determine whether a linear model is appropriate in a given situation?

*Power Standards:*

**S.ID.1**Represent data with plots on the real number line (dot plots, histograms & box plots).**S.ID.2**Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.**S.ID.3**Interpret differences in shape, center and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).**S.ID.7**Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.**S.ID.8**Compute (using technology) and interpret the correlation coefficient of a linear fit.

Advertisements