Colorado Springs School District 11
Year 10 Integrated Algebra & Geometry
Curriculum Map – Last revised Sept. 04, 2009
Q1P1 – Linear Functions
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Changing representations between: tables, graphs, function equation, and English word description.
Using distribution property to write equations from point-slope form to slope-intercept form.
Writing and applying linear equations to solve word problems.
Understanding real-world meaning of y-intercept and slope.
Applying equations, table of values and graphs to solve real-world problems.
Identify linear patterns by recognizing constant differences and write a formula for the nth term.
 Apply linear patterns to find a regression (line of fit) for a set of data.
 Identification of independent and dependent variables from context.
 The special case when the y-intercept is zero (direct variation, proportional reasoning, and geometric
similarity).
Embedded
 Systems of Linear Equations in two variables (Standard and Slope-intercept)
 Function notations and vocabulary (domain, range, etc)
 Unit conversions (example, mph to feet/sec, gallons/hr to gallons/min)
 Algebraic manipulation
Q1P2 – Exponential Functions
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Identify exponential patterns
Writing and applying exponential equations to solve word problems (investment and loan
scenarios, population growth scenarios, and other scenarios involving exponential growth or decay)
 Discriminate between linear and exponential patterns.
Embedded
 Function notations and vocabulary (domain, range, etc)
 Algebraic manipulation
 Exponent rules
 Scientific notation
Extension
 Logarithmic Functions
Q2P1 – Quadratic Functions
 Identify quadratic patterns.
 Writing and applying quadratic equations to solve word problems (projectile motions, area problems).
 Discriminate between linear, exponential and quadratic patterns.
 Locate roots, x- and y-intercepts and vertex. Determine their meanings.
 Relate transformations (reflection over x-axis, horizontal and vertical translation) to changes in the
equation.
Embedded
 Function notations and vocabulary (domain, range, etc)
 Algebraic manipulation
 Multiplying binomials
Q2P2 – Statistics and Probability
Decide when the use of the normal model is appropriate
Using standard deviation as a measure of the spread of the data
Making predictions based on the normal model
Finding probabilities using sampling distributions
Find weighted mean
Recognize distortions and deceptions in displays of data.
Analyze how additional pieces of data, subtraction of data, modification of data or outliers will affect
each measure of central tendency.
 Finding expected values (or what is the mean outcome?).
Embedded
 Create sample spaces (systematic list, area models and tree diagrams)
 Apply the basic counting principle (examples: menu choices, clothing options)
 Sampling with and without replacement
 Finding the probability of dependent and independent events (and and or).
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Q3 – Transformational Geometry
P1
 Angle relationships
 Similarity and congruence of triangles
 The language of transformations (rotation, reflection, translation, dilation)
 Indirect measurement using right triangle trigonometry
Embedded
 Unit Conversions
 Pythagorean Theorem
Extensions
 Inverse Trig (finding the angle measure)
P2
 Polygon angle sum as a function of number of sides in the polygon
 Area of a regular n-gon as a functional relationship
 Functional relationships involving attributes of polygons
 Finding surface area of cones, cylinders, prisms, and pyramids
 Finding volume of cones, cylinders, prisms, and pyramids
 Finding, describing and analyzing the effect of changing one or more dimensions.
Embedded
 Perimeter (including circumference)
 Plane area
 Nets
 Using formulas
 Visualizing rotation of 2-D figures
 Unit Conversions
 Trigonometry
 Equivalent equations
Extensions
 Conservation of volume
 Rotating a plane figure and finding the volume and difference of volume (y-axis vs x-axis rotations)
Q4 – Analytic Geometry
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Transformations using coordinate geometry
Slopes of parallel and perpendicular lines
Finding the distance between two points
Finding the midpoint of a line segment
Inverse Trig (finding the angle measure)
Finding missing angle measures and side lengths in right triangles and triangles that can be divided
into right triangles
 Determining what constitutes “proof”
 Using coordinate geometry in proof
Embedded
 Pythagorean Theorem
 Pythagorean triples
 Classification of triangles