Colorado Springs School District 11
Year 09 Integrated Algebra & Geometry
Curriculum Map – Last revised June 09, 2009
Approximately 17 – 20 days per unit
Overall mathematical curricular approaches to tying various mathematical
concepts together are:
NUMERACY
MULTI-REPRESENTATIONS
 TABLE
 GRAPH
 EQUATION
 DESCRIPTION
INTERPRET INTERCEPTS (REAL-WORLD MEANINGS)
MEASUREMENT
FIRST SEMESTER
Quarter 1 Part 1
FUNCTIONS
 What is a function? (condense from last year into just a few lessons)
o Domain/range/independent & dependent variables
 Drawing examples of linear and non-linear functions with a
given domain and/or range
 function notation (embed order of operations)
 Numeracy with and without calculator -- Include scientific notation,
lots more practice with order of operations (including integer
operations, fractions, decimals, distributive property, combining like
terms); translating words into expressions
o Extension: binomial distribution (FOIL)
 Contextual meanings when a variable is equal to zero
o y-intercept as the “start value”
 make explicit that the domain value is zero
o x-intercept as a significant domain value
 make explicit that the range value is zero
 include negative values for the x-intercept
 Bank of short, quick-hitting naked problems to use as warm-ups or
tickets out the door
 Assessment will be non-calculator
Quarter 1 Part 2 (embed dimensional analysis throughout)
 Solving equations (1- & 2-step)
 Slope/rates
 Continue work interpreting x- and y-intercepts
 Writing Equations to model situations and data (embed order of
operations)
 Direct variation/ (review of proportions)
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Dimensional analysis needs to be more explicitly embedded – connect
to rates – give them conversion factors
Lots more practice with solving equations, (single listing of the variable
only)
Literal equations introduced (match science common curriculum) eg:
F=ma, solve for m; include examples of standard and slope-intercept
forms for manipulation purposes only: 2x+3y=5, solve for y; y=x/3-2,
solve for x.
Quarter 2 Part 1
 Given 2 points, write the equation of a line
 Graphing lines from equations in multiple forms
 Lines of best fit
 Point-slope form of an equation for a line
o Distributive property
o Geometric patterns—reinforcement of linear functions
o Use point-slope form rather than “walk back” to stage 0
 Graphing equations from table, graph, situation
Quarter 2 Part 2
o Theme: one dimensional measurement – be explicit about functional
approach – create linear situations: A(h) = (1/2)(10)(h), areas of all
triangles with base length 10, what’s the domain, range?
 Perimeter
o Include standard form equations: 2W+2L=P
o Scale change effects in perimeter
 Pythagorean Theorem
o Inverse in reverse with squares
 Angle relationships (including measurement with a protractor)
o In what ways is measuring an angle the same as measuring a
line segment?
o Naming conventions for angles
 Convention for congruent angle notation in figures
o Complementary and supplementary angles
 Teaching proportions
o Variables on top and bottom
 Similar figures
o Extensive, including indirect measurement
o Naming convention for polygons (especially triangles)
o The angle sum of a triangle is 180 degrees
o Special case: congruence when scaling factor equals 1
 Convention for congruent side notation in figures
 Dimensional analysis needs to be more explicitly embedded
 Create situations that yields equations with multiple listings of the
variable to practice combining terms
Quarter 3 Part 1
o Theme: two and three dimensional measurement – be explicit about
functional approach– create linear situations: V(h) = (5²)(h), volumes
of all rectangular prisms with a square base of side length 5, what’s
the domain, range?
 Area, surface area, volume, (embed scientific notation)
o Measurement
o Literal equations (look for opportunities for standard form)
o Equation manipulation
o Scale changes in volume and area
o Include expressing answers in terms of pi
o Dimensional analysis needs to be more explicitly embedded
o Pyramids, cones, prisms, cylinders and spheres
 Create situations that yields equations with multiple listings of the
variable to practice combining terms
 Work with more complex compound figures for find areas and volumes
by dissection
Quarter 3 Part 2
 Probability & statistics
o Geometric (area model)
o Theoretical vs. observed (the big idea for this unit)
o Guiding question: “What do you expect?”
 Measures of center
 Given a central tendency statistic, work backwards to find
a missing data point
 Mechanisms for communicating data (that could be used as a basis for
observed probability)
o 5 number summary
o Interpretation of data:
 Stem & leaf plot
 Histograms
 Bar graph
 Pie chart
o Which display is most appropriate for a given situation or
purpose?
 Misleading statistics
o Sampling
o Bias
 Observed probability – trials and successes
o Connect to data displays
o Collect to misleading statistics
 Theoretical probability
o Sample space
o Independent vs. dependent events
o Counting principle
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Expected value (based on both theoretical and observed prob.)
o Connect to proportional reasoning
o Connect expected value to mean
QUARTER 4 Part 1
 Systems of Equation: only slope-intercept form
o Continue work with contextual interpretations of x and y
intercepts
 Make explicit that either the domain or range value is zero
o Solving by substitution
o Explain the solution in the context of the problem
o Consistent and inconsistent systems
 Parallel – systems with no solutions (perpendicular unnecessary)
o Variables on both sides
o Graphical solutions
o Use a solution to provide advice to someone
QUARTER 4 Part 2
 Systems of Equation: include standard form and point-slope form
o Consistent and independent (unique solution), consistent and
dependent (infinitely many solutions) and inconsistent systems
o Solving by substitution (with one of the equations in standard form)
o Solving by elimination
o Solving by graphing (equations in standard form)
o Word problems resulting in systems
o Inequalities – 1 & 2 dimensions
 Graphing
 Solving