Milwaukee Public Schools Suggested Curriculum Pacing Guide for Discovering Algebra (Block and Regular schools)
Time / Lesson/Activity / MPS Learning Targets / Benchmarks Embedded in Chapter Lessons / District Model CABS / Suggested vocabulary /Chapter 0: Fractions and Fractals
0.1 The Same Yet Smaller / CHAPTER 0
LT 5: Compare, perform, explain and evaluate mathematical operations (+, -, *, /, exponents, roots) and properties on real numbers, emphasizing negative and positive numbers; ratios, proportions and percents; and exponents and roots in mathematical and real-world applications. / CHAPTER 0
5.2 Solve problems with fractions, decimals and percents. / integer, ratio, proportion, expression
Reflections/
Feedback
Chapter 0, continued
0.2 More and More
0.3 Shorter Yet Longer
0.4 Going Somewhere?
0.5 Out of Chaos / LT 2:Use a variety of mathematical and technological tools to determine measurements directly (ruler, protractor, compass) and to check reasonableness of answers. When students apply technology, e.g. computers and graphing calculators, they will interpret results appropriately.
LT 5: Compare, perform, explain and evaluate mathematical operations (+, -, *, /, exponents, roots) and properties on real numbers, emphasizing negative and positive numbers; ratios, proportions and percents; and exponents and roots in mathematical and real-world applications. / 2.1 Estimate measurements with precision, using appropriate units.
2.2 Measure lengths using a metric/English ruler (to the appropriate degree of tenths of cm and sixteenths of an inch).
5.1 Solve problems using integers and absolute values.
5.2 Solve problems with fractions,
decimals and percents.
5.5 Solve problems involving
exponents and roots.
5.8 Use the order of operations to evaluate and simplify expressions. / Fractals and Fractions / estimate, length, centimeter, metric unit, meter, exponent, power
Reflections/
Feedback
Chapter 0, continued
Review
Assessment
Chapter 1
Data Analysis
1.1 Bar Graphs and Dot Plots
1.2 Summarizing Data with Measures of Center / CHAPTER 1
LT 3*: Use data in a variety of formats to summarize, predict, and analyze real-world applications.
LT7*: Create and use tables, graphs,
equations and formulas to describe
relationships between variables. / CHAPTER 1
3.3 Create and interpret bar graphs
and circle graphs.
3.4 Determine the means, median
and mode of a set of data.
3.6 Use measures of center and
measures of variation to interpret,
analyze and make predictions from
the data.
7.5 Interpret the meaning of tables,
graphs and equations using data
from real-world applications. / mean, median, mode, graph, range, data, outliers
Reflections/
Feedback
Chapter 1, continued
1.3 Five-Number Summaries and Box Plots
1.4 Histograms and Stem-and-Leaf Plots
Assessment
1.5 Activity Day: Exploring a Conjecture / LT 3: Use data in a variety of formats to summarize, predict, and analyze real-world applications. / 3.1 Organize information into
tables and stem-and-leaf plots.
3.2 Create histograms and describe the distribution.
3.5 Calculate the 5 number summary (quartiles) and create a box and whisker plot.
3.10 Compare and contrast two
sets of data using measures of
central tendency from a box and
whisker plot and a stem and leaf
plot.
3.11 Choose a graph given a set of
data and justify its
appropriateness. / Bob’s Blocks / data, box and whisker plot, histogram, quartiles, stem and leaf, inter-quartile range
Reflections/
Feedback
Chapter 1, continued
1.6 Two-Variable Data
1.7 Estimating
1.8 Using Matrices to Organize and Combine Data / LT 3: Use data in a variety of formats to summarize, predict, and analyze real-world applications.
LT7*: Create and use tables, graphs,
equations and formulas to describe
relationships between variables. / 3.7 Display and interpret data
using line graphs and scatter plots.
3.8 Use the line of best fit to make
predictions from data on a graph.
3.9 Compare and contrast two
sets of data using measures of central tendency from a box and whisker plot and a stem and leaf plot.
7.2 Create graphs, including real-
world data, using equations and
tables.
7.5 Interpret the meaning of tables,
graphs and equations using data
from real-world applications. / graph, scatter plot, line of best fit, matrices
Reflections/
Feedback
Chapter 1, continued
Review
Assessment
Chapter 2: Proportional Reasoning and Variation
2.1 Proportions
2.2 Capture/
Recapture
2.3 Proportions and Measurement Systems / CHAPTER 2
LT 2: Use a variety of mathematical and technological tools to determine measurements directly (ruler, protractor, compass) and to check reasonableness of answers. When students apply technology, e.g. computers and graphing calculators, they will interpret results appropriately.
LT 5: Compare, perform, explain and evaluate mathematical operations (+, -, *, /, exponents, roots) and properties on real numbers, emphasizing negative and positive numbers; ratios, proportions and percents; and exponents and roots in mathematical and real-world applications. / CHAPTER 2
2.2 Measure lengths using a metric/English ruler (to the appropriate degree of tenths of cm and sixteenths of an inch).
2.4 Justify reasons to interpret reasonableness of answers to
mathematical and real-world applications.
5.3 Solve problems with ratios and proportions.
5.4 Solve real-world application problems using scale factors and scale drawings. / dimension, conversion, centimeter, kilometer, inch, foot, yard, mile,
percent
Reflections/
Feedback
Chapter 2, continued
2.4 Direct Variation
Assessment
2.5 Inverse Variation
2.6 Activity Day: Variation with a Bicycle / LT 7*: Create and use tables, graphs, equations and formulas to describe relationships between variables. / 7.2 Create graphs, including real-
world data, using equations and
tables.
7.5 Interpret the meaning of tables,
graphs and equations using data
from real-world applications.
7.10 Describe patterns of change
from a table of ordered pairs.
7.12 Write a linear equation to
represent a pattern in which there
is a constant rate of change
between variables.
7.13 Identify the difference between direct and inverse variation in tables, graphs, and equations. / equation, table, coordinates, coordinate system, rate of change, variable
Reflections/
Feedback
Chapter 2, continued
2.7 Evaluating Expressions
2.8 Undoing Operations
Review
Assessment / LT5. Compare, perform, explain and evaluate mathematical operations (+, -, *, /, exponents, roots) and properties on real numbers, emphasizing negative and positive numbers; ratios, proportions and percents; and exponents and roots in mathematical and real-world applications.
LT 9: Model and solve mathematical and real-world applications that can be represented by linear equations and systems of equations, linear inequalities, and quadratic equations. / 5.10 Translate verbal expressions into algebraic expressions.
9.1 Solve one-step equations using
inverse operations.
9.2 Solve two-step equations using
inverse operations and explain the
meaning of the solution in context.
9.3 Solve multi-step equations using inverse operations and explain the meaning of the solution in context. / inverse properties, inverse
Reflections/
Feedback
Chapter 3: Linear Equations
3.1 Recursive Sequences
3.2 Linear Plots / CHAPTER 3
LT 7: Create and use tables, graphs, equations and formulas to describe relationships between variables. / CHAPTER 3
7.2 Create graphs, including real-
world data, using equations and
tables.
7.5 Interpret the meaning of tables,
graphs and equations using data
from real-world applications.
7.10 Describe patterns of change
from a table of ordered pairs.
Reflections/
Feedback
Chapter 3, continued
3.3 Time-Distance Relationships
Assessment
3.4 Linear Equations and the Intercept Form
3.5 Linear Equations and Rate of Change / LT 7: Create and use tables, graphs, equations and formulas to describe relationships between variables. / 7.1 Create tables, including real-
world data, using equations and
graphs.
7.2 Create graphs, including real-
world data, using equations and
tables.
7.5 Interpret the meaning of tables, graphs and equations using data from real-world applications.
7.6 Find and describe intercepts on a graph.
7.7 Find and describe slopes as constant rates of change,
7.9 Write an equation from tables
and graphs using real-world data.
7.12 Write a linear equation to
represent a pattern in which there
is a constant rate of change
between variables. / slope-intercept, pattern, model, perimeter, area
Reflections/
Feedback
Chapter 3, continued
3.6 Solving Equations Using the Balancing Method
3.7 Activity Day: Modeling Data
Review
Assessment / LT 9: Model and solve mathematical
and real-world applications that can
be represented by linear equations
and systems of equations, linear
inequalities, and quadratic equations. / 9.1 Solve one-step equations using
inverse operations.
9.2 Solve two-step equations using
inverse operations and explain the
meaning of the solution in context.
9.8 Solve linear equations, inequalities, quadratic equations and systems of linear equations related to real-world applications
9.9 Model real-world situations
using linear equations, systems of
equations and inequalities. / Toothpick Hexagons / substitution, formula
Reflections/
Feedback
Chapter 4:
Fitting a Line to Data
4.1 A Formula for Slope
4.2 Writing a Linear Equation to Fit Data
4.3 Point-Slope Form of a Linear Equation / CHAPTER 4
LT 7: Create and use tables, graphs, equations and formulas to describe relationships between variables. / CHAPTER 4
7.7 Find and describe slopes as constant rates of change.
7.11 Use formulas to calculate
slope and intercepts from a set of
ordered pairs
7.12 Write a linear equation to represent a pattern in which there is a constant rate of change between variables. / point – slope
Reflections/
Feedback
Chapter 4, continued
4.4 Equivalent Algebraic Equations
Assessment / LT 5: Compare, perform, explain and evaluate mathematical operations (+, -, *, /, exponents, roots) and properties on real numbers, emphasizing negative and positive numbers; ratios, proportions and percents; and exponents and roots in mathematical and real-world applications.
LT 9: Solve mathematical
and real-world applications
represented by linear and systems of equations, linear inequalities and quadratic equations. / 5.7 Identify the properties of real numbers.
5.8 Use the order of operations to evaluate and simplify expressions.
5.9 Simplify expressions using the commutative, associative, and distributive properties.
9.2 Solve two-step equations using inverse operations and explain the meaning of the solution in context.
9.3 Solve multi-step equations using inverse operations and explain the meaning of the solution in context.
Reflections/
Feedback
Chapter 4, continued
4.5 Writing Point-Slope Equations to Fit Data
4.6 More on Modeling
4.7 Applications of Modeling
Assessment / LT 3: Use data in a variety of formats to summarize, predict, and analyze real-world applications.
LT 7: Create and use tables, graphs, equations and formulas to describe relationships between variables. / 3.9 Use the line of best fit to make predictions from data on a graph.
7.5 Interpret the meaning of tables,
graphs and equations using data
from real-world applications.
7.9 Write an equation from tables
and graphs using real-world data.
7.11 Use formulas to calculate
slope and intercepts from a set of
ordered pairs
7.12 Write a linear equation to
represent a pattern in which there
is a constant rate of change
between variables.
Reflections/
Feedback
Chapter 4, continued
4.8 Activity Day: Data Collection and Modeling (OPTIONAL)
Review
Assessment
Chapter 5,
Systems of Equations and Inequalities
5.1 Solving Systems of Equations / CHAPTER 5
LT 7: Create and use tables, graphs, equations and formulas to describe relationships between variables.
LT 9: Solve mathematical and real-world applications represented by linear and systems of equations, linear inequalities and quadratic equations.
LT 10: Evaluate
information, analyze
patterns, identify
relationships, and represent
them using algebraic
expressions, functions, and
equations, e.g., linear,
exponential and quadratic,
recognizing that a family of
functions can model a
variety of real-world
applications. / CHAPTER 5
7.2 Create graphs, including real-
world data, using equations and
tables.
9.6 Solve a system of linear equations and explain the meaning of the solution in context (methods: graphs, table, substitution, elimination, or matrices).
10.5 Identify and interpret the intersection of a system. / systems of equations
Reflections/
Feedback
Chapter 5, continued
5.2 Solving Systems of Equations Using Substitution
5.3 Solving Systems of Equations Using Elimination
Assessment / LT 7: Create and use tables, graphs, equations and formulas to describe relationships between variables.
LT 9: Solve mathematical and real-world applications represented by linear and systems of equations, linear inequalities and quadratic equations. / 7.5 Interpret the meaning of tables,
graphs and equations using data
from real-world applications.
9.6 Solve a system of linear
equations and explain the meaning
of the solution in context
(methods: graphs, table,
substitution, elimination, or
matrices).
9.9 Model real-world situations
with linear equations, systems
of equations, and inequalities.
Reflections/
Feedback
Chapter 5, continued
5.4 Solving Systems of Equations Using Matrices
Assessment
5.5 Inequalities in One Variable / LT 9: Solve mathematical and real-world applications represented by linear and systems of equations, linear inequalities and quadratic equations. / 9.4 Solve linear inequalities in one
or two variables and graph the
results.
9.6 Solve a system of linear
equations and explain the meaning
of the solution in context
(methods: graphs, table,
substitution, elimination, or
matrices).
9.8 Solve linear equations, inequalities, quadratic equations
and systems of linear equations related to real-world applications / Umbrella Problem / inequality
Reflections/
Feedback
Chapter 5, continued
5.6 Graphing Inequalities in Two Variables
5.7 Systems of Inequalities ( optional)
Review
Assessment / LT 9: Solve mathematical and real-world applications represented by linear and systems of equations, linear inequalities and quadratic equations.
LT 10: Evaluate
information, analyze
patterns, identify
relationships, and represent
them using algebraic
expressions, functions, and
equations, e.g., linear,
exponential and quadratic,
recognizing that a family of
functions can model a
variety of real-world
applications. / 9.4 Solve linear inequalities in one or two variables and graph the results.
10.2 Identify the characteristics of an inequality graph.
Reflection and Feedback
[End of First Semester] / Exam Review and Exams / CHAPTERS 0-5
Learning Targets:
Semester One (to be
assessed)
LTs: 2, 3, 5, 7, 9
LT1: Process should be
incorporated in
constructed response type
items.
Vocabulary: - MPS
Academic Vocabulary for
Math covered in this
semester should be assessed
Reflection
and
Feedback:
Semester One
Developed by the Milwaukee Mathematics Partnership with support by the National Science Foundation under Grant No. 0314898.
Draft 08/25/08