Elementary
Algebra
Course Map
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*Last updated on February
22, 2005
Month |
Core Standard |
Learning
Activity |
Assessment |
August- September |
1.2.1-Compare and find approximate
locations of rational numbers on a number line 1.1.3,
1.3.2, 1.3.3-Apply
properties and operations in simplifying rational numeric decimal, fraction,
percent, and exponential expressions including integer exponents 1.3.3-Use physical models and
calculators to review perfect squares and square roots, including variable
expressions 1.3.1, 1.3.2-Introduce rational
numbers using physical models, number lines, and patterns to develop a sense
of “betweenness.” Classify numbers as rational or irrational. 2.1.1-Write Algebra
expressions to model and generalize visual patterns, manipulative patterns,
numeric patterns, and data sets.
A. 1.1.1, 1.1.2, 1.1.3-Extrapolate values using these algebraic
expressions
B. 1.2.2, 1.3.2-Simplify algebraic expressions using properties 2.2.7-Simplify simple
algebraic exponential expressions including those with integer exponents |
Problem
Solving:
Use appropriate methods for computing, make a model, draw a diagram or
picture, eliminate possibilities, estimate solutions to determine
reasonableness, find a pattern. Reasoning/Proof: Examine various
patterns, make conjectures, draw reasonable conclusions. Communication: Use precise
language and notation, organize and consolidate mathematical thinking,
clearly express ideas verbally and in writing, group discussion. Connections: Establish
connections between physical models, diagrams and symbols, formulate
real-world applications. Representation: Represent
verbally, numerically, algebraically, use technological representations. |
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October |
2.1.1-Use a variety of real-world or student-created
data sets to write one variable equations 2.2.2-solve multi-step one variable equations
including algebraic first degree proportions and absolute value equations
using: a) guess and check, b) manipulatives, c)
technology, d) algebraically. 2.1.1-Represent real world situations using
inequalities. 2.2.2-Solve multi-step one variable inequalities and
graph solutions on a number line. 2.1.2, 2.3.4, 4.1.3, 5.1.1-Write Algebraic
equations to represent and generalize linear relations derived from
manipulatives, geometric, and other visual models and data sets. Find
appropriate domain and range. |
Problem Solving: Use manipulatives, guess and check, solve a simpler problem,
choose appropriate operation, work backwards, use proportional reasoning,
choose appropriate operations, make a model or simulation. Reasoning/Proof: Explain and justify problem solving procedures, link problem
solving to the sequence of steps, draw reasonable conclusions. Communication: Employ precise language to justify reasoning, express ideas
clearly. Connections: Formulate real-world situations, make a connection between
models and mathematical expressions and procedures. Representations: Use physical models and appropriate symbolic notations,
represent verbally, numerically, and algebraically. |
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November |
2.2.2, 4.1.3-Solve real world problems involving constant
rates of change 2.1.4, 4.1.1, 4.1.3-Review slope as a
rate of change using A. 4.1.2-real world problems
including manipulatives B. Technology C. 2.3.11, 4.1.2-Direct
variation D. 3.2.3, 4.1.2-Measurement and
geometric ratios 2.3.1-Identify the slope of a line when given A. A set of two ordered pairs B. A table of values C. The graph of a linear function D. The equation of a linear function 2.3.3-Identify horizontal and vertical lines from
given equations 2.3.10, 4.1.3-Determine and explain the
meaning of intercepts using real world examples |
Problem Solving: Use manipulatives, use proportional reasoning, make a model or
simulation, estimate to determine reasonableness, solve a simpler problem,
ask questions like “where have we seen this before?”, “why do you think so?”,
eliminate possibilities. Reasoning/Proof: Examine patterns, draw reasonable conclusions, make and
investigate conjectures, note regularities and irregularities Connections: Use extended real world investigations, connect mathematical
expressions and technological and physical models to other curricular areas
and outside classroom. Communication: Clearly express mathematically ideas verbally and in writing,
group discussion. Representations: Use technological representations, represent numerical,
graphically, and algebraically with the correct symbolic notation. |
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December |
2.3.7-Determine X- and Y-intercepts A. From a graph B. From an equation 2.3.8-Graph linear functions using X- and Y-intercepts 2.1.2-Represent equations in slope-intercept form 2.3.8-Graph linear equations by A. 2.3.8, 5.1.1-Generating a
table of values and plotting points B. Using slope-intercept form of an
equation C. Using slope and any point on the
line 2.3.6-Explore how changing the value of m and b
affects the graphs of linear relations |
Problem Solving: Reflect and evaluate mathematical thinking processes, make a
model or simulation, tables, graphs, develop clarification, determine
reasonableness of an answer. Reasoning/Proof: Look at patterns and make conjectures, link problem solving to
the steps. Connections: Explore historical and multicultural contributions, establish
connection among mathematical expressions, models, pictorial, and real world
situations Communication: Class and group discussions, use precise language and notation. Representations: Represent verbally, numerically, graphically, and algebraically
use a variety of visual representations, graph paper, and technology. |
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January |
2.3.4-Identify the domain and range from a graph,
equation, table, and set of ordered pairs and discuss appropriate domain and
range for data 2.3.2-Write the equation of a line when given A. The graph of a line B. The slope and a point on the line C. A set of ordered pairs 2.1.2-Represent linear equations in standard form 5.1.3-Interpret the correlation between two variables
as being positive, negative, or having no correlation 5.1.4-Explore the line of best fit A. 4.1.3-Find the line of best
fit by estimation, choosing two points, and using technology for given sets
of data B. 5.1.5-Analyze the meaning of
the slope and Y-intercept of a line of best fit as it relates to the data C. 5.1.6-Make predictions based
on the line |
Problem Solving: Solve a related problem; look for a pattern; develop vocabulary; make
a list, table, graph or equation; reflect and evaluate mathematical thinking
processes. Reasoning/Proof: Note regularities and irregularities of patterns, explain and
justify. Connections: Use real-world situations and connect to other curricular
areas. Communication: Organize and consolidate mathematical thinking. Representations: Represent problem situations verbally, numerically,
graphically, or algebraically using technology and appropriate symbolic
notation. |
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February |
2.2.6-Solve common linear formulas and literal
equations for a specified variable 2.3.9-Graph linear inequalities and identify the
boundary line and solution area 3.2.3, 5.1.1-Collect, record, organize, and display various
sets of linear and nonlinear data including pi 5.1.2-Determine if the patter of the data is linear or
nonlinear when given in a list, table, and graph 3.2.1, 4.1.1-Find the approximate midpoint by measuring 3.2.1-Find the coordinates of a midpoint given two
points 2.2.5, 3.3.1, 4.1.1, 4.1.3-Explore the
Pythagorean Theorem and solve problems using the Theorem |
Problem Solving: “How are these related?” Look for a pattern; make a list,
table, graph or equation. Reasoning/Proof: Examine patterns; make and investigate mathematical conjectures
examining slope; justify eliminating possibilities. Connections: Find applications in other sources. Communication: Class discussion; use precise language and rotation in verbal
and written explanations. Representations: Represent problem situations verbally and in writing; express
numerically, graphically, and algebraically using technology. |
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March |
2.2.5, 3.2.1-Find the distance between two points. 3.2.2, 4.1.1-Solve problems using the distance formula. 1.3.3-Simplify irrational numeric expressions. 1.3.2-Apply properties and operations in simplifying
irrational expressions. 3.3.2, 2.2.5-Solve systems of two linear equations A. Graphically, estimate solutions to
determine reasonableness. B. Technology, estimating solutions. C. 2.2.5-Numerically from a
table and guess and check D. Algebraically, computing solutions |
Problem Solving: Check reasonableness of answer; reflect and
evaluate mathematical thinking processes. Consider thinking strategies
of others; use a model or simulation; make a list, tables, graphs, and
evaluations. How is this related to ideas before? Reasoning/Proof: Justify sequence of steps, realize that extrapolating isn’t
proof. Connections: Use real world situations. Communication: Group discussions, oral presentations, written reports. Representations: Represent verbally, numerically, graphically, geometrically,
and algebraically using technology, formulate conjectures, use physical
models, visualizations, and appropriate symbolic notations. |
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April |
2.2.3-Solve systems of two inequalities A. Graphically, estimate solutions to
determine reasonableness B. Technology, estimating solutions C. 2.2.5-Numerically from a
table and guess and check D. Algebraically, computing solutions 3.3.3, 4.4.1-Illustrate multiplication of polynomials using
area models 3.3.4-Use area models to factor polynomials A. Identify the greatest common
monomial factor B. Find factors of the form _{}when _{} 5.1.2-Determine and express the probability of an
event as a fraction, percent, ration, and decimal. 5.2.2-Identify the probability of an event as being
between 0 and 1 5.2.3-Recognize the sum of probability of an event and
its complement is equal to 1 |
Problem Solving: Use proportional reasoning; look for patterns; make a model or
simulations; make a list, table, graph, or equation; consider thinking
strategies of others, multi-step problems, estimate to determine
reasonableness, use counter examples. Reasoning/Proof: Make conjectures, identify conclusions as valid or invalid,
justify sequence of steps. Connections: Use physical models, pictorial representations and real world
situations, connect models to mathematical expressions. Communication: Use precise language and notation, written and group
discussion. Representations: Represent verbally, numerically, graphically, geometrically,
and algebraically, use a variety of visual representations. |
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May- June |
5.2.4-Determine if a game or process is fair. Review for CRT |
Problem Solving: Reflect and evaluate mathematical thinking processes, draw a
picture or diagram, use a model or simulation, choose an appropriate
operation, estimate solutions, consider the thinking of others. Reasoning/Proof: Explain patterns, explain regularities and irregularities,
determine whether conclusions are valid or invalid, make and investigate
conjectures. Connections: Use real world investigations, recognize and apply mathematical
ideas and relationships in other curricular areas. Communication: Organize and consolidate mathematical thinking, group
discussion, oral written reports using appropriate notation. Representations: Represent problem situations verbally, numerically,
geometrically, or algebraically using technology; use visual representations;
use correct notation. |
Daily feedback on Daily assignments, homework, quizzes (30%) Unit tests (70% of grade) |