| 2.8 Use Algebraic Methods to Describe Patterns
and Functions |
2.8 Grade 3
(Algebra and Functions) |
2.8 Grade 5
(Algebra and Functions) |
2.8 Grade 8
(Algebra and Functions) |
2.8 Grade 11
(Algebra and Functions) |
| A. Equations |
A1. Use concrete objects and trial and error to solve number
sentences and check if solutions are sensible and accurate. |
A1. Use concrete objects and combinations of symbols and numbers
to create expressions that model mathematical situations. |
A1. Apply simple algebraic patterns to basic number theory and
to spatial relations. |
A1. Analyze a given set of data for the existence of a pattern
and represent the pattern algebraically and graphically. |
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A2. Substitute a missing addend in a number sentence. |
A2. Describe a realistic situation using information given in
equations, inequalities, tables, or graphs. |
A2. Discover, describe, and generalize patterns, including linear,
exponential, and simple quadratic relationships. |
A2. Give examples of patterns that occur in data from other
disciplines. |
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A3. Create a story to match a given combination of symbols and
numbers. |
A3. Select and use appropriate strategies, including concrete
materials, to solve number sentences and explain the method of solution. |
A3. Create and interpret expressions, equations, or inequalities
that model problem situations. |
A3. Formulate expressions, equations, inequalities, systems
of equations, systems of inequalities, and matrices to model routine and
non-routine problem situations. |
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A4. Use concrete objects and symbols to model the concepts of
variables, expressions, equations, and equalities. |
A4. Use the understanding that an equality relationship between
two quantities remains the same as long the same change is made to both
quantities. |
A4. Use concrete objects to model algebraic concepts. |
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A5. Select and use a strategy to solve an equation or inequality,
explain the solution and check the solution for accuracy. |
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| B. Patterns and functions |
B1. Recognize, describe, extend, create, and replicate a variety
of patterns including attribute, activity, number, and geometric patterns. |
B1. Recognize, reproduce, extend, create, and describe patterns,
sequences, and relationships verbally, numerically, symbolically, and graphically,
using a variety of materials. |
B1. Solve and graph equations and inequalities using scientific
and graphing calculators and computer spreadsheets. |
B1. Use equations to represent curves such as lines, circles,
ellipses, parabolas, and hyperbolas. |
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B2. Demonstrate simple function rules. |
B2. Connect patterns to geometric relations and basic number
skills. |
B2. Represent relationships with tables, graphs in the coordinate
plane, and verbal or symbolic rules. |
B2. Identify whether systems of equations and inequalities are
consistent or inconsistent. |
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B3. Analyze simple functions and relationships and locate points
on a simple grid. |
B3. Form rules based on patterns (e.g., an equation that relates
pairs in a sequence). |
B3. Graph a linear function from a rule or table. |
B3. Analyze and explain systems of equations, systems of inequalities,
and matrices. |
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B4. Explain the use of combinations of symbols and numbers in expressions,
equations, and inequalities. |
B4. Generate a table or graph from a function and use graphing
calculators and computer spreadsheets to graph and analyze functions. |
B4. Determine patterns generated as a result of an experiment. |
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B5. Generate functions from tables of data and relate data to
corresponding graphs and functions. |
B5. Show that an equality relationship between two quantities
remains the same as long as the same change is made to both quantities;
and explain how a change in one quantity determines another quantity in
functional relationship. |
B5. Use matrices to organize and manipulate data, including
matrix addition, subtraction, multiplication, and scalar multiplication. |
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B6. Determine patterns generated as a result of an experiment. |
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B6. Demonstrate the connection between algebraic equations and
inequalities and the geometry of relations in the coordinate plane. |
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B7. Select, justify, and apply an appropriate technique to graph
a linear function in two variables, including slope-intercept, x- and y-
intercepts, graphing by transformations, and the use of a graphing calculator. |
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B8. Write the equation of a line when given the graph of the
line, two points on the line, or the slope of the line and a point on the
line. |
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B9. Given a set of data points, write an equation for a line
of best fit. |
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B10. Solve linear, quadratic, and exponential, equations both
symbolically and graphically. |
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B11. Determine the domain and range of a relation, given a graph
or set of ordered pairs. |
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B12. Analyze a relation to determine whether a direct or inverse
variation exists and represent it algebraically and graphically. |
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B13. Represent functional relationships in tables, charts, and
graphs. |
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B14. Create and interpret functional models. |
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B15. Analyze properties and relationships of functions (linear,
polynomial, rational, trigonometric, exponential, and logarithmic). |
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B16. Analyze and categorize functions by their characteristics. |