Download MS 104

MS 104
Unit Plan 4
Unit Name:
Say it with Symbols
Essential
Question:
How can we
represent and
simplify
expressions and
equations in
multiple ways?
Grade: 8
Duration: 4 weeks
Big Ideas/Enduring Understandings:
 Algebraic equations and expressions can be used to solve problems.
 Equivalence is useful when solving equations and problems. Equivalent
expressions can be generated using properties of operations. Examining
equivalent forms of an expression can reveal new information about the context
of a problem.
 Equivalent expressions can be used to develop and relate formulas for geometric
shapes including volumes of cones, spheres, and cylinders.
 Equations can have one solution, no solution, or an infinite number of solutions
which can be identified by examining the equation or its graph.
 The underlying pattern of change in a relationship or function can be represented
by a symbolic representation or equation. Different types of functions, such as
linear, inverse, exponential, or quadratic, have specific characteristics in their
symbolic representations.
Common Core Learning Standards:
8.EE.C.7: Solve linear equations in one variable.
8.F.A.3: Interpret the equation y = mx + b as defining a linear function, whose graph is a straight
line; give examples of functions that are not linear.
8.F.B.4: Construct a function to model a linear relationship between two quantities. Determine
the rate of change and initial value of the function from a description of a relationship or from
two (x, y) values, including reading these from a table or from a graph. Interpret the rate of
change and the initial value of a linear function in terms of the situation it models, and in terms
of its graph or a table of values.
8.F.B.5: Describe qualitatively the functional relationship between two quantities by analyzing
a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a
graph that exhibits the qualitative features of a function that has been described verbally.
8.G.C.9: Know the formulas for the volumes of cones, cylinders, and spheres and use them to
solve real-world and mathematical problems.
Student Objectives:
EQUIVALENCE
 Develop understanding of equivalent expressions and equations.
 Model situations with symbolic statements
 Recognize when two or more symbolic statements represent the same context
 Use the properties of real numbers, such as the Distributive Property, to write equivalent expressions
 Determine if different symbolic expressions are mathematically equivalent
 Interpret the information that equivalent expressions represent in a given context
 Determine the equivalent expression or equation that is most helpful in answering a particular
question about a relationship
 Use algebraic equations to describe the relationship among the volumes of cylinders, cones and
spheres that have the same height and radius
 Solve linear equations involving parentheses
 Determine if a linear equation has a finite number of solutions, an infinite number of solutions, or no
solution
 Recognize how and when to use symbols, rather than tables or graphs, to display relationships,
generalizations, and proofs
FUNCTIONS
 Develop an understanding of specific functions such as linear, and exponential functions.
 Develop proficiency in identifying and representing relationships expressed in problem contexts with
appropriate functions and use these relationships to solve the problem
 Analyze equations to determine the patterns of change in the tables and graphs that the equations
represent
 Relate parts of a symbolic statement or expression to the underlying properties of the relationship they
represent and to the context of the problem
REGENTS Activities/Tasks
Investigation 1: Creating Expressions
1.1 Area expressions, including review of the distributive property
Investigation 2: Combining Expressions
2.1 and 2.2: Substituting terms and expressions, then simplifying
2.3 Volumes of cylinders, cones and spheres
2.4 Solving volume problems
Investigation 3: Solving Equations
3.1 Solve Complex Equations with like terms and distributive property, including equations that have one,
none, or infinitely many solutions
3.2 Inequalities
3.3 Quadratics: find roots, vertex, axis of symmetry, y-intercept, complete the square, use the quadratic
formula, factor and FOIL, include sum and difference of squares
Investigation 4: Looking Back at Functions
4.1 Looking for patterns of change
4.2 Using equations
4.3 Linear, exponential, quadratic
4.4 modeling with functions
Include piece-wise, step, and absolute value functions and graphs
Investigation 5: Reasoning With Symbols
5.1 Using algebra to solve a puzzle
5.2 Odd and even revisited
5.3 Squaring odd numbers
8th Grade Activities/Tasks
Investigation 1: Creating Expressions
1.1 Area expressions, including review of the distributive property
Investigation 2: Combining Expressions
2.3 Volumes of cylinders, cones and spheres
2.4 Solving volume problems
Investigation 3: Solving Equations
3.1 Solve Complex Equations with like terms and distributive property
Investigation 4: Looking Back at Functions
4.1 Looking for patterns of change
4.2 Using equations
4.3 Linear, exponential, quadratic
4.4 modeling with functions
Investigation 5: Reasoning With Symbols
5.1 Using algebra to solve a puzzle
5.2 Odd and even revisited
5.3 Squaring odd numbers
Benchmark 4: Performance Task 2: T-Shirt Sale
Key Terms/Vocabulary:
Break-even point, Distributive Property, Like Terms, Functions, Domain, Range
Resources:
CMP3: Say it with Symbols
Glencoe Math
Common Core Mathematics
Big Ideas Math