ALEX Classroom Resource

  

Equivalent Expressions Using Exponents

  Classroom Resource Information  

Title:

 Equivalent Expressions Using Exponents

URL:

 https://aptv.pbslearningmedia.org/resource/mgbh-math-ee-8exp/equivalent-expressions-using-exponents/

Content Source:

 PBS
Type: Interactive/Game

Overview:

Apply your critical thinking skills to learn about multiplication and division of exponents. This interactive exercise focuses on positive and negative exponents and combining exponents in an effort to get you to recognize patterns and determine a rule.

This resource is part of the Math at the Core: Middle School collection.

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 6
15. Write, read, and evaluate expressions in which letters represent numbers in real-world contexts.

a. Interpret a variable as an unknown value for any number in a specified set, depending on the context.

b. Write expressions to represent verbal statements and real-world scenarios.

c. Identify parts of an expression using mathematical terms such as sum, term, product, factor, quotient, and coefficient.

d. Evaluate expressions (which may include absolute value and whole number exponents) with respect to order of operations.
Unpacked Content
Evidence Of Student Attainment:
Students:
Given contextual or mathematical problems both when known models exist (for example formulas) or algebraic models are unknown,
  • Interpret the parts of the model in the original context.
  • Create the algebraic model of the situation when appropriate.
  • Use appropriate mathematical terminology to communicate the meaning of the expression.
  • Evaluate the expressions for values of the variable including finding values following conventions of parentheses and order of operations.
Teacher Vocabulary:
  • Expressions
  • Term
  • Coefficient
  • Sum
  • Product
  • Factor
  • Quotient
  • Variable
  • Constant
  • Difference
  • Evaluate
  • Order of Operations
  • Exponent
  • Absolute Value
Knowledge:
Students know:
  • Correct usage of mathematical symbolism to model the terms sum, term, product, factor, quotient, variable, difference, constant, and coefficient when they appear in verbally stated contexts.
  • Conventions for order of operations.
  • Convention of using juxtaposition (5A or xy) to indicate multiplication.
Skills:
Students are able to:
  • Translate fluently between verbally stated situations and algebraic models of the situation.
  • Use operations (addition, subtraction, multiplication, division, and exponentiation) fluently with the conventions of parentheses and order of operations to evaluate expressions for specific values of variables in expressions.
  • Use terminology related to algebraic expressions such as sum, term, product, factor, quotient, or coefficient, to communicate the meanings of the expression and the parts of the expression.
Understanding:
Students understand that:
  • The structure of mathematics allows for terminology and techniques used with numerical expressions to be used in an analogous way with algebraic expressions, (the sum of 3 and 4 is written as 3 + 4, so the sum of 3 and y is written as 3 + y).
  • When language is ambiguous about the meaning of a mathematical expression grouping, symbols and order of operations conventions are used to communicate the meaning clearly.
  • Moving fluently among representations of mathematical situations (words, numbers, symbols, etc.), as needed for a given situation, allows a user of mathematics to make sense of the situation and choose appropriate and efficient paths to solutions.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.6.15.1: Define algebraic expression and variable.
M.6.15.2: Convert mathematical terms to mathematical symbols and numbers.
M.6.15.3: Translate verbal and numerical expression using all operations.
M.6.15.4: Define coefficient, constant and term.
M.6.15.5: Match mathematical terms with correct mathematical symbols.
M.6.15.6: Convert mathematical terms to mathematical symbols and numbers.
M.6.15.7: Calculate an expression in the correct order. with or without a calculator (Ex. exponents, mult./div. from left to right, and add/sub. from left to right).
M.6.15.8: Choose the correct value to replace each variable in the algebraic expression (Substitution).
M.6.15.9: Calculate a numerical expression, with or without a calculator (Ex. V=4x4x4).
M.6.15.10: Recognize the correct order to solve expressions with more than one operation.

Prior Knowledge Skills:
  • Recognize key terms to solve word problems.
    Examples: times, every, at this rate, each, per, equal/equally, in all, total.
  • Recognize key terms to solve word problems.
    Examples: times, every, at this rate, each, per, equal/equally, in all, total.
  • Define simple expression.
  • Recall simple equations.
  • Recognize properties of addition and multiplication.
  • Recall addition, subtraction, multiplication, division symbols.
  • Define parentheses, braces, and brackets.
  • Define numerical expression.
  • Recognize expressions.
  • Apply properties of operations as strategies to add and subtract.
  • Recall properties of operations as strategies to add and subtract.
  • Represent addition and subtraction with objects, mental images, drawings, expressions, or equations.
  • Use addition, subtraction, multiplication and division to solve one- and two-step word problems.
  • Recognize key terms to solve word problems.
  • Apply properties of operations as strategies to multiply and divide.
  • Apply the area and perimeter formulas for rectangles in real-world and mathematical problems.
  • Recall the formula for area (L × W).
  • Recognize that unit squares are equal.
  • Recall the formula for perimeter (P= L+L+W+W or P=2L + 2W).
  • Recall basic addition and multiplication facts.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.6.15 Evaluate algebraic expressions when given specific values for the variables (e.g. x + 2, where x = 4).
Mathematics
MA2019 (2019)
Grade: 7
Accelerated
14. Develop and apply properties of integer exponents to generate equivalent numerical and algebraic expressions. [Grade 8, 3]
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Use their understanding of exponents as repeated multiplication to create equivalent expressions and justify integer exponent properties.
Teacher Vocabulary:
  • Integer Exponent
Knowledge:
Students know:
  • That whole number exponents indicate repeated multiplication of the base number and that these exponents indicate the actual number of factors being produced.
Skills:
Students are able to:
  • Develop integer exponent operations in order to generate equivalent expressions through addition, multiplication, division and raising a power by another power with expressions containing integer exponents.
Understanding:
Students understand that:
  • Just as whole number exponents represent repeated multiplication, negative integer exponents represent repeated division by the base number.
  • The exponent can be translated (visually. i.e. listing out the factors) to represent the exact number of factors being repeated so that the use of integer exponent operations ("rules") can be proven/make sense.
Diverse Learning Needs:
Mathematics
MA2019 (2019)
Grade: 8
3. Develop and apply properties of integer exponents to generate equivalent numerical and algebraic expressions.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Use their understanding of exponents as repeated multiplication to create equivalent expressions and justify integer exponent properties.
Teacher Vocabulary:
  • Integer Exponent
Knowledge:
Students know:
  • that whole number exponents indicate repeated multiplication of the base number and that these exponents indicate the actual number of factors being produced.
Skills:
Students are able to:
  • Develop integer exponent operations in order to generate equivalent expressions through addition, multiplication, division and raising a power by another power with expressions containing integer exponents.
Understanding:
Students understand that:
  • just as whole number exponents represent repeated multiplication, negative integer exponents represent repeated division by the base number.
  • The exponent can be translated (visually, listing out the factors) to represent the exact number of factors being repeated so that the use of integer exponent operations ("rules") can be proven/make sense.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.8.3.1: Define exponent, power, coefficient, integers, equivalent, and numerical expression.
M.8.3.2: Restate negative exponents as positive exponents in the form 1/x2 .
M.8.3.3: Restate zero exponents as 1 (x0 = 1).
M.8.3.4: Recognize to add exponents when multiplying terms with like bases (Property of product of powers).
M.8.3.5: Recognize to subtract exponents when dividing terms with like bases (Property of quotient of powers).
M.8.3.6: Compute a numerical expression with positive exponents.
M.8.3.7: Restate exponential numbers as repeated multiplication.
M.8.3.8: Compute problems with adding and subtracting integers.

Prior Knowledge Skills:
  • Define exponent, numerical expression, algebraic expression, variable, base, power, square of a number, and cube of a number.
  • Compute a numerical expression with exponents, with or without a calculator.
  • Restate exponential numbers as repeated multiplication.
  • Choose the correct value to replace each variable in the expression (Substitution).
  • Calculate the multiplication of single or multi-digit whole numbers, with or without a calculator.
  • Define integers, positive and negative numbers.
  • Demonstrate the location of positive and negative numbers on a vertical and horizontal number line.
  • Give examples of positive and negative numbers to represent quantities having opposite directions in real-world contexts.
  • Discuss the measure of centering of 0 in relationship to positive and negative numbers.
  • Discover that the opposite of the opposite of a number is the number itself.
  • Show on a number line that numbers that are equal distance from 0 and on opposite sides of 0 have opposite signs.
Mathematics
MA2019 (2019)
Grade: 8
Accelerated
2. Rewrite expressions involving radicals and rational exponents using the properties of exponents. [Algebra I with Probability, 2]
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Convert from radical representation to using rational exponents and vise versa.
Teacher Vocabulary:
  • Radical
  • Rational exponent
  • Expression
Knowledge:
Students know:
  • the denominator of the rational exponent is the root index and the numerator is the exponent of the radicand. For example, 51/2=5 and 163/2=(161/2)3= (16)3=43=64.
  • The root index of the radical is the denominator of the rational exponent and the exponent of the radicand is the numerator of the rational exponent. For example, 4103= 103/4.
Skills:
Students are able to:
  • Rewrite expressions from radical representations to rational exponents and vice versa.
Understanding:
Students understand:
  • The meaning of rational exponents and how to convert between them and radical representations.
Diverse Learning Needs:
Mathematics
MA2019 (2019)
Grade: 9-12
Algebra I with Probability
1. Explain how the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for an additional notation for radicals using rational exponents.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Explain how the meaning of rational exponents follows from extending the properties of integer exponents.
  • Use rational exponent notation to represent radicals.
Teacher Vocabulary:
  • Exponent
  • Root
  • Rational Exponent
  • Radical -nth root
  • Rational exponent
Knowledge:
Students know:
  • Techniques for applying the properties of exponents.
Skills:
Students are able to:
  • Correctly perform the manipulations of rational exponents by analyzing and applying the properties of integer exponents.
  • Use mathematical reasoning and prior knowledge of integer exponents rules to develop rational exponent notation for radicals.
Understanding:
Students understand that:
  • The properties of exponents apply to rational exponents as well as integer exponents.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
ALGI. 1.1: Define exponent, integer, rational number, and radicals.
ALGI. 1.2: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values.
ALGI. 1.3: Use notation for radicals in terms of rational exponents.
ALGI. 1.4: Apply the properties of integer exponents to generate equivalent numerical expressions.
ALGI. 1.5: Know the properties of integer exponents.
ALGI. 1.6: Write numerical expressions involving whole-number exponents.
ALGI. 1.7: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used.

Prior Knowledge Skills:
  • Demonstrate difference of scientific notation symbol between paper and calculator.
  • Discuss the real-world application of scientific notation (very large or very small quantities).
  • Recall properties of exponents.
  • Recall how to write numbers in scientific notation.
  • Demonstrate that when dividing powers of like bases; subtract the exponents (Property of quotient of powers).
  • Restate exponential numbers as repeated multiplication.
  • Define exponent, integer, rational number, and radical.
Alabama Alternate Achievement Standards
AAS Standard:
M.A.AAS.11.1 Determine the value of a quantity that is squared or cubed (limited to perfect squares and perfect cubes).

Mathematics
MA2019 (2019)
Grade: 9-12
Algebra I with Probability
2. Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Given expressions involving radicals and rational exponents, use reasoning and properties of exponents to demonstrate that various forms of radicals and roots actually represent the same quantity,
Teacher Vocabulary:
  • Rational exponent
  • Power of a power
  • Product of a power
  • Power of a product
  • Zero exponent
  • Negative exponent
  • Quotient of a power
Knowledge:
Students know:
  • Properties of exponents.
  • The meaning of algebraic symbols such as radicals and rational exponents.
Skills:
Students are able to:
  • Use mathematical reasoning to justify the equality of various forms of radical expressions.
  • Correctly perform the manipulations of exponents which apply properties of exponents.
Understanding:
Students understand that:
  • The properties of exponents are true regardless of the type of numbers being used.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
ALGI. 2.1: Rewrite expressions involving radicals using the properties of exponents.
ALGI. 2.2: Rewrite expressions involving rational exponents using the properties of exponents.
ALGI. 2.3: Recognize the properties of exponents.

Prior Knowledge Skills:
  • Compute problems with adding and subtracting integers.
  • Restate exponential numbers as repeated multiplication.
  • Compute a numerical expression with positive exponents.
  • Recognize to subtract exponents when dividing terms with like bases (Property of quotient of powers).
  • Recognize to add exponents when multiplying terms with like bases (Property of product of powers).
  • Restate zero exponents as 1 (Xo = 1).
  • Restate negative exponents as positive exponents in the form 1/xy .
  • Define exponent, power, coefficient, integers, equivalent, and numerical expression.
  • Identify perfect squares and square roots.
  • Recall how to compare numbers.
  • Identify properties of exponents.
  • Define square root, expressions, and approximations.
  • Identify and give examples of rational numbers.
  • Recognize the mathematical operations of rational numbers in any form, including converting between forms. (Ex. 0.25=1/4 =25%).
  • Define rational numbers.
  • Restate exponential numbers as repeated multiplication.
  • Define exponent.
Alabama Alternate Achievement Standards
AAS Standard:
M.A.AAS.11.1 Determine the value of a quantity that is squared or cubed (limited to perfect squares and perfect cubes).

Tags: division of exponents, exponent properties, multiplication of exponents, positive and negative exponents
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Comments

This resource contains multiplying exponents worksheets.

  This resource provided by:  
Author: Kristy Lacks
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