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Grade 6 Mathematics Module 4, Topic B: Special Notations of Operations

  Classroom Resource Information  

Title:

 Grade 6 Mathematics Module 4, Topic B: Special Notations of Operations

URL:

 https://www.engageny.org/resource/grade-6-mathematics-module-4-topic-b-overview

Content Source:

 EngageNY
Type: Lesson/Unit Plan

Overview:

In Module 4, Topic B, students experience special notations of operations. They determine that 3x = x + x + x is not the same as x3, which is x times x times x.  Applying their prior knowledge from Grade 5, where whole-number exponents were used to express powers of ten (5.NBT.A.2), students examine exponents and carry out the order of operations, including exponents. Students demonstrate the meaning of exponents to write and evaluate numerical expressions with whole-number exponents (6.EE.A.1).

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 6
14. Write, evaluate, and compare expressions involving whole number exponents.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Write whole numbers with indicated exponents and their equivalent form without exponents, and justify the equivalence.
Teacher Vocabulary:
  • Numerical expression
  • Exponent
Knowledge:
Students know:
  • Conventions of exponential notation.
  • Factorization strategies for whole numbers.
Skills:
Students are able to:
  • Use factorization strategies to write equivalent expressions involving exponents.
  • Accurately find products for repeated multiplication of the same factor in evaluating exponential expressions.
Understanding:
Students understand that:
  • The use of exponents is an efficient way to write numbers as repeated multiplication of the same factor and this form reveals features of the number that may not be apparent in multiplied out form, (showing the prime factorization of two numbers with exponents helps determine how many of each factor).
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.6.14.1: Define exponent, numerical expression, algebraic expression, variable, base, power, square of a number, and cube of a number.
M.6.14.2: Compute a numerical expression with exponents, with or without a calculator.
M.6.14.3: Restate exponential numbers as repeated multiplication.
M.6.14.4: Choose the correct value to replace each variable in the expression (Substitution).
M.6.14.5: Calculate the multiplication of single or multi-digit whole numbers, with or without a calculator.

Prior Knowledge Skills:
  • Product, power of 10.
  • Recognize decimal place value using visual representations.
  • Recall multiplication and division facts of 10.
  • Skip count forward and backward by 10.
  • Recognize decimals as parts of a whole.
  • Compare whole numbers.
  • Read whole numbers.
  • Write whole numbers in words and expanded form.
  • Define expanded notation and standard form.
  • Convert a number written in expanded to standard form.
  • Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
  • Recall basic multiplication facts.
  • Recall basic addition, subtraction, multiplication, and division facts.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.6.14 Match an algebraic expression with one variable to its real-world situation.

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).
Tags: algebra, evaluate, exponents, expressions, formula, operations, wholenumber
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Author: Hannah Bradley
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