ALEX Classroom Resource

  

Grade 6 Mathematics Module 4, Topic F: Writing and Evaluating Expressions and Formulas

  Classroom Resource Information  

Title:

 Grade 6 Mathematics Module 4, Topic F: Writing and Evaluating Expressions and Formulas

URL:

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

Content Source:

 EngageNY
Type: Lesson/Unit Plan

Overview:

Students write and evaluate expressions and formulas in Module 4, Topic F. They use variables to write expressions and evaluate those expressions when given the value of the variable (6.EE.A.2). From there, students create formulas by setting expressions equal to another variable. For example, if there are 4 bags containing c colored cubes in each bag with 3 additional cubes, students use this information to express the total number of cubes as 4c + 3.  From this expression, students develop the formula t = 4c + 3, where t is the total number of cubes. Once provided with a value for the amount of cubes in each bag (c = 12 cubes), students can evaluate the formula for t:  t = 4(12) = 3, t = 48 + 3, t = 51. Students continue to evaluate given formulas such as the volume of a cube, V = s3 given the side length, or the volume of a rectangular prism, V = lwh given those dimensions (6.EE.A.2c).

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: 6
18. Determine whether a value is a solution to an equation or inequality by using substitution to conclude whether a given value makes the equation or inequality true.
Unpacked Content
Evidence Of Student Attainment:
Students:
Given situations that have been modeled with equations or inequalities:
  • Substitute given specified values for the variables and the evaluate expressions.
  • Determine if the resulting numerical sentence is true when the specified values are substituted for the variables.
  • Explain with mathematical reasoning why a specified value is or is not a solution to a given equation or inequality.
Teacher Vocabulary:
  • Substitution
  • Equation
  • Inequality
Knowledge:
Students know:
  • Conventions of order of operations.
  • The solution is the value of the variable that will make the equation or inequality true.
  • That using various processes to identify the value(s) that when substituted for the variable will make the equation true.
Skills:
Students are able to:
  • Substitute specific values into algebraic equation or inequality and accurately perform operations of addition, subtraction, multiplication, division and exponentiation using order of operation.
Understanding:
Students understand that:
  • Solving an equation or inequality means finding the value or values (if any) that make the mathematical sentence true.
  • The solution to an inequality is often a range of values rather than a specific value.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.6.18.1: Define exponent, numerical expression, algebraic expression, variable, base, power, square of a number, and cube of a number.
M.6.18.2: Compute a numerical expression with exponents, with or without a calculator.
M.6.18.3: Restate exponential numbers as repeated multiplication.
M.6.18.4: Choose the correct value to replace each variable in the expression (Substitution).
M.6.18.5: Calculate the multiplication of single or multi-digit whole numbers, with or without a calculator.

Prior Knowledge Skills:
  • Use comparison symbols.
    Examples: >, =, or < .
  • Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
  • Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits using >, =, and < symbols to record the results of comparisons.
  • Comparison symbols.
    Examples: >, =, and < .
  • Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits using >, =, and < symbols to record the results of comparisons.
  • Compare two fractions with the same numerator or the same denominator by reasoning about their size.
  • Recognize that comparisons are valid only when the two fractions refer to the same whole.
  • Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
  • Convert fractions to decimals.
  • Compare two decimals to tenths.
  • Compare whole numbers.
  • Identify comparison symbols.
    Examples: >, <, and = .
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.6.19 Match equations and inequalities to real-world situations.

Tags: algebra, evaluate, expressions, formula, inequality, substitution
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Author: Hannah Bradley
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