ALEX Learning Activity

  

Burgers with a Side of Variables

A Learning Activity is a strategy a teacher chooses to actively engage students in learning a concept or skill using a digital tool/resource.

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  This learning activity provided by:  
Author: Samantha Wallace
System:Limestone County
School:Cedar Hill Elementary School
  General Activity Information  
Activity ID: 2446
Title:
Burgers with a Side of Variables
Digital Tool/Resource:
Fast Food Variables Slide
Web Address – URL:
Overview:

In this activity, students will be writing equations using variables that represent different food items.  They will develop the foundational understanding of variables being used as a symbol to represent a number.  They will also write expressions using variables and then evaluate the expressions at specific values for the variables.

This activity was created as a result of the ALEX Resource Development Summit.

  Associated Standards and Objectives  
Content Standard(s):
Mathematics
MA2015 (2016)
Grade: 6
17 ) Use variables to represent numbers, and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or, depending on the purpose at hand, any number in a specified set. [6-EE6]


NAEP Framework
NAEP Statement::
8A4a: Solve linear equations or inequalities (e.g., ax + b = c or ax + b = cx + d or ax + b > c).

NAEP Statement::
8A4b: Interpret "=" as an equivalence between two expressions and use this interpretation to solve problems.



Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.6.17- Match a phrase to the corresponding one- step one-variable expression (e.g., "a number plus 3" matches "x + 3").


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).


Learning Objectives:

Students will be able to use variables to represent numbers.

Students will be able to write expressions to solve real-world problems using variables.

Students will be able to evaluate expressions at specific values of their variables.

  Strategies, Preparations and Variations  
Phase:
Before/Engage
Activity:

Begin by explaining to the students that today they will be learning about how to use letters in math.  When we use a letter to represent a number in math, it is called a variable. If students are using math journals, they can write the word variable and define it.  Explain that it's more common to use lowercase letters for variables and that any letter can be used as a variable.

 

Display the slide with the food images.  Ask a student to pick two items she might want to order.  For example, the student might choose a burger and a hotdog.  Write a lowercase "b" under the burger and a lowercase "h" under the hotdog.  Write the expression "b + h" and explain that this expression represents what the student ordered.  Continue this procedure, allowing students to pick items and write the expressions using the appropriate variables.


Once students are comfortable with using the variables and writing expressions, explain that the students are going to see how we might apply this to the real world.  Assign each food item with a price and write the amounts under the pictures.  For example, under the burger, you should write "b = $3".  Continue asking students to pick food items, but now they need to find the total cost of the meal.  Model the first two examples and then allow the students to work independently.  Make sure to write the equations with the variables and then a separate equation with the substituted amounts.

Assessment Strategies:

Evaluate student understanding through questioning during the activity.  Observe to see if students are able to use variables to write an expression to represent the meal they've ordered and if they can solve the equations by substituting the correct values for the variables.  

 

At the end of the activity, you can place an order out loud for all of the students to solve independently as an exit ticket. For example, you might say, "I want to order 2 burgers, a hotdog, and a taco."  The students should write "b+b+h+t" and calculate the total price of the meal.


Advanced Preparation:

You will need a projector and board to display the slide.  To label the items and write the expressions, you can use a board with the appropriate technology or chart paper taped to the board.  You can also enlarge the images and then print and tape them to a dry erase board.

Variation Tips (optional):
 
Notes or Recommendations (optional):
 
  Keywords and Search Tags  
Keywords and Search Tags: equation, expression, variable