6th Grade Task: Car Lot

6th Grade Task: Car Lot

Standards & Objectives

Academic standards
CCSS.Math.Content.6.EE.A.1
Write and evaluate numerical expressions involving whole-number exponents.
CCSS.Math.Content.6.EE.A.2
Write, read, and evaluate expressions in which letters stand for numbers.
CCSS.Math.Content.6.EE.A.3
Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to...
CCSS.Math.Content.6.EE.B.5
Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or...
CCSS.Math.Content.6.EE.B.6
Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can...
CCSS.Math.Content.6.EE.B.7
Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all...
CCSS.Math.Content.6.EE.B.8
Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that...
CCSS.Math.Content.6.EE.C.9
Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one...
CCSS.Math.Content.6.G.A.3
Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same...
CCSS.Math.Content.6.NS.C.6
Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to...
CCSS.Math.Content.6.NS.C.7
Understand ordering and absolute value of rational numbers.
CCSS.Math.Content.6.NS.C.8
Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and...
CCSS.Math.Content.6.RP.A.1
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings...
CCSS.Math.Content.6.RP.A.2
Understand the concept of a unit rate a/b associated with a ratio a:b with b != 0, and use rate language in the context of a ratio relationship....
CCSS.Math.Content.6.RP.A.3
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams,...
GLE 0606.1.1
Use mathematical language, symbols, and definitions while developing mathematical reasoning.
GLE 0606.2.3
Understand and use ratios, rates and percents.
GLE 0606.3.1
Write and solve two-step equations and inequalities.
GLE 0606.3.2
Interpret and represent algebraic relationships with variables in expressions, simple equations and inequalities.
GLE 0606.3.3
Extend order of operations to include grouping symbols and exponents.
GLE 0606.3.4
Use expressions, equations and formulas to solve problems.
GLE 0606.3.5
Use multiple representations including symbolic algebra to model and/or solve contextual problems that involve linear relationships.
GLE 0606.3.6
Understand and use the Cartesian coordinate system.
SPI 0606.2.6
Solve problems involving ratios, rates and percents.
SPI 0606.2.7
Locate positive rational numbers on the number line.
SPI 0606.2.8
Locate integers on the number line.
SPI 0606.3.1
Represent on a number line the solution of a linear inequality.
SPI 0606.3.2
Use order of operations and parentheses to simplify expressions and solve problems.
SPI 0606.3.3
Write equations that correspond to given situations or represent a given mathematical relationship.
SPI 0606.3.5
Translate between verbal expressions/sentences and algebraic expressions/equations.
SPI 0606.3.9
Graph ordered pairs of integers in all four quadrants of the Cartesian coordinate system.
TSS.Math.6.EE.A.2
Write, read, and evaluate expressions in which variables stand for numbers.
TSS.Math.6.EE.B.5
Understand solving an equation or inequality is carried out by determining if any of the values from a given set make the equation or inequality true. Use...
TSS.Math.6.EE.B.6
Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an...
TSS.Math.6.EE.B.7
Solve real-world and mathematical problems by writing and solving onestep equations of the form x + p = q and px = q for cases in which p, q, and x are all...
TSS.Math.6.EE.B.8
Interpret and write an inequality of the form x > c or x
TSS.Math.6.EE.C.9
Use variables to represent two quantities in a real-world problem that change in relationship to one another.
TSS.Math.6.G.A.3
Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side that joins two vertices (vertical or...
TSS.Math.6.NS.C.6
Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent...
TSS.Math.6.NS.C.8
Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value...
TSS.Math.6.RP.A.1
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, the ratio of wings to beaks...
TSS.Math.6.RP.A.2
Understand the concept of a unit rate a/b associated with a ratio a:b with b != 0. Use rate language in the context of a ratio relationship.
TSS.Math.6.RP.A.3
Use ratio and rate reasoning to solve real-world and mathematical problems.
 
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Essential and guiding questions: 

Whole Group Questions:

  • What strategies did you use to solve this problem? How did you know your strategy would work?
  • How are ratios in part B similar to what you know about fractions? How are the ratios different than what you know about fractions?
  • What kinds of numbers can you use in your expressions for the variable? Is the variable in your expression for the number of cars related to the variable in your expression for the number of trucks?

Activity/Task Variations

Blooms taxonomy level: 
Understanding
Differentiation suggestions: 

Entry/Extensions:

Assessing and Advancing Questions

If students can’t get started….

Assessing Questions

  • Let’s look at what is already on the car lot. How many cars and how many trucks do you have? What is the ratio of cars to trucks now? Why?

Advancing Questions

  • How can you change that ratio? What would you need to do to change that ratio?

If students finish early….

Assessing Questions

  • Show me how you determined the expressions for the patterns you found.
  • What kinds of numbers can you use in your expressions for the variable?
  • Is the variable in your expression for the number of cars related to the variable in your expression for the number of trucks?

Advancing Questions

  • Suppose the ratio of trucks to cars was 3:2. How would this change your answers? Would you have different patterns? Why or why not?