# The Cost of a Great Looking Floor

This lesson challenges students to construct a tile floor and calculate the cost using pattern blocks. Students will use geometric shapes, ratios, proportions, and percents. Students must rationalize inthis lesson because all cost estimates are based on the purchase of full boxes of tile. Cost also includes labor and taxes and students must weigh cost against design. this lesson provides opportunities for differentiation.

### Standards & Objectives

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.A.1
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction...
CCSS.Math.Content.6.NS.C.5
Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature...
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,...
CCSS.Math.Content.7.EE.B.3
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and...
CCSS.Math.Content.7.NS.A.1
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a...
CCSS.Math.Content.7.NS.A.2
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
CCSS.Math.Content.7.NS.A.3
Solve real-world and mathematical problems involving the four operations with rational numbers.1
CCSS.Math.Content.7.RP.A.1
Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different...
CCSS.Math.Content.7.RP.A.2
Recognize and represent proportional relationships between quantities.
CCSS.Math.Content.7.RP.A.3
Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and...
CCSS.Math.Content.8.EE.A.2
Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number....
CCSS.Math.Content.8.NS.A.1
Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational...
GLE 0606.1.8
Use technologies/manipulatives appropriately to develop understanding of mathematical algorithms, to facilitate problem solving, and to create accurate and...
GLE 0606.2.1
Understand and explain the procedures for multiplication and division of fractions, mixed numbers, and decimals.
GLE 0606.2.2
Solve multi-step mathematical, contextual and verbal problems using fractions, mixed numbers, and decimals.
GLE 0606.2.3
Understand and use ratios, rates and percents.
GLE 0606.2.4
Understand and convert between fraction, decimal, and percent forms of rational numbers.
GLE 0606.2.5
Develop meaning for integers; represent and compare quantities with integers.
GLE 0606.3.6
Understand and use the Cartesian coordinate system.
GLE 0606.4.1
Understand and use basic properties of triangles, quadrilaterals, and other polygons.
GLE 0706.1.2
Apply and adapt a variety of appropriate strategies to problem solving, including estimation, and reasonableness of the solution.
GLE 0706.1.5
Use mathematical ideas and processes in different settings to formulate patterns, analyze graphs, set up and solve problems and interpret solutions.
GLE 0706.1.8
Use technologies/manipulatives appropriately to develop understanding of mathematical algorithms, to facilitate problem solving, and to create accurate and...
GLE 0706.2.1
Extend understandings of addition, subtraction, multiplication and division to integers.
GLE 0706.2.2
Understand and work with the properties of and operations on the system of rational numbers.
GLE 0706.2.3
Develop an understanding of and apply proportionality.
GLE 0706.2.4
Use ratios, rates and percents to solve single- and multi-step problems in various contexts.
GLE 0706.2.5
Understand and work with squares, cubes, square roots and cube roots.
GLE 0706.3.5
Understand and graph proportional relationships.
GLE 0706.4.2
Apply proportionality to converting among different units of measurements to solve problems involving rates such as motion at a constant speed.
GLE 0706.4.4
Understand and use ratios, derived quantities, and indirect measurements.
GLE 0806.2.1
Extend understanding of the real number system to include irrational numbers.
SPI 0606.2.1
Solve problems involving the multiplication and division of fractions.
SPI 0606.2.2
Solve problems involving the addition, subtraction, multiplication, and division of mixed numbers.
SPI 0606.2.4
Solve multi-step arithmetic problems using fractions, mixed numbers, and decimals.
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 0606.3.9
Graph ordered pairs of integers in all four quadrants of the Cartesian coordinate system.
SPI 0706.1.3
Recognize whether information given in a table, graph, or formula suggests a directly proportional, linear, inversely proportional, or other nonlinear relationship.
SPI 0706.2.1
Simplify numerical expressions involving rational numbers.
SPI 0706.2.3
Use rational numbers and roots of perfect squares/cubes to solve contextual problems.
SPI 0706.2.5
Solve contextual problems that involve operations with integers.
SPI 0706.2.6
Express the ratio between two quantities as a percent, and a percent as a ratio or fraction.
SPI 0706.2.7
Use ratios and proportions to solve problems.
SPI 0706.3.4
Interpret the slope of a line as a unit rate given the graph of a proportional relationship.
SPI 0706.3.5
Represent proportional relationships with equations, tables and graphs.
SPI 0806.1.1
Solve problems involving rate/time/distance (i.e., d = rt).
SPI 0806.1.3
Calculates rates involving cost per unit to determine the best buy.
SPI 0806.2.2
Identify numbers and square roots as rational or irrational.
SPI 0806.4.2
Apply the Pythagorean theorem to find distances between points in the coordinate plane to measure lengths and analyze polygons and polyhedra.
SPI 0806.4.4
Convert between and within the U.S. Customary System and the metric system.
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.A.1
Interpret and compute quotients of fractions, and solve contextual problems involving division of fractions by fractions (e.g., using visual fraction models...
TSS.Math.6.NS.C.5
Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below...
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.7
Understand ordering and absolute value of rational numbers.
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.
TSS.Math.7.EE.B.3
Solve multi-step real-world and mathematical problems posed with positive and negative rational numbers presented in any form (whole numbers, fractions, and...
TSS.Math.7.NS.A.1
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a...
TSS.Math.7.NS.A.2
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
TSS.Math.7.NS.A.3
Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for...
TSS.Math.7.RP.A.1
Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. For...
TSS.Math.7.RP.A.2
Recognize and represent proportional relationships between quantities.
TSS.Math.7.RP.A.3
Use proportional relationships to solve multi-step ratio and percent problems.
TSS.Math.8.EE.A.2
Use square root and cube root symbols to represent solutions to equations of the form x 2 = p and x 3 = p, where p is a positive rational number. Evaluate...
TSS.Math.8.NS.A.1
Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show...

Alignment of this item to academic standards is based on recommendations from content creators, resource curators, and visitors to this website. It is the responsibility of each educator to verify that the materials are appropriate for your content area, aligned to current academic standards, and will be beneficial to your specific students.

Learning objectives:

Learning Objectives

Students will:

• Manipulate pattern blocks to create a design without gaps between tiles.
• Accurately calculate the cost of their design using predetermined pricing structures.
• Calculate cost using percentages, rounding, and other numeric skills.
Essential and guiding questions:

Questions for Students:

• What can we say about the sides of the various shapes?
• If a hexagon tile is too expensive or the wrong color, what other tiles could you use to achieve the same shape?
• How many triangles are needed to make a trapezoid?
• How many triangles are needed to make a big rhombus?
• What shape or shapes could be used in place of the small rhombus? How is the small rhombus different from the big rhombus?

### Lesson Variations

Blooms taxonomy level:
Understanding
Extension suggestions:

Extensions:

• Flooring contractors estimate their material at 10% over the required amount. Have student recalculate their projects by adding 10% more of each tile and recalculating. Remind students that the labor costs are calculated from whole boxes, so if only part of a box is used, it's possible that they've already paid 10% extra.
• When you calculate the cost of your design, would you calculate sales tax on materials and labor or just materials?
• [The answer to this question will vary by state and location. If you want this activity to be as realistic as possible consider checking with a local flooring company as to how tax is calculated. You could also assign this task to a student as an extension activity.]
• Propose to your students that the customer has indicated the cost is too high. Ask what changes they would reduce the cost of their design by 25% if possible. If a 25% reduction is not possible, what percentage is possible?
• What would happen to the total cost of the floor if labor was 20% higher?
• Invite a local flooring contractor to come in and talk to the students about how projects such as these would be bid and what costs are associated with a bid.