Practical Frac-Tile

Printable ResourcesPractical Frac-TileAppendix A: Pre/Post Test

Appendix B Pre/Post Test Answer Key

Appendix C Engineering Design Challenge

Appendix D Engineering Design Process

Appendix E Design Rubric

Appendix F Budget Template

Appendix G Floor Plan

Appendix H Calculation Worksheet

Appendix I: Customer’s Request to Minimize Expenses

Appendix J Day #1 Exit Slips

Appendix K Day #3 Exit Slips

Appendix L Day #4 Exit Slips

Appendix M Day #5 Exit Slips

Appendix N Day #6 Exit Slips

Appendix O Day #7 Exit Slips

Appendix P Vocabulary Cards

Draft: 5/6/2023 Page 1

Practical Frac-Tile

Draft: 5/6/2023 Page 2

Practical Frac-TileAppendix A: Pre / Post - Test

Name _____________________________

1. Julian placed 1-centimeter square tiles along the sides of a triangle, as shown. What measurement is Julian trying to determine?

A. the area, which is 16 centimeters squaredB. the perimeter, which is 16 centimetersC. the area, which is 16 square centimeters squaredD. the perimeter, which is 16 square centimeters

2. A window washer has 2 more rows of windows to finish washing on the side of the building shown.

What fraction of the windows on this side of the building does the window washer have left to wash? Explain how you found your answer.

Draft: 5/6/2023 Page 3

Practical Frac-Tile

Name the decimal, fraction and percent for the figure to the right.

3. Fraction: __________________

4. Decimal: __________________

5. Percent: __________________

6. Which fraction is equivalent to 1/3?

A. 1/6B. 3/9C. 3/6D. 9/3

7. Calculate the following fractions ¾ plus 6/8  = ?

Solve numbers 8 – 10. Show your answer in the simplest form:

8. 27 times 1/5 =

9. 9/28 divided by 3 =

Draft: 5/6/2023 Page 4

Practical Frac-Tile

10.15/20 divided by 4/5 =

11.Draw a rectangle with a length of 5 centimeters and a width of 3 centimeters. Find the area of this rectangle.

12.On a blank sheet of paper, draw a square with a side lenth of 6 ¼ inches. Find the area of this sqare.

13.Use the box on the right to calculate the area of this shape.

14.Describe a tessellation pattern you have seen. Then create a regular tessellation pattern using 10 triangles.

Draft: 5/6/2023 Page 5

Practical Frac-Tile

Draft: 5/6/2023 Page 6

Practical Frac-TileAppendix B: Pre / Post–Test, ANSWER KEY

20 Points Total

1. B (1pt)

2. 1/5, student explanation provided (2pts)

3. Fraction: 7/100 (1pt)

4. Decimal: 0.07 (1pt)

5. Percent: 7% (1pt)

6. B (1pt)

7. 1 ½ (1pt)

8. 5 2/5 (1pt)

9. 3/28 (1pt)

10.15/16 (1pt)

11.15 cm2, student drawing provided (2pts)

12.39 1/16 in2, student drawing provided (2pts)

13.78 cm2 (3pts)

14.Answers will vary. Check for understanding. (2 points)

Draft: 5/6/2023 Page 7

Practical Frac-TileAppendix C: Engineering Design ChallengeYour design team is challenged to design a cafeteria floor plan that shows cafeteria functions and creates a traffic pattern for student movement. You will be given a specific area for your cafeteria as well as predetermined stationary objects that would be in the cafeteria to work around. The design must include various shaped tiles and be completed under a specified budget. You will decide the necessary components and organization of the cafeteria, as well as what is needed in the floor design (for example, possibly including a location for milk purchases). You will also need to think about how people move throughout the cafeteria and show this through a tessellating tile pattern (for example, what direction students will walk to go through the line and then return their lunch trays?). You will design a floor pattern to show these elements by tessellating different shaped tiles. Good luck and have fun! This is your DREAM cafeteria!

Your team’s floor plan must include: at least three cafeteria elements specified by the colored areas on the floor,

as discussed after completing Exit Slip 1 a path on the floor that shows the direction people should walk through the

cafeteria at least two different shaped tiles that will tessellate with each other at least three different colored tiles at least two different sized tiles 5-10 eating 18 square feet tables. The table location should be shown with

tiles on the floor.

You have the following materials to use: You can use red, green, blue, white, and black tiles 6x6 inch tiles are $2.00 each 12x12 inch tiles are $7.50 each 18x18 inch tiles are $15.25 each

Hints for your challenge: You will need to work around the fixed pillars on the floor plan. You may cut the tiles into different shapes. You may not have any empty spaces on your floor. Your floor plan must come in under a budget of $6,500.00. Think about how people could walk through your school’s cafeteria. What

directions make the most sense? Remember, even if you cut a tile and do not use all of it, you pay for the entire

tile. It must all be included in your budget. Make sure paths are wide enough for two-way traffic.

Draft: 5/6/2023 Page 8

Practical Frac-TileAppendix D: Engineering Design Process

Draft: 5/6/2023 Page 9

Practical Frac-TileAppendix E: Rubric

Name _____________________________CATEGORY 4 3 2 1

Cafeteria Elements

The cafeteria design clearly shows a minimum of 3 cafeteria elements specified by colored areas.

The cafeteria design shows only 2 cafeteria elements specified by colored areas.

The cafeteria design shows only 1 cafeteria element specified by colored areas.

The cafeteria design does not meet the engineering design requirements of cafeteria elements.

Traffic Pattern The cafeteria design exceeds challenge expectations and clearly shows a traffic pattern for student movement using colored areas.

The cafeteria design clearly shows a traffic pattern for student movement using colored areas.

The cafeteria design clearly shows a traffic pattern for student movement using colored areas. However, minor errors are evident.

The cafeteria design’s traffic pattern for student movement is unclear.

Tessellations The cafeteria design uses more than two different shaped tiles that tessellate.

The cafeteria design uses two different shaped tiles that tessellate.

The cafeteria design uses two different shaped tiles that tessellate. However, minor errors are evident.

The cafeteria design uses only one shaped tiles that tessellate.

Tile Colors The cafeteria design uses more than 3 different colored tiles.

The cafeteria design uses at least 3 different colored tiles.

The cafeteria design uses at least 2 different colored tiles.

The cafeteria design uses only one colored tiles.

Tile Sizes The cafeteria design uses more than 2 different sized tiles.

The cafeteria design uses at least 2 different sized tiles.

The cafeteria design uses at least 2 different sized tiles. However, minor errors are evident, indicating an incomplete understanding.

The cafeteria design uses only one different sized tile.

Floor Plan Key The cafeteria design includes a clear key to identify and explaining what each color represents.

The cafeteria design includes a clear key to identify what each color represents.

The cafeteria design includes a key to identify what each color represents. However, the key is difficult to follow.

The cafeteria design’s key to identify what each color represents is unclear.

Eating Tables The cafeteria design uses tiles to show the locations for 8 of the 18ft2 eating tables.

The cafeteria design uses tiles to show the locations for 6-7 of the 18ft2eating tables.

The cafeteria design uses tiles to show the locations for 3-5 of the 18ft2eating tables.

The cafeteria design uses tiles to show the locations for 1-2 of the 18ft2eating tables.

Budget/Budget Redesign

The cafeteria design fully meets the budget restrictions, and provides justifications.

The cafeteria design fully meets the budget restrictions.

The cafeteria design is within 10 % of the budget restrictions.

The cafeteria design more than 10% outside of the budget restrictions.

Calculation Worksheet

Team members accurately calculated the area, fraction, decimal, and percent for all colored areas of the floor design.

Team members accurately calculated the area, fraction, decimal, and percent for at least 2 or the majority of the colored areas of the floor design.

Team members accurately calculated the area, fraction, decimal, and percent for only 1 of the colored areas of the floor design.

Attempt was made, but team members did not accurately calculate the area, fraction, decimal, and percent for any of the colored areas of the floor design.

Draft: 5/6/2023 Page 10

Practical Frac-Tile

Draft: 5/6/2023 Page 11

Practical Frac-TileAppendix F: Budget Template

Name _____________________________

Tile CostsRed Green Blue Black White6”x6”$2.00

6”x6”$2.00

6”x6”$2.00

6”x6”$2.00

6”x6”$2.00

12”x12”$7.50

12”x12”$7.50

12”x12”$7.50

12”x12”$7.50

12”x12”$7.50

18”x18”$15.25

18”x18” $15.25

18”x18” $15.25

18”x18”$15.25

18”x18”$15.25

Budget Calculations

Color Size # Tiles Tile Cost Total Cost Budget Amount

Red 6x6 inches $2.00

Red 12x12 inches $7.50

Red 18x18 inches $15.25

Green 6x6 inches $2.00

Green 12x12 inches $7.50

Green 18x18 inches $15.25

Blue 6x6 inches $2.00

Blue 12x12 inches $7.50

Blue 18x18 inches $15.25

White 6x6 inches $2.00

White 12x12 inches $7.50

White 18x18 inches $15.25

Black 6x6 inches $2.00

Black 12x12 inches $7.50

Black 18x18 inches $15.25

Draft: 5/6/2023 Page 12

Practical Frac-TileAppendix G: Floor Plan Name _____________________________Scale: ¼ inch = 1 foot

Draft: 5/6/2023 Page 13

Practical Frac-TileAppendix H: Calculation Worksheet

Name _____________________________Directions: Fill out the table with the calculations for each of the colored sections on your floor plan. Write each fraction in its simplest form. Write each decimal rounded to the nearest hundredth. Write each percent rounded to the nearest whole percent. You must show your work on a separate sheet of paper attached to this worksheet.

Total Area of Floor Plan: ___________

Color of Section

Total Number of

tilesArea or

each colorFraction of each color

Decimal of each color

Percent of each color

Red

Green

Blue

White

Black

Draft: 5/6/2023 Page 14

Practical Frac-TileAppendix I: Customer’s Request to Minimize Expenses

Dear Engineering Teams:

Thank you for submitting your cafeteria floor plan ideas. We are impressed with the visual aesthetics of each design submitted.

Unfortunately, due to economic restraints, or budget has been significantly cut. Although each team came in under the given budget of $6,500.00, we are unable to cover any of the budgets that were submitted.

We are requesting that you lower the budgets of your designs by as much as possible while still keeping the uniqueness of your team’s floor plan. the design with the lowest budget and comparably highest visual quality will be chosen to be contracted for the final project.

We look forward to your revised cafeteria floor plan design submissions.

Thank you for your hard work!

Draft: 5/6/2023 Page 15

Practical Frac-TileAppendix J: Day #1: Exit Slips

Name _____________________________

Draft: 5/6/2023 Page 16

What are five things that you think every cafeteria should have?

How does using graph paper assist you with your project design?

Practical Frac-TileAppendix K: Day #3: Exit Slips

Name _____________________________

Draft: 5/6/2023 Page 17

What information do you intend to communicate given your chosen colors and patterns.

How are you using math to make decisions and create your design?

Practical Frac-TileAppendix L: Day #4: Exit Slips

Name _____________________________

Find the area and perimeter of the shape below.

Find the fraction, decimal and percent for the shaded area in the figure below.

Draft: 5/6/2023 Page 18

How have you used the engineering design process up to this point?

Practical Frac-TileAppendix M: Day #5: Exit Slips

Name _____________________________

Draft: 5/6/2023 Page 19

What challenges or problems could designers and contractors experience during this type of project?

How does calculating the area affect your spending?

Practical Frac-TileAppendix N: Day #6: Exit Slips

Name _____________________________

Draft: 5/6/2023 Page 20

What changes did you make to your design to meet the new budget incentive?

How does the idea of the budget incentive fit into the engineering design process?

Practical Frac-TileAppendix O: Day #7: Exit Slips

Name _____________________________

Draft: 5/6/2023 Page 21

How do computer programs, like the one used today, make this type of designing easier?

Reflect upon the work your group completed today. What went well? What was difficult?

Practical Frac-TileAppendix P: Definitions

Name _____________________________

AreaThe number of square units needed to cover a surface or

figure.Formula: A=lw

Units2

DecimalNumerals to the right of the

decimal point (represent parts of a whole).

2.5

DenominatorThe number below the fraction bar in a fraction (represents the

total number of parts in the whole).

Engineering Design Process

A process or set of steps used to devise creative solutions to solve

problem and/or develop innovative products.

Equivalent Having the same value or amount.

FractionA symbol such as ½ or 5/8, used to describe one or more parts of a whole that is divided into equal

parts.

Draft: 5/6/2023 Page 22

Practical Frac-Tile

Mixed NumberA number written with a whole

number and a fraction.2 ½

NumeratorThe number above the fraction

bar in a fraction (represents how many out of the total parts).

PercentA ratio in which the first term is compared to 100 (out of 100).

50% or ½

PerimeterThe distance around the outside

of any polygon. Measured in linear units.

Formula: Sum of Sides

SimplestForm

A fraction for which the greatest common factor of the numerator

and denominator is 1.Example: 26 = 13

TessellationsAn arrangement of shapes which

fit together to completelyfill a space with no gaps or

overlaps remaining (often forms a repeating pattern).

Draft: 5/6/2023 Page 23