Final exam Project – First Semester (Math - Mrs. McNabb)
Name: ______Period______
Starting Date ______
MCC6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
MCC6.RP.2 Understand the concept of a unit rate / associated with a ratio : with ≠0 (b not equal to zero), and use rate language in the context of a ratio relationship.
MCC6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
MCC6.RP.3a Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
MCC6.RP.3b Solve unit rate problems including those involving unit pricing and constant speed.
MCC6.RP.3c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole given a part and the percent.
MCC6.RP.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
MCC6.EE.1 Write and evaluate numerical expressions involving whole-number exponents.
MCC6.EE.2c Evaluate expressions at specific values for their variables. Include expressions that arise from formulas in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).
MCC6.EE.4 Identify when two expressions are equivalent
MCC6.EE.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 inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
MCC6.EE.6 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.
MCC6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form += and = for cases in which p, q and x are all nonnegative rational numbers.
MCC6.EE.8 Write an inequality of the form or to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form or have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
MCC6.EE.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 quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.
MCC6.G.1 Find area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
Dream House
Task/Objective: The students will act as Junior Architect/Interior Designer to design a room of their personally designed home.
Part I / Select a house:
1) Go to http://www.eplans.com/house-plans/epl/catalogsearch/advanced to select the house. Start with an advanced search to customize your house. Select the following: Class work 25pts.
2) BDR, BA, ½ BA, # of stories, Garage... Optional: Essential rooms, interior layout, and style. After all selections have been decided upon, click View. Email this to yourself to print at home. Bring to your next math class.
3) Print the blueprint floor plans for each level, the exterior, and About the Plan. Home Enrichment 25pts.
4) What is the square footage of the house? Sentence 12.5pts.
5) What is the cost of the house? Sentence 12.5pts.
6) How much does your house cost per square foot? Use 3pp. 12.5pts.
7) Is this rate or unit rate? Explain how you know. 12.5pts. (Total ______pts.)
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Part II / Room (Home Enrichment)
8) The students will need to decide upon a room to design. Mrs. McNabb will need to approve the room. A 2D interior decorating sketch will be needed. 30pts.
9) Label the following original dimensions on the sketch: Length, width, and height. 30pts.
10) Compute the room’s area and perimeter. Write the algebraic equation, substitute, and then solve using 3pp. 30pts.
11) Use color and accessories. 10pts. (Total ______pts.)
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Part III /Scale – Down: (class work and Home enrichment)
12) Use originals dimensions of the room (Length, Width, and Height) to scaled down.
13) All rates are to follow this guide:
a. If the length and width measurement is less than (< ) 10ft, then the scale is 1.5inches to every one foot.
b. If the length and width measurement is greater than (>) 10ft, then the scale is 2 inch to every one foot.
c. Ceiling 1 – A standard ceiling height is 9ft.
d. Ceiling 2 – A vaulted/cathedral ceilings height are 12ft.
14) Write this sentence. My room’s length and width is ______; therefore, I will scaled down using ______. I also chose ______ceiling height; therefore, I will scale down using ______. 10pts.
15) After determining which inequality applies, use 3pp to compute all dimensions (Length, Width, and Height). Set-up as follows: exact measure/scaled down measure. 40pts.
16) What is the scaled down area and perimeter of the room? Write the algebraic equation, substitute, then solve using 3pp. 30pts
17) Cut yarn to represent the dimensions of your 3D structure.
18) Discover the percentage decreased. Use 3pp and the proportion - Original area/New area = n/100. 20pts. (Total ______pts.)
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Part IV (Class work and Home enrichment)
19) Create a ratio table or double number line (labels and titles) to show the model's hypothetical expansion when expanding 4 factors. 25pts. Start with scalded down numerical data. Mathematical justification - show how each expansion is proportioned. 25pts. Needed: List and/or label ordered pairs and construct a graph/coordinate grid. 25pts.
20) Was your room scaled down proportionately? Use sentences to explain how you know. 25pts.
Part V – choose one of the four. Each 25pts. (Class work and Home enrichment)
21) Mathematical scenario #1: The room needs painting. Eight gallons of paint is required. Home Deep has a sale for 30% off the regular price of $30 per gallon if you purchase 5 gallons at one time. If you don't buy 5 gallons, then the price is $34.99 per gallon. Happy House of Color sells paint for $24.99 per gallon. Which store offers the better deal? How much is being saved? Use 3pp to defend the responses.
22) Mathematical scenario #2: You have a short period of time for you to get this paint job completed. The paint sprayers come in two sizes: pints and quarts. The pints are 4 for $15.50 or one quart for $9.50 each. Which sprayer will you purchase? Give an explanation for why your chose is the best for you. Make certain all proof requiring computation uses 3pp.
23) Mathematical scenario #3: If your parents pay $11.50 per hour for the painting. You take 10 hours total. Beyond 8 hours, they will pay an additional 25% of your hourly wage for every hour over you paint. How much did you earn if the government taxed 12%?
24) Mathematical scenario #4: Who got more for their buck? Get the square footage and price of two others (Names). Compare the unit rate of your house to the others. Unit rate – Which house is a better buy? (Total ______pts./25pts.)
Part VI – 3D model Home enrichment.
24) Be creative while recycling, reusing, and reducing. Try not to purchase anything. DO NOT use edible insect attracting materials. 10pts.
25) Make a replica using the scaled down measurements and your floor plan decorating.
26) The structure must have accurate measurements (string) 30pts.
27) The structure must be self-sufficient (stand alone). 30pts.
25) Decorate using appropriate sizes, 2D, and/or 3D. 30pts. (Total ______pts.)
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Part VII – Presentation (class)
28) PPT or Prezi: Introduction - page 1, house (exterior and interior) - page 2, total cost and cost per square footage - page 3, mathematical scenario and results - page 4, and (reflect) what you learned, challenges, enjoyed - page 5. 75pts.
26) Show and describe 3D visual. 25pts. (Total ______pts.)
Note: The final exam grade will be an average of parts of this project.
Student ______Homeroom ______
Start Date: December ______, 2014
Letter date: December ______, 2014
To: Sixth Grade Parent(s)/Guardian(s) and Student
From: Mrs. McNabb
Re.: First Semester Final Exam Project
The Sixth Grade Math Students will have a project for their first semester final exam. This project will allow students to adequately apply first semester standards to real-world mathematics.
➢ To ensure your student receives the highest score possible, the parent needs to make available a computer, printer, art supplies, and various other supplies as it needed for this project. Check with your student regularly on their progress for at-home sections. Please check the math webpage and student agenda. Sign below and send back with your student on his/her next math class.
➢ To ensure the highest score possible, Mrs. McNabb will supply materials, instruction/direction, and will be available per request for additional sessions during your non-band/strings days.
➢ To ensure the highest score possible, each students needs complete all tasks on time with accuracy, and bring their IMN to class daily to use as a reference. Please check the math webpage and record in your agenda daily. If the student falls behind on an in-class section, he/she must attend additional sessions during non-band/strings days. Bring this sheet back signed below the next math class.
Note: 6/7A’s project is Dream House and 6th ‘s project is Cartoon Scale Factor.
All involved parties will complete below acknowledging their responsibility to the success of this project. This will earn your student a score of 100/A. If not returned the next math class, a deduction of 10pts. per day will apply.
Parent/Guardian sign ______Print ______
Teacher Sign ______Print ______
Student sign ______Print ______
Score earned ______%
Project – Cartoon Scale Factor
(Mrs. McNabb’s - Math)
MCC7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.
MCC7.RP.2 Recognize and represent proportional relationships between quantities.
MCC7.RP.2a Decide whether two quantities are in a proportional relationship
MCC7.RP.2c Represent proportional relationships by equations.
MCC7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
MCC6.EE.4 Identify when two expressions are equivalent as it pertain to geometry.
MCC6.EE.1 Write and evaluate numerical expressions involving whole-number exponents.
MCC6.EE.2c Evaluate expressions at specific values for their variables. Include expressions that arise from formulas in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).
MCC6.EE.4 Identify when two expressions are equivalent
Project – Cartoon Scale Factor (Mrs. McNabb’s - Math)
Name: ______Period______
Starting Date ______
MGSE7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.
MCC7.RP.2 Recognize and represent proportional relationships between quantities.
MCC7.RP.2a Decide whether two quantities are in a proportional relationship
MCC7.RP.2c Represent proportional relationships by equations.
MCC7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
MCC6.EE.4 Identify when two expressions are equivalent as it pertain to geometry.
MCC6.EE.1 Write and evaluate numerical expressions involving whole-number exponents.
MCC6.EE.2c Evaluate expressions at specific values for their variables. Include expressions that arise from formulas in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).
MCC6.EE.4 Identify when two expressions are equivalent
(Home enrichment)
1. Review what’s expected for this project - Reference: http://www.basic-mathematics.com/scale-drawings.html and a Scale drawing PPT is attached.
2. Choose a cartoon enclose in a rectangular or a square border. (Home enrichment)
3. Parent sign the rubric acknowledging the sixth grade final exam project. Sent 11-16-15
Part 1- Measurements:
(Class assignment)
1. If you want scale down, then the cartoon's length and width has to be no greater than your forearm. (Nonstandard estimated measure)
2. If you want scale up, then the cartoon's length and width has to be no greater than the length of your hand. (Nonstandard estimated measure)
3. The cartoon must have medium complexity, colorful, and be approved by Mrs. McNabb.
4. Tape the cartoon to white paper.
5. If scaling up then:
a. Measure the length and the width of cartoon using mm units. Precise measurements required. L=______mm W= ______mm Use 3pp to convert. L= ______cm W= ______cm
b. Label on the smaller rectangle below in cm.
c. Problem: How large will you increase the cartoon w/o it exceeding the drawing paper?
d. What is the measure of the large paper that will be used to recreate the cartoon?
L= ______mm W= ______Use 3pp. to convert. L= ______cm W= ______cm
e. Your scale recreation will be drawn ______times the area of your exact cartoon. Label the new L and W on the larger rectangle.
6. If you scale down, then:
a. Measure the length and the width of cartoon using mm units. Precise measurements required. L=______mm W= ______mm Use 3pp to convert. L=______cm W=______cm.
b. Label on the larger rectangle below.
c. Problem: How small will you decrease the cartoon w/o exceeding the drawing paper?
f. What is the measure of the smaller paper that will be used to recreate the cartoon?
L= ______mm W= ______mm
Use 3pp. to convert. L= ______cm W= ______cm
d. Your scale recreation will be drawn ______divided the area of your exact cartoon.