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Union City High School Honors Course Summer Assignment

Mathematics

UCHS Honors Summer Assignment: Honors Geometry

Course Title: Honors Geometry

Goals and Objectives

1. To develop number sense and perform standard numerical operations in a variety of ways

2. To represent and analyze relationships among variable quantities and solve problems involving patterns, functions, and algebraic concepts.

3. To develop an understanding of the concepts and techniques of data analysis and probability and use them to model situations, solve problems, analyze and draw appropriate information from the data.

4. To find the area of various shapes and be able to make conjectures about them

5. To use statistics to make inferences and predictions 6. To apply geometry to real world problems 7. To make connections between geometry and algebra

and extend this to other topics 8. To employ technology to solve problems 9. To learn in a cooperative setting 10. To communicate mathematics

Essential

Questions • How can real numbers and operations help solve real

world problems? • How are shapes related? • How are formulas and equations useful in solving

practical problems? • How can statistics be used to model, analyze and

communicate real world applications?

Assignment Description

You will need to complete 10 open-ended questions contained in this packet. Work out each problem neatly. All responses must be properly labeled and complete.

Useful websites: www.mathforum.com www.math.com www.coolmath.com www.sosmath.com


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Timetables & Deadlines;

Pacing Guide

You will be expected to turn in the assignment with all the applicable work on the first day of class. Do not wait until the end of the summer to start this assignment.

Assessments Rubric is attached.

Instructional Materials

Problems are attached

Grading Weight for MP1

This summer assignment will count as your first test grade.


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1. Carlos owns a rare stamp collection. There are 45 rare stamps in his collection. He wants to divide the stamps among his three children. He requested that the oldest child receives 4/5 of the collection, the middle child receives 1/10 of the collection and the youngest child receives 1/15 of the collection. His children met and tried to figure out how to distribute the stamps according to their father’s specification.

1) How many stamps should each child get?

2) Did Carlos choose the fractional parts each child was to receive in the best way? Explain why or why not.

3) Suggest an alternative way that the stamps could be distributed.


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2. Continental Airlines advertises that its flights are on time. The chart below displays a consecutive 12-day period and is representative of most 12-day periods for the last 3 months. Study the chart, which shows the touchdown times for Flight 288, which had on time departures at 10 am for the 2 hour and 40 minute flight to Florida from Newark.

Touchdown Times To Florida Date 8/1 8/2 8/3 8/4 8/5 8/6 8/7 8/8 8/9 8/10 8/11 8/12

Touchdown Times

12:15 pm

1:00 pm

1:10 pm

12:15 pm

12:30 pm

1:00 pm

12:55 pm

12:18 pm

1:15 pm

12:10 pm

1:20 pm

12:45 pm

1) Explain why the advertising claim of on time arrivals is incorrect for this flight.

2) Determine the probability of arriving in Florida late if this flight is

taken.

3) If Flight 288 is late, predict how many minutes late the flight will

be and explain how you made this prediction.


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3. Juan’s mom lives in Union City and she needs his help. She wants

to build a vegetable garden in her backyard. She wants her kids to still be able to play in the backyard and therefore only wants to use 24 feet of fencing. 1) Draw all possible rectangular areas that can be made using the

entire fencing and label the sides. (Use whole numbers for the dimensions of the rectangle)

2) Find the area of each rectangle. Which has the greatest area?

3) If Juan’s mom uses all 24 ft of fencing and tries a circular shape

for the vegetable area, what will the length of the diameter be? Draw a circle and label it. Find its area. Compare its area with the area of the rest of the rectangles.

4) What shape should Juan’s mom decide to make the vegetable

garden? Explain


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4. On its opening day, a video store is offering prizes. Every twentieth paying customer will receive a free T-shirt and every fiftieth paying customer will receive a free DVD. The store had 500 customers that day. 1) How many customers will receive a free T-shirt on opening day?

Explain your answer. 2) How many customers will receive a free DVD on opening day?

Explain your answer.

3) How many customers, if any, will receive both a free T-shirt and

free DVD that day. Explain your answer. 4) If the cost of a T-shirt is $4.99 and the cost of a DVD is $12.99,

how much did the store give away on opening day? Explain your answer.


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5. Roberto’s refrigerator is not working. In the phone book, he locates two companies that fix appliances. Company A charges $75 for the visit plus $35 for each hour or part of an hour of labor. In the phone book, there is a coupon for 10% off the bill that Roberto can apply if he uses Company A to repair the refrigerator. The other company, company B, charges $60 for the visit plus $45 for each hour or part of an hour of labor. This company offers a discount of $20 for charges over $150. 1) Compute the charges of each company for 1,2,3,4, and 5 hours.

Show all your work. 2) Last time Roberto had the refrigerator fixed, the repairman was at

his house for 2 hours and 10 minutes. If he expects this repair to take just as long, which company should he choose to do the work? Show your work.

3) If it takes the repairman between 1 and 2 hours to do the work,

which company will do the work for less money? Show your work.


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6. The Prom Committee is setting up card tables for the prom. One table seats 4, 2 tables together would seat 6, 3 tables 8. No table seats more than 12. Show 3 different ways that 16 couples could be seated for the Prom.


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7. Here is a sketch of a city park. It is 400 ' long and 300 ' wide. The sidewalks are 6 ' wide.

A. What is the surface area of the sidewalk?

B. What is the ratio of the sidewalk to the area of the park?

C. How ratio will change if width of sidewalk doubled?


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8. In planning her new vegetable garden, Diana designs it in the shape of a rectangle that is 10 percent longer and 20 percent shorter then her previous rectangular garden.

A. Is the new garden larger or smaller then last years?

B. By what percent?

C. Explain your solution.


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9. During a bowling tournament, a prize is give to anyone who finishes with a mean of 180 or better. In her first five games, Rita has scores of 168, 172, 182, 144, and 156. She has one more game to bowl.

A. Find the mean of the first five scores.

B. What score does she need in her last game to qualify for the prize, given that the maximum possible score in a game is 300?

C. Do you think she can win the prize? 10. Kyle is raising money for a local children’s charity. He is taking orders


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for candles and bouquets of flowers. He will earn $1.25 for each candle he sells and $2.25 for each bouquet he sells. He would like to raise more than $400.

A. Let c equal the number of candles and let b equal the number of bouquets that Kyle sells. Write an inequality to show how many candles and bouquets Kyle needs to sell to raise more than $400.

B. If Kyle sells 200 candles, how many bouquets does he need to sell to make his goal? Use the inequality you wrote for part a to explain your reasoning.

C. On a coordinate graph, draw a line that contains all the different combinations Kyle can sell to make a total of exactly $400. Let the horizontal axis represent the number of bouquets sold. Let the vertical axis represent the number of candles sold. Show or describe the calculations you used to find the data points on your graph.

Rubric for Open-ended Problem Solving


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