Constructed
Response
Items
Volume 2
Mathematics Constructed Response
Name: ______Hour: _____ Score: ______
Money
(Number Operations and Relationships, Measurement )
Remembering:
List 1 thing you could buy for $1.00, $2.00 and $5.00 or less.
Understanding:
Draw the coins that you would use to pay for the items.
Applying:
Draw the coins you could receive as change if you paid $1.00,
$2.00 and $5.00.
Analyzing:
Determine and record the operation that you used to calculate
change.
Evaluating:
What criteria would you use to evaluate if your answer is correct?
Mathematics Constructed Response
Name: ______Hour: _____ Score: _____
Distance
(Number Operations and Relationships, Measurement)
You may use the formula d = rt to solve this problem.
John's remote control car travels at a rate of 30 feet per second.
How many seconds does it take the car to travel 300 feet?
Answer: ______seconds
In the formula d = rt , how does the value of t change if the car's rate
decreases but the distance traveled remains the same?
Mathematics Constructed Response
Name: ______Hour: _____ Score: _____
Exponents
(Number Operations and Relationships)
Lydia was given the expression: 82 x 4 x 23 . In simplifying the expression, she solved it to be equal to 210 . Circle the step where Lydia made her mistake and express your correct solution as a power of 2.
Step1 82 x 22 x 23
Step 2 (23)2 x 22 x 23
Step 3 25 x 22 x 23
Step 4 27 x 23
Step 5 210
Mathematics Constructed Response
Name: ______Hour: _____ Score: _____
Baseball Trivia
(Geometry, Measurement)
The greatest distance that a baseball has been thrown is 445 feet,
10 inches. Is this greater or less than the length of a football field (100 yards) from goal line to goal line? By how much? Explain how you made your decision.
Mathematics Constructed Response
Name: ______Hour: _____ Score: _____
Rectangle
(Geometry)
Which of these choices contains the dimensions of a rectangle with the same perimeter as a rectangle whose dimensions are 5 m by 3 m?
· 10 m by 8 m
· 7 m by 1 m
· 6 m by 4 m
· 8 m by 2 m
Show your work.
Mathematics Constructed Response
Name: ______Hour: _____ Score: _____
What Do You Need?
(Geometry)
What do you need to know to solve this? You have kite ABCD.
Angle B is at the top of the kite and measures 80 degrees. Angles A
and C are on the sides and Angle D (whose measurement is a whole number)
is at the bottom of the kite. What is the largest size that Angle A or C could be?
Mathematics Constructed Response
Name: ______Hour: _____ Score: _____
Yum
(Statistics and Probability)
Determine the number of pizza combinations you could get with 4 different toppings. Each pizza must have at least 2 toppings. Make a chart to display
your results.
Mathematics Constructed Response
Name: ______Hour: _____ Score: _____
Planet Krayon
(Algebraic Relationships)
Zemo, Orb, Yuko, and Sam are friends who live on neighboring space stations of the planet Krayon. They commute to school every day by space shuttle. Orb's space station is one half as far from Krayon as Zemo's space station. Yuko travels as far as the total distance traveled by Zemo and Orb. Sam travels 3 times the distance that Zemo travels. How many space miles does each friend travel to school if the friends together travel 888 space miles? Write an algebraic equation and solve.
Mathematics Constructed Response
Name: ______Hour: _____ Score: _____
How Old am I?
(Statistics and Probability)
The average age of a group of teachers and students is 20. The
average age of the teachers is 35. The average age of the students
is 15. What is the ratio of teachers to students? Express your
answer as a fraction in simplest form.
Mathematics Constructed Response
Name: ______Hour: _____ Score: _____
Change
(Number Operations and Relationships, Measurement)
Sadie went to the store with a $10 bill. She spent $4.76. Give 6 possible ways
she could get her change. You cannot use the same number of coins twice.
(i.e. you cannot say 5 one dollar bills, 2 dimes, 4 pennies, and then a $5 bill,
2 dimes and 4 pennies.) You must use each type of US coin at least once.
Mathematics Constructed Response
Name: ______Hour: _____ Score: _____
Meow!
(Geometry)
Draw a cat. You may only use regular polygons and you must use at least
6 different ones.
Mathematics Constructed Response
Name: ______Hour: _____ Score: _____
Toothpick Fun
(Geometry)
Carl is given 24 toothpicks and told to construct a geometric solid. He must use
all of the toothpicks. Which solid could he make? Draw a picture to support your answer. How many balls of clay would he need to hold his structure together?
Mathematics Constructed Response
Name: ______Hour: _____ Score: _____
Dots
(Algebraic Relationships)
Oblong numbers can be represented by rectangular arrays in which the number
of dots in each row is one more than the number of dots in each column. The
first 3 oblong numbers 2, 6 and 12, are represented below.
** *** ****
*** ****
****
Show the next oblong number. How many dots are needed to represent the tenth oblong number?
How many dots are needed to represent the 100th oblong number?
Mathematics Constructed Response
Name: ______Hour: _____ Score: _____
Car Rental
(Algebraic Relationships)
Sam needs to rent a car for his upcoming trip. Cheap Wheels charges $20.25
per day plus $.14 a mile. Easy Rider charges $18.25 a day plus $.22 a mile.
Sam plans to do a lot of driving on his 3-day trip. Which company should Sam
go with? Explain your choice. Does the difference in cost go up or down as
mileage increases? Support your answer.
Mathematics Constructed Response
Name: ______Hour: _____ Score: _____
Error Analysis
(Algebraic Relationships)
Find the errors and correct them. Be sure to show the properties that you are using in your explanation.
9 (3 – 5) = 9(3) – 5
= 27 – 8
= 22
-2 (7 – 8) = -2(7) – 2(8)
= -14 – 6
= -30
Mathematics Constructed Response
Name: ______Hour: _____ Score: _____
Stepping Up
(Algebraic Relationships)
Study this picture. How many blocks would you need for a 20-step staircase?
Set up an algebraic equation to solve.
Mathematics Constructed Response
Name: ______Hour: _____ Score: _____
Diagonally Speaking
(Geometry)
What is the maximum number of diagonals in an octagon? Solve this without drawing the shape. (Start with smaller polygons and search for a pattern)
Once you have determined the pattern, what is the maximum number of
diagonals in a ten sided figure? A 12 sided figure?
Mathematics Constructed Response
Name: ______Hour: _____ Score: _____
House of Angles
(Geometry)
Draw a picture of a house with exactly 24 right angles, 6 acute angles, and 2 obtuse angles.
Mathematics Constructed Response
Name: ______Hour: _____ Score: _____
Hexagonal Tiles
(Geometry)
In the center of Memorial Park is a fountain in the shape of a hexagon. Workers are ringing the fountain in hexagonal tiles. The first ring of the tiles is made of black tiles. The next ring is made of white tiles. The next black, and so on. How many hexagonal tiles will the workers use in the fourth ring? In all, the workers completed 15 rings. What color were the tiles in the fifteenth ring? How many did they need for this ring?
Mathematics Constructed Response
Name: ______Hour: _____ Score: _____
Mowing Lawns
(Number Operations and Relationships)
Ron and Darrell mow lawns to earn money in the summer. Ron has a riding mower. He charges $18 a yard and pays his little brother $7 to help. He is able to do 9 yards in a day. Darrell has a walking mower. He charges $20 a yard and does 8 yards in a day. Who earns the most money? Explain your answer.
Mathematics Constructed Response
Name: ______Hour: _____ Score: _____
Center Tree
(Geometry)
Tom Terrific has a garden in the shape of a rectangle. He wanted to plant a tree
in a specific spot. He wanted it to be in the exact center of the garden. Describe one way to find the center without using ANY measurements.
Mathematics Constructed Response
Name: ______Hour: _____ Score: ______
ChooChoo Train
(Algebraic Relationships)
The table below shows the number of passengers who traveled from Chicago
to Milwaukee on the ChooChoo train during a five year period.
Year / Passengers2001 / 14,857
2002 / 15,290
2003 / 15,703
2004 / 16,199
2005 / 16,588
How did the number of passengers change from year to year? Describe any trends in the data?
ChooChoo executives need to predict the number of passengers for the year
2008. Explain how they can use the trend and mathematics to do this.
Mathematics Constructed Response
Name: ______Hour: _____ Score: ______
Find a Function
(Algebraic Relationships)
Find an equation for the table below. The line of the equation must pass through (0,2). Find four other points that lie on the line.
x / y2 / 1
Graph the equation of the line.
Mathematics Constructed Response
Name: ______Hour: _____ Score: ______
Shoe Sale
(Number Operations and Relationships)
There is a sale at The Foot Closet, your favorite shoe store. The store gives
you a choice of $10 off each pair of shoes or 15% off your purchase. Give an example to illustrate when it would be better to use each of the deals.
Mathematics Constructed Response
Name: ______Hour: _____ Score: ______
Set Your Sails
(Geometry)
For a certain sailboat race, the ratio of the height (h) of the sail and the base (b) must be at least 1.3 : 1 (see diagram below). Using the centimeter side of your ruler, draw an accurate representation of a sail that would meet the criteria.
Mathematics Constructed Response
Name: ______Hour: _____ Score: _____
Ordering Cups
(Algebraic Relationships)
You work at a frozen yogurt store during the summer. You need to order 5-oz
and 8-oz cups. The storage room will only hold 10 more boxes. A box of 5-oz cups costs $100 and a box of 8-oz cups costs $150. A maximum of $1200 is budgeted for yogurt cups. Write a system of linear inequalities that shows the number of boxes of 5-oz and 8-oz cups that could be bought. Graph your result.
Mathematics Constructed Response
Name: ______Hour: _____ Score: _____
Karl’s Diner
(Number Operations and Relationships, Measurement)
Karl’s Diner
Our Roast Beef
Sandwich is
400%
Bigger than this ad.
Come in and try it!!
This ad was in last week’s Journal-Sentinel. What do you think is the size of
Karl’s sandwich? Draw and show the dimensions of the sandwich. Use the
back of this paper if necessary.
Is this a reasonable sized sandwich? Explain.
Is the ad misleading? Explain.
Bags of Sugar
Each point on this graph represents a bag of sugar.
1. Which bag is heaviest?
2. Which bag is the cheapest?
3. Which bags are the same weight?
4. Which bags are the same price?
5. Which of F or C would give the better vaIue for money? How can you tell?
6. Which of B or C would give the better value for money? How can you tell?
7. Which two bags would give the same value for money? How can you tell?
43
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant No. 0314898.
The Bake Sale
Your class is having a bake sale to raise money for a camping trip. You plan to make chocolate chip and/or oatmeal raisin cookies. These are the only
ingredients that you have:
Ingredients on hand:
4 1/2 cups of butter 1 can (50 teaspoons) baking powder
4 1/2 cups of sugar 6 cups of chocolate chips
12 eggs 6 cups oatmeal
11 cups flour 6 cups raisins
Here are the lists of ingredients for the two recipes that you want to use.
Recipes for One Batch
Chocolate Chip Oatmeal Raisin
1 cup butter 3/4 cup butter
1 cup sugar 3/4 cup sugar
3 eggs 2 eggs
2cups flour 2 1/4cups flour
1 teaspoon baking powder 1 teaspoon baking powder
1 1/2 cups chocolate chips 1 1/2 cups oatmeal
Makes 2 dozen cookies 1 cup raisins
Makes 3 dozen cookies
In order to have the most cookies, how many batches of each cookie should
you make? Show your work and explain your reasoning.
43
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant No. 0314898.
Building a Wheelchair Ramp
Below is a side view of a wheel chair ramp.
• Federal regulations require that a wheelchair ramp’s ratio of Rise to Run can
not exceed 1 inch of Rise to 1 foot of Run.
• The ramp will go to the front door, which is 29 inches above the ground.
Using the diagram and the facts given above, determine the length of the
Ramp and the Run of the ramp. Round both to the nearest inch.
.
43
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant No. 0314898.
Cut in Pay
Samuel was called in by his manager. The manager explained that due to the recession, Samuel would have to take a 10% cut in pay until times got better. Samuel’s salary was $30,000. A few months later, the manager called Samuel
in and told him he would be getting a 10% increase in his salary. When Samuel
received his paycheck after the increase, he was angry.
1. Why was Samuel angry when he saw his paycheck? Use mathematics to
substantiate your answer.
2. What percent increase would Samuel need to get in order for him to return to
his original salary? (Round to the nearest tenth.)
3. If Samuel received a 10% increase every year for four years, how much would
his salary be, and what would be his percent of increase at the end of four
years?
Mathematics Proficiency Examination Practice Materials
43
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant No. 0314898.