1 - University of Arizona
Math 302A Final Exam Review
When reviewing all types of addition, multiplication, subtraction, and division problems (with or without fractions) do the problems using pictures and non-traditional methods. Check your answers with the traditional algorithms.
Review tests, test reviews, notes,worksheets, explorations, quizzes, test 1 and test 2 reviews, and homework in addition to this review.
Solve the following word problem in two ways: a) by using algebra and b) by using a conceptual approach.
If one block of ice is [pic] dollars, how much is [pic] block ice?
a) Explain how we could use manipulatives to solve [pic].
b) Solve [pic]. (Recall that A=10)
a) Give a brief definition of GCF(a,b).
b) Find GCF(45, 150) in two different ways.
A student attempts to multiply [pic] and does the following:
[pic] and the answer is then 800+140+120=1060
It is easy to check that the answer is not correct. What is the student wrong? Draw a picture or use algebra to defend your answer.
Each of the following is a sentence involving a fraction and pictures. Fill in the missing part of each sentence.
a. xxxxx
xxxxx is ______of xxxxxx
xxxxx
b. xxxxxx
xxxxxx is 3/5 of
c. is 5/4 of xxxx
xxxx
Write a realistic story problem for [pic] using the partitioning model of division. Solve the problem using a conceptual approach.
You have given the following question to your students:
Ali can build a model airplane in 3 hours. Tom can build one in 4 hours. How long can they build one together?
One student gives the following answer:
Well Ali can build one in 180 minutes and Tom can build one in 240 minutes. So together they can build one in 210 minutes.
Is this answer correct? Why or why not? If it is not correct, then what is the correct answer?
In certain county, 3/5 of all registered voters are Males. Five-sixths of all Females voted in the last election, but 25% of Males did not vote. What percent of the registered voters did vote in the last election?
A child is trying to solve 52 – 28. He adds two to the 28 to make the problem 52 – 30 and gets 22. Then he subtracts 2 from 22 and gets 20 as the answer. What would you say to the child to help him understand why adding 2 at the end is the correct step to take?
Show the child the correct way by solving [pic] by applying the method correctly.
In a class 2/9 of the students are female and there are 15 more male students than females. How many students are there in the class? Solve the problem in two ways:
a. By having a proportion:
b. By using a diagram:
In 2000, City A, with population 55,489 reported 214 violent crimes. In the same year, City B, with population 185,217 reported 639 violent crimes. Which city has the worse crime rate? Explain your answer in 1 sentence.
When I write the fraction 5/7, if I am thinking of this fraction as a part-whole quantity, what does the numerator represent? What does the denominator represent?
Without getting common denominators, how could you tell which is bigger of:
a. 4/7 or 4/9
b. 9/11 or 7/9
c. 3/5 or 7/16
d. 2/7 or 1/3
e. 3/8 or 4/7
solve using diagrams
14. Justin poured 3/4 pounds of sugar into a container. The container he used will only hold up to 2 1/3 pounds of sugar. What fraction of the container did he fill?
23. Justin also had 1 1/2 cups of oil available. If he only needed 1/6 of the oil that he had. How many cups of oil did he use?
24. Justin then used 1/2 tsp. of vinegar. This was 2/3 of all of the vinegar that he had. How many tsp. of vinegar did he have to start with?
14. Consider the fraction 6/10 depicted below:
Show what the portion size would need to be in order to have the following fractions:
a. 3/5
b. (1 1/5) / 2
c. (1 1/2) / (2 1/2)
15. Consider the following situation: Jessica has 2 1/2 dozen eggs. She used 8 eggs for cooking. If you were to write down the fraction of the total number of eggs that Jessica used, indicate what fraction would result from thinking of the portion size as:
a. 2 eggs
b. 1/2 dozen eggs
c. 4 eggs
16. How could you use a picture to prove to someone that 9/12 and 6/8 represent the same fractional quantity (note, pictures can be deceiving, how could you prove that you are not just taking artistic license to make them look the same?)
17. Say that X X X X X X X X X X X X represents 3/5. Show 3/4.
18. Say that represents 1 1/3. Show 1/4
19. Say that represents 1 2/3. How would you find 1/2?
a. If the following picture represents 2 2/3 of some whole quantity, what picture would represent 1/4 of that whole?
1. (4 pts) Use a discrete model of fractions to show that the following three fractions represent the same amount: 3/4, 6/8, (1 1/2) / 2
3. Order the following fractions in order from least value to greatest value without converting to decimals for finding common denominators. Explain your reasoning:
a. 6/7, 5/11, 2/3
b. 2/5, 5/6, 4/7, 7/8, 3/10
4. For each of the following, justify your reasoning.
c. Name three fractions between 1/8 and 1/9.
d. Is 10/13 closer to 1/2 or to 1?
e. Name a fraction closer to 1/2 than to 5/12.
f. Name a fraction close to 1 than to 7/8
g. Name a fraction between 1/4 and 1/2 that has a denominator of 11.
8. A recipe calls for 3/4 cups of flour. You only have 3/8 cups of flour on hand. What fraction of the recipe can you make?
9. Looking through the fabric store, you find some fabric that you want to buy. The piece is 1 1/2 yards long, but you only need 2/3 yards. What fraction of the piece of fabric do you need to buy?
6. Without actually doing any computation (use your fraction sense), determine whether
h. 5 5/8 + 4 3/42 is greater than 10 or less than 10
i. 7/8 + 3/4 + 1/16 is greater than 2 or less than 2.
j. 1/4 + 1 9/10 is greater than 2 or less than 2.
k. 8 1/2 – 2 2/3 is between which numbers, 5 and 5 1/2 or 5 1/2 and 6.
P 301 green book
2 don’t do mentally, do with a) the traditional algorithm and b) using a picture
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