Review for the Final 302A, Fall, 2007

What is on the test? From book: 1.2, 1.3, 1.4, 1.7; 2.3; 3.1, 3.2, 3.3, 3.4; 4.2, 4.3; 5.2, 5.3, 5.4; 6.1, 6.2 From Explorations: 1.1, 1.4, 1.7; 2.8, 2.9; 3.1; 3.13, 3.15, 3.19, 3.20, 4.2, 4.3, 5.8, 5.9, 5.10, 5.12, 5.13, 5.14, 5.15, 5.16, 6.3, 6.4, 6.5, 6.7 From Class Notes: Describe the strategies used by the students--don’t need to know the names.

Chapter 1 A factory makes 3-legged stools and 4- legged tables. This month, the factory used 100 legs and built 3 more stools than tables. How many stools did the factory make? 16 stools, 13 tables

Chapter 1 Fred Flintstone always says “YABBADABBADO.” If he writes this phrase over and over, what will the 246th letter be? D

Chapter 2 Explain why 32 in base 5 is not the same as 32 in base in base 5 means 3 fives and 2 ones, which is 17 in base in base 6 means 3 sixes and 2 ones, which is 20 in base 10. So, 32 in base 5 is smaller than 32 in base 6.

Chapter 2 Why is it wrong to say 37 in base 5? In base 5, there are only the digits 0, 1, 2, 3, and 4. 7 in base 5 is written 12.

Chapter 2 What error is the student making? “Three hundred fifty seven is written ” The student does not understand that the value of the digit is found in the place: is actually 3 hundred-thousands plus 5 hundreds and 7 ones. Three hundred fifty seven is written hundreds plus 5 tens plus 7 ones.

Chapter 3 List some common mistakes that children make in addition. Do not line up place values. Do not regroup properly. Do not account for 0s as place holders.

Chapter 3 Is this student correct? Explain. “ : add one to each number and get = 408.” No: is the same as because = , and = 0. The answer is 406.

Chapter 3 Is this student correct? “ = = = 456.” No, the student is not correct because = (497) - (40 - 1) = (497) = 458. An easier way to think about this is = 460, and then subtract the 2 from 499, to get 458.

Chapter 3 Is this student correct? “ is the same as So, = = 363.” Yes, this student is correct. This is analogous to 390 = = 27; = Note: to avoid this negative situation, we regroup.

Chapter 3 Multiply using at least 5 different strategies. Lattice Multiplication Rectangular Area Egyptian Duplation = (30 + 9)(10 + 2)

Chapter 3 Divide 259 ÷ 15 using at least 5 different strategies. Scaffold Repeated subtraction Repeated addition Use a benchmark Partition (Thomas’ strategy)

Chapter 3 Models for addition: Put together, increase by, missing addend Models for subtraction: Take away, compare, missing addend Models for multiplication: Area, Cartesian Product, Repeated addition, measurement, missing factor Models for division: Partition, Repeated subtraction, missing factor

Chapter 4 An odd number: An even number:

Chapter 4 Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, … 2 factors ONE IS NOT PRIME. Composite numbers: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, … at least 3 factors Square numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, … an odd number of factors

Chapter 4 Prime factorization: many ways to get the factorization, but only one prime factorization for any number. Find the prime factorization of , or

Chapter 4 Greatest Common Factor: The greatest number that can divide evenly into a set of numbers. The GCF of 50 and 75 is 25. You try: Find the GCF of 60, 80, and : 60 = 20 3, 80 = 20 4, 200 =

Chapter 4 The Least Common Multiple is the smallest number that is divisible by a set of numbers. The LCM of 50 and 75 is 150. You try: Find the LCM of 60, 80, and : = 1200, = 1200, = 1200.

Chapter 4 What is the largest square that can be used to fill a 6 x 10 rectangle. 2 x 2: You can draw it to see why. (Which is involved here, GCF or LCM?)

Chapter 5 Fractions models: Part of a whole Ratio Operator Quotient Make up a situation for 6/10 for each of the models above.

Chapter 5 Name the model for each situation of 5/6. I have 5 sodas for 6 people--how much does each person get? Out of 6 grades, 5 were As. I had 36 gumballs, but I lost 6 of them. What fraction describes what is left? In a room of students, 50 wore glasses and 10 did not wear glasses.

Chapter 5 There are three ways to represent a fraction using a part of a whole model: part-whole discrete, number line (measurement) Represent 5/8 and 11/8 using each of the above pictorial models.

Chapter 5 Errors in comparing fractions: 2/6 > 1/2 Look at the numerators: 2 > 1 Look at the denominators: 6 > 2

Chapter 5 Appropriate ways to compare fractions: –Rewrite decimal equivalents. –Rewrite fractions with common denominators. –Place fractions on the number line. –Sketch parts of a whole, with the same size whole

Chapter 5 More ways to compare fractions: –Compare to a benchmark, like 1/2 or 3/4. –Same numerators: a/b > a/(b + 1) 2/3 > 2/4 –Same denominators: (a + 1)/b > a/b 5/7 > 4/7 –Look at the part that is not shaded: 5/9 < 8/12 because 4 out of 9 parts are not shaded compared with 4 out of 12 parts not shaded.

Chapter 5 Compare these fractions without using decimals or common denominators. 37/81 and 51/90 691/4 and 791/7 200/213 and 199/214 7/19 and 14/39

Chapter 5 Remember how to compute with fractions. Explain the error: 2/5 + 5/8 = 7/13 3 4/7 + 9/14 = 3 13/14 2 7/ /8 = 7 11/8 = 8 1/8 5 4/6 + 5/6 = 5 9/6 = 5 1/2

Chapter 5 Explain the error: 3 - 4/5 = 2 4/ /7 = 3 6/7 3 7/ /4 = 1 6/4 = 2 1/2 9 1/ /4 = 9 2/ /8 = 8 12/ /8 = 1 4/8 = 1 1/2

Chapter 5 Explain the error: 3/7 4/9 = 7/16 2 1/4 3 1/2 = 6 1/8 7/12 4/5 = 35/48 4/7 3/5 = 20/35 21/35 = 420/1225 = 84/245 = 12/35

Chapter 5 Explain the error: 3/5 ÷ 4/5 = 4/3 12 1/4 ÷ 6 1/2 = 2 1/2

Chapter 5 Decimals: Name a fraction and a decimal that is closer to 4/9 than 5/11. Explain what is wrong: 3.45 ÷.05 = 0.69

Chapter 5 True or false? Explain. 3.69/47 = 369/ /30.04 = 502/3004

Chapter 5 Order these decimals: 3.95, 4.977, 3.957, 4.697, Round to the nearest tenth. Explain in words, or use a picture.

Chapter 6 An employee making $24,000 was given a bonus of $1000. What percent of his salary was his bonus? 1000/24,000 = x/ ,000 = 24,000x x ≈ 4.17%

Chapter 6 Which is faster? 11 miles in 16 minutes or 24 miles in 39 minutes? Explain.

Chapter 6 Ryan bought 45 cups for $3.15. “0.07! That’s a great rate!” What rate does 0.07 represent? Describe this situation with a different rate--and state what this different rate represents.

Chapter 6 Which ratio is not equivalent to the others? (a)42 : 49 (b)12 : 21 (c)50.4 : 58.8 (d)294 : 357

Chapter 6 Write each rational number as a decimal and a percent. 3 4/5 1/11 2 1/3

Chapter 6 Write each decimal as a fraction in simplest form and a percent

Chapter 6 Write each percent as a fraction and a decimal. 48% 39.8% 2 1/2% 0.841%

Chapter 6 A car travels 60 mph, and a plane travels 15 miles per minute. How far does the car travel while the plane travels 600 miles? (Hint: you can set up one proportion, two proportions, or skip the proportions entirely!) Answer is the car travels 40 miles--the car travels 1 miles for each 15 miles the plane travels. 1/15 = x/600.

Chapter 6 DO NOT set up a proportion and solve: use estimation instead. (a) Find 9% of 360. (b) Find 5% of 297. (c) Find 400% of 35. (d) Find 45% of 784.

Chapter 6 DO NOT set up a proportion and solve: use estimation instead. (e) What percent of 80 is 39? (f) What percent of 120 is 31? (g) 27 is what percent of 36? (h) 87 is 20% of what number? Now, go back and set up proportions to find the exact values of (a) - (h). Were you close?

Chapter 6 David has 150 mg of fools’ gold. Find the new amount if: He loses 30%? He increases her amount by 90%? He decreases her amount by 40%?

Study Hard, and show up on time!