302A final exam reviewWhat is on the test?Chapter 1Slide 4Chapter 2Slide 6Slide 7Chapter 3Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Chapter 4Slide 16Slide 17Slide 18Slide 19Slide 20Chapter 5Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Slide 32Slide 33Slide 34Chapter 6Slide 36Slide 37Slide 38Slide 39Slide 40Slide 41Slide 42Slide 43Slide 44Slide 45Percent & Proportion QuestionsEstimateTry this oneSlide 49Last oneGood Luck!302A final exam review302A final exam reviewWhat 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, 5.15, 5.16, 6.3, 6.5, •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 tablesChapter 1•Fred Flintstone always says“YABBADABBADO.” If he writes this phrase over and over, what will the 246th letter be?•DChapter 2•Explain why 32 in base 5 is not the same as 32 in base 6.•32 in base 5 means 3 fives and 2 ones, which is 17 in base 10.•32 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 300507.”•The student does not understand that the value of the digit is found in the place: 300507 is actually 3 hundred-thousands plus 5 hundreds and 7 ones. Three hundred fifty seven is written 357--3 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.•“347 + 59: add one to each number and get 348 + 60 = 408.”•No: 347 + 59 is the same as 346 + 59 because 346 + 1 + 60 - 1 = 346 + 60 + 1 - 1, and 1 - 1 = 0. The answer is 406.Chapter 3•Is this student correct?•“497 - 39 = 497 - 40 - 1 = 457 - 1 = 456.”•No, the student is not correct because 497 - 39 = (497) - (40 - 1) = (497) - 40 + 1 = 458. An easier way to think about this is 499 - 39 = 460, and then subtract the 2 from 499, to get 458.Chapter 3•Is this student correct?•“390 - 27 is the same as 300 - 0 + 90 - 20 + 0 - 7. So, 300 + 70 + -7 = 370 + -7 = 363.”•Yes, this student is correct. This is analogous to 390 = 380 + 10 = 27; 300 - 0 + 80 - 20 + 10 - 7 = 300 + 60 + 3. Note: to avoid this negative situation, we regroup.Chapter 3•Multiply 39 • 12 using at least 5 different strategies. •Lattice Multiplication•Rectangular Array•Egyptian Duplation•Lightning-Cross•39 • 10 + 39 • 2•40 • 12 - 1 • 12•30 • 10 + 9 • 10 + 30 • 2 + 9 • 2 = (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 factorChapter 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 factorsChapter 4•Prime factorization: many ways to get the factorization, but only one prime factorization for any number.•Find the prime factorization of 84.•2 • 2 • 3 • 7, or 22 • 3 • 7Chapter 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 200.•20: 60 = 20 • 3, 80 = 20 • 4, 200 = 20 • 10.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 200.•1200: 60 • 20 = 1200, 80 • 15 = 1200, 200 • 6 = 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 wholeRatioOperatorQuotient•Make up a real-world problem for each model above for 6/10.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-wholediscrete,number line (measurement)•Represent 5/8 and 11/8 using each of the pictorial models above.Chapter 5•Errors in comparing fractions: 2/6 > 1/2•Look at the numerators: 2 > 1–Two pieces is more than one piece.•Look at the denominators: 6 > 2–We need 6 to make a whole rather than 2.•There are more pieces not shaded than shaded.–If we look at what is not shaded, then there are more unshaded pieces.The pieces are smaller in sixths than in halves.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 wholeChapter 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