1. 8.1 REVIEW: COMPARING FRACTIONS Monday, February 24 th

2. Math Message Label the top of your page, 8.1 and include the date. For the following fractions, rewrite and indicate whether it is closer to 0, ½, 1 ½, or 2. 1) 2/10 is closer to…. 2) 3/10 is closer to… 3) 5/3 is closer to… 4) 9/8 is closer to…

3. Renaming Fractions as Decimals How would you find equivalent fractions without using the Fraction-Stick chart or Decimal Number- Line chart in SRB pgs. 399 & 401? Use a multiplication table Look up fractions in the table of Equivalent Fractions, Decimals, and Percents (SRB pg. 401) Use the Multiplication Rule- Multiplying the numerator and denominator of a fraction by the same (nonzero) number yields an equivalent fraction

4. Quick Common Denominator The QCD is the product of the denominators you are renaming. For example, compare 2/3 and 3/5 1) Find the QCD: 3 * 5 = 15 2) Rename 2/3: 2/3 * 5/5 = 10/15 3) Rename 3/5: 3/5 * 3/3 = 9 /15 4) Because 10 > 9, 10/15 > 9/15, and 2/3 > 3/5

5. 8.2 ADDING MIXED NUMBERS Tuesday, February 25th

6. Math Message Label the top of your page, 8.2 and include the date. Rename each fraction as a whole number or mixed number and each mixed number as an improper fraction. 1) 3/3 = 2) 2 ½ = 3) 13/8 = 4) 11 ¼ =

7. Adding Mixed Numbers with fractions having LIKE denominators One way to find the sum of mixed numbers is to treat the fraction and whole number parts separately. Example: 3 1/8 1) add the whole number parts + 5 3/82) then add the fraction parts 8 4/8

8. Let’s try this one… 2 7/8 + 3 5/8

9. Adding Mixed Numbers with fractions having UNLIKE denominators 3 ¾ + 2 7/8 1) Find a common denominator for ¾ and 7/8 2) Rename the fraction parts of the mixed numbers so they have the same denominator 3) Add 4) Rename the sum

10. Watch this! Learn more about how to add and subtract Mixed Numbers using this link… http://studyjams.scholastic.com/studyjams/jams/math/fracti ons/add-sub-mixed-numbers.htm

11. 8.3 SUBTRACTING MIXED NUMBERS Thursday, February 27th

12. Math Message Label the top of your page, 8.3 and include the date. Number your paper 1-3 and name a common denominator for the following: 1) halves and sixths (1/2 & 1/6) 2) fourths and eights (1/4 & 1/8) 3) halves, thirds, and fourths (1/2, 1/3, ¼)

13. Subtracting Mixed Numbers with renaming 3 1/3*Since the top fraction is smaller - 1 2/3 than the bottom fraction, you can rename 3 1/3 to make the fraction part larger. 2 4/3 – 1 2/3 = 1 2/3 *Some sums might have to be renamed to write them in simplest form. Example: 4 7/4 = 4 + 4/4 + ¾ = 5 ¾ 4 7/4 and 5 ¾ are both equivalent

14. Let’s try some problems together…. Sample: 8 – 3 2/3 8 = 7 3/3 7 3/3 – 3 2/3 = ? Solution: 4 1/3 1) 6 – ¼ = 2) 4 3/5 – 1 4/5 = 3) 6 5/12 – 3 11/12 =

15. 8.4 CALCULATOR PRACTICE: COMPUTATION WITH FRACTIONS Friday, February 28 th

16. Math Message Label the top of your page, 8.4 and include the date. When comparing each fraction pair, write down which fraction is closer to 2. 1) 1 4/5 and 1 15/16 2) 8/7 and 1 1/6 3) 1 ½ and 15/8 4) 18/5 and 1 9/10

17. Calculator Practice In class, we will refer to SRB pg. 260 to practice converting fractions on a calculator.

18. 8.5 FRACTIONS OF FRACTIONS Monday, March 10 th

19. Math Message Label the top of your page, 8.5 and include the date. Solve the following Fraction-of problems: 1) There are 12 counters in a set. How many counters are in ½ of the set? _________ 2) If 3/5 of a set is 18 counters, how many are in the whole set? __________ 3) If ¾ of a set is 6, what is 1/8 of the set? ____

20. Using Unit Fractions to find a fraction of a number We will refer to SRB pgs. 74 & 75 for practice.

21. Modeling how to find a fraction of a fraction Example: What is 2/3 of ½? 1) The denominator of the second fraction is 2, so fold the paper into halves and shade one side. 2) The denominator of the first fraction is 3, fold the paper horizontally into thirds. 3) Unfold the sheet and shade the bottom 2/3. You are shading 2/3 of the entire sheet and also 2/3 of each half. 4) Write an X in each of the two parts of the sheet that was shaded twice. These parts represent 2/3 of ½ 1) 2) 3) 4) X X

22. 8.6 AN AREA MODEL FOR FRACTION MULTIPLICATION Tuesday, March 11 th

23. Today’s Lesson: Multiplying Fractions Multiplying Fractions One way to multiply two fractions is to multiply the numerators, and record the product as the product numerator. Multiply the denominator and record the product as the product denominator. For example: 3/5 of 7/8  3*7 = 21 (product numerator) 5*8 = 40 (product denominator) So, 3/5 of 7/8 = 21/40

24. An Area Model for Fraction Multiplication Another way to multiply fractions is to use area models! Let’s say we have the problem 2/3 of 1/5 2/3 of 1/5= 2/15

25. Math Work In your math notebook, title the page 8.6, answer the following questions. 1) 3 sets of 4 coins. How many coins in all? 2) 8 rows of 8 stamps. How many stamps in all? 3) 3 bags of 12 oranges for each of 3 classrooms. How many oranges in all?

26. 8.7 MULTIPLICATION OF FRACTIONS AND WHOLE NUMBERS Wednesday, March 12 th

27. Using an Area Model to Represent the Product of a Fraction and a Whole Number 2/3 * 2 = ? The whole is 2. The denominator of the fraction is 3. The numerator of the fraction is 2. 2/3* 2 = 4/3 or 1 1/3

28. Math Work In your math notebook, title the page 8.7, answer the following questions. 1) 1/5 of ½ = 2) 1/8 of ½ = 3) ½ of 2/14 = 4) 2/3 of ¾

29. Using an Algorithm to Multiply a Fraction and a Whole Number 2/3 * 2 = ? Rewrite the whole number as a fraction. 2/3 * 2/1 Next, multiply the numerators together. 2*2 = 4 After, multiply the denominators together. 3*1 = 3 Finally, place the numerator on top of the denominator. 4/3

30. 8.8 MULTIPLICATION OF MIXED NUMBERS Thursday, March 13 th

31. Multiplying with Mixed Numbers Method 1 6 * 4 3/5 = ? Calculate the partial products and add. 1. Think of 4 3/5 as 4 + 3/5  6 * (4 + 3/5) 2. Write the problem as the sum of partial products. (6*4) + (6* 3/5) 3. Calculate the partial products.  24 + 18/5 4. Convert 18/5 to a mixed number.  24 + 3 3/5 5. Add.  27 3/5

32. Multiplying with Mixed Numbers Method 2 6 * 4 3/5 Convert whole number and mixed numbers to improper fractions. 1. Think of 6 as 6/1 and 4 3/5 as 23/5 2. Rewrite the problem as a fraction multiplication. 6/1 * 23/5 3. Use a fraction algorithm.  6*23/ 1*5 4. Multiply.  138/5 5. Simplify the answer by converting 138/5 to a mixed number.  27 3/5

33. Math Work In your math notebook, title the page 8.8, write each mixed number as a fraction. 1) 1 2/3= 2) 8 7/10= 3) 6 4/7 = 4) 3 7/9 =

34. FINDING A PERCENT OF A NUMBER Monday, March 17 th

35. Finding the Percent of a Number: The flu hit Roosevelt School hard. 40% of the 480 students were absent at least one day last week. How many students were absent at least one day? Write 40% of 480= # of students absent The unit-percent approach  480 is 100% 1% of 480  4.8 40% of 480  is 40 * 4.8 = 192 students.

36. Finding the Percent of a Number: 10- percent approach. 480 is 100%, or the whole. 10% of 480= 48 40% of 480  4*48 = 192 students Equivalent- fractions approach. 40% = 2/5 40% of 480  2/5 * 480 = 192 students Equivalent-decimal approach. 40% = 0.40 40% of 480  0.40*480 = 192 students

37. Using Fractions to Find the Percent of a Number A percent can be thought of a fraction with a denominator of 100. For example, 43% is 43/100 Many commonly used percents are equivalent to easy fractions: For example, 25% = 1/4, 50% = 1/2 Finding the percent of a number can be thought of as finding a fraction of that number. For example, 50% of 18 = ½ of 18 = 9

38. Math Work In your math notebook, title the page 8.9, write each percent as a decimal and as a fraction in simplest form. 1) 20% = 2) 45%= 3) 35%= 4) 110%=

39. 8.10 RELATING FRACTIONAL UNITS TO THE WHOLE Tuesday, March 18 th

40. Math Work In your math notebook, title the page 8.10, solve fraction- of problems. 1) How many days are 2/7 of a week? 2) How many counters are 2/6 of 18 counters? 3) How many seconds are 1/6 of a minute? 4) How many ounces are ¾ of a cup? 5) How many inches are 4/9 of a yard?

41. Using Unit Fractions to Find the Whole Unit fraction = any fraction with a numerator of 1. Unit percent = 1% of a whole. If a unit fraction (1/n) is known, the whole is equal to the value of 1/n times the denominator(n). If the unit percent is known, the whole is equal to the value of 1% times 100.

42. Example #1 Alton collected 252 marbles but lost 4/7 of them on his way to school. When he arrived at school, how many marbles did Alton have left? 1. Find 4/7 of 252  4/7* 252  1,008/7= 144. 2. Then subtract 252-144 = 108 marbles.

43. Example #2 If 31 pages are 1/8 of a book, how many pages in the book? 1/8 * p = 31 p = 31 1/8  31* 8 p = 248 248 pages

44. 8.12 FRACTION DIVISION Wednesday, March 19 th

45. Division with Fractions How many ½-pound boxes of candy can be made from 6 pounds of candy? Each part= 1/2 lb. The whole rectangle = 6lbs. 6 ½ = 12 boxes

46. Common Denominator Division Step 1. Rename the numbers using a common denominator. Step 2. Divide the numerators. 4 divided by 2/3 1. Rename 4 using common denominators. 12/3 2. Rename the problem. 12/ 3 divided by 2/3 3. Divide the numerators. 12 divided by 2 = 6 4. Place the numerator on top of denominator. 6/1 = 6

47. Math Work In your math notebook, title the page 8.12, write each set of numbers and then rename them using a common denominator. 1) 2/3, 3/4, ___ 2) 3/4, 2, ___ 3) 1/8, 2/3, ___

48. UNIT 8 REVIEW Thursday, March 20 th

49. Concepts to Review Convert among fractions, decimals, and percents. Convert between fractions and mixed or whole numbers. Find common denominators. Order and compare fractions. Use an algorithm to add mixed numbers. Use an algorithm to subtract mixed numbers with like denominators. SRB Pages to Review  pages 66-75