# # Fourth Grade. Understanding Fractions. Slide 1 / 162 Slide 2 / 162. Slide 4 / 162. Slide 3 / 162. Slide 5 / 162. Slide 6 / 162

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1 Slide / 62 Slide 2 / 62 Fourth Grade Fraction Decimal oncepts Slide 3 / 62 Slide 4 / 62 Table of ontents lick on the topic to go to that section - Understanding Fractions - Mixed Numbers - ompare and Order Fractions - Equivalent Fractions - onvert Decimals to Fractions - onvert Fractions to Decimals - Number Line Location Understanding Fractions click to return to table of contents Slide 5 / 62 Slide 6 / 62 Mr. Number Line is taking a short nap. He's a little tired from a long day of problem solving! 2 3 What type of numbers is he using to count sheep? 4 5 Positive lick WHOLE for Numbers While napping, Mr. Number Line is dreaming of pepperoni pizza! What type of numbers would you use to help Mr. Number Line count the total number of pizzas in his dream? Fractions and/or lick for Mixed Numbers Talk to an elbow partner and share how you would count the pizzas. How are fractions different from whole numbers? # # # #

2 Slide 6 () / 62 Slide 7 / 62 While napping, Mr. Number Line is dreaming of pepperoni pizza! What type of numbers would you use to help Mr. Number Line count the total number of pizzas in his dream? Fractions represent what is ETWEEN whole numbers. fraction is a PRT of a WHOLE. The first fractions we will learn about are PROPER FRTIONS. Examples of proper fractions are shown below in word form: Fractions and/or lick for Mixed Numbers Talk to an elbow partner and share how you would count the pizzas. Teacher Notes Students could use one of the following strategies to count the halves. Using only fractions: /2 2/2 3/2 4/2 5/2 6/2 7/2 one half...two halves...three halves... Using fractions and whole numbers: /2 3/2 2 5/2 3 7/2 one half... one...three halves...two... How are fractions different from whole numbers? Using fractions, whole numbers and mixed numbers: Great way to go over difference between whole numbers, fractions and mixed numbers one half...one...one and one half...two # # three eighths three fourths one quarter one half Proper Fractions in Standard Form: 3 8 four fifths two thirds five tenths one sixths Slide 2 to the 5right to 4reveal fractions 3 in standard form Slide 7 () / 62 Slide 8 / 62 Fractions represent Students what may need is ETWEEN to review standard whole form. numbers. Practice fraction is with the 8 fractions a PRT on this of slide. a WHOLE. Have students explain The first fractions how a fraction we will is learn written about in standard are PROPER form. If important FRTIONS. vocabulary (numerator and denominator) does not come Examples easily, of proper the slides fractions that follow are will shown go over below these terms. in word The form: most important thing is that students know that standard three form is the typical one way we see fractions. four number on five top and a number on the bottom and a line segment in between. y the way this line segment is called the eighths quarter vinculum or fraction fifths bar. tenths IMPORTNT: The word document "Proper Fraction - Flash ards" contains the 8 fractions on this slide plus three eight additional one proper fractions. two Students can work in one groups to write the standard form on each flash card. fourths Once students half cut out these flash thirds cards, they can write sixths "Proper[This Fraction" object is on a pull the tab] blank side. Proper Fractions in Standard Form: 3 Slide 2 to the 5right to 4reveal 3 8 fractions 3 in standard form. 2 4 Teacher Notes Let's look at the 8 proper fractions we discussed on the previous slide Talk to an elbow partner and share what you know about these proper fractions. Write down any important ideas you discuss with your partner so that you can share these ideas with the whole class We will organize our ideas on the next slide Slide 9 / 62 Slide 0 / Let's review what we know so far about fractions.. ll Proper Fractions can be found between 0 and on a number line. Proper Fractions { Whole numbers are the first types of numbers we learn about. Whole numbers are found in the real world, but fractions are used much more frequently. rainstorm with a partner where we can find fractions in the real world.

3 Slide / 62 Slide 2 / 62 c 3/4c /2c /4c Slide 3 / 62 Let's review some important vocabulary to help us better understand fractions. Noomy the Numerator and Deeno the Denominator are here to help us. Noomy the numerator represents the top part of a fraction. He shows the PRT of the fraction that we are looking at. PRT and Purple both start with P. Deeno the denominator represents the bottom of a fraction. He shows the WHOLE (or ONE) that we are looking at. ONE and Orange both start with O. Slide 4 / 62 Every fraction is division and every division problem can be shown as a fraction. Even the division sign looks like a fraction. lick on the top part of the division sign. NUMERTOR lick on the bottom part of the division sign. DENOMINTOR Slide 5 / 62 Slide 6 / 62 Fractions can also be used to name a part of a collection of objects. Fractions can be used to name a part of a whole object. of the balls are You ate of the pie. needed for practice.

4 Slide 7 / 62 Naming Fractions Slide 8 / 62 Which number is the numerator in the fraction? 2 3 top number = numerator bottom number = denominator Slide 8 () / 62 Which number is the numerator in the fraction? Slide 9 / 62 2 Which number is the denominator in the fraction? 2 Slide 9 () / 62 2 Which number is the denominator in the fraction? Slide 20 / 62 3 Which fraction has a 5 in the denominator? 7

5 Slide 20 () / 62 3 Which fraction has a 5 in the denominator? Slide 2 / 62 4 Which fraction has a 3 in the numerator? Slide 2 () / 62 4 Which fraction has a 3 in the numerator? Slide 22 / 62 5 What fraction of this set is blue? Slide 22 () / 62 5 What fraction of this set is blue? Slide 23 / 62 6 What fraction of this set is purple? 3 7

6 Slide 23 () / 62 Slide 24 / 62 6 What fraction of this set is purple? 7 What fraction of this set is red? 2 5 Slide 24 () / 62 Slide 25 / 62 7 What fraction of this set is red? 3 6 Mixed Numbers click to return to table of contents Slide 26 / 62 Take out the following number of pattern blocks Slide 27 / 62 If a hexagon is worth, what are 3 trapezoids worth? trapezoid 9 click for answer hexagon rhombus 8 triangle

7 Slide 28 / 62 Slide 29 / 62 If a hexagon is worth, what are 4 rhombi worth? click for answer 8 If a hexagon is worth, what are 5 triangles worth? click for answer Slide 29 () / 62 Slide 30 / 62 8 If a hexagon is worth, what are 5 triangles worth? 9 If a hexagon is worth, what are 5 trapezoids worth? click for answer Slide 30 () / 62 Slide 3 / 62 9 If a hexagon is worth, what are 5 trapezoids worth? 0 If a hexagon is worth, what are 8 rhombi worth?

8 Slide 3 () / 62 0 If a hexagon is worth, what are 8 rhombi worth? Slide 32 / 62 If a hexagon is worth, what are triangles worth? Slide 32 () / 62 If a hexagon is worth, what are triangles worth? Slide 33 / 62 2 If a hexagon is worth, what are 9 trapezoids worth? Slide 33 () / 62 2 If a hexagon is worth, what are 9 trapezoids worth? Slide 34 / 62 Sometimes the hexagon is not worth one. What do we do if a unit other than one is given? First figure out what one is worth, then solve the problem. click

9 Slide 35 / 62 3 If the triangle is, what shape is ONE? Slide 35 () / 62 3 If the triangle is, what shape is ONE? hexagon rhombus trapezoid hexagon rhombus trapezoid Slide 36 / 62 4 If the triangle is, what is a trapezoid worth? Slide 36 () / 62 4 If the triangle is, what is a trapezoid worth? 3 4 Slide 37 / 62 5 If the triangle is, what is the hexagon worth? Slide 37 () / 62 5 If the triangle is, what is the hexagon worth? 6 4

10 Slide 38 / 62 Slide 39 / 62 Fractions that are greater than one are often called improper fractions, even though there is nothing improper about them. mixed number is a number that has a whole part and a fractional part. Improper Fraction Mixed Number For example: 6 is the whole part is the fractional part Slide 40 / 62 Slide 4 / 62 To convert an improper fraction to a mixed number. To convert an improper fraction to a mixed number. First divide 3 by 6 First divide 30 by 4 Divisor Quotient Remainder Then write in the form: quotient remainder divisor Divisor Quotient Remainder Then write in the form: quotient remainder divisor click for mixed number Slide 42 / 62 Slide 43 / 62 Match the Mixed Numbers and Improper Fractions.

11 Slide 43 () / 62 Slide 44 / 62 Slide 44 () / 62 Slide 45 / 62 Slide 45 () / 62 Slide 46 / 62

12 Slide 46 () / 62 Slide 47 / 62 Slide 47 () / 62 Slide 48 / 62 Slide 48 () / 62 Slide 49 / 62 ompare and Order Fractions click to return to table of contents

13 Slide 50 / 62 Slide 5 / 62 The first step when comparing fractions is to look at the numerators and denominators. numerators denominators When the denominators are the same: - the unit fractions are the same size - only need to compare the number of pieces # (numerators) need to be compared Slide 52 / 62 Slide 53 / 62 Reorder the following fractions from least to greatest. 22 Which of the following is ordered least to greatest? Slide 53 () / Which of the following is ordered least to greatest? Slide 54 / Which of the following is ordered greatest to least?

14 Slide 54 () / Which of the following is ordered greatest to least? Slide 55 / 62 When the numerators are the same: - there are the same number of pieces - compare the size of the denominator The larger the denominator, the smaller the size of each piece. The smaller the denominator, the larger the size of each piece. Slide 56 / 62 Slide 57 / 62 Reorder the following fractions from least to greatest. 24 Which of the following is ordered least to greatest? Slide 57 () / Which of the following is ordered least to greatest? Slide 58 / Which of the following is ordered greatest to least?

15 Slide 58 () / Which of the following is ordered greatest to least? Slide 59 / 62 If numerators and denominators are not the same, we need to use other methods to compare fractions. Use benchmarks to see if the fraction is close to 0, /2, or and then order them. 0 2 Slide 60 / Which fraction is closest to zero? Slide 60 () / Which fraction is closest to zero? D D Slide 6 / Which fraction is closest to one? Slide 6 () / Which fraction is closest to one? D D

16 Slide 62 / Which fraction is closest to a half? Slide 62 () / Which fraction is closest to a half? D D Slide 63 / Which fraction is closest to one? Slide 63 () / Which fraction is closest to one? D D D Slide 64 / Which fraction is closest to a half? Slide 64 () / Which fraction is closest to a half? D D

17 Slide 65 / 62 3 Which fraction is closest to zero? Slide 65 () / 62 3 Which fraction is closest to zero? D D Slide 66 / 62 Slide 67 / 62 Use benchmarks of 0, /2 and to order the fractions least to greatest. Use benchmarks of 0, /2 and to order the fractions least to greatest. Slide 68 / Which of the following is ordered least to greatest? Slide 68 () / Which of the following is ordered least to greatest?

18 Slide 69 / Which of the following is ordered least to greatest? Slide 69 () / Which of the following is ordered least to greatest? Slide 70 / 62 Slide 7 / 62 lick below to use this interactive number line. Equivalent Fractions If the previous strategies don't work to compare fractions, we need to find equivalent fractions in order to compare them. click to return to table of contents Slide 72 / 62 Slide 73 / 62 fraction stick is a model for the whole, or ONE. Fraction Stick hart Use it to find equivalent fractions. Find equivalent fractions for

19 Slide 73 () / 62 Fraction Stick hart Slide 74 / Find an equivalent fraction for Teacher Notes Use a print out of a fraction stick chart or use manipulatives as shown here to aide students in their understanding of equivalent fractions. Slide 74 () / Find an equivalent fraction for Slide 75 / Find an equivalent fraction for 6/8, 9/2, etc. Slide 75 () / Find an equivalent fraction for Slide 76 / Find an equivalent fraction for 6/32, 24/48, etc.

20 Slide 76 () / Find an equivalent fraction for Slide 77 / Find an equivalent fraction for 2/6, 3/9, etc. Slide 77 () / Find an equivalent fraction for Slide 78 / 62 fraction stick is a model for the whole, or ONE. Use it to compare fractions. 4/2, 2/8, etc. Which number is larger? or 38 Which number is larger? Slide 79 / Which number is larger? Slide 79 () / 62

21 39 Which number is larger? Slide 80 / Which number is larger? Slide 80 () / Which number is larger? Slide 8 / Which number is larger? Slide 8 () / 62 Slide 82 / 62 Slide 83 / 62 Splitting Fractions Sticks to Make Equivalent Fractions If a horizontal line is drawn to divide each part of the rectangle into 2 parts, what fraction of the whole is shaded? What fraction of the whole is shaded? Has the shaded amount of the rectangle changed?

22 Slide 84 / 62 4 What fraction of the whole is shaded now? Slide 84 () / 62 4 What fraction of the whole is shaded now? 4 2 Slide 85 / What fraction of the whole is shaded? Slide 85 () / What fraction of the whole is shaded? 4 Slide 86 / Use these two horizontal lines to divide the whole. What fraction of the whole is shaded now? Slide 86 () / Use these two horizontal lines to divide the whole. What fraction of the whole is shaded now? 3 2

23 Slide 87 / Is the shaded region the same in each of these? Slide 87 () / Is the shaded region the same in each of these? Yes No Yes No Yes Slide 88 / 62 Slide 89 / 62 What do you notice about the denominators in each set of equivalent fractions? What patterns have you noticed in the previous examples about making equivalent fractions? What important idea do we know about multiplying by? Slide 90 / 62 Slide 9 / 62 Use the multiplication table to make equivalent fractions. Multiplication Rule To find an equivalent fraction, multiply both the numerator and the denominator of the fraction by the same number. 2 5 =?? Pull

24 Slide 9 () / 62 Use the multiplication table to make equivalent fractions. Slide 92 / 62 Find three equivalent fractions. 2 5 =?? Teacher Notes To see fractions equivalent to 2/5, move the fraction circle along the strips between 2 and 5. Pull Slide 93 / Which two fractions are equivalent to? Slide 93 () / Which two fractions are equivalent to? D D & D Slide 94 / What fractions are equivalent to? Slide 94 () / What fractions are equivalent to? D D D

25 Slide 95 / 62 Slide 96 / What is a fraction equivalent to? Slide 97 / 62 Slide 98 / What is a fraction equivalent to? What important idea to we know about dividing by? How can we use division to find equivalent fractions? Slide 99 / 62 Slide 00 / 62 Steps to Simplifying Fractions. Find the GF of both numbers. 2. Divide the numerator and denominator by that number. 3. will be the fraction in simplified form. GF = 2

26 Slide 0 / What is in simplified form? Slide 0 () / What is in simplified form? /3 Slide 02 / 62 5 What is in simplified form? Slide 02 () / 62 5 What is in simplified form? /2 Slide 03 / What is in simplified form? Slide 03 () / What is in simplified form? /2

27 Slide 04 / What is in simplified form? Slide 04 () / What is in simplified form? /5 Slide 05 / What is in simplified form? Slide 05 () / What is in simplified form? /8 Slide 06 / 62 Slide 06 () / 62

28 Slide 07 / 62 Slide 07 () / 62 Slide 08 / 62 Slide 08 () / 62 Slide 09 / 62 Slide 09 () / 62

29 Slide 0 / 62 Slide 0 () / 62 Slide / 62 Slide () / 62 Slide 2 / 62 Slide 3 / 62 onverting a Decimal to a Fraction onverting Decimals to Fractions. Put the digits in the numerator. 2. The denominator represents the place value. 3. Simplify fraction if you can. Example: 0.9 = 0.25 = click to return to table of contents

30 Slide 4 / 62 Match the following decimals with their fraction equivalents. 0.6 = Slide 5 / 62 6 What fraction is equivalent to the decimal below? (e sure answer is in simplified form.) 0.3 = 0.7 = 0.06 = 0.03 = Slide 6 / What fraction is equivalent to the decimal below? (e sure answer is in simplified form.) Slide 7 / What fraction is equivalent to the decimal below? (e sure answer is in simplified form.) 0.44 = 0.2 = Slide 8 / What fraction is equivalent to the decimal below? (e sure answer is in simplified form.) Slide 9 / What fraction is equivalent to the decimal below? (e sure answer is in simplified form.) 0.05 = 0.33 =

31 Slide 20 / 62 Slide 2 / 62 onverting fractions to decimal form by changing the denominator. onverting Fractions to Decimals Steps:. Use mental math, the multiplication rule or the division rule to change each fraction to an equivalent fraction having a denominator of 0 or Write the new fraction as a decimal. click to return to table of contents Slide 22 / 62 Slide 23 / 62 Examples: x 4 x 4 x 5 x 5 _ 6 _ 6 Slide 24 / 62 Slide 25 / 62

32 Slide 25 () / 62 Slide 26 / 62 Slide 26 () / 62 Slide 27 / What is the fraction in decimal form? Slide 27 () / 62 Slide 28 / What is the fraction in decimal form? 0.2

33 Slide 28 () / 62 Slide 29 / 62 Slide 29 () / 62 Slide 30 / 62 Slide 30 () / 62 Slide 3 / 62

34 Slide 3 () / 62 Slide 32 / 62 Slide 32 () / 62 Slide 33 / 62 onvert the following fractions to decimals. When you can not make an equivalent fraction with a denominator of 0 or 00, then you must divide to find the decimal equivalent. Slide 34 / 62 Slide 35 / 62

35 Slide 36 / What is the fraction in decimal form? Slide 36 () / What is the fraction in decimal form? Slide 37 / What is the fraction in decimal form? Slide 37 () / What is the fraction in decimal form? 0.25 Slide 38 / 62 Slide 39 / 62 3 Use a calculator to convert these fractions to decimals to see the repeating pattern. fraction calculator display decimal Notice what happens with this division. This is called a repeating decimal and it is written as 0.3 and is read as point three repeating.

36 Slide 40 / 62 Slide 40 () / 62 Slide 4 / 62 Slide 4 () / 62 Slide 42 / 62 Slide 42 () / 62

37 Slide 43 / 62 Slide 44 / 62 On the following number line, draw a line and move the decimals to their correct location. Number Line Location click to return to table of contents Slide 44 () / 62 Slide 45 / 62 On the following number line, draw a line and move the decimals to their correct location. On the following number line, draw a line and move the decimals to their correct location Steps:. Divide the number line into smaller parts using tick marks ompare the decimals 0.42 and place them correctly Teacher Notes Slide 45 () / 62 Slide 46 / 62 On the following number line, draw a line and move the decimals to their correct location. Label the numbers on the number line. Steps: Divide the 6.46 number line into smaller parts using tick marks ompare the decimals and place them correctly. Teacher Notes 2 3

38 Slide 46 () / 62 Slide 47 / 62 Label the numbers on the number line. Label the numbers on the number line. Teacher Notes 2 Steps: 3. onvert numbers to same form. 2. Divide the number line into smaller parts using tick marks. 2. ompare the numbers and place them correctly. Slide 47 () / 62 Label the numbers on the number line. Slide 48 / Where would the following number be correctly placed on the number line? Teacher Notes Steps:. onvert numbers to same form. 2. Divide the number line into smaller parts using tick marks. 2. ompare the numbers and place them correctly. D Slide 48 () / Where would the following number be correctly placed on the number line? Slide 49 / Where would the following number be correctly placed on the number line? D D

39 Slide 49 () / Where would the following number be correctly placed on the number line? Slide 50 / 62 8 Where would the following number be correctly placed on the number line? D D Slide 50 () / 62 8 Where would the following number be correctly placed on the number line? Slide 5 / Where would the following number be correctly placed on the number line? D D Slide 5 () / Where would the following number be correctly placed on the number line? Slide 52 / Where would the following number be correctly placed on the number line? D D

40 Slide 52 () / Where would the following number be correctly placed on the number line? Slide 53 / Where would the following number be correctly placed on the number line? D D Slide 53 () / Where would the following number be correctly placed on the number line? Slide 54 / Where would the following number be correctly placed on the number line? D D 0 2 e careful of the scale of the number line! Slide 54 () / Where would the following number be correctly placed on the number line? Slide 55 / Where would the following number be correctly placed on the number line? D 0 2 D 0 2 e careful of the scale of the number line!

41 Slide 55 () / Where would the following number be correctly placed on the number line? Slide 56 / Where would the following number be correctly placed on the number line? D 0 2 D Slide 56 () / Where would the following number be correctly placed on the number line? Slide 57 / 62 Steps to reate Your Own Number Line. onvert numbers all to the same form. D Order the numbers to determine the range of numbers you need to include. 3. Draw a number line and divide it into equal size pieces. 4. Put a dot and label each number. Slide 58 / 62 Example: Plot and label the numbers in the box on a number line.. onvert numbers all to the same form. In this case, all to decimal will be the easiest..5, 0.75, 0.2,.2, Order the numbers to determine the range of numbers you need to include. 0.2, 0.45, 0.75,.2,.5 We need a number line from 0 to 2 Slide 59 / Draw a number line and divide it into equal size pieces. Label 0, and 2 Divide in between the whole numbers into tenths Put a dot and label each number

42 Slide 60 / 62 Example: Plot and label the numbers in the box on a number line.. onvert numbers all to the same form. In this case, all to decimal will be the easiest..2, 0.6, 0.4,.8, 2. Order the numbers to determine the range of numbers you need to include. 0.4, 0.6,,.2,.8 We need a number line from 0 to 2 Slide 6 / Draw a number line and divide it into equal size pieces. Label 0, and 2 Divide in between the whole numbers into two-tenths Put a dot and label each number Slide 62 / 62 Plot and label the following sets of numbers on a number line. Make a separate number line for each set. Set Set 2 Set 3