How else can I represent the same portion? You have been working with various ways to represent portions of a whole.  These multiple representations are shown in the diagram at right.  It is called a web.  For some problems, you might prefer to work with a percent, while at other times, it might make sense to use a fraction or a decimal.  Today you will represent portions in multiple ways and consider which of them allows you to work most efficiently.  As you work on today’s lesson, use these questions with your team to focus your discussions:  How else can I represent the same portion? How do I know the portions are equivalent (the same)?

55. BUILD IT, WRITE IT, DRAW IT Sometimes it is easier to compare portions when they are written in a particular form.  For example, 0.25 and 0.8 can be compared easily when both are drawn on a 100% block or are both in percent form.  In this problem, your team will work with all of the representations on the web and find ways to change one representation into another.  You may want to explore using Base Ten Blocks (CPM). For each portion of a whole described below: Build the portion on top of a 100% block. Draw the representation on your Lesson 3.1.3B Resource Page . Write the portion as a percent, fraction, decimal, and as a description in words. 3 tenths and 1 hundredth 0.56 -- 3% Place each of the portions described in parts (a) through (d) on a number line.  The number line should range from 0 and 1 be marked in tenths.  Which representation (fraction, decimal, or percent) is most convenient to use when placing values on a 0-to-1 number line?  Explain your choice. 

56. LOCATION, LOCATION, LOCATION Sally was helping her younger sister Susie, who had been absent from school, to understand decimals.  When Susie came to the problem 0.37 + 0.7, she got very excited.  “I know, I know!” Susie shouted, “37 and 7 make 44, so the answer is 0.44!” “Well,” Sally said, “You’re right that 37 and 7 make 44, but 0.37 is not 37 and 0.7 is not 7.  The value of numbers depends on where they are located,” Sally explained, “That is why you have to line up the place values, by lining up the decimal point, when you add or subtract.” What does Sally mean?  What explanation can you give for lining up decimals when adding or subtracting?  Write a note to Susie explaining why 0.37 + 0.7 is not 0.44.  Include the correct answer and an explanation of what each number in the problem represents.  Hint: It might help to rewrite each number as a sum of fractions or draw them with hundred blocks.   

57. Susie’s next question impressed Sally 57. Susie’s next question impressed Sally.  “So does that mean that if I want to add 1.003 and 0.47, instead of adding 47 and 3, I need to add 470 and 3?  Is this similar to adding fractions, so I have to write them in equivalent forms?” What do you think?  Is Susie right?  Use what you know about representing these numbers with fractions, percents, and 100% blocks to justify your answer.  Find the answer to 1.003 + 0.47. 58. Complete each of the following computations using your understanding of decimal place value and representations of portions. 0.375 − 0.2 18.6 + 0.04 2.008 − 0.46

59. Maya and Logan are playing “Guess My Decimal” again 59. Maya and Logan are playing “Guess My Decimal” again.  You will play along with them in parts (a) and (b) below. Maya challenges Logan by saying, “The decimal I’m thinking of is what you would get if you subtract 0.01 from 0.3.”  Visualize what her number might look like on a 100% block.  What decimal is Maya thinking of?  Explain how you know.   Logan continues the game with this challenge: “The decimal I am thinking about is halfway between 18 hundredths and 3 tenths.”  Help Logan solve this puzzle and show any work that might help explain your thinking.   60. Additional Challenge:  Work with your team to rewrite   as a decimal and as a percent.  Be prepared to explain your strategies to the class.

“Representations of a Portion” 61. LEARNING LOG Title this entry… “Representations of a Portion” Include today’s date.  In your Learning Log, copy the web. Since it is a web that shows the connections between all the different ways a portion can be represented, its technical name is “Representations of a Portion web.”  After copying the web, show as many representations of the number 15% as you can.  

Tonight’s homework is… 3.1.4 Review & Preview, problems # 62 – 66 (text page 121) Label your assignment with your name and Lesson number in the upper right hand corner of a piece of notebook paper. (Lesson 3.1.4) Show all work and justify your answers for full credit.