Lesson 3.1.4 – Teacher Notes Standard: 6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. Chapters 5 and 7 – Multiplying and dividing decimals Lesson Focus: The Portions Web is introduced in this lesson. However, the focus of the lesson is understanding place value and the importance of the decimal location when adding and subtracting decimals. (3-58) I can fluently add and subtract multi-digit decimals using the standard algorithm with speed and accuracy. Calculator: No Literacy/Teaching Strategy: Give 1/Get 1 and Whiparound

BELLWORK

3-50. Use the Lesson 3.1.3B Resource Page to shade in the amounts represented by the following descriptions, and then write them in the stated form. 3-50 HW eTool (CPM). Homework Help ✎ Shade 7 hundredths, and write the portion as a percent. Shade 7 tenths, and write the portion as a fraction. Shade 28%, and write the portion as a fraction. Shade 31.5%, and write the portion as a decimal

3-51. Given the numbers 18% and 0 3-51. Given the numbers 18% and 0.7, explain which number is larger by using words and/or pictures.

3-52. Explain what 78. 5% would look like on a 100%-block 3-52. Explain what 78.5% would look like on a 100%-block.  Then write it as a decimal.

3-53. What is the sum of 2 2 + 3 3 ?  Represent your ideas in multiple ways.

3-54. Owen loves to eat hamburgers 3-54.  Owen loves to eat hamburgers.  He goes to his neighborhood grocery store to buy ground beef and buns to make hamburgers at home.  He buys a package of hamburger buns for $1.29 and a package of ground beef for $5.82.  He only has a $10 bill and wonders if he can buy some ketchup and mustard, too.  The ketchup is $1.89, and the mustard is $2.69.  He does not have to pay sales tax on food.  Homework Help ✎ Does Owen have enough money to buy both the ketchup and the mustard? If he does, how much money will he have left over? If not, then what could he buy and how much would it cost?

p. 106 3-55 and 3-58 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.

How else can I represent the same portion? 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)?

3-56. 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.”

3-56. (cont.) 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.

3-57. Susie’s next question impressed Sally 3-57. 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.

3-58. 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

3-61. LEARNING LOG The web below shows the connections between all the different ways a portion can be represented. Its technical name is “Representations of a Portion web.” Using the web, show as many representations of the number 15% as you can.

PRACTICE 1) 1.2 + 5.16 = ______ 3) 4.52 + 6.62 = _______ 5) 5.106 + 4.51 = ______ 7) 12.4 + 5.216 = ______ 9) 5.424 + 9.81 = ______ 2) 8.8 – 0.25 = ______ 4) 8.49 – 5.06 = _____ 6) 6.1 – 4.23 = _____ 8) 5.0 – 1.61 = _____ 10) 6.5 – 2.7 = _____

PRACTICE (cont.) Sally bought three books at the store yesterday, one for herself and two for her mother. The total bill came to $45.90 prior to tax. The book that Sally bought for herself cost $17.95. What was the total for the two books she bought for her mother?

PRACTICE (cont.) Timothy bought four books and one journal. The books cost $4.95, $5.75, and $14.99. The total of the five items was $44.39. How much was the journal?

HOMEWORK