1 In mathematics, there is often more than one way to express a value or an idea. For example, the statement, “Three out of ten students who are going on the field trip have turned in their permission slips,” communicates the same portion as the phrase, “30% of the students who are going on the field trip have turned in their permission slips.” While three out of ten and30% might look and sound very different, they are both representations of the same portion of a whole. (In this case, the whole is the entire number of students who are going on the field trip.) Throughout this section, you have been representing numbers in different ways. In Lesson 3.1.2, for example, you used a diagram and a percent ruler to express your team’s guess about the portion of raisins in a jar. In this lesson, you will use a 100% block to create models of the size of various numbers on the 100% block. Today you will be investigating several ways to represent portions of wholes, including percents, fractions, and decimals.

2 As you work, keep these questions in mind: How can I build it? Is there another way to represent this portion? What is the whole? 36. BUILD IT, DRAW IT, WRITE IT, SAY IT For your work in this section, you will use this 100 block to represent one whole or 100%, also described as 1, as 100/100, or as one hundred out of one hundred. The block will be referred to as the 100% block. Since a whole block represents 100%, 50% (50/100, 5 out of every 10, or ) can be represented by the diagram right.

3 36. BUILD IT, DRAW IT, WRITE IT, SAY IT When the large square block represents 100%, what do each of the other blocks you have worked with represent? Obtain a set of Base Ten Blocks or use: For each of the portions listed below: Build the portion on a 100% block. Draw a diagram of the portion on your resource page. Write the portion in at least two different equivalent representations. Write out how you could use words to say or name the portion two different ways. a. b. c. 80 pieces out of 100 total pieces d. 150%

4 37. Erik and Tate cannot agree on the amount shaded on the 100% block shown at right. Erik says, “It shows 2 tenths of the 100% block… and 3 hundredths of the block,” while Tate says, “It shows 23 hundredths of the whole block. a.”What would you tell Tate and Erik? Justify your response with words and pictures. b.Another representation of the number shown on the 100% block above is a decimal, which would be written as Compare this number to how Erik and Tate described the value. What similarities do you notice?

5 38. If 0.23 can be represented with 2 tenths and 3 hundredths, how can the number 0.19 be represented? What about 0.5? Get a Lesson 3.1.3B Resource Page and draw a picture of each of these numbers on the 100%- block diagrams. Explore using: Base Ten BlocksLesson 3.1.3B Resource PageBase Ten Blocks Jessa was working with a percent ruler when she had an idea. “Can we use this idea for the other representations of a portion?” she asked. Discuss this idea with your team. Decide how to label each end of the ruler (the 0% end and the 100% end) if it is being used to measure fractions or decimals. Draw a large percent ruler on your paper and mark each of the portions listed on the ruler. a.80% b.40% c.99 hundredths d.100% e.9 tenths f.3 tenths and 9 hundredths g.10 hundredths h.25 out of 100 i.10 tenths j.

6 #40. - #44

Vocabulary: A percent is a way of expressing a number as a fraction out of 100. Tonight’s homework is… Review & Preview, problems #45 – 54 Label your assignment with your name and Lesson number in the upper right hand corner of a piece of notebook paper. (Lesson 3.1.3) Show all work and justify your answers for full credit. 7