Licensing information Users should treat this material as a working draft. This material can be used in its current form, customized, and/or printed or displayed by the user. The author(s) request feedback on all materials so that they can be continually improved and updated. This material is licensed under the Creative Commons Attribution-Share Alike license: (http://creativecommons.org/licenses/by-sa/3.0/). Author: Kevin Hall Wording for the legal statement above is adapted from the legal statement for Trigonometry, published in 2009 by The CK-12 Foundation: http://about.ck12.org/

Teaching notes Before getting to class, be sure to print out the answers and have them handy. While students are practicing the drill questions, you want to be walking around praising and prompting them, not trying to solve the questions for yourself. On the drill slides, 4 questions come up at a time. It’s ok if some students only do the first couple, as long as they get them right. Again, these are designed to let you walk around the room and see how students are doing while the classes discusses and/or practices.

At that rate, out of 54 songs, you’ll like 1). Trayon took 25 total shots, and made 18 of them. What percent did he make? 2). You figure out that you like about 4 out of every 9 songs that you hear on your WJLB. At that rate, if you hear 54 songs, how many will you like? out of 100 18 • 4 = 72 Copy _____ times ?? 6 • 6 = 24 18 made 18 18 18 18 shots made x x you like 4 you like = 9 total 54 total Copy _____ times ?? 6 • ?? 6 25 total shots _____ total shots 25 + 25 + 25 + 25 = 100 Copy _____ times 4 ?? Answer: At that rate, out of 54 songs, you’ll like 24. 72 100 He made , or 72% Answer:

Solving Proportions with Equivalent Fractions × 5 × 5 × 5 25 × 5 Step 1: Copy Problem. Step 2: What is it multiplied by? Step 3: Multiply numerator and denominator Step 4: Calculate answer. × 7 × 11 3). 4). 5). 6). 2 30 × 2 × 7 × 11 ×6 × 6 56 99 × 2 × 6

40 35 72 15 49 72 100 45 6 is one 4, plus half of 4. So it’s 1.5 • 4 × 5 ×9 × 1.5 7). 8). 9). 10). ×5 × 5 × 5 40 9 × × 1.5 35 72 15 × 5 27 is two 12’s, plus a quarter of 12. So it’s 2.25 • 12 × 8 × 20 × 2.25 11). 12). 13). 14). 49 × 7 × 8 × 20 2.25 × 72 100 45 × 7 Two 20’s, plus a quarter of 20, is 45.

Compare them with a calculator 7 0.142857… 0.143 Rounded Divide and Conquer • In high school, we often use the fraction bar, not the dividing sign. • The biggest problem people have with dividing is knowing which number to write first. 21 ÷ 3 is not the same as 3 ÷ 21. 21 3 3 21 is not the same as Compare them with a calculator 7 0.142857… 0.143 Rounded Not even close!

.2 Split up: 1 1 ÷ 5 means you have ___ , and 1 .2 5 .2 It adds A Picture for Dividing • What does dividing do? Dividing splits up an amount into equal parts. • Draw a picture to represent 1 ÷ 5 .2 Split up: 1 1 ÷ 5 means you have ___ , and you’re splitting it into ____ pieces. 1 .2 5 .2 It adds up to 1 .2 1 ÷ 5 = .2 .2 5 pieces

2.60 ÷ 4 ??? 4 ÷ 2.60 2.60 $ = 0.65 $/song 4 song A Real-Life Example • SCENARIO: For $2.60, you can buy 4 songs online. What is the price per song? 15). Why do we DIVIDE to answer this? How would you explain it? We’re splitting up a total into 4 parts. $0.65 16). What expression shows the answer? Total: $2.60 $0.65 2.60 ÷ 4 or ??? $0.65 4 ÷ 2.60 ?? $ Please explain your thinking: $0.65 $0.65 We’re dividing it into 4 pieces, 4 songs 1 song so we divide BY 4. What we know Want to find out 17). Please write the answer as a fraction and a decimal. 2.60 $ 4 song = 0.65 $/song