2. The World of Ratios p. 19 Using what you know to find something new!

3. L S LL S S S S S S S S Draw circles for the counters. Use “L” to stand for the large dogs. Use “s” to stand for the small dogs. Throughout this unit, using LABELS will be very important!

4. L L S S S S S SS S 6 6 44 6 6 4 1414

5. This is the SAME ratio written in three DIFFERENT ways!

6. 268268 Part: Red Part: Blue Whole: Total Organizational tool Let’s look at that first example a little more. There is a lot of information that is hidden in that simple 2:6 ratio. The red and blue clips are parts that make up the whole number of clips. 2:6 is a part:part ratio. What would 8:2 be expressing? What type would it be? Use the side margin of your text page to draw this ratio box……. All the clips:Red clips Whole:part ratio

7. Just as you can simplify fractions by dividing out shared factors, ratios should also be simplified. Before simplifying, this shows 2 reds for 6 blues. Dividing the shapes shows the simplified ratio of one red for each 3 blues.

8. 4 6 10 Part: suns Part: moons Whole: Total 4:6 = 2:3 There are 2 suns for each 3 moons. Order matters!!!!!!!! Draw this box in your text!!

9. Categorical data is a fancy way to say we are putting the values into “categories.” Naming the color of the paper clips was categorizing the data. Differentiating between suns and moons was categorizing. LABELS ARE VERY IMPORTANT when working with ratios! USE THEM! It is not an option!

10. The flavors are the categories. Notice they are asking for something not given in the chart! Finding the “hidden” total is a good way to complete a ratio table like this. Total 21

11. The flavors are the categories. 8 3 6 7 8 24 Total 24 8 8 1 24 8 3 1 3

12. Part: Whole: total 32

13. Where did the 5 come from? part 2 part 3 total? 5 What does the 30 represent? Ratio Real 30 There are 5 groups of 6 to total the 30 flowers. Now you can see how the text example used 2 groups of 6 and 3 groups of 6. WE had to come up with the value of 6 by using the hidden total and the 30.

14. pens:pencils 6: 8 3:4 For every three pens there are 4 pencils. pennies:dimes 3: 9 1:3 There is 1 penny for each every three dimes.

15. Apples9 Bananas5 Peaches4 Total 18 Bananas: Total 5: 18 5 of the 18 pieces of fruit were bananas.

16. Part: 3 Part: 4 Total : 728 How many in each group? 444 4444 12 16 x 4 = 12 x 4 =16 x 4 =

19. We ARE RATIOS!! Comparison of numbers by division!!

20. Let’s look at the practice problems on p. 300. I am choosing to use my organizational chart. Centers 3 Forwards 5 Guards 6 Total14 We are asked to write ratios in three different ways. This means we can write them as a fraction, with a colon, or with “to” separating the values. It is “wise” to label your values. forwards:guards centers to total centers:guards part:part part: whole part:part 5 : 6 5 to 6 3 : 14 3 to 14 3 : 6 3 to 6 Cover what you don’t need!

21. 7 525 35 = As you can see, ratios are similar to fractions. 7 5 We walk like Fractions. We can multiply or divide them to create equivalent ratios. 7 525 35 We talk like fractions 25 35 We even Taste like fractions.... but we are NOT fractions! 7 5 2 5 1