2. I CAN EXPLAIN WHY A FRACTION A/B IS EQUIVALENT TO A FRACTION (N X A) / (N X B) BY USING FRACTION MODELS Standard 4NF1

3. Say What? Let’s try it with numbers instead of letters. ½ is equivalent to (2 x 1) / (2 x 2) So, ½ is equivalent to 2/4.

4. The Goose/Gander Rule With equivalent fractions, there is always one important rule that must be followed. I call it the Goose / Gander rule What’s good for the goose is good for the gander. BTW the goose is the girl and the gander is the boy. FYI – a boy duck is called a drake. With fractions this means that what you do to the bottom number (the denominator) you must also do to the top (the numerator).

5. Example: This is what you usually get in a math book. 1 3 --- = --- 3 ? 1 x 3 = 3 on the top, so… 3 x 3 = 9 on the bottom. 9 is your missing denominator.

6. Working it out When you work the problem out, it should look something like this: 1 (x3) 3 --- = --- 3 (x3) 9 Since 1 x 3 = 3 on top, you multiply 3 x 3 to get 9 on the bottom.

7. Sometimes you have to go backwards. Check this out: ? 8 --- = --- 5 20 Don’t freak out! You’re doing the opposite of what you did before. So what’s the opposite of multiplying? DIVIDING! Feel better?

8. Working it out To solve this one, you must divide. 20 divided by 4 is 5 What you do to the bottom, you do to the top. 8 divided by 4 is 2, so… The missing numerator is 2

9. Showing your work When you work this problem out, it should look kind of like this: 8 (/4) 2 --- = --- 20 (/4) 5 I switched the fractions around, you don’t have to do that, but what the hey. This is what you look like right now.

10. Model It! You should be able to do this with numbers, but… Drawing a picture can be very helpful.

11. Modeling Here’s a model of ½ Notice that the top of the model is hued (darker) and the bottom of the model is in pastel (lighter) Now, just imagine making an equivalent fraction of this model by drawing a line down the middle. Ah heck, I’ll just show you on the next slide 1 2

12. The Next Slide Told you I’d show you Now you may notice that there are a total of 4 boxes in the model… Only 2 of the 4 boxes are hued (darker), and… The model is still the same size as before, so… ½ is equivalent to 2/4 12 34

13. Your Turn! Solve these 2 equivalent fraction equations. ½ is equivalent to ?/10 ?/24 is equivalent to ¼ Take your time… I’ve got all day… You can do it… At least I think you can… Are we there yet???

14. How did you do? ½ is equivalent to 5/10 6/24 is equivalent to ¼ Here’s your yearbook picture