1. What’s another way to write 4 5 using addition?
LearnZillion Notes:
--This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific. For example, the hook could be “How do you know if 2/3 is greater than 5/8?” rather than something more generic such as “How do you compare fractions?”
--You can fill in an example using the blue text or you can delete that text box and include some other image that explains what you’re talking about.

3. 3 8
1 8
1 8
1 8
We already know how to decompose a fraction into unit fractions. For example we have 3/8, We can see that this rectangle is divided into 8 equal parts. So, we want to find out how many eighths are in 3/8. We have 3 eighths – so we have 1/8 + 1/8 + 1/8

4. 3 4 =
A common mistake is that when given a fraction, we tend to think that the only way to decompose a fraction is to write the unit fractions. A unit fraction is a fraction that has 1 as the numerator and another digit as the denominator like 1/3, 1/5 or 1/6. Students sometimes see a fraction such as ¾ and think that the only way that they can break the fraction down is to record unit fractions. ¼ + ¼ + ¼

5. We are going to decompose a fraction into a sum of fractions and what we are going to use to help us is an area model. To decompose is to break a fraction down into a sum of fractions. An area model is a picture representation to show fractional parts. Here are some examples of area models.

6. = 3 8
= 3 8
We are going to use an area model so we can see visually the different ways to show the sum of fractions.
We already know how to decompose a fraction into unit parts. Ex. 3/8
Let’s look at this fraction using an area model
It can be written as 1/8 + 1/8 + 1/8 another way that we can show this decomposition is to group these unit fractions (circle two of the eights) together and which would be 1/8 + 1/8 which is 2/8 and we are left (circle the remaining eighth)with 1/8

7. 4 5
Let’s go back to our initial question. What’s another way to write 4/5 using addition? We will make our area model – the denominator tells us how many parts- in this fraction we have 5. The numerator tells us what we are referring to – in this fraction we are referring to 4 parts out of the five. If we name each unit fraction we are going to have 1/5 + 1/5 + 1/5 + 1/5. Our next area model we are going to shade in 3 parts and shade the fourth part a different color to show that we are decomposing this fraction differently than the initial decomposition. This fraction using an addition sentence is 3/5 + 1/5. Finally we are going to show two parts shaded in to show 4/5 that would our decomposition to be 2/5 + 2/5

9. Using an area model decompose 8 10 into a sum of fractions with the same denominator.

10. Using an area model, decompose into a sum of fractions with the same denominator using an area model. Show all possible decompositions.

11. Max had 1 8 + 1 8 + 4 8 as one of his decompositions
Max had as one of his decompositions. What are some other ways he could decompose his fraction? What is the fraction that he had to decompose?

13. Show two ways to decompose into a sum of fractions with the same denominator using an area model.
Show two ways to decompose into a sum of fractions with the same denominator using an area model.