Converting Fractions to Decimals

May has been quite the month for me! I have had two interviews and just was asked back for a second round today. Anyways, for one of the interviews, I had to teach a fifth grade math lesson. I was very pleased with how my lesson went and wanted to share it with all of you!

We were given the choice between three topics, and I chose to focus on converting fractions to decimals. I based my lesson upon the Common Core standard:

CCSS.Math.Content.5.NF.B.3 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b) ex. by using visual fraction models or equations to represent the problem.

I decided to take a risk and use manipulatives. I really wanted to show the scope of moving from the concrete, to the pictorial, to the abstract. Since I was not familiar with the class, I was a little nervous, but everything went relatively smoothly. 

To begin, I explained to students that we can represent the same amount as either a fraction or a decimal. Then, I asked students to share what they already knew about fractions and decimals; to see what I was working with. After listening to several student responses, I asked students what the line between the numerator and the denominator stood for. I used that to lead into the focus of the lesson: We can convert fractions into decimals by dividing the numerator by the denominator. 

I wanted to incorporate technology into my lesson, so I modeled using base ten blocks on the Smartboard. I find this makes the manipulatives much easier for students to see. For my first example, I used 1/2 because it was the simplest to explain. I gave the example in a story problem to help make the activity more meaningful: One cookie had to be shared among two people, therefore 1 divided by 2.

To start, I showed a hundreds flat. This represented the whole cookie. We couldn't break this hundreds flat in half, so we needed to trade it in for 10 ten rods. The ten rods represent one-tenth.

Then, I separated the ten rods into two groups, representing the two people. Next, I counted the number of ten rods in each group. There were five ten rods in each group, which represented five-tenths. 1/2 is the same as five-tenths because 1 divided by 2 is five-tenths.

I continued with two more story problems in the same fashion. This time students solved the problems with assistance from me, as guided practice. I circulated throughout the room assisting students. When students had finished solving the problem, we went over it together on the Smartboard. If you have not heard of the "infinite cloner" feature on the Smartboard, you need to check it out. Then, you can just keep making copies of each base ten block by clicking on it.

For the independent practice/assessment portion of the lesson, students solved a story problem on their own using base ten blocks. Overall, I was very pleased with the lesson. Even if they are nerve-wracking, I prefer performance interviews. If you would like a copy of the lesson plan, click here. (I had to turn in a formal copy!) For a copy of the Smartboard notebook file, click here.

How do you use manipulatives to teach conversions?

Decimals, Fractions, Percents, Oh My!

This past week my fifth graders and I worked on converting between fractions, decimals, and percents. Initially my students found this skill very challenging, but we worked through it together!

To start, we began with a basic overview of the conversions. I wish I could take credit for this brilliant visual, but I found it on pinterest. I do not think the original location is known, but you can see it here on pinterest.

Now, to explain the conversions in more detail, we used a blank hundreds grid.

For the first one, I had the students color in 23 squares. Then, I asked them what the number would be as a fraction out of 100. The hundreds grid provided a great visual for this. Next, we moved onto the decimal. We discussed how we could divide the numerator by the denominator, but that with this one, the kids knew it automatically. (We divided to double-check.) For the final step, we identified the percent. We talked about how a perfect score on a test is 100%. Percents are the same as fractions out of one hundred.

We repeated the same procedure for 25 squares. This time we had to simplify. Then, I switched things up on my students. I had them color in 1/2 of the squares. Before we could move on, we had to identify what that would be as a fraction out of 100. Then, we were able to figure out the decimal and percent rather easily. This provided a great opportunity to explain why it is 0.5, not 0.05. Just look at the squares!

I let one of the students come up with the last one. He chose to have us color in 72 squares. This made for a little more complex simplifying, but the kids were up for the challenge. 

We continued to practice converting with several problems. Then, I introduced the number line.

I selected three numbers. (one fraction, one percent, and one decimal) As a group, we thought through all the conversions and used our basic number sense to figure out where to place the numbers on the number line. For this one, we began with 25%. We knew this was halfway between 0 and 1/2. Then, we placed 0.63. We knew it was more than 1/2, but less than 3/4. Finally we had to figure out 1/5. We divided 1 by 5 to determine that it would be 0.20 as a decimal. (which is less than 25%)

This activity required students to use a whole lot of math, but they loved it! There is something way more fun about a giant laminated number line with hot pink paper than number lines on a worksheet.

We continued to work on converting between fractions, decimals, and percents. I have to admit that I am very impressed with how the students' understandings are developing. If you would like a copy of the numbers I used for the number line activity, click here.

Also, check out this great giveaway at The Teacher's Chair! Lots of amazing bloggers are offering some fantastic prizes that you will not want to miss! I might have something in there too...  ;)

Is everyone else as glad as I am that it is March?

Equivalent Fraction Fun!

Now I know what you are thinking. Fraction Fun? That just cannot be possible. Well, I almost didn't believe my ears when my fourth graders told me they were having fun with fractions during our intervention lesson. Before we started fractions they were all in agreement that they absolutely abhorred fractions. (Which usually just means they do not understand them.)

My favorite thing about this lesson is how simple it is. Sometimes the simplest ways are the best!

To begin, I created an equivalent fraction chart. I laminated enough copies of the chart for each of my students to have one. You can get your own copy by clicking on the image above.

I began by giving students a fraction. (ex. 1/2) Students colored this fraction in on their chart with dry erase markers. Then, I asked them how many sixths would be equivalent to one-half. Students colored in the one-sixths until they lined up with the one-half. Then students could see that three-sixths was equivalent to one-half. We continued working through several problems this way.

Eventually I asked students if they noticed a pattern. One student explained that we divided both the numerator and the denominator by the same number. I asked the students why they thought we did that. This is the really beautiful part about this fraction chart. The students were able to see that one-half was three times as big as one-sixth. Their explanations were fabulous! I am so glad I let them figure the process out for themselves.

As we continued solving problems students actually began using the chart without even coloring the fractions in. Soon we will be ready to move on to the abstract phrase!

My school is currently very into Singapore Math. Their methods focus on moving from concrete, to pictorial, to abstract. This lesson would fall under the pictorial stage. We had already used pattern blocks to explore the concrete stage of equivalent fractions. 

I would also highly recommend the book Teaching Primary School Mathematics: A Resource Book. We got this book from or math curriculum director. It provides really great reasoning behind many mathematical concepts. Supposedly this is the textbook preservice teachers use in Singapore. (The price is not usually as high as it is currently listed on Amazon. The book seems to be back-ordered and independent sellers are taking advantage of this.)

The black and white copy of the equivalent fraction chart is provided for free, but if you would like color copies and copies without numbers you may purchase a pack at my Teachers Pay Teachers store.

I hope you found this lesson helpful! Is anyone else's district implementing Singapore Math techniques?  

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