##
* *Reflection: Developing a Conceptual Understanding
Understanding The Whole Through the iPad - Section 5: Educreations: Show me what you understand

When I first wrote this lesson, the Candy Factory part was intended to be just an opening warm up. They were so engaged in the ap that I realized that I needed to take this ap and build their conceptual understanding of what the whole meant. As the lesson progressed, they revealed they didn't understand that halves can be two different sizes when talking about something similar like two candy bars. I am certain that if I compared a half an elephant with a half a mouse, it would be obvious. In CCSS real life situations are important to utilize in our teaching. In their world, they will compare halves of candy bars and so it is relevant to their lives. However, I was so amazed at the answers I got. I was concerned my drawing was throwing them off because I wasn't making the two bars immensely different. They focused on the fractions, knowing that fourths are bigger pieces than twelfths to the same size whole, not realizing that the two wholes were different.

Eventually they work around it. I worked hard with questioning, probing and pushing them to see. Their video explanations were clear that they had mastered this portion of the standard. This concept is so vitally important to understand before we talk about equivalent fractions because the idea that we are comparing fractions to the same size whole will now be meaningful.

*Getting them to understand was rough!*

*Developing a Conceptual Understanding: Getting them to understand was rough!*

# Understanding The Whole Through the iPad

Lesson 2 of 12

## Objective: SWBAT understand that a fraction can be two different sizes when we compare it to two different sized wholes.

#### Warm Up: The Candy Factory

*10 min*

Today, I opened up my lesson with a new app on our iPads called Candy Factory. This app helps students manipulate fractions to find equivalent fractions. It's main idea is to get students to understand parts to the whole better, and pay attention to the number and size of those parts.

*However, I learned that unguided, they will just push buttons, move candy bars and nothing about this app will have meaning. It is really an app that is a teaching tool! After it is taught and guided through, students will understand the meaning behind the concept, strengthening their fraction understanding and build upon understanding equivalent fractions. Guiding them to think this app through is important so they don't get frustrated. It is a little challenging at first!*

#### Resources

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**Review:** Before I continued with the Core Lesson, I wanted to be sure they understood the parts of the fraction and how they function.

**Quick Write:** In their math journal, I asked students to write on the top of a clear page "Fractions and Decimals." They would be using this section of their journal for this entire unit. I wrote on the board. **What does it mean to be a fraction of something?** I gave them three minutes to write their answer in their journal under the topic. We call this a "Quick Write" and it is followed by a "Quick Share". Students shared that a fraction is part of a whole. * I was concerned, in order to master this standard completely, that students understood that the size of the whole mattered when comparing the same fractional amount.*

**I wrote 1/2 on the board and pointed to the top number asking what it was called.** Students shouted out their answers and we finally agreed it was the numerator. Then I asked the Common Core question: **Why is it called the numerator?** No one knew.** I pointed to it and asked what word they see within the word?** Everyone saw the word "number" and so I asked what "number" means and led them to understand that it meant "to order" or "count." We continued with the word denominator and I again asked the same** "why?" **question about the denominator. This time one student said " It is the number that shows how many pieces something is cut up into.

I asked them to write in their own words, what it means to be a numerator and a denominator in their journal. We did another quick share. I heard them say wonderful things about the same topic in different ways.A written response sample

So, I stopped and said: "Notice how each of us had our own words about the same topic? It is great to hear that we understand the same idea but can express it differently. When we learn about equivalent fractions, it is sort of the same idea."

#### Resources

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I drew a Kit Kat Bar ( fourths) and a Hershey Bar (twelfths) just like they look when you unwrap them. I asked a student to come up and show me half the Kit Kat Bar by circling it. The second student was asked to come up and do the same with the Hershey Bar. Kit Kat Half?

** I asked: Are these both 1/2 of the candy bar? Are they the same size?** They told me yes to both of the question.

*Oh no! I looked at my drawing to make sure I had clearly drawn two different size candy bars thinking I wasn't clear enough. Nope. They were clearly two different sized bars. The width is the same, but the length was clearly different. The Hershey bar was larger.*

I rephrased my question to help them understand what I meant.

**If I were going to have a half of either of these candy bars and wanted the biggest piece, which bar would I choose**? Kit Kat was the answer. "Fourths are larger than twelfths," one student said, "and even though we have half, it's 2/4ths."

**I went to the board and drew the Kit Kat bar into twelfths by drawing lines horizontally. I asked: How many of you think these are the same size pieces** **as the Hershey Bar? **I told them to stand to show their thinking. All stood but one.

*Finally, that one student raised his hand and explained that even though 6/12 was equivalent to 2/4, the Hershey bar piece half was larger than the Kit Kat bar half. *

*I supported what he said by asking him, " So do you think it is true that 1/2 of one thing can be a different size than 1/2 of another? *

*"Well, yah!"* he said.

**Does it always work that way? **Students looked confused. I happened to have two apples on my desk. One was much larger. I held them up and asked: What are these? They said, "apples." I smiled and continued," If I cut them both in half for Ringo ( our class tortoise), would all the halves be the same size?"There was a chorus of "No!"

**I concluded:** **It always works that way. Size of the whole matters if we are comparing the same fractional part. A half of one thing can be larger than a half of another because it is dependent on the size of the whole.**

#### Resources

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To assess their understanding of the concept that the size of the whole matters when it comes to comparing fractions, I decided that creating a video would be effective and fun.

**The Assignment: Make a video of yourself talking about the same fractional amount represented in two different sized wholes.**

I opened up Educreations on my iPad and did a video example and "think aloud" using pizzas. I often use a "think aloud" so they can see a clear example of what I am thinking as I am solving or writing in math.

When I was done, I told them that the video had to clearly show that they were using two different sized wholes and the same sized fraction, as I had done in my video.

Students set to work using Educreations, although I told them they could use the video camera on their iPad and draw using a little whiteboard or paper. Educreations seems to be the ap of choice because you can draw as you talk. It is engaging and easy. Here is a sample of one of my student's work. Even though he has the concept correct, the pizzas he drew are not clearly two different sizes. He knows what he is talking about because I checked on his sample work, so I am not sure if he just didn't realize that the one pizza should be a little larger than it is so it is clear. He chose to cut it into fourths. Other students used pies, candy bars, and glasses of milk.

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- UNIT 1: Place Value and Multi-Digit Addition & Subtraction
- UNIT 2: Metric Measurement
- UNIT 3: Graphing and Data
- UNIT 4: Concepts of Multiplication
- UNIT 5: Geometry
- UNIT 6: Fractions 1: Understanding Equivalence in Fractions and Decimals
- UNIT 7: Fractions 2: Addition and Subtraction Concepts/ Mini unit
- UNIT 8: Fractions 3 Mini Unit: Multiplying Fractions by Whole Numbers
- UNIT 9: Division Unit
- UNIT 10: Addition and Subtraction: Algorithms to One Million
- UNIT 11: Place Value
- UNIT 12: Addition and Subtraction Word Problems
- UNIT 13: Multiplication Unit

- LESSON 1: Pre-Test Fractions 1. & Eggsciting Spiral Review
- LESSON 2: Understanding The Whole Through the iPad
- LESSON 3: The Equivalence: The Domino Effect
- LESSON 4: 2 Games that Compare Fractions with a Little RTI on the Side
- LESSON 5: Quiz 1: Creating and Comparing Equivalent Fractions
- LESSON 6: Fractions: Using Graph Paper to Prove Equivalency of Hundreths and Tenths
- LESSON 7: Comparing Fractions on a Numberline
- LESSON 8: The Depth of Decimals: Comparing Using A Fractional Model
- LESSON 9: Decimal War: Comparing Fractions Using Place Value
- LESSON 10: Comparing Decimals Using a Numberline
- LESSON 11: Quiz 2 Showing Our Understanding of Decimals
- LESSON 12: Fractions 1: Comparing Fractions and Decimals Assessment