## How many hundredths is two tenths? - Section 4: Human number line

*How many hundredths is two tenths?*

# Decimal War: Comparing Fractions Using Place Value

Lesson 9 of 12

## Objective: SWBAT compare decimals to hundredths using a number line or place value understanding.

*50 minutes*

#### Warm Up: Number Sense

*10 min*

Today, to warm up, we stood in a circle and played "Buzz". Buzz is a game that is great for thinking about place value and counting. I set the rules that we would start adding by 7's starting with the number 28. If a sum has a five in it, you say "Buzz" and the person next to you keeps adding from your number. So, they have to listen really well.

We started with our 28. People really stumbled. I stopped them and asked about adding strategies.

One person said they could add by tens and then subtract three. I told him that was an idea, but how about if we add by 5's and then add 2 more. One student said that he couldn't subtract in his head very fast.

We kept going and started adding by 5 and then added in the 2. I had to coach when we reached the hundreds. W didn't "Buzz" very much. 105 came along and someone forgot because we were so worried about adding! So we laughed. I didn't make them sit out. I may have made this too hard to start with. We stopped when we reached the entire circle. It's challenging!

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To quickly review how we compare decimals using a number line and how we should think about place value, I used this Learnzillion lesson as a resource. I used this because the number line is very clear and easily understood. This lower group needed to be taught whole class. The other students who had mastered comparing decimals on their pre test, were busy on working on their game design assignment from a lesson earlier in the week about word problem.

As I talked through the lesson, there were pages I stopped and used my marker on the SB to help to get them to understand the difference between tenths and hundredths and how they are notated. I heard a "Oh...I see it on there!" I wanted them to know that .06 looked different on a number line than .6. I wanted them to understand that they needed to extend the place value out to hundredths to compare because it helps us understand the value of the number.

So we practiced with the number line on Learnzillion. I asked someone to compare .05 and .5 by solving it on the number line. Then when we did, we continued the video to see that we were correct.

Then, I turned the SB off and went to the white board to extend their thinking about place value just a little more because it has been my experience that they understand this confusing idea until they have to practice it alone. We played "True or False" & 'Why"

I wrote .4 =.04 and stood back.

I said: " Is this true or false and why? They all yelled false! I called on one person to explain why. She came to the board and wrote a zero on the end of the .4. She said that she wanted to make them both in the hundredths place. That way she could see it.

I continued with .16 > .7 True or False? This time it was quieter. Finally someone said it was false. I asked why they were hesitating? One student explained that she needed to think about it. I asked if she remembered the last "place value strategy?" I turned to the girl who talked about the last problem. She continued by coming up to the board and writing a zero on the end of .7 and increasing it's place value. I heard three "OH!'s" I thought "Yay!"

I told them that we were going to practice comparing decimals by value in a card game.

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#### WAR!

*20 min*

**War!**

**Materials:** A deck of about 50-75 note cards with decimals written on them. I wrote some with whole numbers included.

I explained that they would play the game of WAR. I instructed them to take turns being the dealer and to pass one card to each person. The dealer would announce "flip". Everyone was to flip their card over on the floor and the person with the largest value would win the card. Then all were to put their cards back into the deck and play again. The person with the most cards at the end of the game would win. Everyone was to agree it was the largest value in order to win the card. This rule helps students be accountable to one another for their learning. It also is an example of practicing MP3 as they critique each other's reasoning.

There was a lot of hooting and hollering as they slapped down the cards, compared the decimals to their own, and argued about value. I roved back and forth between the teams. It was great! They really were having fun and I could tell from the results that they were understanding the comparisons. One boy was rather quiet and didn't seem to be trying, and so I approached him. He said that he couldn't think as fast as everyone else. I told the group to be sure and check that everyone had a chance to look, since I suspected one or two students were dominating the game. So, to avoid anyone dominating, I mixed up the groups again, counting off by 2's and grouping them again. It was a chance, but it worked. The boy who was quiet was now mixed with a group that was more passive and focused,and the other team got noisy and the fun kept going.

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#### Human number line

*10 min*

I stopped students from their game playing. I asked for an "aha!" moment. One student raised her hand and said that she didn't think she could think about decimals that fast. Another student said that he understood that 4 tenths was larger than 13 tenths now. I said "You mean hundredths?"

We all agreed the game was really helpful and fun. I told them that I had one more task for them. I asked them to pick up a card and then create a human number line across the front of the room. They quickly grabbed cards and the hooplah started up again. *Watching them working on the standard at this level of thinking and fun*. I listened as I heard one boy say, "Well I 've got 2.58 and you have 2.47, so I bet we are on the end down there!" I heard them comparing their cards, chattering about where to go. Very quickly, they had themselves in order, except for one. Where should he go? I asked questions to see if I could get him to think about creating the hundredths place. How many hundredths is two tenths? shows how were working to figure it all out. I worked with students to read the numbers in fractional form.How many hundredths is .06?

When we were done, we posed for a picture! We got it together!

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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