Feed the Frog: A lesson in understanding how to use place value to compare numbers.
Lesson 7 of 14
Objective: SWBAT compare two multi-digit numbers using their understanding of place value.
We warmed up today with a really cool ap called Zoom that really does a great job of making kids aware of numbers on the number line from 0 to 1,000,000. This ap got my kids in the mindset of thinking about larger and smaller and where numbers fit on the number line. They worked for about 8-10 minutes on this app. I love the pictures and the whole "pinch" part of this activity that expands and contracts the number line. You really have to think about which way you have to go and it is a challenge! Check it out!
I roved around the class and observed their progress. I could see that they could manipulate the app and place numbers really well. It was challenging for them when they moved into decimal numbers. I stopped them after 10 minutes and I asked them what thinking skills they needed to use in order to place the numbers in the correct order on the number line?
One student mentioned that he had to count out loud sometimes. Another student said he had to think about which number was larger and which was smaller and how the number would fit in between. I asked students if they thought any part of it was challenging? I asked this to help with their development of critical thought about number sense and their understanding of the meaning of the game. One student said that when decimal numbers popped up on his, he had a hard time. I love this app because it exercises future skills as well as increases fluency in number sense.
Gather and/or Make Ahead Materials: A large mouthed puppet and/or simple paper puppet. It's an easy origami puppet mouth, but I suggest practice making it ahead of time. I was able to easily instruct the class how to make this puppet the day before. It took about 15 minutes from start to finish and they had fun. Make number cards on large note cards. Create two sets of 0-9 written in large black ink. Draw commas on 4 cards.
Which way does that greater sign point? Before CCSS, we taught kids to compare numbers using the idea that the "mouth" of the sign "ate" the larger number. And for the most part, they remembered that. I wanted to know if they could identify the greater than sign without numbers because I wanted them to extend their thinking about the signs. To start my lesson, I wrote the greater than symbol on the board and asked them to tell me which sign it was. They didn't know. They guessed. When I asked why they said what they said, two students said " you have to have numbers to tell. To satisfy 4.NBT.A.2 fully, students need to understand the meanings of the symbols that we are using. I think they should be able to identify > as the greater sign, but I think it is a hard concept to understand without a model.
I told them that we would learn how to remember which sign was which today by using our Big Mouth Puppets. I introduced my frog puppet, Francois. I told them his story...
M Francois, ( used in our lesson was a handsome prince from the Dark Ages in France. An old hag jumped out in front of him one day as he was riding his steed in the forest. She held a magic orb and asked him to tell her what the product was inside the math orb. She warned him that if he couldn't answer correctly, he would be transformed into a frog and sent to the 21st century...a fourth grade math class in Wisconsin. Shaking in his saddle, he was wishing he had learned his facts as his teacher had preached, but now it was too late. He couldn't think on his saddle. And of course she asked him what 6x7 is...the hardest math fact to remember! Poof! He is now our frog...and when he learns his math facts, he will return to France, a handsome prince.
They love this story and Francois visits throughout the year, helping them to drill math facts or help with games.
I continued the lesson with Francois's help.
As we moved forward to our lesson goal of using the signs correctly, I focused on Francois again and we talked a little bit about the greater than siqn as I pointed his mouth in the correct direction and outlined it on the whiteboard. I placed 21 on the left and 14 on the right. They laughed when I told Francois that he makes a great model! I love this puppet because he has buggy eyes that roll around and he is charming! I asked again:Do you know which sign is which? I explained that this arrow is the greater than sign. 21 is greater than 14.
Identifying larger numbers using the "greater than" sign.
I passed out the number and comma cards to each student, until they were all distributed.
*I wrote two three digit numbers on the board and asked the students with those cards to come forward and create the two three digit numbers by standing next to one another, lining up the numbers in their correct place value.
* I asked them which number was larger? I took Francois and pointed his mouth in the correct direction as they all were answering which direction I should point him. * I continued by asking: How did you compare smaller multi-digit numbers in the past? They shared how different teachers in the past got them to remember which direction the opening of the sign should point. So, Francois was wanting to eat the larger number. I made gobbling noises and pretended that Francois was gobbling up the larger number.
Remembering a past concept: I drew an equation on the board by using 345 =345 and asked them to recall what they had learned about the meaning of the equals sign. Two students shared the words "balance" and then "same as". So I continued to ask what does the > really mean?
No one could connect the idea of inequality. I wrote this word on the board and asked them to copy it in their notebooks. We defined it as a class as meaning "not equal." We drew examples around the word to show what it is. Then I asked them to explain what it isn't. That was easy. They all said "It isn't equal!". So we drew an example of what it isn't near the word and labeled it; What it isn't. I remarked that it was time to exercise some strategies to figure out which symbol we should use and how place value works in figuring it out.
At this point, I asked 6 students to come up and create two three digit numbers. I split them, leaving three to figure out the largest number they could create with their three cards. As they turned around and faced everyone, I added one more digit to both sides from the audience creating a 4 digit number. We began comparing by having students hold up their cards place value by place value. We were comparing 4,345 to 4, 325. We stopped at the tens place. I gave a student Francois and had them stand between them and open his mouth the right direction.We read the numbers like this to practice language and number reading skills:Three hundred fifty three thousand, six is greater than three hundred fifty six thousand, one.
We kept doing this over and over, building larger numbers until it was time to stop and at least everyone has had a turn to come up and be a part.
* I like to have the students read the numbers aloud to practice reading numbers again. This rote reading reinforces their number reading skills and helps with applying the symbol to the concept thus mastering the standard.
Before we were all done, I took it one step further to increase their understanding of value by reciting the numbers like this as well:Three hundred fifty three thousand, six is greater than three hundred fifty six thousand, one, because six ones has a greater value than one ones.
Now they are explaining "why" the number is greater and this helps master the standard more deeply. If I hold them accountable to this, I am hoping their thinking will deepen on all levels.
We closed the lesson with a round of applause for such good number reading. A few of my students were struggling yet because I could see them get quiet, but eyes were intent and I think they made progress in getting better at reading numbers because they were interested in what we were doing. Francois certainly added to the fun!
Assignments for three levels
I assigned IXL Math at two levels. All the work must be written on paper to prove their thinking.
IXL Math: Higher level: F A.9 ( You will find this in 4th Grade Level)This uses the chart to compare numbers and makes them think a little harder because there is language incorporated. Do 20.
Lowest Level and Special Needs: F A.8 This is a simple basic number line and helps them reason greater than and less than. Do 20.
OR Students could choose to create numbers by rolling up to six dice. On each roll they create the largest number and then write it down. Then they compare using the concept of place value and value. They can play in partners, but must figure out their work alone. I told them I wanted at least 20 numbers to compare.
I encouraged anyone to use their paper puppet to help them visualize the signs or just for fun. If they have a puppet at home, they can use that puppet and work with an adult for support.