Data comparison can be tricky because it is so abstract. It is all based on pictures! Starting with this fun, concrete game means that students get hands on practice with the concept of how many more before working on comparing data.
Students will play a game with a partner to get them thinking about comparing 2 quantities.
1. Each partner rolls a dice.
2. Each partner builds a tower of cubes to show that number.
3. Who has more? How many more?
You can watch a video of 2 students playing here: Playing the Game You will see that these 2 students are struggling to figure out what I mean by "how many more". You'll see how I explained the concept to them a different way.
After students play, we will quickly share out a few partner group games. Watch how students explain their thinking here: Sharing Thinking
This is a great example of having students constantly practice MP3, Construct viable arguments and critique the reasoning of others. Students have to be explain what they did and how they did it! Putting this in every lesson means students get continuous practice with it.
Yesterday we used graphs to figure out how many MORE votes one choice got than another. Today, we are going to look at the question: How many MORE again, and we are going to use that question with how many fewer.
This is another question that helps us see how the numbers are different. Sometimes we want to know how many it won by, other times we want to know how many it lose by.
Your goal today is to be able to answer “how many more” and “How many fewer” questions.
Definition (on chart paper):
How many MORE: How many extra, Winning!
How many FEWER: How many you are losing by, how many you need to catch up
Present problem: I have a graph here about the number of points some kids have in a basketball game. Peter has 8 points, Mike has 4 and Elizabeth has 7.
We need to figure out how many extra points Peter has. Where are the extra points he has on the graph?
How many MORE does Peter have?
I’ll model using number sentence: Peter has 8 points, take away the 4 Mike has and that leaves 4 extra. 8-4=4. The equation is mostly just exposure right now, but it does help student start to work towards modeling with mathematics (MP4).
Revisit Problem: But Mike wants to know how many FEWER he has. He needs to know how many he needs to catch up to Peter.
How many would Mike need to score to catch up to Peter?
Scaffold questions: What boxes would I need to color in so Mike could have the same as Peter?
Model number sentence: Peter had 8 points, take away the 4 mike has and that leaves the 4 that Peter needs to catch up. 8-4=4.
Think Aloud: Wait, Peter had 4 more and Mike has 4 less. Both the answers are 4! That’s because 4 tells us how their numbers are different.
Now let’s take some data about our class and compare it using “how many more” and “how many fewer” language.
Survey Question: What would you rather do for our next classroom celebration?
Choices: Painting Party, Free Choice Centers or Crafty Friday
Data Analysis: I'll ask the data analysis questions whole group but have students record their answers and how they know on whiteboards. I use whiteboards as one form of formative data collection. Students are all responding on their individual white boards, so I can quickly spot misconceptions, take note of students to check in with, and notice any class wide trends.
How many more people voted for _____ than ______?
How many fewer people voted for ______ than ______?
How many people voted in all?
Students analyze another pretend classroom’s data.
Intervention: Students who need intervention will do this activity in small group. The primary scaffold they need to remember is to circle the extras, otherwise their knee jerk reaction will just to be count how many each group has!
These questions focus on combining data as well as comparing it. For example, how many votes did Painting Party and Crafty Friday get all together?
I'll use technology at the end of this lesson to be in step with the Common Core emphasis on incorporating technology in the classroom and give students another way to practice the material.
I'll project the Brainpop Jr Tally Charts and Bar Graphs video. After watching the video, we will play the Picture Maker game and answer how many more/how many fewer questions about the graphs we make.