##
* *Reflection: Complex Tasks
Larger Numbers: A Tie to Social Studies - Section 2: Working in Small Groups

The idea of converting dollars to yen was a complex problem for students to solve. Some groups immediately wanted to get out their calculators. I asked them to first tell me what they were going to do with the calculator. If students knew that they were going to do repeated addition, or multiplication, and which numbers they were going to use, I let them get the calculator. If they did not, I asked them to think first about how they might solve the problem and what the calculator might help them with.

I also watched students attempt repeated addition of 98, 20 times. One child asked if she could use the calculator to perform this task.

Another child tried to use the small, small big strategy that we have used before. She set up the chart and put in all the 98s. Again, she was using repeated addition.

Another child wrote it as a multiplication problem and tried to solve it in columns, even though we have not done anything like that. She related it to double digit addition on her own. She was able to multiply the tens place, but then did not know what to do next.

Each group kept working and working to solve the problem. The willingness to persevere in spite of the difficulty level of the problems was a testimony to the student's meeting the Common Core standard of persevering in solving difficult problems in mathematics (MP1).

*Variety of Strategies*

*Complex Tasks: Variety of Strategies*

# Larger Numbers: A Tie to Social Studies

Lesson 5 of 14

## Objective: SWBAT compare larger numbers within the context of geography.

## Big Idea: I want my students to realize that numbers are everywhere and math is applicable to almost all other subjects. Geography offers a perfect opportunity for students to make this connection.

*50 minutes*

#### Japan Introduction

*15 min*

Students are about to begin a new unit on Japan. They have been gathering fuel to travel on a plane to Japan by reading at home each night. The hours they read convert to 10 miles each, allowing each child to help read to Japan. It usually takes the class from September to February to have enough miles to arrive in Tokyo.

As our plane has now arrived, I want to introduce students to Japan. I tell them that Japan is made up of many small islands. I show them the numerical area of Japan in square miles, and the numerical area of the United States in square miles. I ask them to look at these two very large numbers and decide which is larger. Because of the plea value difference, students are able to see that the US is larger in area.

I hold up 4 rulers to identify what a square foot is and tell students that if we could make Japan a square and measure it in miles it would be 145, 882 square miles in size meaning that inside my square (I point to my rulers) there would be 145,882 squares. I remind students that my little square is only a square foot, but if we were to get in the bus and drive to the beach and then to Coastal Ridge School and then to Stonewall Kitchen and back to school ( each leg of the trip about a mile - you can do this with landmarks about a mile from your school) that would be a total of 1 square mile. If we made our country square it would be a total of 3,790,000 miles inside the square. I ask students how they know which is larger? (again, students use their plea value understanding to identify that 3 million is way bigger than a number in the thousands)

Next I say that Japan is smaller. Can you think of a tool (MP5) we could use to figure out how much smaller Japan is than the US? (calculator). I ask students to take out their calculators and I ask which number would be put in first? (3,790,000) We do this together. Now do we add or subtract to find out how much smaller (subtract) Ok so hit the - key. Now can you type in Japan's size? Don't forget to hit equal. And what do you get? (Students just had to make sense of very large numbers together to solve the problem (MP1)

Next I tell students that Japan is very crowded. There are 127,600,000 people in Japan and 313,900,000 people in the US. Which has more? (The US.) I draw a picture of the US as a square and put a large person in it. Next I draw a small square to be Japan and I put a person that is almost as big as the US person in the little space. I explain that Japan has more people for each square mile than the US. (This is an introduction so I am just giving students a quick visual of how size and population of the US and Japan are not evenly proportional.)

Students were working with very large numbers today. I did not expect them to manipulate such large numbers on their own. We worked together, but I did want them to see that larger numbers can refer to real things. I am hoping students will gain more insight into place value with larger numbers during this introductory lesson.

I show students some introductory pictures of Japan and tell them that if they had just arrived by plane, they would first need to get some money because Japan uses the yen and not the dollar. I tell them that then they might travel by very fast train, the bullet train, around Japan. I tell them that they will work with partners to figure out their money and how far they can travel.

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#### Working in Small Groups

*20 min*

I give students a paper with 3 questions on it. I tell them they may work with one other person for 5 minutes and may use tools from their math suitcases to help them. I tell them that if they are going to use the calculator tool, they will need to first write the equation they will type into the calculator, and share it with me and then they could use that tool, if it is the one they select.

The problems are:

18 children travel to Japan. They each have $20.00 to spend. At the bank they trade their dollars for yen. Each dollar is worth 98 yen. How much money will each student have in yen to spend in Japan?

The bullet train (shinkansen) can go 320 km/hour. How far could you go in 2 hours?

How far could you go in 4 hours?

If you want to travel to Mt. Fuji from Tokyo, it is 100 km. About how long will it take to get there if you travel on the bullet train?

I walk around to help partners who are struggling with the problems. At the end of 10 minutes, I suggest that students combine with another group and share their work so far.

At the end of another 10 minutes I call the group together to share how they solved the problems.

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#### Closing

*15 min*

I bring students together to share their strategies for solving these complex tasks. We look at several different strategies and talk about why they did or did not work. I want students to walk away with a sense of pride in their attempts to solve these difficult problems, rather than feeling bad if they did not get the correct answer.

I reinforce how hard these problems were, and how proud I was of everyone for trying to figure them out.

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- UNIT 1: What and Where is Math?
- UNIT 2: Adding and Subtracting the Basics
- UNIT 3: Sensible Numbers
- UNIT 4: Sensible Numbers
- UNIT 5: Everything In Its Place
- UNIT 6: Everything in Its Place
- UNIT 7: Place Value
- UNIT 8: Numbers Have Patterns
- UNIT 9: Fractions
- UNIT 10: Money
- UNIT 11: The Numbers Are Getting Bigger
- UNIT 12: More Complex Numbers and Operations
- UNIT 13: Area, Perimeter and More Measurement
- UNIT 14: Length
- UNIT 15: Geometry
- UNIT 16: Getting Ready to Multiply
- UNIT 17: Getting Better at Addition and Subtraction
- UNIT 18: Strategies That Work

- LESSON 1: Using A Pattern to Solve A Problem
- LESSON 2: Skip Counting Patterns
- LESSON 3: Extending Partners of 10 and 100
- LESSON 4: Patterns in Larger Numbers
- LESSON 5: Larger Numbers: A Tie to Social Studies
- LESSON 6: Doubles and Halves are Patterns Too
- LESSON 7: Smiley Faces and Up
- LESSON 8: Put It Together and Take It Apart
- LESSON 9: Pets, Pets and More Pets
- LESSON 10: Larger Number Patterns
- LESSON 11: Let's Review
- LESSON 12: Patterns in Nature
- LESSON 13: Writing and Solving Number Stories
- LESSON 14: Trimester Assessment Day