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- Look at the two tables your class made. How are the two class tables different? How are they alike? Discuss this with a partner and with the class.
- List the areas each group found from smallest to largest.
- Compare the coat areas using the list from Question 8.
- About how much larger is the area of the largest coat than the smallest coat?
- Is it more or less than 500 square centimeters larger?
- Is it more or less than 1000 square centimeters larger?
- If the material costs 10¢ for every 100 square centimeters, about how much will it cost to cover your group's coat? Show how you found your answer.
- Your group has a 6000 square centimeter piece of material. About how much will be left over after you cut out enough material to cover your group's coat?
- Use base-ten shorthand and the Fewest Pieces Rule to show your number from Question 5. Then write the number. How are these two ways of showing the number different? How are they the same?
Place Value
Our number system is a place value system based on tens. It has a code built into it. When we write numbers in standard form in our base-ten system, the place that each digit sits in the number tells us its value. Here is a four-digit number in standard form:
The 5 is in the thousands place. It means 5 thousands: 5 × 1000 = 5000.
The 3 is in the hundreds place. It means 3 hundreds: 3 × 100 = 300.
The 2 is in the tens place. It means 2 tens: 2 × 10 = 20.
The 4 is in the ones place. It means 4 ones: 4 × 1 = 4.
Adding the value of each place gives the number:
Writing a number as a number sentence in this way is called expanded form.