Section B: Practice Problems Place-value Relationships through 1,000,000
In this section, we worked with numbers to the hundred-thousands.
First, we used base-ten blocks, 10-by-10 grids, and base-ten diagrams to name, write, and represent multi-digit numbers within 1,000,000. We wrote the numbers in expanded form so that we can see the value of each digit. For instance:
Next, we learned that the value of a digit in a multi-digit number is ten times the value of the same digit in the place to its right. For example:
Both 14,800 and 148,000 have 4 in them.
The 4 in 14,800 is in the thousands place. Its value is 4,000.
The 4 in 148,000 is in the ten-thousands place. Its value is 40,000.
The value of the 4 in 148,000 is ten times the value of the 4 in 14,800.
We used both multiplication and division equations to represent this relationship.
Finally, we analyzed the “ten times” relationships by locating numbers on number lines.
Problem 1 (Lesson 6)
Write the name of the number 8,500 in words.
How many hundreds are there in 8,500? Explain how you know.
Problem 2 (Lesson 7)
Count by 10,000 starting at 6,500 and stopping at 66,500. Record each number:
Pick two numbers from your list and write their names in words.
Problem 3 (Lesson 8)
If each small square represents 1, what number does the picture represent?
If each small square represents 10, what number does the picture represent?
Problem 4 (Lesson 9)
Write the names of the numbers 702,150, and 73,026 in words.
How is the value of the 7 in 702,150 related to the value of the 7 in 73,026?
Problem 5 (Lesson 10)
What is the value of the 6 in 65,247?
What is the value of the 6 in 16,803?
Write multiplication and division equations to represent the relationship between the value of the 6 in 65,247 and the value of the 6 in 16,803.
Problem 6 (Lesson 11)
Locate and label each number on the number line:
Which numbers were easiest to locate? Which were most difficult? Why?
Problem 7 (Exploration)
For each question, use only the digits 1, 0, 5, 9, and 3. You may not use a digit more than once and you do not need to use all the digits.
Can you make three numbers greater than 3,000 but less than 3,500?
Can you make three numbers greater than 9,000 but less than 10,000?
Which numbers can you make that are greater than 39,500 but less than 40,000?
Problem 8 (Exploration)
Estimate the value of the number labeled A on the number line. Explain your reasoning.