Activities

1. What is the value of the digit 4 in the number 439.5?
   
   
2. What does the 4 represent in the number 6,460.9?
   
   
3. Write a number with a 7 in the thousands place.
   
   
4. True or false.  80 is 1/10 of 800.
   
   
5. The underlined place value is 1/10 of which place value if all digits are the same?    AB,CDE

6. Compare the value of the digit 5 in the numbers 54 and 5.
   
   
7. Using base ten blocks, draw a model for the value of the digit 7 in the number 8,873
   
   
8. What is the value of the first and second 5 in the number 553?
   
   
9. Does the 8 in the hundreds place represent 1/10 of the value of the 8 in the tens place of the number 880?
   
   
10. What fractional part of the thousands place is the hundreds place?
    
    
11. What fractional part of the hundreds place is the tens place?
    
    
12. Write a number that has a 3 in the hundreds place and the digit in the tens place is 1/10 the value of the hundreds place.
    
    
13. Does the 8 in the hundreds place represent 1/10 of the value of the 8 in the thousands place of the number 8,809?
    
    
14. Write a number that has a 6 in the thousands place and the digit in the hundreds place is 1/10 the value of the thousands place.
    
    
15. How many numbers can meet the following conditions?

• Has a 7 in the hundreds place
• The tens place digit is 1/10 the value of the hundreds place digit
• Is less than 780
• Is a whole number  

16.  Compare the value of the digit 4 in the first number to the value of digit 4 in the second number.  What are the patterns with respect to location and value?  

                        3,476               9,748
                        14,305             456
                        12,947             84

17. Determine the value of the digit 6 in the following numbers:   6,857       5,687     3,765
    As a digit moves from the thousands to the hundreds to the tens place, what happens to the value? 
    
    
18. Explain the difference in the value of a digit as it moves from the thousands place to the hundreds place.  Does this work for any digit? Why or why not?
    
    
19. Using the blocks below, write the number represented in each circle and then describe what fractional part one is of the other by comparing the value of the digit 7.

20. What whole number would be represented if the highest place value is the hundreds place and the value of the digit in the hundreds place is 10 times the value of the digit in the tens place? The digit in the ones place is the same digit as the hundreds place.  Is this the only number that meets these conditions?  Explain your thinking.
    
    
21. List two whole numbers that meet the following criteria.  Explain your reasoning.

• The number is less than 30,000
• Each digit in any place is 1/10 of what it represents in the place to its left

22. List two whole numbers that meet the following criteria.  Explain your reasoning.

• The number is less than 44,000
• Each digit in any place is 10 times what it represents in the place to its right

23. In the empty circle, draw a model of the number that meets the following conditions.  Explain your thinking.

• Each digit in any place is 1/10 of what it represents in the place to its left
• A whole number less than one hundred twenty.

24. How many whole numbers have each digit in any place is 1/10 of what it represents in the place to its left?  Explain your thinking.
    
    
25. How many whole numbers have each digit in any place is 10 times what it represents in the place to its right?  Explain your thinking.

Answer Key/Rubric

1. 400
   
   
2. Hundreds or 400
   
   
3. Answers will vary.
   
   
4. true
   
   
5. A

6. Answers will vary but must contain reference to 50 and 5
   
   
7. Seven longs should be drawn
   
   
8. 500 and 50
   
   
9. No
   
   
10. 1/10
    
    
11.  1/10
    
    
12. Answers will vary.  Example: 331 - Answer must have a 3 in the hundreds and tens place.
    
    
13. Yes
    
    
14. Answers will vary.  Example:  6,600 - Answer must have a 6 in the thousands and hundreds place.
    
    
15. ten

16. The second number is 1/10 the value of the first number with respect to the 4 digit.
    
    
17. Values:  6,000; 600; 60.  The number is 1/10 the value of the preceding number with respect to the 6 digit. 
    
    
18. The number is 1/10 the value as you move from the thousands place to the hundreds place.  Yes, this will work for any digit, because the value of the digit is not relevant to the pattern as long as the digit remains the same as movement occurs.
    
    
19. 70 in the first circle and 7 in the second circle.  The second is 1/10 of the first.     
     
20. 111, 222, 333, 444, 555, 666, 777, 888, 999 are all possible answers.  Since the hundreds digit is ten times the value it must be the same digit as the tens (i.e 700 and 70 because 700 is ten times 70) and the hundreds digit is the same as the ones digit all three places have the same digit.
    
    
21. 22,222 or 11,111 are possible answers.  The number must be under 30,000 so the first possible number must be 29,999.  Since each digit in any place is 1/10 of what it represents in the place to its left (i.e 7,000 and 700 because 700 is 1/10 of 7,000) this requires all places to have the same digits.
    
    
22. 33,333; 22,222; 11,111 are possible answers.  The number must be under 44,000 so the first possible number must be 43,999.  Since each digit in any place is 10 times what it represents in the place to its right (i.e 300 and 30 because 300 is ten times 30) this requires all places to have the same digits.
    
    
23. Explanations will vary according to the number chosen to model from the following possibilities:  11, 22, 33, 44, 55, 66, 77, 88, 99, 111.  The number must be under 120 so the first possible number must be 119.  Since each digit in any place is 1/10 of what it represents in the place to its left (i.e 70 and 7 because 70 is 1/10 of 7) this requires all three places to have the same digits.

24. An infinite number.  The condition is that every digit in the number is identical and there are infinite numbers where this is the case.  (Student must explain why the previous must be the case.)  Since each digit in any place is 1/10 of what it represents in the place to its left (i.e 70 and 7 because 7 is 1/10 of 70) this requires all places to have the same digits.
    
    
25. An infinite number.  The condition is that every digit in the number is identical and there are infinite numbers where this is the case.  Since each digit in any place is 10 times what it represents in the place to its right (i.e 300 and 30 because 300 is ten times 30) this requires all places to have the same digits.