Grade 05 Mathematics - EC: M05.A-T.1.1.2
Grade 05 Mathematics - EC: M05.A-T.1.1.2
Continuum of Activities
The list below represents a continuum of activities: resources categorized by Standard/Eligible Content that teachers may use to move students toward proficiency. Using LEA curriculum and available materials and resources, teachers can customize the activity statements/questions for classroom use.
This continuum of activities offers:
- Instructional activities designed to be integrated into planned lessons
- Questions/activities that grow in complexity
- Opportunities for differentiation for each student’s level of performance
Grade Levels
5th Grade
Course, Subject
Mathematics
Related Academic Standards / Eligible Content
Activities
- When multiplying a number by a power of 10, does the decimal point move to the right or left?
- When dividing a number by a power of 10, does the decimal point move to the right or left?
- How many places and in which direction does the decimal move when multiplying a number by 104?
- How many places and in which direction does the decimal move when dividing a number by 103?
- When finding a solution for .29 ÷ 102 does the decimal move to the left or the right?
- 92.05 ÷ 106 =
- 445.87 x 102 =
- 6.003 x 10? = 6,003
- How many zeros are in the product when 3.587 is multiplied by 105?
- How many zeros are in the solution to 36.5 ÷ 102?
- 102.05 ÷ 10? = .0000010205
- What is the original number if 5,402,000 has already been multiplied by 103?
- What is the original number if 462,000 has already been divided by 104?
- What is the difference between 3.45 divided by 104 and 3.45 divided by 106?
- What is the difference between 24 multiplied by 103 and 24 divided by 102?
- Explain why the decimal moves two places to the right when multiplying 54.999 by 102. This is the same as multiplying by what number? Why?
- Give multiple reasons why the solution to 4.093 x 103 cannot be a less than 4,000. Provide a thorough explanation for your reasons.
- Determine the value of the digit 5 in the following numbers: 5,763 6,587 8,657
As a digit moves from the tens to the hundreds to the thousands, what is the value increased by? Represent the increase mathematically in two different ways. Explain your thinking. - Explain the difference in the value of a digit as it moves from the hundreds place to the thousands place. What must it be multiplied by? Does this work for any digit? Why or why not?
- Explain why the decimal moves three places to the left when dividing 86.243 by 103. This is the same as dividing by what number? Why?
- Give multiple reasons why the solution to 5,109.3 ÷ 103 cannot be a greater than 10. Provide a thorough explanation for your reasons.
- Compare the two expressions without doing the calculations. Which one is greater? Explain your answer (do not calculate an actual answer).
5,109.3 ÷ 103 .05124 x 103 - Multiplying or dividing 234.5 by what power of 10 will allow the number to become greater than 23? Is there one solution to this questions or multiple solutions? Explain your thinking. Can you use multiplication and division? Why or why not?
- Marietta explains to the class that the way she figures out the solution to 45.02 ÷ 106 is to divide 45 by 10, then add the decimal portion of the number to it, and finally move the decimal 5 places to the left. Is she correct? Why or why not?
- Compare the two expressions. Which one represents a larger number if a> b>0? Explain?
ab.cdef ÷ 103 bb.acde ÷ 102
Answer Key/Rubric
- right
- left
- 4 to the right
- 3 to the left
- left
- .00009205
- 44,587
- 3
- Two
- None
- 8
- 5,402
- 4,620,000,000
- Answers may vary. Examples: division by 102, division by 100, .00034155
- Answers may vary. Examples: 23,999.76, the decimal in the first is moved 3 places to the right and in the second it is moved 2 to the left
- The base ten number system is used so 102 represents two places in a base ten system. The movement to the right of the decimal is because the value of the number is increasing when multiplying by 100. Actually multiplying by 100 where 100 = 102.
- 103 is equivalent to 1000 and 4 x 1000 equals 4000. Multiplying by 103 means the decimal is moved 3 places to the right so the answer is 4093.
- 5,000 500 50. The value is increased by 10. 10 and 101. As the place value goes from the ones to tens to hundreds to thousands the value of the number is increased 10 times.
- The value of the digit is 10 times greater. It must be multiplied by ten. This will work for any digit. The value of the digit is irrelevant it is the value of the place it holds – it increases by ten times.
- 103 is equivalent to 1000 and division by 1000. The base ten number system is used so 103 represents three places in a base ten system. The movement to the left of the decimal is because the value of the number is decreasing when multiplying by 1000.
- 103 is equivalent to 1000 and 5109.3 divided by 1000 means the decimal is moved 3 places to the left so the answer is 5.1093. Another method is to use estimation 5000 divided by 1000 is 5.
- Division by 103 is three decimal places to the left and 5109.3 decimal is moved 3 places to the left so the answer is approximately 5. In the second expression multiplication by 103 is three decimal places to the right so the answer is approximately 51. The second expression is greater.
- Example answer: Multiplying by 10 to the zero power. There are multiple solutions. Since the number is greater than 23 already, multiplying by one will allow the number to remain the same. You can use multiplication and division. Student explains using examples. (Multiplying by any power greater than or equal to 0 will work; and dividing by 10 will also work).
- Incorrect. When 45 is divided by 10 the decimal is removed, thus eliminating the division by 10 for that portion of the number – mathematically incorrect.
- Second expression is greater. The first expression is equal to .0abcdef and the second is .bbacde therefore .0a must be less than .bb.
