For any number, the place of a digit tell show many ones, tens, hundreds, and so forth are represented by that digit.
How does a place value chart help to find the answer?
Each place value to the left of another is ten times greater than the one to the right (e.g.,100=10x10).
If a grade level brought in 44,444 pennies, explain the relationship of each 4 in terms of multiples of 10.
Mathematical explanations can be given using words, objects, pictures, numbers, or equations.
Which strategy did you use to decide how many pennies the 4th grade donated for the garden project?
Are there any other strategies that can be used to find the answer?
Why did you use multiplication in this problem?
Why did you use addition in this problem?
The value of the digits can be added together to find the value of the number.
What number is represented by (6x10,000)+(1x1,000)+(2x10)+(7x1)?
Explain what is shown when a number is written in expanded form. For any number, the place of a digit tell show many ones, tens, hundreds, and so forth are represented by that digit.
How did you know how to make the largest 6-digit number?
What are the values of each digit in that number?
How did you know how to make the smallest6-digit number?
What are the values of each digit in that number?
Each place value to the left of another is ten times greater than the one to the right(e.g.,100=10x10).
Why does it matter which order the digits are in when determining the value of the multi-digit whole number?
Mathematical explanations can be given using words, objects, pictures, numbers, or equations.
What advice would you give to a student who is struggling to read multi-digit whole numbers?
For any number, the place of a digit tells how many ones, tens, hundreds, and so forth are represented by thatdigit.
What effect does the location of a digit have on the value of the digit?
Which number is larger: 380 or 38? How do you know? Why?
What conclusions can you make about the places within our base ten number system?
Each place value to the left of another is ten times greater than the one to the right (e.g.,100=10x10).
What can you conclude about the value of a digit in the ones place compared to the value of the same digit in the tens place?
What can you conclude about the value of a digit in the tens place compared to the value of the same digit in the hundreds place?
What can you conclude about the value of a digit in the hundreds place compared to the value of the same digit in the thousands place?
How does moving one place to the left change the value of the same digit in a multi-digit number?
How does moving one place to the right change the value of the same digit in a multi-digit number?
How does this relate to division?
Mathematical explanations can be given usingwords, objects, pictures, numbers, or equations.
How did you choose to represent your reasoning in this task?
For any number, the place of a digit tells how many ones, tens, hundreds, and so forth are represented by that digit.
Why did you choose to use a place value chart?
Why did you choose to use a number line?
How can place value understanding help us with comparing, ordering, and rounding?
Each place value to the left of another is ten times greater than the one to the right (e.g.,100=10x10).
How do you know the value of the digit 3 in each mountain height?
Which 3 digit has a greater value in the mountain heights?
Which 3 digit has a lesser value in the mountain heights?
Mathematical explanations can be given using words, objects, pictures, numbers, or equations.
How can numbers be expressed, ordered, and compared?
What symbols can I use to compare numbers?
The value of the digits can be added to get her to find the value of the number.
What is the expanded form of 22,837?
Can you explain how the standard form relates to the expanded form?
Why are plus signs needed when writing numbers in expanded form?
For any number, the place of a digit tells how many ones, tens, hundreds, and so forth are represented by that digit.
How can place value understanding help us with comparing, ordering, and rounding?
Mathematical explana9tions can be given using words, objects, pictures, numbers, or equations.
How did you choose to show your reasoning about rounding? Explain.
Rounding whole numbers is a process for finding the multiple of 10,100, and soon closest to a given number.
How do you know that Gianna is correct in saying that all these numbers round to the same number?
How do you know that Zachary is correct in saying that all these numbers round to different numbers?
What is the highest number possible that would round to 500,000, when rounding to the highest place value?
What is the smallest number possible that would round to 500,000, when rounding to the highest place value?
What do we get when we round 25 to the nearest ten? Why? Is 25 closer to 30 or 20? (Neither It’s right in the middle.) Why do you think it rounds to 30? (It’s a mathematical convention.) These questions can stimulate a discussion of where some of our rules come from.
For any number, the place of a digit tell show many ones, tens, hundreds, and so forth are represented by that digit.
What is the value of the 7 in the number 762,398? The 6? The 2? Etc?
How is this knowledge useful in rounding?
Mathematical explanations can be given using words, objects, pictures, numbers, or equations.
How is a number line useful when rounding?
Are there any other representations that can behelpful when rounding?
Rounding whole numbers is a process for finding the multiple of 10, 100, and soon closest to a given number.
When rounding to the thousands place, which digit determines the value in the thousands place? (i.e. which digitis used to make the decision?) For example, when rounding 13,671 tothousands which digit determines if the answer is 13,000 or 14,000?
If the Liberty Bell weight was rounded up to 2000 lbs, what possible values could have been in the hundreds place of the actual weight?
If the Liberty Bell weight was rounded down to 2000 lbs, what possible values could have been in the hundreds place of the actual weight?
When is rounding useful in real life?
For any number, the place of a digit tells how many ones, tens, hundreds, and so forth are represented by that digit.
Can you tell me what each digit stands for in 10,430?
Each place value to the left of another is ten times greater than the one to the right (e.g., 100=10x10).
What do the zeros in each person’s rounded number tell you about how they rounded?
Do all of the zeros have same meaning in the rounded numbers?
Mathematical explanations can be given using words, objects, pictures, numbers, or equations.
How could a number line be used to help explain rounding numbers?
Are there any other representations that might be helpful when rounding?
Rounding whole numbers is a process for finding the multiple of 10,100, and soon closest to a given number.
How do you know that all 3 people can be correct?
If everyone was asked to round to the highest place value, could they have different correct answers? Why or why not?
Can you round 85,273 to each place value?
Do you get different answers for each place value? Why or why not?
For any number, the place of a digit tells how many ones, tens, hundreds, and so forth are represented by that digit.
What does the 5 digit stand for in the population of Dyer County?
What does the 3 digit stand for in the population of Cheatham County?
What does the 8 digit stand for in the population of Warren County?
Each place value to the left of another is ten times greater than the one to the right (e.g.,100=10x10).
What are the values of the 8s in Dyer and Warren counties populations?
How can the same digit be worth different amounts?
Mathematicale xplanations can be given using words, objects, pictures, numbers, or equations.
How is expanded form useful when comparing numbers?
How is a number line useful when comparing numbers?
How is a number line useful when rounding numbers?
The value of the digits can be added together to find the value of the number.
How is expanded form useful when comparing numbers?
Rounding whole numbers is a process for finding the multiple of 10,100, and soon closest to a given number.
What words would you use to describe the activity of “rounding to the nearest ten thousand”? (Emphasize the phrase “close to” or “closest to”)
What words would you use to describe the activity of “rounding to the nearest ten”?
How many digits must be zeros when rounding to the nearest ten thousand? Why?
