Gr 3 Place value

[Karen Gartland]

I am working with a grade 3 teacher on her interpretation of the place value standards for elementary students. It is clear that students in grade 2 work with numbers to 1,000 but then the next reference to place value (other than rounding) is in grade 4. The grade 4 standard focuses on understanding the relative value of digits in the base ten system, but does not state if students should understand numbers to a particular place.
The teacher that I am working with is hoping for clarification from me (hence, here I am!) about the expectations for place value in grades 3 and 4. Can you assist me?
Thanks in advance.

[Cathy Kessel]

Have you looked at the NBT Progression here: https://www.math.arizona.edu/~ime/progressions/? It was written by CCSS writers.

[Cathy Kessel]

The updated NBT Progression (as part of a larger document) is here: http://mathematicalmusings.org/wp-content/uploads/2019/02/Progressions_CC_to_RP_02072019.pdf.

[Karen Gartland]

Hi,
Thanks for replying. I have read the progressions documents a number of times over the years! Unfortunately my question is not answered in this document. If you have any other suggestions please don’t hesitate to let me know.
Thanks in advance.
Karen

[Cathy Kessel]

For grade 3, students add and subtract within 1000 and multiply one-digit whole numbers by multiples of 10 in the range 10–90. For that, they need only numbers within 1000.

On page 29 of the CCSS document, the footnote for NBT in grade 4 says, “Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.”

[carriew]

I had this question as well. I didn’t see anything about comparing numbers (within 1,000), ordering numbers, or writing numbers in their various forms. It is mentioned in 2nd and 4th, but not in 3rd. Is it good practice to have them do this as a review of place value to help them remember the meaning of the places and their values? The only straight out “place value” standard calls for the students to round. Comparing and ordering and word forms aren’t mentioned, but I would assume to help them bridge over from 2nd to 4th you would do this as a practice/review?

[carriew]

I had this question as well. I think what Karen is referring to are the usual “Place Value” standards such as writing numbers in word form, comparing them, and ordering them. These are mentioned in grade 2 and again in grade 4, but aren’t mentioned directly in the 3rd grade base ten standards. Only rounding is mentioned (besides getting into the operations themselves).

Would you suggest doing these as a way to review/practice the meanings of place and their values? This would obviously help bridge between grades 2 and 4 and also help them remember place value for when they use the operations. (Sorry if this posts more than once, the first time I hit Submit, nothing happened and my reply was lost.)

[carriew]

One more question (sorry that the earlier post was doubled, I thought it was lost and retyped what I remembered): If you do a place value review as mentioned above, do you go over the thousands place? Since 3rd graders are working within 1,000 for adding/subtracting and 100 for multiplication/division, I didn’t know if they were expected to know that. Assuming they round a 9 in the hundreds place up, they would obviously need to know the thousands. Just wanted to see what you all thought. Thanks!

Carrie

[Cathy Kessel]

Whether or not to have a place value review of the kind you describe is a curricular decision. Work with rounding might serve some or all of the same purposes because students need to use closest numbers (thus they need to compare numbers) and the meanings of places when rounding.

I can’t see that any grade 3 standard indicates that students need to work past 1,000 for NBT.

[Karen Gartland]

Cathy,
Totally agree that a place value review is a curriculum decision. However, WHAT place value to work within in grade 3 in particular is the question. It seems that the standards state working to 1,000 in grade 2 and then to 1,000,000 in grade 4 is a big jump. It is a good hint that students to work with add/sub to 1,000 but does not specifically state whether they need to know how to work with numbers beyond 1,000. Thanks for CarrieW for continuing this thread as well.
Karen G.

[Cathy Kessel]

Thanks, Karen. What you and CarrieW seem to be getting at is: Do the standards really intend to have a jump from 1,000 in grade 2 to 1,000,000 in grade 4?

I think that what is going on is related to focus (treating fewer topics in more depth). Here are the descriptions of the critical areas in grades 2–4:

In Grade 2, instructional time should focus on four critical areas: (1) extending understanding of base-ten notation; (2) building fluency with addition and subtraction; (3) using standard units of measure; and (4) describing and analyzing shapes.

In Grade 3, instructional time should focus on four critical areas: (1) developing understanding of multiplication and division and strategies for multiplication and division within 100; (2) developing understanding of fractions, especially unit fractions (fractions with numerator 1); (3) developing understanding of the structure of rectangular arrays and of area; and (4) describing and analyzing two-dimensional shapes.

In Grade 4, instructional time should focus on three critical areas: (1) developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; (2) developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; (3) understanding that geometric figures can be analyzed and classified based on their properties. . . .

The NBT overview in grade 4 says:

Generalize place value understanding for multi-digit whole numbers.

Use place value understanding and properties of operations to perform multi-digit arithmetic.

The NF overview in grade 4 includes:

Understand decimal notation for fractions, and compare decimal fractions.

So, in grade 4, students extend and use their understanding of place value in several arenas: multi-digit addition and subtraction; multi-digit multiplication and division (using 3.OA.7, fluency with single-digit multiplication); and decimal notation for fractions (using understanding of fractions from grade 3).

[Cathy Kessel]

So, in grade 4, students extend and use their understanding of place value in several arenas: multi-digit addition and subtraction; multi-digit multiplication and division (using 3.OA.7, fluency with single-digit multiplication); and decimal notation for fractions (using understanding of fractions from grade 3).

This allows greater depth than would have been possible in grade 3.

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