One way to make sure students get the most out of expanded form is to also have them label and draw what each of the digits in a number represents. In the example below, my second grade student split the number into 2 hundreds, 0 tens and 3 ones and had her draw a picture of each.
I would argue that zeroes are just as important as the non-zero digits. Zeroes matter! Expanded form is too valuable to stop using after the place value unit ends. Two areas where expanded form supports increased understanding is with addition and decimals. Students benefit from using expanded form here because the emphasis remains on the place value of the numbers they are working with.
The pictorial representation provides scaffolding for students who need something to help them count the sum. You can also return to expanded form when teaching decimals. This means partitioning a number before carrying out an addition or multiplication.
More like this. What is place value? Place value arrow cards. What is partitioning? Adding two-digit numbers using partitioning. Put up your right hand and pledge that you will not skip to the abstract too fast. Manipulatives are not something we need to wean the students off of as quickly as possible. Manipulatives provide a means for deep, conceptual understanding.
Will it take longer to work problems using manipulatives? Absolutely, but the understanding is cemented when the learning is concrete. Within the file, there are three sets of cards—6-, 9-, and digit. One idea is to copy each set on a different color card stock to easily differentiate. You could also mix and match the cards for greater variety and create a deck with 6-, 9-, and digit numbers. Looking to extend the activity? Have kiddos make their own card decks on index cards.
Grab your freebie here. Thanks for this lesson and the freebie. I start back next week and this will be perfect for my 4th and 5th graders! This is a great explanation of how to cement student learning in a concept and a wonderful lesson to guide teachers. Thank you! Thanks for the matching cards Donna. This is just what we were looking for, for the expanded notation TEKS. Now that we know how TEA is going to test it. Do you have any ideas for TEKS 3. Although base 10 blocks only go to thousands, if they get the concept with smaller numbers, it should translate to larger ones.
That TEK might be better revisited later in the year. I love this! We a easy transition to multiplication with multiples of ten as well. We used your post as discussion at our math team meeting this week. We move into decimals in another week and will use the expanded notation with them as well. Thanks for the amazing insight!
Donna, Can you explain the difference between expanded form and decomposing the number? Great question, Jan! While numbers can, and should, be decomposed in many ways, I think expanded form shows the actual value of each digit. So the value of the 2 in is Does that make sense? This was so helpful and came for me at the perfect time in my teaching sequence. I teach 3rd grade math. I also never had to represent a number like that my whole career in school.
I think tea should have thought this through before placing in the teks. I also have taught 1st grade math and I found it incredibly difficult to teach expanded form when they were not use to dealing with an addition symbol. I think common core is better thought out than the teks.
I could really use those too! Another option is to teach place value concepts at the beginning of the year, but bring in the expanded notation piece a little later, when students are studying multiplication.
Using drinking straws is another great option. The ones that bend are great for angles! Basically they will be assessed for mastery of all place value concepts next week, and I am feeling the stress. I love your blog and activities btw, and thank you for the reply! Thanks for helping me understand the difference between expanded form and notation.
The CCSS only call out standard form specifically for 4th grade, so I am not sure we need to teach expanded notation. Is it your opinion that we should teach it anyway? If so, how do you help students understand the difference? I want to add that I realize that this lesson is designed to help students learn about both expanded form and notation.
However, my question was more about how to have students remember the difference. Sometimes students get confused when mathematical terms are similar. Written like the above on my word wall and directly below the explanation of each and a visual of expanding the word. I tweaked some of your questioning to help my 1st grade teachers with expanded form. Why would they take it away then?
Thanks for this article to help me provide them with appropriate questioning that builds a foundation for upper grades.
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