It’s back to school, which means back to place value! In our district scope and sequence, grades 2 through 5 all start the year with place value. What’s changing about place value under Common Core and the new TEKS (Texas standards) is the emphasis on understanding the relationships between the digits in a number.
“Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.” CCSSM 4.NBT.1
Notice that Common Core doesn’t really specify the magnitude of number a student must be able to work with, while in Texas it’s 6-digit for 3rd, 9-digit for 4th, and 12-digit for 5th. You may wonder why common core doesn’t specify. Here’s my thinking. If you truly understand the patterns in the place value system, reading numbers to the trillions is the same as reading numbers to the hundred thousands, right? You might want to take a minute and check out this post on reading larger numbers. You can also grab a free place value chart while you’re there.
I made a little match-up activity that reinforces the concept of reading 3-digit numbers and knowing period (groups of 3 digits in a number) names. Notice in the word form card, the 3-digit numbers are underlined and the period names (thousand, million, billion) are bold. This is also a strategy for helping kids learn to attend to precision in matching up the different forms of numbers. They need to be taught to chunk the numbers into periods and compare each period when trying to, for example, match number form to word form.
Here’s how I would use this activity in the classroom. Prior to this activity, I would have had the lesson on reading large numbers (maybe the previous day), but I would not have had a lesson on forms of numbers (standard, word, expanded). That kind of throws it into a little bit of problem solving. There 10 groups of 3 cards in the set, for a total of 30 cards. If your class is smaller than 30, take some cards out, but make sure you keep sets of 3. Hand out one card to each student. Since it’s the beginning of the year, and you’re working on establishing routines, this would be a good time to have a mini-lesson about your expectations for how students should move around the room and how you will get their attention. I would also give them a list of talking points to discuss once they find the students with matching cards, because I want that time to be productive and I want to start right away letting them know that we are expected to talk about math. Here are some sample talking points:
- What process did you use to find matching cards?
- How did you check to make sure your cards matched once you grouped up?
- Why are some words bold?
- Why are some words underlined?
- If you have a zero in your number, what does the zero mean?
- If you have the same digit more than once in your number (for example two 3s), do the digits mean the same thing?
- What patterns do you notice?
- Is there anything interesting about your number you’d like to share?
At your signal, the students will move around and try to find the students with cards showing the other forms of their number, at which time the group will discuss their number using the talking points. After all the students have matched up and had time to discuss their numbers, pull the group back together and allow the groups to share out. Don’t skimp on the time for discussion…that’s your mathematical practices in action!
To bring the lesson to a close, create an anchor chart with help from the kiddos listing the different forms of the numbers (standard, word, expanded) and an example of each. Have a discussion about what expanded form is, and I’d include a definition. A good kid-friendly way to describe expanded form is that it “shows the value of each digit”.
There are lots of other uses for the cards. Use them another day to practice ordering numbers (don’t forget to include conversations about how kids knew the right order). Use them for an activity on comparing numbers or in small group instruction. Have students write the number form or expanded form from the word form. So many possibilities!! You can grab a set with 6-digit numbers, 9-digit numbers, and 12-digit numbers.