Counting Strips

The opening discussion really focuses on the CCSS Mathematical Practice standard, "Look for and make use of structure" (MP7). Students use what they notice about the patterns that exist in the numbers to help them write other numbers and identify mistakes. 

Let’s look really closely at one of the rows on our hundreds chart. Let's start counting at 21 and go to 30.

Partner Talk: What do you notice as we count on from 21 to 29? Only look at this first row. How are the numbers changing or staying the same?

Present my counting strip: I wrote these numbers in order from 21 to 30 on my counting strip. Let’s look at it together. Notice how I write 21 at the top and then wrote the numbers down the strip.

• Check my counting strip. What patterns do you see?

• What if I wrote my counting strip like this? (Teacher writes a new counting strip starting at 21 but reverses one number—example: 21, 22, 23, 24, 52, 26, 27, 28, 29)

• Is this correct? How do you know? (Push students to see that the 25 breaks the pattern)

Restate: Right! I needed to watch the patterns. All these numbers have a 2 in the front so I accidentally switched these numbers. Looking for these kinds of patterns will help you make sure that you write the numbers in the right order.

Explain the activity: 

I'll give students 3 numbers to choose from. The 3 numbers will each force students to cross a decade and focus on numbers changing, which is one of the main spots where children have misconceptions. I chose 18, 24, and 35. 

I'll model writing that number on the top of my counting strip. Students often get mixed up because they try to write the numbers horizontally. The idea here is that students are writing the numbers up and down (see this picture for another teacher's example). I have students write the numbers on either sentence strips or a strip from a cashier paper roll. 

I'll have students work on these at desk for 4-5 minutes. As students work, teacher looks for misconceptions. Examples: Do students write…

• 24, 25, 26, 27, 28, 29, 210 (confusion on the decades)
• 24, 25, 26, 27, 28, 29, 20 (confusion on the decades)
• 24, 25, 62, 27, 28 (reversals)

I"ll bring student back together and choose a few counting strips to correct as a class. I'll choose counting strips that have different misconceptions (as listed above).

As students look at the counting strips, I'll ask these guided questions:

• Do you see any mistakes?
• How are you sure that this number is incorrect? (I have students give 2 reasons they are sure. This pushes them to provide evidence for their claims, a huge emphasis of the CCSS)
• How would I write this number correctly in standard form? (Teacher circles the mistake and writes it the way the student tells him/her to)
• Is this correct now? How do you know? 

Today’s thinking job was: What patterns do I notice to help me write my numbers?

I'll choose 2-3 counting strips to share as exemplars. Students practice counting the numbers on those strips.

I'll choose 1 of the strips for students to discuss with a partner why it is correct, and then display the exemplars for students to refer to later.