Today I had a great day of planning with a kindergarten and 1st grade teacher for lessons we are teaching together on Thursday and WOW, has it been such a learning experience for me! The best part is, we have a whole day to get feedback from anyone who would like to offer it before we try this all out!

In Kindergarten, the students have been counting collections, counting dot images in various ways and since I have been obsessed with the clothesline lately, we thought this could be the perfect mash-up! When I read the counting and cardinality learning progressions, however, I did not see anything in there about number lines in Kindergarten but I did find this in the measurement progression:

*“Even when students seem to understand length in such activities, they may not conserve length. That is, they may believe that if one of two sticks of equal lengths is vertical, it is then longer than the other, horizontal, stick. Or, they may believe that a string, when bent or curved, is now shorter (due to its endpoints being closer to each other). Both informal and structured experiences, including demonstrations and discussions, can clarify how length is maintained, or conserved, in such situations. For example, teachers and students might rotate shapes to see its sides in different orientations. As with number, learning and using language such as “It looks longer, but it really isn’t longer” is helpful. Students who have these competencies can engage in experiences that lay the groundwork for later learning. Many can begin to learn to compare the lengths of two objects using a third object, order lengths, and connect number to length. For example, informal experiences such as making a road “10 blocks long” help students build a foundation for measuring length in the elementary grades.”*

In thinking about this, I tweeted out about number lines in Kindergarten and immediately was reminded by Tracy of her post on this work from last spring! Awesome stuff! I sent the link on to Nicole, the teacher I am planning with, and we were both filled with so many ideas! We were both thinking about relative location on the number line but hadn’t thought more specifically about the equal distances between each number! We also were originally going to do the number line as a whole group, but after reading Tracy’s post we changed our plan to allow for more discovery and exploration of the number line!

Here is the plan….

- Students will be in groups of 4. Each group will have a strip of tape on the floor in different areas around the room.
- We decided to put the tape the length of 5 tiles to see if any group uses the tiles in thinking about space.
- We will hand each group the same card one by one and ask them to decide, as a group, where it should be placed.
*We went back and forth with this one…we wondered whether we should just let them start placing, but we really were so curious to see their moves and adjustments with each card. We also thought that since they have been ordering numbers lately, the majority would just put each card next to one another on the line.* - Now, the order of the cards…this was so much fun to talk about….
- 1 – to see if they place it at the beginning and then the adjustment when 0 comes up.
- 10 – to see if students put it at the end of the line and how they determine the distance from 1
- 0 – to see if students place it to the left of 1 and if they have to move the 1.
- 3 – to see if students but it closer to 1 than 10, how close to 3 they place it, and if they put it less than half.
- 9 – to see if students think about 1 less than 10.
- 5 – THIS IS THE CARD I CANNOT WAIT TO SEE! Since they have been doing ten frames so much, some students are comfortable with 5 and 5 is 10, so do they apply that logic here?
- 7 – to see if students put it right in the middle of 5 and 9.
- 6 – one less than 7 or one more than 5.
- 2 – between 1 and 3.
- 4 – again, one more or one less
- 8 – same

- During all of the placing time, we will be listening and recording any important ideas we want to have students talk about when we go to the whole group discussion.

After each group has placed the cards, we will have them do a gallery walk to the other groups’ lines and ask them to talk about what is the same, what is different at each line. We will then gather on the carpet.

We have a clothesline up, much longer than their strips of tape to do the same cards as a whole group. We will give each pair of students one card to talk to each other where they would put it (based on their work in the earlier group work). *Something we did not think of until I just typed this was how we partner the students up…we should match them with a student from a different number line to vary the convo.

We will call the cards up in the same oder they did their group work and ask the pair to explain where they decided to put their card and why. After all the cards are placed, we will ask them what was important to them as we made our number lines and record that for future conversations.

As a future conversation, we thought it would be really cool to see what connections the students make between the number line, ten frame, and dot images they have been working with so much!

Also, if anyone knows of a children’s book that has something moving a distance of 10 or 20 units, I would love to hear about it! Every single book I read dealt with 10 as collections of things, never distance.

-Kristin

Too late to type up the 1st grade one now, but it will be around this Dot Addition game in Investigations: http://www.smusd.org/cms/lib3/CA01000805/Centricity/Domain/198/Dot%20Addition.pdf Will type that one up tomorrow!!

Cynthia Garland-DoreTry the book Ten Beads Tall

https://www.google.com/search?q=ten+beads+tall&ie=UTF-8&oe=UTF-8&hl=en-us&client=safari

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mathmindsblogPost authorThanks Cynthia!! I will check it out!

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mathmindsblogPost authorOk, so here is my problem, and it could completely be the way I think about this distance on a number line….In that book, they are counting blocks to see how many, so they really don’t have to go to the end of the block to say “it went the distance of one and then to get to two I have to travel the equal distance, and then three is another interval of the same amount…” Does that make sense? I am looking for something that gets beyond counting the number there to measure but instead thinks about the distance to get there. Please tell me if I am completely off or thinking about this completely wrong!!

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howardat58A stick should do the job. It doesn’t matter about “how big is the gap”, only that the gaps are the same. No real need to talk about length at this stage. Remember Piaget.

Strictly speaking, a number line for whole numbers does not need to have equal sized gaps, and it doesn’t need to be straight !

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Paula Beardell KriegImagining this activity, with the tape and tiles on the floor, an image that came to mind was of being out on the playground in grade school and drawing hopscotch boards on the pavement. As I think of it now, it was something like a number line. Is this an activity that children do anymore?

I enjoy reading posts about number lines. I think anything that educators can do to elevate the importance of the number line is time well spent. I like that you are thinking about using the number line as a measure of distance. As students get older and this number line that has been integrated into their being by being so vibrantly represented in your class, more and more they will be using the number line to represent TIME. I wonder if there is a way to play with the time concept now? I’ll look forward to reading how it goes.

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Amy YoungbloodYou might be able to make Counting Crocodiles work. It doesn’t directly talk about length, but the monkey does have the crocodiles line up across the Sillabobble Sea so he can cross to another island to get bananas.

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