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    place value activities
    By Jessica

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    1) Look for the Marilyn Burns Replacement Unit on place value. It's listed as 1-2. All of these units are great resources.

    2) Here is one way that worked for me. A whole week worth's of activities were centered around the "place value mat." I used these activities with 2nd and 3rd graders in a multiage.

    The place value mat is from a book in the series "Developing Number Concepts" from Dale Seymour Publications. I think it is in Book 3. These are also good resources for primary teaching.

    You can make the "pv-mat" by taking a large piece of white construction paper (11x13, I think) and covering half of it with dark blue paper. Each student gets their own. So, on the left side is the tens block (the blue) and the right side is the ones block (white.) To help students keep track of their sides, draw a small smiley face in the upper right hand corner (on the white.) The students love this little smile and it keeps their mats the right direction. Sometimes to get them focused, I say put your finger on the smiley face.

    Next, you see what the students can do with the concept of "tens" by this activity: 1) Ask them to build a tower of (n) unifix cubes. I would start with a number in the teen. 2) Ask them to break it into tens and ones. The ten part stays together on the left side, and the ones are broken up on the right side. I would model this first.

    I did this in small groups of about 9. Here's a tip. Some kids always finish faster than the others, building their tower. Ask them to check their tower with the person sitting across from them, to make sure everyone has the correct number of cubes.

    I worked with my small groups for 1/2 hour everyday for a week. Each day, we repeated these "decompositions." Observe your students, and make judgement of what they need more of.

    I also do a lot of estimating with tens. We estimate how many towers of ten will fit across the table, across the room...It is important to record their predictions-you will be able to see who can manipulate the thought of "one ten" because some students will say "7 tens will go across the table," and some will say "123 tens will go across the table." By recording the predictions and then returning to them at the end, students have the opportunity to learn about "tens" in a different context. Students really get into this activity.

    When students are VERY comfortable with breaking two-digit numbers into tens and ones, I do a kind of enrichment activity that relates to multiplication. Our place value mats are no longer dedicated to tens and ones, but to whatever values the students desire.
    Ex: I write the number 23. I ask the students, "How many tens, how many ones?" I then ask, "What is another way you can see this? (Students answer that they can look at the number in the tens place and ones place."

    After this, I ask them to build a tower of 23, and break it down as they wish. Sometimes students break down the number into five sets of 4 and 3 ones. The best part is that everyone comes up with something different, and they love to share! As the students share, I record their set. Sometimes I have to write, for 23,
    2+2+2+2+2+4+4+1+1+1+1+1 = 23

    After writing this out, I say "Whew! My hand is so tired-is there an easier way I can write this?" I let the students think and invent their own ways--but I have had students convert this into multiplication format, ie:
    (2 x 5) + (4 x 2) + (1 x 5) =23.

    At first, I give a lot of guidance, then I let the students do this on the board. It's really fun to see what they come up with, and everyone is thinking about different combinations of numbers. It reinforces the idea that there can be sets of numbers, even sets like tens and ones.

    Good luck! It is so fun to see place value click.
    The key is using tens and ones in different contexts-working with it on paper and with manipulatives.


    PS-I have my students sit at long tables across from eachother with tubs of cubes in between. We talk EVERYDAY about using the cubes as math tools and not toys. I reinforce that if a students plays with the cubes, they cannot participate in the group. This works, but just make sure that your students have had time to play with and manipulate the cubes before you come to the small groups. Students always need to have free experiences with manipulatives before you can effectively incorporate them into instruction.

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