Monday, December 15, 2014

Early Place Value Experiences

I've been working with my firsties on understanding numbers to 50. We've practiced counting forwards and backwards, writing and reading the numbers, as well as comparing numbers.  By far our biggest challenge, however, has been understanding the meaning of the digits in a 2-digit number.  Children can count out 26 counters and relate the counters to the number 26 long before they understand that the digits represent 2 tens and 6 ones.  We have been using linking cubes and ten-frames to try to make meaning of these early place value understandings.

Here's what we were up to today.  I gave each pair of students four empty ten-frames and a pile of counters.  I asked them to talk to their partner and decide what the biggest number would be that they could show with their ten-frames.  This turned out to be a great question!  It was an awesome formative assessment.  As I listened to the conversations, I heard that some students immediately said 40, while other responses were all over the board (20, 100, 50, etc.).  I reminded students that they needed to explain their answers, even when talking with a partner ("I think it's 40 because...").  My Tier III kiddos were not even in the ballpark, so I scaffolded...
[Putting out one ten-frame] If I have one ten-frame, what's the biggest number I could show? (10)
[Adding a second ten-frame] Okay, if I have two ten-frames, what's the biggest number I could show? (20)
At this point, I thought they would make the connection, so I asked them to look at their ten-frames, talk with their partner, and decide the biggest number they could show with four ten-frames.  They still did not come up with 40.  This was fascinating to me!  Once again I repeated my questions about one and two ten-frames.  I added a third empty ten-frame and asked what the largest number I could show would be (30).  I then asked them the original question again ("What is the largest number you could show with your four ten-frames?").  They finally decided 40, but this just shows how much support our Tier III kiddos need!
Back to the planned lesson...I wrote the number 26 on my whiteboard and chose a student to read the number.  I have learned not to assume students can read 2-digit numbers when they see them in isolation.  Then I asked the students to work with their partner to build the number.  While all the students successfully built the number, it was fascinating to see that most students were counting by ones as they put their counters on the ten-frames. After they had built the number, I asked them if they had to count by ones and reminded them that if the ten-frame was full, it was ten.  We continued practicing this throughout the lesson ("If it's 26, how many filled ten-frames will you have?  Which digit shows you how many filled ten-frames you will have?").

On my whiteboard, where I had written 26, I wrote the equation 26 = 20 + 6.  I asked the students to talk to their partners about what this equation meant.  They were able to tell me that the 20 was the two filled ten-frames and the 6 was the counters on the ten-frame that wasn't full.  It is not obvious to children that a filled ten-frame can be called a ten, and that when we have two filled ten-frames it is two tens but represents 20 counters.  HUGE concept and hurdle in understanding.
Next, I wrote 32 on the whiteboard and asked them to build the number.  It was interesting to see that some students knew to fill another ten-frame automatically, while others were counting by ones.  After building the number, I again asked how many filled ten-frames they had (3) and asked a student to help me finish the equation.

Finally, I thought I'd throw a little problem solving into the mix, so I wrote 45 on the board and asked them to build it (remember they only had four ten-frames).  My Tier II kids just added 5 counters below the fourth filled ten-frame, but my Tier III students were lost without another ten-frame to hold the five counters.  So interesting. I gently led them through questioning and they figured it out.

As a final activity with my Tier II students, I wrote 20 + 4 on the board and asked them to build it.  I just wanted to see if they could look at it from the other perspective, and I thought it would help them better understand that the 20 is represented by 2 tens in the number.

We will practice this a LOT more!  It is so important that they really understand these early place value concepts. 

Monday, December 8, 2014

iHeart Math Holiday Hop

Image Map
I am so excited to be linking up with a group of wonderful math bloggers to bring you nearly a month of holiday surprises!  Each day, a different blogger's post will go live.  Be sure to check out each and every one.  You can click on the images in the picture above to go directly to each blogger's post.

Stocking Stuffer #1--Giving Back Idea

Who are the hardest working people in a school building?  If you said the custodians and cafeteria workers, I'd probably agree!  Last year, we started a wonderful tradition at our school.  Each staff member picked up a few extra holiday groceries during our weekly shopping trip, and we assembled baskets of food for our custodians and cafeteria staff.  The administration chipped in a ham for each basket, and we presented the baskets at our holiday luncheon.  They were overwhelmed!  Try this on a small scale.  I work breakfast duty in the cafeteria, and every year I like to bake the ladies in the cafeteria a treat!

Stocking Stuffer #2--Holiday Math Tip

Face it, there is almost no way to keep a normal schedule during the last couple of weeks before the Christmas break.  Be prepared for those crazy schedules with a few easy go-to math games that you can pull out in a moment's notice.  I like these games for practicing addition and multiplication facts. Laminate them, and all you need is a wipe off marker for 10 minutes of engaging math fun!  Click here to grab yours. 

My special gift to you this holiday season is a special version of my themed number cards.  This set ranges from 1-20 and includes cards showing numerals, number words, and a ten-frame representation. Here are some idea for using them:

  • Have students choose a number word or ten-frame card and write the corresponding numeral
  • Students can play War with the cards
  • Students play a Memory game either matching different representations or matching cards that make a 10
  • Have students randomly choose 4 numeral cards and put them in order
  • Students choose a numeral card and use counters to show the number
  • Students draw two numeral cards and write an addition or subtraction story using the numbers

I'm sure you can think of lots more uses for these cards!  Click here to grab your set.

The next stop on this festive hop is over at Lessons With Coffee. You can check out her post by clicking on the image below!

Lessons With Coffee

Friday, December 5, 2014

Winter Freebie Ebooks...A Holiday Gift!

Again this year, Teachers Pay Teachers has sponsored their Winter Holidays Tips & Freebies ebooks!  This annual Christmas present has grown from one book with 50 pages (and freebies!) to FIVE books for separate grade bands containing over 200 pages.

For those of you not familiar with the format of the ebooks, each page contains a holiday tip and a link to a freebie.  The books include pages from some of your favorite sellers as well as some talented new sellers.   I am honored to have been included in this year's Grades 1-2 book.  You will find the links to the other ebooks (PreK-K, 3-5, 6-12 ELA/SS, and 6-12 Science/Math) from the Grades 1-2 book page.

My freebie is a winter-themed Capture 4 game for the meaning of the equal sign.  Such a hard concept for kiddos to grasp, so lots of practice is important.  The strategy component of Capture 4 games adds a problem solving element to the activity.  Consider putting ten-frames and counters in the workstation with the game for students who need concrete support.
Click here to go directly to the freebie or here for the link to the Grades 1-2 ebook.   Happy holidays!!

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