Learning Mental Adding and Subracting

One way to help students practice the skill of mentally adding and subtracting is to become more familar with the 100's chart.

1.       The 100’s chart is a difficult chart to navigate. Your eyes must go down to the end from left to right, and then skip all the way back to the next row on the far left again.  This action is similar to reading, but that needs to be pointed out to the children.  They want to continue back from the right to the left (back and forth).  Many times I will color code the number 20 and 21 the same color to make the connection. See the chart below:

   On the large grid, the children walk on the chart to simulate where their eyes must travel. This kinesthetic learning style is very effective with young children. 

2.        We discuss in a whole group class what the children notice as far as patterns on the chart. For example:

a)      What happens when I start on the number 5 and walk down the column one step…more steps?  What if I walk down the 6 column?  Does this pattern happen on every column?  How many squares will I travel from 46 to 56…let’’s count it as S___ walks on the mat.  Let’s try it again…M__ walk from 53 to 63.  Oh, so what can I expect when I walk down one row on each column? +10

b)      What can I expect to happen went I walk up one step?  Let’s check  to see if you are correct in your prediction. 

c)       Proceed with a step to the right and one step to the left.

d)      Let’s try it together. J--- start on the number  26. Everyone else in the class, put your finger on your laminated 100”s chart and “walk with us.”  26…one step to the right… what happened?  Yes, it did increase by 1.  Go back to 26… one step to the left… what happened?

Yes, it decreased by 1. Who can predict what will happen when we walk one step below our number in the same column?   Yes, I agree. Let’s try it to make sure.

Hopefully you can see how this kinesthetic activity really helps students understand how to navigate the 100’s chart.  When student become this familiar with the chart, I believe that the image of the chart becomes part of their “Brain files.”  Why do I think that?  If you have ever seen a child mentally adding and subtracting that is using their brain file 100’s chart you will notice their head bobbing like they are taking steps on the chart.  54 + 13 =

54…down one row to 64.. and then 3 more steps…65,66,67.  The answer is 67.  Of course the head bobbing goes away as they become more and more familiar with adding mentally in this way.  I find that I personally add number s this way in my head since I taught it with Everyday Math. I add the tens first and then the ones. 

3.        The chart can be used by students in a center to practice mentally adding and subtracting as a manipulative after you have used it several times with the class.  Have them complete a 2 digit plus two digit problem worksheet, actually walking on the chart to find their answers (with a partner so they can discuss their learning together.) 

4.       An assignment in Everyday Math, utilizes a small 3 to 5 segment grid and asks the students to “fill in the missing number.”  I have also cut out small parts of the grid with blank boxes. They place the small grid over the large chart.  Then they self-check their answers.  (I originally made these small missing piece grids when I made a mistake in one of the charts I was making, and recovered from my error by using cut up pieces of the chart in this way.) You can even create incorrect grid sections that they must correct using a Vis-à-vis water based marker. After you check their work, the students use a damp cloth to wipe off the marker from the vinyl surface.

Children's Writer's Word Book

I just wanted to tell you about a resource that we used while writing standardized test questions for our state test, the ISAT. It is a book titled, "Children's Writer's Word Book." 

This book helps you immediately determine if you are using the right vocabulary and language for the audience that you are writing the test questions. The part that I liked the best was that you can find appropriate words for children of various ages, and discover substitute words that might work even better in the thesaurus section.


 

The book cover  states that the price is $16.99, so it is a reasonable cost to make sure you are creating documents that differentiated for your students.

Deborah

Everyday Math Kindergarten Activity Cards

Here is a chart that I made to help you find the exact description of the corresponding activity  in your teacher manual.about each "Kindergarten Center Activity Card."  My suggestion is to highlight the paragraph since they are located at various pages throughout the book. I've listed the heading of the correct paragraph to highlight to help you.  Look in Part B of the lesson. (Common Core State Standards Edition of Everyday Math)

Click here to print a copy of the chart.

Deborah

Dual Language Resource for Kindergarten

Here's a great resource for Dual Language Class parents to help their children at home. My friend, Luz, who is a dual language teacher shared it with me... and now I want to share it with you.

The website is www.literacycenter.net

All these activities are available in English, Spanish, and German

 

When I was in Luz's class, I sat down at the computer next to one child. He had on his earphones and was working on his colors. He was merrily clicking on one color after another. I asked him, "Are you just learning your color names or are you practicing?"

"Practicing," he replied.



"Then try it this way. First, before you click on the color try to say the name of the color. Then click on the color and see if you are right. When you predict the color first, you find out how much you already know and if you need to practice that color anymore or not."

 

And then he tried it that way and rewarded me with a big smile.

 

It just reminded me that sometimes we need to teach children how to help themselves learn.

 

Deborah

 

 

 

 

Learning Teen Numbers with Ten Frame Cards

It is very common for students to have difficulty with the numbers 11- 19. Their names do not follow a pattern and must be considered sight words/ numbers of mathematics. Teachers must ACTIVELY help students develop meaning for both the words and the corresponding numerals.

There are many intervention strategies to help students make sense of the "teen numbers from 11-19."

www.mathwire.com has the following suggestions:
1. First, work on rote counting from 10-20.

• Identify the student's comfort zone: add 1-2 numbers at a time to the 1-10 sequence until the student can reliably count on using the correct names.
• Sing songs and extend counting songs: for example, Ten Little Indians can be modified and extended to be 11 little, 12 little, 13 little teddy bears (or dinosaurs or valentines, etc.). Singing is great reinforcement for many students and helps them acquire fluency with these extended numbers more easily than simply counting aloud.
• Who Has The Number?: Give students the large demo-size cards (#10-20) and have them hold up the cards as you sing the song so that students hear and see the numbers.
• Teen Line-up: distribute the large demo-size cards (#10-20) and ask students to line up in the correct order. NOTE: numbers 10 and 20 of the teen demo cards are boxed in bright orange [see picture at left] to visually reinforce the notion that the teen numbers are between 10 and 20. Reinforce this notion often when working with the teen demo cards.

2. Learn to recognize the teen numbers.

• Matching Station: Provide many copies of the teen number cards for students to match to teen numbers in sequential order.
• Matching Sing-along: As students sing extended teen number songs, have students point to teen number cards to imprint written number with the oral name.
• Teen Line-Up: students shuffle number cards, then place them in sequential order. After this, students point to each number and name it.
• Teen Swiper: One student places the teen numbers in sequential order on the floor then removes a card while the other student has eyes closed. This student opens eyes and names the missing number. He/she must then locate that number in a second pile of all teen numbers and place it in the correct place. For this game, it is helpful to have two decks printed on different color paper, or in different color fonts for easy separation into two complete decks.

3.  Next, attach meaning to the number.

• Four-handed Teens: Have student pairs represent teen numbers. One student holds up both hands to represent 10 fingers. The other student shows additional fingers to represent the teen number.
• Stamping sets: Give student number cards and have student stamp that many objects on the card.
• Teen Number Posters: Hang number posters for numbers 11-20 on classroom walls. These posters include the base-ten representation of each number. Regularly include these in rote counting activities, counting 1-20 while pointing to the posters. Introduce the teen numbers as between 10 and 20.
• Teen Number Mats: Provide number card mats for each number 11-19 and have students count aloud as they place counters on the mat. (Modification would be providing dots on which students place the counters as they count aloud.) NOTE: There is no effort to group materials or make tens at this stage. Students are simply attaching rote counting to one-to-one correspondence and the beginning of number recognition.

4.  Learn to model numbers to make sense of the number value and number sequence.

• Use of Base-Ten Blocks: This should follow lots of practice with non-grouped materials and students should use base-ten blocks and a place-value mat concretely, writing only the answer to modeling the numbers to attach meaning to how many ones and how many tens they have.
• Pictorial Representation: Be sure to model for students how they can use simple lines and dots to represent the base-ten blocks to record their thinking. This semi-concrete step is often skipped when teachers go from concrete (base-ten blocks) to abstract (numbers on a page). Students who use this pictorial step have access to more powerful mathematical reasoning by using this intermediate step to think through problems beyond what they have learned.
• Overhead practice: after students have had lots of hands-on experience, use an overhead to present either the blocks alone or the number alone and ask students to quickly model the number on their place-value mats, filling in the missing information.

 

 

I'm going to add my own activity at this point... learning to recognize that teen numbers are composed of "ten and a specific number of "more"... which helps to attach meaning to the number.  In addition,  the teen 10 frames cards also help students to see and interact with the model to make sense of the number value.

 

    Ten frames are an invaluable resources to visualize this concept of ten plus a specific number of more.

So I created a set of eye-catching snowmen demonstration ten + frame cards from 10-20 in both demonstration size and 4 on a page size , a set of expressions strips from 10 + 0 = through 10 + 10 =, and a set of equation cards in which the word for the teen is featured in both English and Spanish, i.e. 10 + 4 = fourteen,  10 + 4 = catorce.

 

4 of the suggestion cards based on Debbie Diller's "I Can" cards



10 frame card set with 8 suggested games

Deborah

 This ten frame set  can be purchased at either my Teachers Pay Teachers store , or you can make your own cards using my pictured examples to help you.

Everyday Math Games Online Organizational Tip

This is a great organizational tip from Teresa Andrade, a teacher in our district. She prints out an additional set of Everyday Math online game cards for her use only. She glues them individually to an index card, then places the cards in alphabetical order, and puts them on a metal ring. 

 

When her class is in the computer lab, she brings the ringed card set with her, so if a student has forgotten their password she can retrieve it quickly. 

 

Thanks Teresa!

 

Deborah Devine

Great Resource for Teachers Using Everyday Math

The Everyday Mathematics Virtual  Learning  Community (VLC) is a website for elementary teachers.  The site was established to provide resources to support mathematics teaching, including a means of communicating with other teachers interested in teaching mathematics; and to encourage teachers to reflect on their practice. It is open to any practicing EM educator free of charge.

 

The address is http://vlc.cemseprojects.org

 

The VLC is maintained by staff at the Center for Elementary Mathematics and Science Education (CEMSE) at the University of Chicago. The VLC's development is supported by generous funding from the National Science Foundation and the Illinois Board of Higher Education.

 

What kind of resources do they have?

Lesson Video

Student Work Examples

Instructional Tools

Professional Development Tools

Photographs and Audio

Sticker Templates to place in your Teacher Activity Manual that feature questions to ask your students with the Common Core Mathematical Practices in mind 

Ongoing Assessment Questions retyped by teachers into a packet format, so they are all together for each unit.

 

Check it out!

Deborah