Our Audience

Over the past several months I have come to see that my comments on my blog have dropped to a minimum. That is OK as there are many times that I just don’t have time to comment on ever blog I read. There have been times I wondered why I even keep my blog going, but when I receive an Email like this out of the clear blue, I realize my audience is larger and reaching those who truly are getting something from my blog. It really encourages me to keep going.

“Hi,

My name is (leaving name out due to permission rights), and I am a math tutor in the San Jose area. I hope it's okay that I'm e-mailing you like this. I just wanted to say thank you for creating your page http://whisperswhispering.blogspot.com/2011/01/math-links-fractions.html because I have been using it a lot to help provide additional resources for my students. :)

While researching, I found these other resources that might be of interest to you:

“Fraction Resources and Games for Kids” – http://www.alwaysmath.com/fraction-resources-and-games-for-kids.php

“The Young Child and Mathematics” – http://www.naeyc.org/store/files/store/TOC/167.pdf

I’m sure they will be of great interest to your readership since I’ve found them helpful in keeping my students engaged and interested in learning math.

If you decide to link them, let me know! Hope you find them to be useful. :)

Best wishes,”

As you can see by clicking on the link that she was referring to a post that I wrote a year ago. To be honest I forgot about the post and even forgot we did this lesson. We still do a lot of work with fractions, since it is an area of math that just seems to come so natural to Selena. I need to share more of these off the cuff lessons we do. This reader really made me stop to think about the reach my blog has, the unknown audience out there that is reading my blog and walking away with information that I have shared. She put the joy back into my blogging. Remember maybe your comments are dropping off, but there are always these hidden readers, who might just be your best followers.

I encourage you to take a peak at the resources she has recommended. The first one at Always Math has some wonderful resources for fractions, some that we may just have to play with and explore.

The second one is a pdf file of a book, which is a must read. I bet there isn’t a one of us who can’t read the examples of the different students and not find our own child in there.

I give a huge Thank you to this reader for taking the time to remind me the impact my blog really does have on an audience I don’t even know is out there.

Learning At It’s Best

Selena was up yesterday morning quite early. She was being quiet so I lingered on the couch half awake and half asleep. Finally I made my way off the couch to find Selena sitting at the table practicing her numbers. We haven’t worked much on writing numbers, since Selena just didn’t seem that interested. Here she sat not being prompted, not being asked, with no assistance from me, writing her numbers.

One of the questions I read over and over again has to do with why isn’t my child writing, why isn’t my child reading? I have commented many times that I feel a child will only do what he/she is ready to do. I have known for some time that Selena was getting ready to break into the writing and learning to write her numbers, while we played around a bit with them, I never pushed the issue. She has always had the tools she has needed from paper, pencils, dry erase, and pens just readily available when ever she wants to use them. The fact that she has sat down and done this on her own, will only boost her self confidence in herself. I can now see real math in our near future.

I love discovering self directed learning in our home. While I love to teach Selena and work with her, nothing seems to make me more proud then when she discovers her own talents and abilities on her own. It is these moments when I know the material will stick a life time.

Math

Selena has been working very hard in her math. She has been making some huge leaps in her abilities. Remember we started this year using her math buddies and story problems for her to begin to learn the simple math. She has now moved beyond her math buddies to doing a little more formal math.

Yesterday, while Selena was taking her bath I set up our math for some review.

She was thrilled when she got out of the tub to discover this set up and could hardly wait to go right to work. I didn’t have to explain very much to her of how it works and she was able to work totally independently.

She would first find the rod that corresponded to the top number in the problem, then locate the one that corresponded to the second number. After she clicked them together then she was able to solve the problem.

Selena wanted to take the last picture of her work. You can get the idea how she was able to solve all her math equations all by herself.

With her writing coming along, who knows she could start writing her numbers as well, then she can log all her answers on paper.

Math Fun and Problem Solving

Selena and I decided to play a game yesterday. We started out with just the two of us and some buttons. I gave her an even number of buttons and she divided them up between the two of us. I then gave her an odd number of buttons and then when we had one button left she had to figure out how we could solve this problem. Her idea was to add another person. She grabbed a little doll to represent Papa.

It wasn’t very long before she realized that this wasn’t working out very well either. I again asked her how we might solve this problem. Her idea was to add another person. She ran off to her bedroom and came out with yet another little person to add to our game.

Let’s just say she was a wee bit surprised when this happened.

She suddenly realized if she added one more person everyone would have the same number of buttons.

I had so much fun just watching her experiment, and try new ideas to make this work out. The only rule I had was she could not add more buttons or take any away from her pile. She had to figure out how she could divide them evenly among the people.

Ready, Set, Go

It looks like Selena is ready to get back to her studies. It was nice to take a break from having to plan activities, but it is even nice to have her asking for school work to do. This morning she suddenly wanted to do her math. For some odd reason we couldn’t find our normal Sam and Jan, which is strange as they were sitting on the same counter this entire time and I remember them there when we started decorating for Christmas. Now they are gone. That didn’t stop us though we just found new ones to take their place. Selena went right to work reviewing the math facts that we had worked on before she suddenly decided she wanted to take a break form school.

I think it is a little ironic that she has such a desire to get back to school, when most will be taking time off for Christmas. Oh well, who am I to deny her educational wants.

New Beginnings

Tuesday was Selena’s first day in AWANA for this year. She was so thrilled to go, and looked so cute in her uniform. Though I must admit her uniform is looking a lot smaller on her this year.

I could go on ahead and buy her a new uniform, but this will be her last year wearing this one, so I think we will just make do. I was hesitant over taking her and just dropping her off, even though we are not from the church, but Selena insisted I not stay. An hour into AWANA my phone rang and I had to jump in the car and head off to the church to calm a nervous little girl down, who had been found to be roaming the church in search of me. My little brave girl who asked me NOT to stay decided she truly was not ready for this step in her life. When I got there she was back in the classroom, happily playing, but truly gave me a huge hug and a kiss before returning back to play. This is making me look at our schedule now and looking as to how we can change some things to make it work better. I know I will be spending 2 hours on Tuesday evenings sitting at church (choke, choke) praying I can sacrifice just a little money to get some needle point or cross stitching to occupy my time there. I can see now where Wednesdays are not going to be a very productive day for neither Selena or myself. This almost makes me wonder are evening or extra activities really worth it?

Yesterday, was a day with a tired crabby Selena, and to be honest I was feeling very tired myself. There was quite a bit I would have loved to have done with Selena but with the way we were both feeling we didn’t even bother trying. We did however have fun with our new stash of buttons.

Selena had made this lovely pile of buttons, and instead of just letting her pick through them, I asked her to put them into piles from large, medium to small. She gladly went through and did just that.

We then took the buttons she put in the large pile and sorted through them again arranging them from largest to smallest.

She did the same thing with the medium sized buttons. At this point though she decided enough was enough and announced she was done playing with buttons. I felt it was an over all good lesson in that while we see things in a general way of large, medium and small, if we look closer we can see that sometimes even these groupings can be broken down even further. Can you see the math skills?

Math/Science

Yesterday was a good day, but because we had to take Pal to the groomers, and I had meetings that evening we did not do math with our math buddies. Instead I pulled out our flash cards. We stayed with the 0 addition facts. Selena impressed herself by figuring out one hand could represent 0 by making a fist, and the other hand could represent the number being added to that 0 in order to get the answer. We made it up to 0+5=5 before Selena announced she was bored. We will do this exercise periodically to reinforce the skills she is learning with her math buddies and story problems.

It was a very nice sunny warm day, so we ventured outside for some fun. I initiated a walk around the yard to investigate what all our plants looked like. It wasn’t long before Selena found this piece of coral sitting in our front flower bed.

She wasn’t happy with just the little piece we found that had broke off to investigate she had to bring in the entire piece. While we were heading in I picked up a couple different rocks, to compare this piece with. Selena’s observations were that it had little holes. We then came and looked coral up on the computer and she learned that this came from the ocean and that indeed little sea creatures once made this their home.

The other rock I picked up came from our red rock, it as well had holes in it. Then the third one was just an ordinary rock.

After she had investigated all three of these, and lost the little piece of coral, we pulled out a dish of water. I asked Selena what she thought would happen when we put the rocks in the water. She looked at me rather puzzled, so I rephrased my question and asked her if she thought the ones with the holes might float. She thought about that and decided possibly because the holes would have air in them. We then began to drop them in.

She dropped the regular rock in first and as she predicted it sank. The red rock she predicted would float, indeed did float.

She got a big surprise when she put the piece of coral in as she predicted it would float as well. She quickly discovered it did not float, but as it sank air bubbles came out of the rock. I truly wanted to explain why this had happened which will wait for another time, but she was too interested in playing with the rocks at this point.

I think by her face you can see she was pretty thrilled with her little science experiment.

Just because I love this picture!

Combining Reading with Math

This year Selena has decided that she loves Math more then Reading. I love the way their interests change from one year to the next. In order to keep her Reading practice going while building on her Math skills, I stayed up Monday night and wrote out several story problems.

On Tuesday morning I explained to Selena what she was suppose to do. At first she looked a little uncertain as I told her she had to read the story problems on her own, set up the math problem using the cheerios, and her math buddies, then solve the problem for me.

Since it was math, Selena jumped right in and read the story problem. After she finished reading it through once, I had her go back and read it a second time, this time she had to set up her math problem.

Then she had to solve the problem and correctly mark the answer at the bottom of the page. She also had to help me write out the problem on the chalk board.

My plan is to continue to work math this way, building more difficult story problems, as well as throwing in challenge problems. I do have to add that I was very proud with Selena’s ability to read and set her math problems up all by herself with no prompts from me. Now to reinforce her skills with a math workbook page this afternoon.

Math Introduction to Simple Subtraction

We returned to school today, and pulled out our math buddies Sam and Jan. After some review of simple addition, this time having Selena read my story problems, then setting them up all by herself, I decided to try some simple subtraction. Selena caught on very quickly.

My story problems were very easy: Sam has five cheerios. He gives Jan three Cheerios. How many Cheerios does Sam have left?

After reading the story problem all by herself, she quickly went to work to solve the problem. She first gave Sam five cheerios.

Referring back to the story problem, she then had Sam give three cheerios to Jan. From there she quickly answered the story problem correctly. She even was able to tell me which symbol to use as we wrote the problem out on paper. I guess all my work last year in which I felt that Selena just was bored or not ready for math truly was not all in vain. She has truly proven that she did retain much of the material. Her maturity this year though is now working in her favor to actually practice what we did last year.

After our math lesson we went out and Selena rode her bike all the way up to our Pastor’s house since we were still letting their dog out. She rode very well and with a lot of confidence up the sidewalk. In fact there were many times the training wheels never even touched the road. Since she doesn’t mind having the training wheels on we decided to not even attempt in taking them off yet. She is going to need a larger bike next year, we wonder if moving to a larger bike will require the use of training wheels for a little bit, but I just know that next summer will be the summer they finally come off.

Selena is playing with Ollie or trying too. Ollie was trying his best to hide from us as he knew that we would put him back in the garage. Which in fact turned into a job itself. He literally refused to go back in. We did get him in after I went and found his ball to coax him in.

Meet Sam and Jan/Math Buddies

What do these two little ginger men have to do with math? Well, let me have the chance to tell you. (I want to say thank you to Ticia at Adventures in Mommydum  for her helpful advice and the inspiration I have received from Phyllis at All Things Beautiful because with them I don’t know if I would have come up with this activity on my own.)

Meet Sam and Jan. Sam is the one wearing green and Jan is wearing blue. I asked Selena to find these little characters before she went to bed Monday night. I told her we were going to use them for math. Come Tuesday morning she was more then excited to start her math lessons, especially when math included not only her two toys, but her breakfast.

With a bowl of Cheerios, chalkboard, chalk, and paper we set out to write our own simple word problems to help Selena understand the concept of simple addition.

We first started with 0 + 0 = ? and worked our way up to the variations of 1 + 1 = ?

For each problem Selena helped me tell the story of her two little people. I wrote it out on the chalk board. Then using paper we wrote the problems out together. Then Selena had to solve the problem.

The best part was Selena’s reward for doing such a great job! Before you get to see that picture, we will be using these two little fellows more often in our math.

I still for the life of me can’t figure out why Selena thinks it is necessary to slowly push all our work back allowing more and more room for her to just climb up on my table and sit. I think it is time I get this area organized and we start doing school here.

I have truly been waiting to share this wonderful feature with you since I still have so much more work to do in this area of the  house, but look below our bookcase, Selena has her own pull out desk. There is more.

Underneath the pull out desk is a drawer just perfect to keep all her school supplies in. This is not only my favorite areas but Selena thinks it is pretty cool too. Now you can all help me by reminding me weekly or daily to get in and get this area organized. It sort of ended up being the place where all the little odd and end stuff ended up getting placed, so now it is where to put it, or find another bin and pack it up.

For those of you looking for my Geography/History Meme, after much consideration, and in order to just keep the flow going in our homeschool, I am going to be discontinuing this Meme. If someone wants to take it over feel free to move forward with the idea.

Patterns

Selena has been so independent on many of the activities she does in the mornings while I am going about cleaning and getting ready to start the day. I never really know what I will find her doing. I asked her one morning, “Selena, what are you doing?” She informed me, “Making patterns, Grandma.”

I went in to see what type of patterns she was making and discovered this:

I am so glad that I made the active choice to keep most of her schooling supplies down within reach for her. Certain items like paint and the messy things are up out of reach, but things like this Selena can grab and work on at her leisure. Have I mentioned how much we are enjoying this new more mature Selena? I am sure I have, but I can’t say it enough, the changes that have taken place here of late are so special. I think Selena is enjoying the changes in herself as well. I know she is enjoying all the new found freedoms.

Understanding The Number Line

A while back I tried to introduce the number line to Selena, but she would have nothing to do with it. She did however love to graph. I just felt that the number line would take her further in her math so on Friday I reintroduced it to her. We first started with the 1 addition facts, from 1=0 through 1+9. I could see the light bulb go on so I moved on to the 2 addition facts.

This time I gave Selena the pen and she had to work through all the problems on her number line by herself. At first it was a little confusing, so I showed her another way of counting her way up the number line by numbering the spaces on top. Again the light bulb went on, and she was able to do all the problems I had on the board.

She took it one more step though and showed me at the end of this exercise the pattern in her answers. I thought that was pretty bright when she caught that.

Just to make sure she was indeed understanding what she was doing and not just finding the pattern in the answers, I mixed up the equations. She worked through each of them on her own.

No longer being confused or scared of the number line, I feel that Selena’s math skills can do nothing more then improve now. Subtraction will be our next hurdle using the number line, after a bit more practice with addition.

Place Value and Counting Beyond 100

Earlier we worked on counting by twos using our bottle caps. Selena surprised me when she counted beyond 100 by twos, so I decided to introduce her to place value and see how far she could count. She loves playing with our bottle caps and it makes her counting so much fun for her. I used our white ones for the ones, blue for the tens, and red for the hundreds. I wrote hundreds, tens, and ones on pieces of papers, explaining to Selena what they stood for.

Selena started out counting from 0 and easily counted clear up to 109. She was a little tired at this point and wanted to stop. I think next time we do this we will start at 100 and see how high we can count from there. That was a lot of counting for Selena, so I was very proud of her. What did she think of this fun activity, well I will let the following picture say it all.

Selena never ceases to surprise me with the drive she has to push on especially into the new territories of her learning. She shows no frustration, but just smoothly moves forward to the next concept, so long as we don’t push, and just let it flow from her. I love it when she takes a lesson I have planned and makes so much more out of it.

Counting by Twos

We went back to our bottle caps for a fun game of counting by twos. I took all the odd numbers and Selena had all the even numbers, we scrambled them up. I would put the first number in place and she would have to find the number that came next to build her number line.

Yes, we went clear up to ten, but at that point I had her place the 0 before the two and using a blue bottle cap for the tens spot she began to count again, 10, 12, 14, 16, 18, then moved on to 20 and so forth. She moved the tens spot or the blue bottle cap down her number line as she counted.

She absolutely surprised me, as she caught on so quickly and actually began to count over 100 with this method, counting 102, 104, 106 and so on. Since we haven’t worked much on counting over 100 I am going to make some more numbered caps so we can have more fun with this and count over 100 using all the numbers, as well as having the hundred spot represented by a red cap. Look for more on this activity to come.