Function Machines and Arithmetic Racks

Using the arithmetic racks 3 times in a week?  *gasp*  I was so excited, so you know the kids were amped!  Today we used the racks as function machines.  You put one number in the machine, the machine changes it by adding or subtracting, and a new number comes out.  This is always one of the most difficult (and frustrating) concepts of the year!  I have to admit, using the rack was a last minute brainstorm on my part, but I think it may have worked.  I'll have to see tomorrow when we revisit the concept!

Personally, I think the written function machine is very overwhelming to students the first time they see it, so I just got out our enormous arithmetic rack and starting posing situations to them:

I put 1 bead in the function machine.  2 beads came out.
I put 2 beads in the function machine.  3 beads came out.
I put 3 beads in the function machine.  4 beads came out.

By now, the students are starting to notice that I'm ending with 2, 3, 4, and can predict that next 5 will come out, then 6, then 7... so we back up. I went over each situation again and asked how the machine changed the number.  They discovered that the machine added 1.

We did this with a few other rules before moving on to the written version:

 

I apologize for part of the chart being covered up... I found the hooks for the rack after we'd already started charting and was excited not to have to hold it up any more!  This picture is showing 18 beads coming out of the machine.

By writing the in and out numbers down, it also allowed me to extend the activity and connect it to missing addends.  When doing function machines, the first several pairs of in and out numbers are given.  The students have to find the rule, which in this case is a missing addend.  We see that the out numbers are bigger than the in numbers, so the machine is adding beads.  Each time I wrote the in and out numbers in blue and once we discovered how the machine altered the in number, we filled in the missing addend into the number sentence (in green).  Missing addends are really tough, too, so maybe using the rack as a visual aid will help!

Next, we did some more problems at the rug, but the students had their own racks as well.  After this, students went to their seats to try to work more independently.  Instead of doing problems as a class, I let them try with partners.  Then we went over them together.  Here is an example from the document camera:

We are working on #1 "Your turn."

First, we got 10 beads ready to go into the machine.

 Next, we slid the 10 beads into the machine (sliding them to the right- acting it out helped some).

 The machine takes 3 beads away and the rest come out.  We can see that 7 beads come out.

Note: There are stars next to 9 and 11 because I asked the students if there was any way to predict what the answer would be before we started using those two numbers. 


Onto #2.

To find the rule, I presented the problem as a missing addend.  We had 5 beads and when we put them in the machine, 10 beads came out.  How many beads did the machine add?  We started with 5 beads and started adding beads until we had 10 total.  The color of the beads was helpful on this one!  Students could easily see that 5 beads had been added.

We then double-checked the rule with the other two pairs of numbers before finding the out number for 16 and then coming up with our own.

This is the 4th year that I have taught function machines, and I have to say that it was not at all frustrating.  Now, that is not to say that every students "got it," but every student participated and came away with some new level of understanding.  I love when I can file something away that has been successful!

Some high points of the lesson:
One student asked to make arithmetic racks again like we did earlier in the year (see my very first post)- I was so happy that it stuck out in their minds!

Another student was disappointed that there were only 2 rows on the arithmetic racks.  Never fear!  Soon we will be able to project our iPads and I have an arithmetic rack app that has more than 2 rows.  Score!

 

Ta-da!  It's the Number Rack app and it's FREE!!!

Using Arithmetic Racks for Doubles and Near Doubles

Two summers ago I attended an Inquiry Math Workshop at Purdue University Calumet.  I learned SO much about how kids' mathematical concepts develop and how inquiry math can foster this growth.  Basically inquiry is all about discovering rules and concepts, rather than just having them be told.  Kids come up with their own strategies and definitions and they are so much more meaningful.

Last week I used arithmetic racks to help kids visually see doubles facts.  We talked about twins (we have 4 sets of twins in first grade and I have one sibling from each set), and that doubles are like identical twins.  The arithmetic rack lends itself to this with its two rows.  We used the arithmetic racks to help fill out our fact cards.

While doing mClass, I discovered that students were not using all the strategies we had learned to solve math facts.  Instead, students were relying on counting all and counting on, which isn't very efficient when you are trying to solve 8+7!  The students who were counting all didn't have enough fingers, and the students who were counting on were susceptible to mistakes with all that counting!  They'd count the seven fingers, then go back and have to remember that they started with 8 and count on.  Needless to say, my students didn't solve very many facts in 60 seconds!  I had to reteach the strategies and try to get them to stick.

We took an extra day on Monday to work on doubles +1 and doubles +2 facts.  In the past, I presented the strategies to the class.  I just simply told them that a fact like 6+7 was a doubles plus 1 fact and showed them how the doubles fact could help them.  I wanted to find a way to make it more meaningful to really help the students see the connection between the types of facts.

What I ended up doing was reviewing doubles facts and then studying the patterns.  We did the doubles facts in order and the students noticed that the sums went up by 2.  I asked students to talk about why this pattern occurred.  I love seeing how excited they get when they discover and understand patterns!  So now I had them right where I wanted them... I wrote 6+7 up on the chart paper and asked what they thought the sum would be and why.  Could they use the doubles facts to help them?   Lo and behold, I had volunteers for how to use 6+6 and how to use 7+7... AND how to use them both, which I didn't think they'd see!  Since they saw the pattern with the sums going up by 2s with the doubles, one pair of smarties realized the sum of 6+7 would be between 12 and 14, the sums of the 6 and 7 doubles facts!  YAY!

Now obviously not all students saw these patterns and relationships, so we busted out the arithmetic racks.  We made doubles plus one facts on the racks and looked to see which doubles facts they were close to.  We paid close attention to how we changed the near doubles to the doubles facts.  I realized that I needed to stop calling them doubles +1 facts when some students were using the larger number to double and then subtracting 1!

We did it! Yay Scholastic!!!

Woohoo!  I am on my way out the door for one of my bestie's birthdays, but I had to share this:

 

Wow, do I love Scholastic!  By combining my January and February book orders, I managed to spend just enough to earn what seems like a million bonus points! My class and I made a wish list of some books we wanted to add to our library for the kids to bookshop from.  I have the best problem this year- lots of high readers and a class full of kids who LOVE to read!  If you read my previous post from last week on the subject, I'm looking to expand my library so that there are more higher level nonfiction and picture books, not just chapter books.  We're working on writing about our reading and reading with our buddies, and chapter books make that a little difficult in first grade.

So between the amazing parents and a little shopping for my niece's birthday to push us over the edge, we did it... 5,030 bonus points earned on this order and 5,340 spent (had some in the bank amazingly)!  I'm excited to put some of the kids' favorite picture books in their personal shopping library.  They adore Piggie and Elephant books, but I didn't have many in the library- problem solved!  I also added a Pigeon pack, which I can already see kids fighting over!  It also excites me that I have kiddos ready to read Knuffle Bunny all on their own!  It will also be easier for me to read what they write about their reading when they are checking out books I am familiar with and love.

Some other titles my class picked:

Magic School Bus Readers

National Geographic Kids Readers

Daisy Dawson

Roscoe Riley

Black Lagoon

Miss Nelson Pack

LEGO Readers

Flat Stanley

Horrible Harry

Pink-, Purple-, Silver-, and Goldilicious

Froggy

Kevin Henkes Pack

Fly Guy

I have to share this... it's my favorite part of my order because it looks like I got more free than I bought.  Actually, that is probably true with Scholastic being as awesome as it is, but when you look at just this catalog, it really stands out because the purchases came on other catalogs, but I chose a lot of free books from this one:

I am home by myself and doing a happy dance and had to share!  Only teachers would understand how excited I am to be getting so many books for my favorite first grade readers to devour.  They are going to be so excited when I show them the order!!!!

Well, I'm off to shop for myself now.  I honestly don't know if I could possibly have more fun than I just did.  Ha!  Enjoy your weekend everyone!!!!

100th Day Aging Booth Adjectives

Back in the day, I used to have the kids draw pictures of what they think they will look like at 100 years old.  That was a really hard thing for kids to picture!  Today at our grade level meeting, Jill (from Cruz'n in First) told me about an aging app to put on my iPad.  Oh my goodness, was it fun! It gives the kids wrinkles and gray hair... and the boys can either be bald or have a mustache.  We were laughing SO hard!

After taking the pictures I printed them out so we could write about them.  We've been working on parts of speech and have already talked a lot about nouns.  Today we learned that adjectives are words that describe those nouns we've been finding.  Of course this ties into word choice in our writing- love when that happens!  We've already been talking about using interesting words in our writing- and we find them all the time in our reading, using context clues to define them!  This is the time of the year that everything really seems like it's coming together. It makes things so much easier to teach when you can integrate. :)

I will share my picture with you- please note that this is an estimate of what I will look like in 2044 or something like that- not what I look like today (though one of my kids said I already have the creases on my forehead).  We described parts of my face (nouns) using adjectives, then I verbally gave them an example of what I would've written (see below).  I really have been trying to keep my minilessons short to give them more independent work time, otherwise I would've finished writing it.  I will write it in before the 2nd part of the lesson on Monday.

Here's my lovely photo before:

And after:

The app not only adds wrinkles, but it makes your nose a little bigger (more noticeable on the kids, not really on me), and it gives you jowls, which makes your chin look pretty weird, too!

Here are some descriptions of the picture that we came up with:
old face
old-grandma face
nice old lady
wrinkly face
mad wrinkles (despite looking nice, some kids thought the forehead wrinkles made me look mad)
saggy skin (one kid said it looked like it was peeling off my skull)

Here is what I will write about my picture:
When I am 100, I will probably have a wrinkly old-grandma face.  I will still look like a nice old lady, even if I have mad wrinkles.  My skin might be saggy, but at least I won't have a bald head or a hairy mustache!

I tried to vary how I started my sentences because we've also worked a little on sentence structure and making our writing flow better and be more appealing by not being so repetitive.

Here are other descriptions for their pictures:
gray hair
white hair
silver hair
bald head
hairy mustache

To have a little fun and show you what the Aging Booth App can do, I made one of myself bald:

My brother says I look like Hulk Hogan!!!

And my personal favorite... the mustache:

 I told my dad that it makes me look just like him!

So, as you can see, you can have a lot of fun with this app and get kids super excited about word choice and parts of speech!

Thanks again to Jill  at Cruz'n In First for the app share- we haven't had this much fun writing in a LOOOOONG time!

Whole Brain Teaching- Loving the behavior!

One of my fellow teachers had a small workshop on Whole Brain Teaching- I was sold!  For those of you who do not know about this, there are 5 simple rules:
1.  Follow directions quickly.
2.  Raise your hand for permission to speak.
3.  Raise your hand for permission to leave your seat.
4.  Make smart choices.
5.  Keep your dear teacher happy.

I'm sure you have seen this all over Pinterest and TpT.  I wasn't sure if I could start this in the middle of the year, but we were almost at break when I went to the presentation.  After break I told the kids about it and they seemed pretty pumped.  They love rule #5!  (And so do I!)  Our favorite part:

The color chart for our behavior!  This is just a test run, so it isn't very pretty yet.  I had to see if it would work- it does!Since taking this picture, I added a Cubs mini-basketball hoop at the top.  Kids that end up on purple or pink get to take a few shots.  Weird incentive, but it's free and it works!

Amazing.  Love it.  I used to have the jerseys with the kids' numbers on them (which I still have) and a strike board with three baseballs labeled 1, 2, and 3.  Three strikes and you're out!  The problem is, once a kiddo gets a strike, what incentive is there to make smart choices for the rest of the day?  And what incentive is there for the kids who are behaving?  On the color chart, everyone starts on green and the goal is to stay on green or move up for making smart choices.  When a not-so-smart choice is made, they move down.  However, there is the opportunity for the rest of the day to move back up.  I have seen so much improvement in behavior, and I already had a pretty fantastic class!  They are working harder to work as a team and help each other, and they even tell me when they think other kids deserve to move up for helping them or for making a smart choice.  Having the 7 level spectrum also gives me some leeway to be a little more picky about the type of behavior I want to see.  Before I wouldn't give strikes unless it was something pretty big, but now I can sort of fine tune behavior, and I love what I am seeing from my kids!  Kids love to get caught "being good" and are so proud when after moving down, they get to move back up.  Our days are just so much more positive now!

I just wanted to share a small success for those who maybe haven't heard of this plan.  Loving it!