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Monday, November 30, 2015

Counting Down 'til the Big Day


Today I am linking up with Focused on Fifth to bring you a fabulous event - Unwrapping Holiday Classroom Ideas: Celebrate the 12 Days of Christmas with Focused on Fifth. For twelve days lots of great bloggers will be joining together to bring you classroom ideas for this holiday season. Today we are blogging about holiday math ideas.
I am just finishing up a class for my math endorsement about using algebra in the elementary classroom. We have been working with variables, functions, and graphs and how they can be introduced into the classroom. I have been amazed at how well my students have taken to thinking algebraically within mathematical tasks. I haven't asked them to graph any functions yet and I wanted to see how they would do with it in an inquiry based lesson. So with no prior teaching of graphing functions, I gave my fifth grade class this problem:

The tasks are to:

1. Create a function table for all houses one through ten.

Here are a few examples of the charts my students made to show how many cookies Santa had eaten after each house. We have created tables in the past, so this was pretty quick and easy for them. If you haven't done them in the past, then you might want to spend your time helping them create a table up to 10 or 12 and then really focus on how many cookies would Santa eat after 45 houses, 100 houses, 124 houses?



2. Find an expression that will tell how many cookies Santa has eaten for any given house. It should work for all numbers.

Some of my student wrote h x 2 = c and others wrote 2 x h = c. In both cases, h stood for the number of houses Santa had visited and c stood for the number of cookies Santa had eaten. This provided for a great discussion about what 4 x 2 means compared to 2 x 4. Then we applied our thinking to h x 2 = c compared to 2 x h = c, which is why some of the students in the pictures above crossed out one of the equations.

3. Create a graph that shows how many cookies Santa has eaten. Include up to house number 12. 

This is our first attempt at creating graphs for our expressions, so I knew it would be interesting. Here are two attempts that were started when most kids were still scratching their heads.
I asked this student how this chart was different from his function table and he didn't have an answer. I never did figure out why he has a column of zeros in there.

This student was giving it a try but she was unsure what to do with the number of cookies Santa ate after every house.
After some of these failed attempts (and there were more), I helped students see that we just wanted to mark the number of cookies Santa had eaten after the first house. Right about then, one young mathematical yelled out, "This graph is only going to go up." That provided for a great conversation as we talked about why he said that. Most of my students agreed that when we multiply with 2 each time, our slope would only go up. Here is an example of what most student graphs looked like by this time.
Most kids did not connect the line until I mentioned that if they wanted to connect the dots, it might help them see the slope.

We went a little further and discussed these questions: What do you notice about this graph? If you kept on graphing the number of cookies Santa had eaten up to house number 100, what would your graph look like? When does the graph stop?  We also talked about some of the features of a graph. We talked about the x-axis and y-axis and the differences between them. One student made my day when I mentioned a dependent variable and she said, "That must be the number of cookies Santa ate." I asked her to go a little further with her thinking and she said that for whichever number of houses he has been to, that gives a specific number of cookies. So the number of cookies is dependent on the number of houses. Not too bad for a first introduction to graphing functions and a such a fun lesson to teach.


To see a schedule of all 12 days, click on the Focused on Fifth blog button below. You will also find directions for linking up with us.

For more holiday math ideas, click on these great blog posts:


Saturday, November 28, 2015

Focused on Fifth: Products for Payday Linky

Today I'm linking up with Focused on Fifth to bring some of our favorite products to you. This is a product I joined up with The Ancient-Minded Professor to create. His expertise on Greek and Latin roots combined with my vocabulary research came together to create some great activities to help build your student's vocabulary.
Clicking on the product cover will take you to Teachers Pay Teachers

We took what research tells us about vocabulary instruction and put it into practical classroom activities.




There's 105 word lists to choose from and lots of different strategies and organizers.




740 × 400 This Products for Payday link just happens to be falling right before a HUGE Teachers Pay Teachers sale. They only have 4 per year and everything in my store will be 28% off, including bundles. Just use the code SMILE. To see more great products from the authors at Focused on Fifth, click on the button below.

Monday, November 23, 2015

Meeting History IRL


Yes, meeting history in REAL LIFE. And it was every bit as cool as I thought it would be. You probably recognize this piece of art work by Norman Rockwell.
The Problem We All Live With by Norman Rockwell

Well, the Museum of Art at the local university opened up a Norman Rockwell exhibit this past week and the opening night included a lecture by none other than....RUBY BRIDGES!!!!! I got in line an hour and a half before they started giving out wristbands for the lecture and barely made it in time to get the wristband that allowed you into the actual museum rather than the overflow. But the weather was pretty cold, so we decided to not stand in line for two more hours to get on the main floor and just accept being inside the museum in the basement instead. We arrived 50 minutes before the lecture only to stand in line for 40 more minutes outside in the cold before getting in. But it was all worth it. Ruby gave a fabulous talk about what she remembered and what she later learned about her experience as the very first colored child in a New Orleans school. She was amazing. Absolutely amazing.

"Racism is a grown-up disease. We need to stop using our children to spread it."

"There is no explanation for racism."

"Babies come into this world with a clean heart, until some adult teaches racism to them"

"We are all responsible for what we see unfolding before us....Are we afraid today of what we might lose? What might change?...We are losing anyway... Racism is a grown-up disease. Let's stop using our children to spread it."

After her talk we were able to stand in line (for only another hour) to meet her and get our books signed. Unfortunately they didn't let you take the time for pictures, so here's my best shots while the line was still moving.

My mom meeting Ruby.

My youngest daughter, Cate, getting her book signed and shaking hands with Ruby.
I am so glad I was able to take my daughter to meet her. I only wish I could have had my entire class listen to her.  One of my students did get to go with her family though. What a powerful learning experience for all the kids who were there. My daughter is a pretty strong believer in social justice and I know this is something she will always remember. I took my signed book to school. Hopefully my fifth graders will pick it up and read it. If they don't take the opportunity now, I'll make sure they do when we get to the civil rights era in US history.


Click to go to Amazon.

Here are a few other civil rights books for when you celebrate Black History Month or teach about the civil rights era. Clicking on any of the covers will take you to Amazon.


Freedom on the Menu is about the Greensboro sit-ins.
White Socks Only is about a young girl who doesn't understand the meaning of the "whites only" sign on the drinking fountain, which puts her in a dangerous situation. This book is also on the National Screen Actors Guild website, www.storylineonline.net.

Martin's Big Words is one of my favorites. I love how the author weaves Dr. King's actual words into this biography.
You cannot gather books about the civil rights era without including Rosa by Nikki Giovanni.
I found this book at the Utah Council of the IRA last year. It's about a young white girl who rides the bus to Washington D.C. to hear Martin Luther King speak. Along the way she experiences the same unfair treatment as those on the bus with her, and she has the opportunity to take a stand against racism.
Kadir Nelson is one of my favorite illustrators and this biography about Nelson Mandela will not disappoint you. I picked it up when it first came out and didn't use it in the classroom because I thought it was above my first graders. I'm excited to use it with my fifth graders this year. Racism isn't just a problem in the U.S., and I think it will be good for my students to think more globally.
I am always looking for great books to use in the classroom.  So if you have other favorite picture books about the civil rights era, please, please, please leave me a comment.  

Sunday, November 15, 2015

Cornucopia of Teacher Tips


I am linking up with the bloggers of Focused on Fifth for a Cornucopia of Teacher Tips. I'm not a guru of organization, but there are a few things that have worked for me in the classroom. 

1. Under the Cupboard Baskets- This is a fabulous way to take some of the dead space in your classroom and make it useful. They came from Lowe's and just slide into the cupboard - no screws, no drilling. The labels for each basket are hanging by paperclips. I use them for my students to turn in their work and I also keep one for things I need to file. So easy and convenient. 




2. Dish Drainer Electronic Holder- This is an idea I actually saw on Pinterest and it works perfectly for storing and charging all of our classroom electronics. 

3. Interactive Notebook Glue- This is a teacher tip that was all over the primary grade blogs a year or two ago. I was teaching first grade at the time and thought I had a great solution for gluing so I didn't give it a try. But when I moved to fifth grade this year I started thinking about the best way to glue in our interactive notebooks. I hate, hate, hate glue sticks. Once they dry, the pieces just fall off. Elmer's Glue will stick, but it's so easy to get too much on and have the pages stick together. So at the beginning of the year I finally decided to try these supposedly fantastic glue sponges. I put a sponge inside each container and then I poured one small bottle of glue over each sponge. After about 24 hours the glue was all soaked unto the sponge and they were ready to use. These sponges work so great, especially with interactive notebook pages. They put just the right amount of glue on every piece. No excess glue, no pages getting stuck together, so easy to use and no mess to clean up. I should have switched to these years ago.



4. Online Parent Helper Calendar- This works amazing for me. I set up a calendar for the entire year on Google slides. I simply selected "anyone with the link can edit" and then sent the link to all of my student's parents. Every two months I adjust the available times and resend the link with a quick note telling parents they can sign up for the next two months. It made scheduling all of my helpers a breeze.



5. Class Website- This is not a pretty website, but my district has us use Google Sites. It's very basic, but it has made things so easy. Lost your spelling list? It's on the website. Need a copy of the weekly reading calendar? Print one off the website. Wondering when your birthday celebration week will be? It's also on the website. Term 2 book project? All the directions are on the website. Policies, schedules, homework, pictures, and more. They are all on the class website. This is my first year using a class website, so it was completely empty when the year started and I just add things as needed. It worked so great that way that I am going to delete everything and start from scratch next year too. Otherwise I worry that my parents and students will have too much to sort through at the beginning of the year. 



For more teacher tips, continue on the hop by visiting Keep Calm and Teach 5th Grade




Saturday, November 14, 2015

Revolutionary Heroes and Heroines

This week my students drew some incredible portraits of Revolutionary War heroes and heroines. They came out so amazing. I blogged about them over at Focused on Fifth this weekend. If you are like me and feel the time constraints, then integrating just makes sense. You can check out my post by clicking on the Focused on Fifth button below.

Sunday, November 8, 2015

November What Are You Reading?

I'm linking up with Focused on Fifth for the monthly "What Are Your Reading?" linky party. I just picked up a great new book that was recommended by one of my team members - The Reading Strategies Book by Jennifer Serravallo.

One of the things I love most about fifth grade is that everyone reads. Coming from first grade, that is a huge, huge thing that I'm not used to. I started the year so excited to be focusing on comprehension. I envisioned all of these great discussions about books with the kids digging deeply into each text. But then when I started my groups, I realized that the deep conversations are more difficult than I expected. My time with each group has been spent more on retelling and summarizing than I wanted it to be. My questions were revolving around trying to make sure everyone understood the story at the most basic levels. There wasn't a lot of digging deeper. That's when I realized that there's a lot of work to be done even with a class of readers. If I'm being completely honest with myself, I wasn't helping them dig deeper. I just kept doing more of the same things with them. More of the things that I could do without putting in a lot of effort. I don't shy away from hard work, but with everything going on in the classroom, I don't have a lot of time to work on each guided reading group lesson. So when I saw this new book by Jennifer Serravallo (thanks to an awesome team member),  I came home and ordered it right away. It is packed and I mean packed with lessons that are easy to implement. It's organized into 13 reading goals with loads of strategies for building fluency, understanding main idea, writing about reading, comprehending fiction and nonfiction and more. A lot more. The strategy lessons range from grades K through 8, so there is something for every reader. And for me, there's something for every group. Guided reading lessons just started feeling a whole lot easier.

Clicking on the cover will take you to Amazon.

To read more book suggestions or to link up a book recommendation of your own, head on over to Focused on Fifth.


Sunday, November 1, 2015

Multiplication and Division Problem Types


Last week I wrote a blog post about using different type of problems with addition and subtraction. You can read it at Busy Bee's Activities. It made me think about writing a post about multiplication and division problem types too, so today I'm blogging for the upper grades.

I'm just finishing up a unit on multiplication and division of whole numbers with my fifth grade class. We have focused a lot of time on developing different strategies for problem solving within these operations. With it being my first year in fifth grade, I had no idea how difficult it would be to help them be more flexible. I have a group of very procedural-minded mathematicians and getting them to look at things differently can be difficult. Sometimes it feel almost impossible! One thing that I think made a HUGE difference in encouraging them to be more flexible is changing up the problem types.

Multiplication Problems

Multiplication (x times y) doesn't always indicate x groups of y. 3 groups of 12 cupcakes or 15 groups of 21 beads is great, but you don't always have discreet objects to put into groups in real life multiplication. While the solutions aren't that different with some of these, it's important for students to work with different conceptions of multiplication. Here are some of the types of multiplication problems I used besides just grouping problems.

Measurement Problems- Because are no objects that can be counted, these are a little more abstract. They can be solved in similar ways even though there technically aren't any countable objects.
  • How many miles does a car travel in 6 hours at an average speed of 72 miles per hour?  
Comparison Problems- These problems are definitely harder. They involve comparing two quantities when one of those quantities is a multiple of the other. Students must understand the meaning of 12 times larger or 4 times as much and they need a strategy that does not involve grouping.
  • The zoo has 2 bears. The black bear weighs 243 pounds. The polar bear weighs 3 times as much as the black bear. How much does the polar bear weigh?
Area Problems- These problems use two factors that are interchangeable. They have no distinct, independent roles and they don't allow student to solve by grouping. They also don't have any discreet objects.
  • I planted a garden that is 14 meters by 9 meters. How big is the area of my garden?
Array Problems- These problems are different from area problems because arrays are made up of discrete objects. My textbook uses pictures of arrays, but my student rarely use them themselves. However, I think using arrays are the best way to demonstrate the commutative property of multiplication. So to get students to use arrays, you need a problem that lends itself to thinking of objects in rows.
  • Last night my daughter's choir concert was really crowded. Every seat was taken. I wondered how many people were there so I did some counting. There were 28 rows and each row had 54 chairs in it. How many people were at the concert?
Combination Problems - These problems require students to think about different combinations that can be made from sets of objects.
  • The special at the ice cream shop includes 2 scoops of ice cream and any 2 toppings in either a cup or a waffle cone. Mom says we can go to the ice cream shop for my birthday party but everyone has to order the special. I didn't want to tell my friends that they only had one option, but Dad said there are tons of options when you order the special. How many options will my friends have?

Division Problems

When students look at a division problem such as 1425 divided by 12, you can't tell what type of division problem it is. I think that's fine when I just want them to get a lot of practice with division. But if I want to force them to think about the problem differently, it has to be put into context. Are they solving by making 12 groups or making groups of 12?

Partitive Division- These problems require students to solve for how many items are in each group.
  • The district athletic department is preparing for their annual celebration dinner. 1,425 athletes have signed up to come. It's being held on the football field and by putting food on both sides of the field, they will have just enough room for 12 rows of tables. How many athletes will they need to put at each table?
Measurement Division- This type of problem requires students to make groups of 12.
  • The PTA made 1,425 cupcakes for the school bake sell. If they package them in boxes of 12, how many boxes will they have?
What about the remainder? What you do with the remainder depends on the context of the problem. Sometimes you do nothing with the remainder. 
  • The school is planning a huge celebration. The cafeteria bought 14 dozen eggs to make cakes. If each cake takes 5 eggs, how many cakes can they make?
Other times, you need to add another trip up to take care of the remainder.
  • 168 people have been invited to a dinner on the 19th floor of a building. The elevator can only hold 9 people at a time. If everyone takes the elevator, how many trips will be needed to get everyone up to the dinner?
And in some instances you will need to deal with a fractional part.
  • During art class, the students will be making sculptures of birds. Mrs. Smith brought in 30 pounds of clay for the class. There are 25 students in the class. How much clay will each student get?
Once I started thinking about multiplication and division problem types, I started exposing my students to problems that required them to think differently. It helped them to be more flexible and it forced them to think a little more deeply about the problem. Not to mention how fun the problem solving has been!