October 30, 2014

Exploring 2-Digit Multiplication with Base Ten Blocks

Guest Blog Post by Dr. Shirley Disseler

The way we do math has changed! The Common Core offers a new way to look at an old subject and encourages us to integrate relevant content. There are many new and exciting ways to get students motivated in the math by teaching in this more constructivist manner. For example, manipulatives like base ten blocks can be used to create area models of multiplication. This method’s focus is based on place value, which is an area of great importance for elementary students if they are to master math concepts in later years. Many teachers are just not comfortable with this new format, so I would like to describe an activity to get students comfortable with the new way to use place value to multiply two-digit numbers using manipulatives.

First the teacher should provide a hands-on practice time so that students begin to get comfortable with the manipulatives. To do that students should be given base ten blocks and provided a problem such as 12 x 14. Students then build the model and write the partial products. Students would draw the model and explain where the partial products portion of the model. It would look like this:

This approach is optimal for students because engagement is ramped up. Students do not realize they are really practicing multiplication of 2 digit numbers, and it affords the teacher the time to walk around and assess the level of struggle going on among students.

Area Model Match-Up Freebie
Once students have begun to understand students can begin to investigate the topic in more of game-like format using the Area Model Match-Up Activity, a lesson included in my book Strategies and Activities for Common Core Math Grades 3-5, Part I. My publisher has allowed me to share this activity as a free download. Click the image on the right to download it and read the complete directions.

In this activity, students play in groups of 2 or 3 to draw a two-digit multiplication problem card. Each student models the problem using base ten blocks and the others try to identify the problem and create a solution. Area Model Match-Up covers the standards included in Numbers in Base Ten for grades 4 & 5, as well as many of the math practices of the current standards. This strategy provides a more hand-on approach to understanding the actual number placement in two-digit multiplication problems. It takes out the misconception that students often have about the zero that serves as a place holder in this computational skill.

Math will always be about numbers, but the fact that students now need to “know” the math, not just “do” the math somehow makes it more fun. At the same time, it makes it somewhat scary for those teachers who did not learn to teach in this way.  Try these activities and see how engaged the students become!  Enjoy and remember… Common Core brings the “do” and the “know” together!

Dr. Shirley Disseler is Assistant Professor of Elementary and Middle Grades Education at High Point University in North Carolina. She has National Board certification as a Middle Childhood Generalist. Dr. Disseler has taught both elementary and middle school math and science, and has received many awards throughout her teaching career. She is the author of Strategies and Activities for Common Core Math Grades 3-5, a 2-part series.

October 29, 2014

Five Ways to Teach Your Students Empathy

Guest post by Emily Liscom

As teachers, we strive to push each of our students to his/her full potential. We have the responsibility to educate each student academically, emotionally, and socially. In my classroom, the single most important thing I can teach my students is empathy. If my students are able to understand the thoughts, feelings, and needs of others, they will be able to interact in a selfless manner. This will also help them to avoid physical and unpleasant conflict. 

Teaching students empathy can be extremely difficult, but it is very rewarding. When your students can practice empathy, it will benefit your instruction because your students will be in tune with the content you are teaching. It will also benefit your community, because your students will feel safe because they have the tools to solve conflicts.

1. Use Reading Standards that focus on character to teach empathy. 
Most reading curriculums include at least one standard that focuses on character and that's where you can sneak in a few lessons on empathy. If you are teaching the CCSS, Anchor Standard Three specifically deals with character. As grade levels increase, that standard narrows its focus to a character and his or her actions in response to an event. Using this standard is the perfect opportunity to assist students in understanding how characters feel and react to different situations. This is a great way to teach empathy, especially for those teachers whom have a tight academic curriculum with little time to incorporate extra learning activities into their curriculum.

 2. Allow your students to share their personal stories from the beginning of the school year.
This helps all students gain a better understanding of who they are personally and why they act as they do. The more students know about each other, the easier it is to understand their actions and/or emotions that may arise throughout the year. This will also help you to understand each of your students.

3. When there is a conflict, have a plan for solution driven conversations.
I have a go-to conversation stem for my students to use when they have a conflict. For example: “When you _________________ it makes me feel _________________. I don’t like to feel _________________ because _________________. Next time, I would like you to _________________.”

Because the conversation stem includes a part where the child can tell why they don’t like to feel a certain way, it really lets students understand that particular emotion.

4. As a class, take the time to focus on one feeling at a time. 
When you introduce one feeling at a time, your students will be able to identify and understand each emotion separately. For each feeling, I will create an anchor chart to guide our class discussion. To encourage participation and ownership, I will have each student write or draw a picture on a sticky for when they felt that way. I will have them put the sticky notes on their desks and then students will participate in a gallery walk around the room to observe pictures. Students then place their sticky notes on the anchor chart. After I finish the lesson, I always hang the anchor chart in a visible place.

5. Accept each student for who he or she is, as an individual. 
Show love and compassion for your students, and they will learn to show it towards each other. Be patient and model respectful conversation and problem solving. Students will not learn this in a day. You are one of their most influential role models so use it to your advantage and know that each interaction you can model is helping build a community of caring students.

Emily Liscom is currently a first grade teacher. She is the author and owner of the website Education to the Core. She loves to share ideas and resources that are both effective and purposeful. 

October 18, 2014

3D Printers - New Dimensions in Learning!

Guest post by Renee Peoples

“What can a third grader do with a 3D printer? How could it help them learn? Isn't it just a fancy toy? When would a teacher find time for such a thing? Who would program it, run it, teach students about it? Where would it go? Why would I want to have one?”

These were just a few of the questions in my mind when I saw that DonorsChoose had a program to try to get a 3D printer in every school. I was not interested.

Then, a few weeks later, I got an email that the program was opened up to every school in the country. I started to get interested and asked an engineer if there was anything for an eight year old to do on a 3D printer. He thought they would find plenty to do.

So I wrote a DonorsChoose proposal and got it approved. The next day, my project was funded because most of it was covered through a grant from the Makerbot, the manufacture of the 3D printer. I had no idea how much our classroom would change! 

3D Printers in a Nutshell
If you haven't seen a 3D printer, let me tell you a little about it before I share how it impacted our classroom. It's not really a printer in the normal sense of the word because it doesn't create 2-dimensional images on a piece of paper. Instead, it creates 3-dimensional models out of plastic. Our printer is a Makerbot Replicator 2 (shown below) and it looks like a large open box.The operator of the printer has to program the printer to create the object, and the object is created inside the box.

Luckily, there is a website, Thingiverse, where people who know how to write the programs put things they have made. In order to make the website better, there are contests. People upload their programs. A teacher (yes, even a third grade teacher) can get the program off that, put it into the 3D printer software, and be ready to print real items.

The "printing" process could take as little as 10 minutes or it might take hours, depending on the size of the object. It's exciting to watch because the item is in view the is in view the whole time it is printing. You can actually see the extruder lay down the plastic!

How 3D Printers Can Impact Learning
Having a 3D printer in the classroom can add a new dimension to the learning process because it allows students to make physical objects that relate to their curriculum. Need to see what a femur looks like? Print one! Studying explorers? Print a Viking ship! Studying geographic features of the earth? Print landform models!

Being able to create models of what they are studying makes a serious impact on students. It turned out that a 3D printer is not really is not a toy; it is technology at its finest. After a few minutes setting it up, maintenance turned out to be fairly easy.

3D learning happens across the curriculum. We read a story about a boy who made a hand with the help of his father. Going online to look at items to print involves a lot of reading. Writing about what students want to create when they grow up is very engaging for students in the classroom, and sure gets their creativity flowing.  Math concepts are embedded. If the project is too big and will take too much time or filament, we reduce it. Proportional reasoning is very interesting when you do it with real items. Vocabulary and science increase as you use the printer. Public speaking skills are enhanced when students explain how it works. “The filament goes into the extruder....”

I have only scratched the surface in the months since we acquired our printer, but I know that there is so much more to learn and do with it, and I can’t wait!

After 30 years of teaching in preK to 5th grade and administration in 4 states, Renee Peoples is now a Teaching and Learning Coach in Swain County at an elementary school, where she coaches teachers and students to integrate technology into their daily activities.

October 13, 2014

Checking for Understanding with Exit Tickets

Guest post by Greg Coleman 
from Mr. Elementary Math

During my early years as a classroom teacher I felt that exit tickets were yet another initiative or showy thing to do. However, as the years progressed I came to realize the importance of exit tickets for both my students and myself as an educator.

As educators, it is essential that we check our students’ understanding along the way. Formative assessments help us to monitor student learning so that we can adjust our teaching practices to improve student success. Formative assessment can be verbal (i.e. students responding to questions), silent signals (i.e. thumbs up and thumbs down), or written (i.e. quick writes or journal writing). Exit tickets are one type of formative assessment educators can use to check for student understanding.

Depending on your purpose, exit tickets can assist you in determining ...
  • what students already know about a topic 
  • what students learned from a specific lesson
  • what misconceptions individual students have about a specific skill or concept
  • what next steps are required for individual students, groups of students, or the entire class
In this blog post, I will focus on written response exit tickets, especially as they might be used in mathematics instruction. However, many of the strategies can be applied to other subject areas as well.

If you are thinking, “How can I get started with exit tickets?”consider the following three questions:
  • What do you want to find out about your students’ understanding at the conclusion of the lesson?
  • How much time do you want to allocate for your students to complete the exit ticket?
  • What format do you want to use for the exit ticket?

Show What You Know Board
One method that has worked well for me has been the Show What You Know Board. At the conclusion of a lesson students respond to a question by recording their answers on post it notes. Using post it notes makes the board reusable and efficient. The image below shows a picture of a board that I used after I taught a lesson on place value.

I wanted to find out whether the students could look at a base ten model, determine its value, and justify their thinking. The students were asked if they agreed or disagreed with the following statement, “Mike believes the model below the board represents the number 1,405. Do you agree or disagree? Explain why in writing or with a picture.” I would recommend having students put their initials at the bottom of their post it notes. This will help you identify which response belongs to which student.

A benefit of using the Show What You Know Board is the ability to see the responses of a group of students in one space. I always find this to be a very effective tool in the classroom because the students are required to take a position and explain their rationale behind it. Besides strategically planning a question that aligns with your learning goal, this method requires very little preparation after the initial setup.

Paper Exit Tickets (and a Freebie!)
Another effective strategy to check for understanding is to provide each student with a paper exit ticket. When creating effective paper exit tickets, I consider the following to be 3 critical components:
  1. What does the student know? In this section students respond to a given question or statement. This is a place for students to show their work. 
  2. What does the student think he/she knows? In this section students rate how well they understood the learning goal. This is a section for students to reflect on their own learning. 
  3. What does the student’s work actually show? In this section the teacher takes notes on the student’s response. This is a place for teachers to reflect. Did the student meet the learning goal? Does this student have any misconceptions? Does the student’s perception of what he/ she knows match what he/she can do?
The image below shows an example of an exit ticket that I created using the 3 critical components.

I have discovered several major advantages to using this exit ticket format. First it helps to guide my understanding of student strengths and areas for growth. I can clearly see the misconceptions that individual students have with a concept or skill. In addition, these exit tickets are great for keeping track of student growth. If you would like to download the template for the Show What You Know Board and the sample exit ticket, click here.

Exit tickets are powerful tools that can be used to:
  • drive discussions during student conferences
  • assist with planning your small group instruction and/or centers
  • provide parents with critical information during conferences
  • provide a quick lesson closure

More Exit Ticket Formats
Take a look at some additional exit ticket formats that can be readily used in the classroom:
  • Guess What I Learned? – Students write a brief note (2 – 3 sentences) to their parents explaining a concept they learned.
  • Draw It & Record It – Students draw one or two concepts from a lesson. The students record 1 – 2 sentences explaining what they drew. 
  • 3 - 2 - 1 - In a journal or on index cards, students record the following:
3 – things you learned 
2 – questions you still have 
1 – idea or thought that stuck with you

Although this process takes time, I challenge you to try using exit tickets at least 2 – 3 times each week. To make the transition easier, consider starting this process with one content area (ie. math ). As you become more comfortable add on other content areas. If you decide to use exit tickets in your classroom, notice the difference they make on how you deliver and modify instruction to meet the needs of your students.

Greg Coleman is a Kdg. – 5th Math Instructional Coach in Atlanta, Georgia. He loves to share math ideas and resources with elementary school teachers. You can find more ideas at his blog, Mr Elementary Math.

October 11, 2014

Is Your Classroom ELL-Friendly?

Guest post by Deb Hanson of Crafting Connections

Do you have any ELLs in your classroom this year? According to the National Center for Education Statistics, an estimated 4.4 million students in the United States are ELLs (English Language Learners)! Today I invite you to ponder some questions in order to determine whether your classroom is as ELL-friendly as it could be!

1. Do you make use of environmental print? 

Use anchor charts. Consider putting the word “horizontal” across the top of your door frame and “vertical” down the side of it. Use your wall space as learning tools!

2. Do you use graphic organizers?

Venn diagrams, flow charts, and Tcharts all assist ELLs learn content because the visual arrangement supports the concept being presented.

3. Do you read aloud to your students? 

As you read aloud, you will model fluency and support comprehension as you “think aloud” about the story’s characters and plot.

4. Do you encourage independent reading? 

As teachers, we all know that students become better readers by reading, and that independent reading is vitally important! Make it a priority in your classroom that students have time to read independently each day, and encourage students to read outside of school, too!

5. Do you provide visual supports as you teach content?

I personally love to use vocabulary cartoons because they engage and motivate students. At the beginning of a unit, give student pairs a vocabulary word. They work together to create a cartoon, linking word, and example sentence that helps explain the meaning of the vocabulary word. Then, you can share and refer to the cartoons throughout the unit!

6. Do you interact with vocabulary? 

For example, if “rotate” and “revolve” are two target vocabulary words in your science lesson, have students get up and move! Play a game of Simon Says where everyone stands in a big circle. At “Simon says ‘rotate’”, students turn their body around once, but at “Simon says ‘revolve’”, students walk in a big circle around a central object.

7. Do you provide sentence frames?

Advanced language structures can be tricky. An anchor chart with easy reference to these structures can be extremely helpful.

8. Do you use popsicle sticks?

Sometimes ELLs like to “fly under the radar” and passively watch as their classmates answer all of the teachers’ questions. Get a can of popsicle sticks and write your students’ names on them. Furthermore, institute a “no-raised hands” policy. Then, when you ask a question, randomly choose a popsicle stick and ask that student to answer your question. Students will quickly realize that all will be held accountable to be active class participants. They will be much more engaged if they know that they could be called on to respond at any moment.

Perhaps you are thinking right now that most of these suggestions are simply good teaching strategies for ALL students... and you are absolutely correct! I once heard someone say the following statement, and it does ring true:

All students can benefit from these strategies, but ELLs depend upon these strategies!

What other ELL-friendly strategies do you use in your classroom?

Deb Hanson has taught 16 years in a school district in Nebraska. She has taught second grade, Reading, and ESL. She has a passion for working with English language learners. Deb is the creator of the Crafting Connections blog where she enjoys sharing her strategies with others.

October 9, 2014

Teaching Division with Partial Quotients: Moving from Concrete to Abstract Models

Guest post by Tara, AKA The Math Maniac

When I started teaching I loved multiplication and hated division. My students felt the same way. When I started my career as a sixth grade teacher, almost half of my class had no idea how to divide. Worse, they had no idea what division was or when to use it. Of course division was not part of my curriculum and it was expected that my kids already knew it. I spent most of the year teaching and re-teaching the procedure for long division but it didn’t seem to do much good. As the school year came to a close, I knew I had to do something different. I started reading books and signed up for a class on multiplicative reasoning and that is when I was introduced to the idea of partial quotients.

The reason I love partial quotients is because they help me move kids from a visual model for division to an abstract one. That had been what was missing for my sixth graders. They had learned division facts using visual models and sharing and grouping strategies but had never connected that to bigger numbers. Instead, they had learned a procedure that had no connection to their definition of division. Partial quotients are a wonderful tool to move kids from what they already know about smaller number division and sharing things out to an efficient algorithm.

The best way to start with partial quotients is to start in context. I like to start with a problem like “Olivia, Mason and Connor made $153 shoveling snow. If they share the money equally, how much will each of them get?” Kids can use concrete manipulatives such as money pieces or base 10 pieces to solve the problem in a hands on way. It is a sharing context which kids are very familiar with. As kids share out the manipulatives, I record what they are doing using the partial quotients structure. If they start by giving each kid $40, and then give each kid $11 more, it is going to look like this.

Other kids will start out by sharing different numbers. Some kids will even share out ten at a time until all the tens are gone and then will share out the ones. Kids who are more fluent in multiplication, especially at the fact level will tend to share out bigger quantities than their classmates who are not yet comfortable. I record the process in a partial quotients format while kids share how they divided up the money. After several pairs have shared how they did it, I let other kids take the opportunity to come up and try to record their thinking.

We do several problems in this range in a similar format and before long, I have students recording their own thinking as they use the manipulatives to solve the problem. The second or third class period we spend on this, kids start making the transition to using just the partial quotients and not needing manipulatives. The key is that they can still visualize the manipulatives if need be, use what they know for multiplication facts and move to a more efficient and more abstract strategy. I also push this a bit by having kids show their partial quotients work and have the other kids explain how many they shared first and then how many they shared and so on. Take a look at this problem. Can you see how many manipulatives were shared initially and how many after that?

Since I have moved to teaching partial quotients, kids have a much better understanding of division. They connect it to what they already know about multiplication and division facts and are ready to tackle bigger problems in a short amount of time. They continue to connect division to sharing, are much more able to solve problems mentally and can get a reasonable estimate to a division problem. Since I learned partial quotients it has also increased my ability to do mental division and to see if my answer or my students’ answers make sense.

Take some time to learn more about partial quotients and to think about how they can move your students from a concrete model to an abstract one. Make math about making connections and not about learning procedures.

Tara, AKA The Math Maniac is a K-6 Math specialist. It is her mission in life to help kids and teachers learn to think about math and not just do it.