Volume

Volume of solid figures is one of our last objectives to cover before our state testing so we typically have very little time to teach it in. I try to pack as much instruction as possible into one class period. I've found that if I provide concrete, hands-on experiences and the opportunities for students to construct meaning on their own, they retain the information very well. Another way that I cope with the lack of time is by including volume questions throughout the year on our mixed-topic review sheets. This gives them a lot of exposure with the concept before I teach it.

In Texas our current standard (4.11C) states that students should be able to use concrete models to measure volume. This connects to 5th grade Common Core standard (5.MD.C.4) that states that students should be able to measure volume by counting unit cubes. I like to extend on our state standard by having students discover the formula for volume. This corresponds to the Common Core standard 5.MD.C.5.B - students should be able to apply the formula V=l x w x h to find the volume of rectangular prisms.

Mini-Lesson:

I started off our lesson by reviewing the formulas for area and perimeter. This activated their prior knowledge about formulas and got them thinking about measurement. I passed out unifix cubes* to each table and displayed a picture of a rectangular prism for students to build. This also gave us a great chance to review the vocabulary rectangular prism. Once they had built the prism we worked together to fill out the dimensions (length, width, height) and volume on a recording sheet. Our working definition of volume was "how many cubes did we use to build this figure?"

*Whenever we use a manipulative in math, I typically set a timer for 5 minutes and let the kids play. They know that if they play with the manipulatives after the timer goes off there will be a consequence. 

Partner Activity:

I had the kids work with their "face partner" (the person sitting across from them). Each pair got a set of task cards that had pictures of rectangular prisms. Their job was to build the prism and then record the dimensions and volume on their recording sheet. I also gave them the challenge of figuring out the formula. This gave my higher kids a challenge to keep them engaged. 

Reflection:

Once time was up, I called the class back to the carpet. First I had several pairs share out one set of their data. Once we had the dimensions & volume for several rectangular prisms recorded, I asked if any students had figured out the formula. After hearing several ideas, my class was able to come up with the correct formula V = l x w x h. Then we used this formula to check their work. 

Extension/Intervention:

After we figured out the formula for volume, I sent students back to their desks with a new set of task cards. This time I had them fill out their recording sheet without using the cubes to construct the prisms. The students who were still struggling with misconceptions worked with me in a small group. We filled out the recording sheets without the cubes and then checked our work by building it. 

Common Misconceptions:

I have found a couple of common misconceptions with my kids when it comes to finding the volume of a solid figure. A lot of students want to count each side of the cube as 1 unit. Another misconception is that when students look at a picture of a rectangular prism, they only count the units they can see. For kids who struggle with this objective, giving them more time and opportunities with manipulatives gives them a solid understanding that they are able to transfer to test format questions.

You can download the materials I used for free my Teachers Pay Teachers store. Just click on the picture below:

Lines Task Cards

Our geometry unit started right after our unit on long division. I had about half of my students who had mastered long division and were ready to move on at the end of the unit. However, the other half still needed some more practice. Our district pacing is pretty set because of the amount of material the state expects us to cover before state testing in April. So I felt the need to move on to geometry, but still needed to work with my students on division.

This led me to the development of task cards. I created different task cards for some of the main topics in our geometry unit. I'm going to focus on the tasks for lines in this post. The way I structured this unit was that the students were all given the same task card to start with. While they were working independently, I was able to pull small groups to reteach division. We spent about a week working on the different task cards. This gave me enough time to help my students reach mastery with division. Some of my more struggling students did not complete all of the task cards because they spent more time working in small groups with me on division. 

Must Do Activities:

Their task card included two must do activities. Every student had to do both of these activities. The first must do was to watch a video that I created using the show me app. This video went over the important vocabulary that they needed to know about lines. This was the direct teach portion of the activity. 

Here is the video:

The second must do activity was to create a foldable for the vocabulary. We do a lot of foldables in my class, so the kids are pretty quick at making them. They had a flap for each vocabulary word and inside the flap they put a definition and a picture. They could use their math textbook as a reference material. When they were finished, they glued their foldables into their math journals.

Can Do Activities

There were 4 choices for "can do" activities. The kids had to pick 2. I tried to come up with activities that appealed to different interests and strengths. Their choices were: 

• Use pipe cleaners to make examples of parallel, perpendicular & intersecting lines. They glued them down on paper and labeled each example. 
• Create their own instructional video using an ipad. They had to explain the different types of lines and how they are different from one another. Some kids used a screen capturing app (like my example in ShowMe) while other kids chose to make an iMovie. They had freedom in choosing which app to create their video in. 
• Complete practice problems on Khan Academy. 
• Draw a map of a town with intersecting, parallel and perpendicular streets. They had to include an explanation of their types of streets. 

Assessment

The last part of the task card was the assessment piece. For this they had 5 different word problems to answer about lines. The assessment piece allowed me to see if they were able to apply their knowledge to word problems. It also gave me data on which students needed additional instruction with me. 

Reflection

I loved this activity. Not only were the kids extremely engaged, but I loved seeing their creativity in the different ways they demonstrated their knowledge. I saw so many kids referring back to their foldables and rewatching the video to ensure they had the content correct. When I wasn't working with a small group, I was walking around talking with kids about their work, answering questions and clearing up any misconceptions. 

After our geometry unit we took a district assessment and 100% of my kids correctly answered the questions over lines! I was amazed at how much learning took place.