I just discovered a new app called Show Me similar to an interactive white board on the ipad. A kindergarten teacher shared with me today how she uses this app in her classroom. She uses a class set of ipads and has the students record themselves talking as they are solving math problems. The app has the ability to record the students’ voices and actions on the screen as they are thinking through their problem. Students can write on the screen with their finger or a stylus in several different colors while they are solving their problem. Pictures can be imported from the ipad files or you could email yourself a picture from another file to have it on your ipad. For example, if you wanted to solve problems with color tiles, then you could build some colored squares in another program and email them to yourself. This particular kindergarten teacher, however, explained how she had students solve CGI problem types on the ipad while they recorded their voice and writing on the screen. She did this in order that she could hear their thinking because she wasn’t always able to make it to every student to hear their thinking. Later she would take the ipad home so she could hear the students solving their problems.
Every year the same thing happens. Students get area, perimeter, and volume confused. Several years ago I went to an NCTM conference and a presenter there suggested this activity. I kind of made it my own since I have been teaching fifth grade a lot lately. She suggested taking index cards and labeling them “AREA” and “PERIMETER”. I added “VOLUME” also. Then read aloud several statements and have students hold up the card so that all including you can see. I had a list of about fifteen statements such as:
- How much sand to fill up a sandbox?
- How far is the distance around the playground?
- How much bulletin board border do you need to go around the bulletin board?
- How much paint do we need to cover the classroom wall?
- How much fabric do you need to make a tablecloth to cover the table?
- How much water is needed to fill a swimming pool?
- How much carpet do I need to buy to make a comfortable reading center?
We did this orally in class for about fifteen minutes and after each statement, I asked the student why the answer was what they held up on his or her card. Sometimes instead of asking why the answer is perimeter, I asked why is the answer not area or volume. At first when we did this activity students had mixed answers and I could tell that they didn’t have an understanding of these terms. After spending a while explaining why or why not an answer was correct, I noticed that most of the students were correct as they held up their cards. I had thought of giving the students three different colored cards so that I could easily tell which word they were holding up, and then I changed my mind. I decided that if I could quickly tell which card that students were holding up, then other students would simply look at the color of the “smart” kids’ cards and not do much of their own thinking.
To extend this activity, I had students keep their cards in their notebooks and add to them the next day. On the back of the perimeter card, students wrote “UNITS”. On the back of the area card, students wrote ” SQUARE UNITS”, and on the back of the volume card, students wrote “CUBIC UNITS”. I used the same fifteen statements and had the students hold up the cards just as before, but this time with the units side facing me. Doing this helped them see the connection between perimeter, area, and volume with which type of units each measured.
After these activities most students were holding up the correct card and had the general understanding that:
- perimeter and units measure distance
- area and square units cover
- volume and cubic units fill.
This activity could be used in other disciplines as well if students are struggling with the meaning of a few terms. The beauty of this is you as a teacher have an immediate quick assessment for students who aren’t understanding as soon as you see their card.
Here is a little something I have been working on–Nothing But Nets. I recently posted this on TPT. I used this to teach a fifth grade class about what nets worked to build a cube without overlapping. Before I used this lesson, I gave students some grid paper and asked them to find as many ways as they could to build a net for one cubic unit. Then we posted all of the nets–ones that worked and ones that didn’t on a chart. We grouped the nets into two sections so we could see the similar characteristics that made a net work or not work. We gathered on the carpet for an up close look at the similarities among the nets. Students made some good generalizations about what would make a net work such as the net must have 6 squares and be flexible enough to surround the cube. Students also made generalizations about cubes that didn’t work. Among students comments were these generalizations–they noticed nets that don’t work may have more or less than 6 faces and have squares clumped together.
After students had made these generalizations about nets, I gave them this activity for them to test their generalizations. Students were given a series of 10 nets. They predicted which would and wouldn’t work. Then they were allowed to cut them out to test their predictions. We grouped the nets again into categories that worked and that didn’t work. Students began to notice more characteristics about the nets which made them work or not work. After these two lessons, students did very well on their nets quiz. Below is the nets activity I used which is available at TPT.
Today marks the first day of my spring break. I have no exciting travel plans. I suppose I will have to live vicariously through someone else’s beach getaway. I will be spending time with my furry friend, gardening, spring cleaning, catching up with friends, adding to my blog and completing some materials for TPT. I may even refinish a piece of furniture somewhere in there. I have been looking forward to working in my yard, and since I live in the south, it has already been VERY beautiful outside–reaching a balmy 83 today . So staying at home will almost be like the beach!
Other updates since I haven’t posted in a while: I have been selected to attend a series of math common core meetings which are led by Linda Griffith. Linda Griffith has had experience working with researchers such as Constance Kami (one of the constructivist researchers I learned about in college). She is an excellent professor who works at a state teachers college here. She is funny, practical, and extremely smart. I have learned so much from her! The teachers and coaches who were selected to attend these meetings are responsible for training others in the district about common core math standards. I will be eventually sharing what I have learned in pieces on my blog. I will have to say that attending her meetings have sparked a passion in me again to teach mathematicians and NOT test takers! I am sure many of you share the same divided feelings that I do when teaching. You want to teach the child to mastery of a skill and ask probing questions to lead students there, however you have to COVER the material. And so we sacrifice mastery for covering material. Then when kids don’t score well, we scratch our heads and say, “Well, I covered it?” Now, the common core standards will allow us to teach to mastery and let students learning and understanding guide our lessons instead of our need to COVER material.
Oh, and Happy St. Patrick’s Day to you all!
So many discounts,, I don’t know what to do. I just stumbled upon this website, which has way more discounts than I ever knew existed for teachers. The website states that the more people that join, the better the offers that they can negotiate for teachers. I am signing up right now! Check the site out at http://myeducationdiscount.com/.
1. Teach students to “Brain Dump”. As soon as students are allowed to begin their test, tell them to write everything down that they worked hard to remember, but are afraid that they might forget during the course of the test. Our state tests give students a math reference sheet, card stock rulers and pattern blocks. Students could write other formulas down on their reference sheet, write the name of the pattern blocks on the pattern blocks, and write the fractional measurements on their rulers. If your state doesn’t provide students with these materials, then they may provide them scratch paper, or they may be allowed to write in the test booklet itself. Students could “brain dump” in these areas.
2. Have a Mathlete’s Challenge. To give students a break from the mundane multiple choice test prep and practice, allow them to work in pairs to discuss which answers are correct. Give the top three student pairs a prize for answering the most questions correctly. The competition helps keep the students focused on the task. Students get the benefit of discussing with their partners which answer is correct. Allow students to move to a quiet corner of the room to work in their pairs. Remind them that because this is a competition, they need to work quietly so that no one steals their answers.
3. Weeks before the test make vocabulary or spelling lists based on most often used language in test questions. Your list might include words such as represent, approximately, elaborate, explain, outline, trace, support etc.
4. Time students like they will be timed when taking their real state tests. Allow students to see the timer as the minutes pass by to help them pace themselves.
5. Practice bubbles. Make sure students are bubbling in the whole bubble. Practice bubbling in bubbles darkly.
6. Practice using the calculator. If students are allowed to use calculators, make sure they know that they are smarter than the calculator and that the calculator is only a tool. For example, many students may have difficulty inputting money in the calculator. Instead of typing 0.50 for 50 cents, students type 50 and then add 1.50 for a dollar and fifty cents. Then they get the wrong answer. Students also build a misconception around the calculator showing 0.5 and thinking that the calculator is showing them that they have 5 cents and not 50 cents.
Another common misconception students have is when they are dividing numbers. Students tend to misread the number behind the decimal as the remainder. On a recent test, I noticed that many students saw 29 and divided it by 5 only to read 5.8 on their calculator screen. Many of the students wrote that the answer was 5 with 8 leftover (as a remainder) in the word problem.
7. Eat a peppermint candy. Peppermint oil is excellent for mental fatigue and depression, refreshing the spirit and stimulating mental agility and improving concentration. It helps for apathy, shock, headache, migraine, nervous stress according to this website. We always give students a few peppermints during testing to give them an extra boost.
In order to make addition and subtraction more engaging, there are several things you can do to help keep students attention. Have students play games such as Close to 100, Close to 0, Close to 20, and other such games. In addition to the games that are already available from many of the Math Solutions books by Marilyn Burns and other authors, I developed some card sorts to help keep students’ attention on solving problems. I have developed a variety of card sorts to teach addition and subtraction within 100. Students match a picture card of unifix or snap cubes to an equation. To make a card sort more challenging, I like to include a card which doesn’t match any other card. This helps target some misconceptions that develop around addition and subtraction. If students solve card sorts in pairs, then this creates much students’ higher thinking as they evaluate each other’s decisions about where to place cards. If you would like to try out one of the these card sorts, just click on the picture below to download a free sample of an addition card sort without regrouping. This link will take you to TPT where you can download the preview file.
I just wanted to share one of my favorite products with you all. I purchased these solids pictured below for our school two years ago and all of the teachers love using these to teach students the plane shapes that make up a solid. They are great for helping students identify nets of solids also. Today I taught a class in which the teacher was absent, and I used these solids that unfold into nets. After looking at these, students took paper nets and listed the shapes they saw in the nets and then labeled the solids with sticky notes. Next they composed their 3 dimensional solids into other shapes such as robots and rocket ships. See the following pictures below to take a peek at some of the students’ creations.