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.
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.
When teaching time, students have difficulty understanding that the day has twenty four hours because there are only 12 numbers on a clock. To help students understand a.m and p.m build a linear clock. To make a large linear clock that involves all of your students, give students each two sentence strips. Have students fold each sentence strip in half three times. This will make eight sections. Overlap the two sections of the sentence strip so that you now have a very long strip with fourteen sections. Assign each student a different hour of the day. For example, one student will have 1 a.m, another 2 a.m. and so on. The folds on the strips will represent five minute intervals. Students should start writing on the second section, so that the blank sections can be attached to the next hour. A student will begin writing the five minute intervals on each fold like so, 1:00, 1:05, 1:10, 1:15, 1:20, 1:25, 1:30, 1:35, 1:40, 1:45, 1:50 1:55. Then there should be a blank section left afterwards so that the last section may be attached to the next hour. Between the five minute intervals, student may draw four little marks to represent the minutes or little tics on a clock between the numbers. Provided you have 24 students, you will now have a complete clock with a.m. and p.m. time. If you hang this linear clock up in your classroom, it will be extremely long and probably wrap around the entire room. When you take the ends of the liner clock and have them meet in a circular fashion, students have a dawning moment and you can hear “oh!” being whispered under breath throughout the room. What I like about building this linear clock is that students are able to see both a.m and p.m. Having the clock hanging up when discussing elapsed time makes finding elapsed time so much more concrete for students who need this support. In addition to teaching elapsed time, students can label different activities that happen throughout the day and post them over the linear clock.
Yesterday I spent some time in a second grade classroom helping students who were adding double digit numbers. When working with one student, I realized he didn’t know he had ten fingers on his hand, and he didn’t know that four fingers on one hand and five fingers on another made one less than ten–nine. While at a CGI (Cognitively Guided Instruction) training today (I am in Year 2 of the training), some things dawned on me about this children. Children do not innately know that they have 10 fingers, nor do they necessarily discover this on their own. With that said, the CGI trainer today told us that she knew of a teacher that has students do finger flashes. She calls out numbers and the students hold up that many fingers. I had never thought to do something so simplistic. I know that in kindergarten we do such activities with dot cards, but I had never thought of finger flashes–WOW!
In this same second grade classroom, I moved on to another little girl who had difficulty counting on from the larger number. Even after I showed this student how to count on, I noticed that when looking at the problem she didn’t know where to get the other number to count on with her fingers. I showed her how to look at the problem to find the number. Again at the CGI training I realized for students to develop the number sense they need to count on, the teacher can push students toward counting on by posing a very large number in a word problem followed by a much smaller number. For example, with the problem 62 + 3, 62 would be easier to start from and just count up 3 more. Once a child is counting up just 3 more, the second number could be increased. As my mentor always used to tell me–You know better, then you do better. That is me.
- K.CC.1. Count to 100 by ones and by tens.
- K.CC.2. Count forward beginning from a given number within the known sequence (instead of having to begin at 1).
- K.CC.3. Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).
- 1.NBT.1. Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.
- 2.NBT.2. Count within 1000; skip-count by 5s, 10s, and 100s.
I developed a set of number charts with missing numbers and number chart puzzles to help students see patterns, become more proficient with number recognition, and become more proficient at counting. Pictured below is a picture I snapped of a kindergarten student putting together the 1-80 chart. Our school district decided to increase the numbers that students learn in kindergarten each quarter instead of working towards 100 the 1st quarter. This quarter our pacing guide says students should learn to count to 75, so students are completing a 1-80 puzzle. When using these puzzles with small children it is necessary to model this otherwise students will cut out each number. If you would like to sample the number charts and puzzles, there are a few pages for FREE on TPT–just download the preview.
The common core standards for first grade state that students must become fluent with adding and subtracting tens. To promote fluency, students need to discover patterns and how they change numbers. Only when students have examined patterns and become comfortable with them should they be given timed “naked number” problems to assess and improve their efficiency in recalling the patterns. Finding the answer to a “naked numbers” problem needs to be merely a by product of knowing the pattern.
When trying to figure out how to teach fluency with adding and subtracting multiples of ten to first graders, I struggled to find resources to do this. Because of the lack of resources, I developed these sheets for next week to lead students and their teachers into guiding discussions about patterns on the hundreds chart. They are simplistic activity sheets but necessary. I will be trying them out this week. I am providing a link to them below. If you would like to try out one of the lesson sheets, the preview file will give you a sample for free at TPT.
I came across these posters in a fourth teacher’s room at my school. She decided to display parts of speech on a shape poster to help students think about what types of words they use when they write. She made a poster for nouns, verbs, adjectives, and adverbs. She had displayed a house for nouns, a blob shape for adjectives, and the kite below for verbs. For some reason my other pictures didn’t turn out, but the kite picture managed to turn out, which is my favorite. Also, pictured below is another chart which she made entitled “RIP” for ‘dead words’ or words that are overused.