This isn't a new idea by any means, but I took the idea and created a template for others to use. I originally took the idea from a Marilyn Burns book, but I've seen the idea on other websites.
Rules: Have a student pick a number from 1 to 31. Show them each individual card. Ask the student if their number appears on the card. After they have replied to each card, watch them become amazed as you tell them their number. Here is the template I made:
If you aren't sure how this works, all you need to do is keep track of the students responses and do some quick adding. If the students number appears on the card, add the number in the upper left each time. For example, if the student's number was 9, they would say "Yes. No. No. Yes. No." You would have to add 1 and 8 because those are the numbers in the upper left that correspond with the students responses.
I printed these cards on card stock, laminated them, and attached them with a ring. I have done this activity numerous times and my students still cannot figure out the trick, yet they keep asking me to play it because they think they can "stump" me. This activity could be tied into lessons on powers of two or even binary numbers.
Survivor
Every teacher has those short, time filler activities to use for various reasons. I will spend my next few posts sharing some that I do because you really can only use them a few times before they lose their luster, and I'm sure some teachers are looking for more.
Survivor
Objective: To be the last person standing at the end of the game.
Materials: Every person, including the teacher, needs a number cube or die. I like to use the die on the SMART Board for mine.
Rules:
1. Every student stands up, then rolls their die.
2. Once the teacher sees that all the students have rolled, the teacher rolls his/her die. Any student that has a number that matches the teacher is eliminated and sits down. For dramatic effect, I like to say "The tribe has spoken."
3. Steps 1 and 2 are repeated, but only with the students who are still standing.
The game is quick and easy. I give out a mini prize to the winners. The probability ideas could be worked into a lesson as well.
Survivor
Objective: To be the last person standing at the end of the game.
Materials: Every person, including the teacher, needs a number cube or die. I like to use the die on the SMART Board for mine.
Rules:
1. Every student stands up, then rolls their die.
2. Once the teacher sees that all the students have rolled, the teacher rolls his/her die. Any student that has a number that matches the teacher is eliminated and sits down. For dramatic effect, I like to say "The tribe has spoken."
3. Steps 1 and 2 are repeated, but only with the students who are still standing.
The game is quick and easy. I give out a mini prize to the winners. The probability ideas could be worked into a lesson as well.
Careers in Math Glogs
I recently had a few of my students do a mini-project using Glogster. They researched careers that have math backgrounds on the "When Will I Use Math?" website. From there, they used the important information to create their own Glog.
Here is a link to a larger version of this glog, as well as a few others that were created - another biologist, statistician, attorney, and physician.
Here is a link to a larger version of this glog, as well as a few others that were created - another biologist, statistician, attorney, and physician.
Accelerating Students Follow Up
Just a follow up on my post about accelerating students from earlier in the school year. Last year my advanced 7th graders had to basically teach themselves concepts from the 8th grade book. I'm totally against it, but it was the situation I walked into. This year those students, along with a few others, are now in Algebra I. Today we talked about the Pythagorean Theorem.
At the beginning of the lesson, I heard a comment, "Oh great, I didn't understand this at all last year. This is not going to be fun."
At the end of the lesson, I heard, "I actually get it this year. It's actually kind of easy."
At the beginning of the lesson, I heard a comment, "Oh great, I didn't understand this at all last year. This is not going to be fun."
At the end of the lesson, I heard, "I actually get it this year. It's actually kind of easy."
Music and Learning Math
It's no doubt that people can remember information better if the information is sung to a tune. Using music in class is such a great tool, but it can be hard for some teachers to create songs because they are not musically inclined (such as myself). I think it would be great to create a compilation of math related songs that teachers have used to help their students learn concepts. I will get started with a few that I have used or plan to use:
Adding Integers Song (sung to the tune of "Row, Row, Row Your Boat")
Same signs - add and keep
Different signs - subtract
Take the sign of the higher number
And then you'll be exact!
The Pi Song performed by The Derivatives. The song is sung to the tune of 867-5309/Jenny. Here's the mp3 download of the song I use.
Fraction Rap by Mr. Duey
Sean Sweeny's Slope Rap sung to the tune of Flo Rida's "Low"
Of course there is the ever-popular Schoolhouse Rock songs for learning multiplication facts.
"What You Know About Math" sung to the tune of T.I.'s "What You Know" - Original Version and Middle School Version. Not really useful for learning specific concepts, but they are good for showing when you have 5 minutes to fill.
What are some songs that you have used in your math class? If we can get enough suggestions, I will start a wiki to build our resources!
Adding Integers Song (sung to the tune of "Row, Row, Row Your Boat")
Same signs - add and keep
Different signs - subtract
Take the sign of the higher number
And then you'll be exact!
The Pi Song performed by The Derivatives. The song is sung to the tune of 867-5309/Jenny. Here's the mp3 download of the song I use.
Fraction Rap by Mr. Duey
Sean Sweeny's Slope Rap sung to the tune of Flo Rida's "Low"
Of course there is the ever-popular Schoolhouse Rock songs for learning multiplication facts.
"What You Know About Math" sung to the tune of T.I.'s "What You Know" - Original Version and Middle School Version. Not really useful for learning specific concepts, but they are good for showing when you have 5 minutes to fill.
What are some songs that you have used in your math class? If we can get enough suggestions, I will start a wiki to build our resources!
Indiana Standards and Resources
For anyone working on refining their curriculum, I was introduced to an excellent resource. The Indiana Department of Education has a standards search engine that provides assessments, activities, and lesson plans that go along with each standard. To find these, search for math standards at your specific grade level, expand each standard, then click "View Resources." The classroom assessments are particularly useful for doing backwards design lesson plans.
Explaining Thought Processes
My students will begin taking the standardized state test for math next week and I thought I would share something that I do with my students to not only prepare them for certain types of questions on the test, but to give them a skill that they will need to use for the rest of their lives.
Our state tests have 2-3 constructed response problems that our students need to solve. They are given a problem of elevated difficulty and they are expected to find the answer and describe how and why they came to their solution (see question #11 or #18 on this sample test). The students in my district typically do very well on the state test, but these types of problems are the ones that seem to give them troubles.
I decided to attack this problem last year. Describing your thought process or explaining why something is correct is hard for students to do, especially if they've never had to do it before. I don't think I ever had to explain my thought process in words until I got to college, and even then I struggled at the beginning. I could do it verbally, but putting those thoughts on paper was just something that was not normally done.
To start the lesson, I discuss with my students about why it is important to be able to explain your answer to a story problem. They need to know why it is important to do this in order for them to buy into this process (and not just for the test either). This year, I gave them the example that President Obama is trying to solve the problem of finding a way for universal health care to work in our economy. If he comes up with a solution, some people may not understand all the details behind his solution. As a result, he needs to be able to effectively communicate his ideas so that everyone can understand his solution.
After that, I ask my students about what makes a good solution to a short answer problem. The ideas my students come up with can be simplified to two main ideas:
1. Use the 6 traits of writing
Our district is big on the 6 traits of writing. Since the solutions to short answer problems involve writing, I feel the 6 traits should also be included. I try to be a little more specific by telling my students to use complete sentences, proper vocabulary, sentence fluency, and labels. I think the question should be restated within the first few sentences of your answer.
Instead of an answer that says "I timesed 6 by 8 to get 48," (which used to be a common answer) I tell them a much better answer would be "To find the area of a rectangle, you multiply the length by width. Since the length is 8 feet and the width is 6 feet, the answer is 48 square feet because 6x8=48." Notice how you can figure out what the question is based on my solution without even seeing the actual question.
One thing that I tell my students is "If you make it sound like you know what you are talking about, even if you don't, chances are you will impress the reader enough to give you a higher score." They seem to buy into that pretty well.
2. Explain your thinking
This is definitely the hardest part for students to do, but as teachers, you have to coach them on how to do this. Like I stated before, many of them could describe the process of getting an answer verbally, but they just don't get how to do it in writing.
In explaining your thinking, this is where sentence fluency helps. I tell them to just describe their steps in order of how they solved it. For example, "First, I did this. Then I did this. Next I did this." Using those transitional words will really help to organize their thought process.
Just because the student describes the steps in order of how they solved it doesn't mean they understand what they are talking about. I also tell them to describe why they did a certain operation. If they said they added 5, 7, 12, and 3, I would want them to describe why they added these numbers. By doing this, it will solidify that they know the concept.
Sometimes I have students that will tell me they still don't know how to explain their answer. I can see they have a solution, but they don't know how to explain it. I will nonchalantly ask them what they did. I might toss in a "Why did you do that?" After they get done telling me, usually I can see they know what they are talking about. I then tell them, "Everything that you just told me, write that on paper." It's a simple strategy, but usually it works.
After we discuss these ideas, I feel it is important to immediately let them try a constructed response problem on their own. I give them a problem and let them work on what they think a good solution would be based on the ideas we just talked about. After 5-10 minutes, depending on the difficulty of the problem, they share answers. Other students and myself provide constructive criticism on their solutions. Modeling a good solution is also a great idea as the students can see what is expected of them.
Sometimes having a teacher generated response isn't the best idea because the students will downplay the expectations as the math teacher is supposed to be the smartest one in the room. Instead, show student responses that meet your expectations. The Massachusetts Comprehensive Assessment System website may be good resource for this as you can search for questions based on grade level, subject level, and question type. If you toggle the answers on, you can also see sample responses from students.
I spent about a one class period going over these expectations, but I also have them practice periodically throughout the year and continue to model good solutions.
Our state tests have 2-3 constructed response problems that our students need to solve. They are given a problem of elevated difficulty and they are expected to find the answer and describe how and why they came to their solution (see question #11 or #18 on this sample test). The students in my district typically do very well on the state test, but these types of problems are the ones that seem to give them troubles.
I decided to attack this problem last year. Describing your thought process or explaining why something is correct is hard for students to do, especially if they've never had to do it before. I don't think I ever had to explain my thought process in words until I got to college, and even then I struggled at the beginning. I could do it verbally, but putting those thoughts on paper was just something that was not normally done.
To start the lesson, I discuss with my students about why it is important to be able to explain your answer to a story problem. They need to know why it is important to do this in order for them to buy into this process (and not just for the test either). This year, I gave them the example that President Obama is trying to solve the problem of finding a way for universal health care to work in our economy. If he comes up with a solution, some people may not understand all the details behind his solution. As a result, he needs to be able to effectively communicate his ideas so that everyone can understand his solution.
After that, I ask my students about what makes a good solution to a short answer problem. The ideas my students come up with can be simplified to two main ideas:
1. Use the 6 traits of writing
Our district is big on the 6 traits of writing. Since the solutions to short answer problems involve writing, I feel the 6 traits should also be included. I try to be a little more specific by telling my students to use complete sentences, proper vocabulary, sentence fluency, and labels. I think the question should be restated within the first few sentences of your answer.
Instead of an answer that says "I timesed 6 by 8 to get 48," (which used to be a common answer) I tell them a much better answer would be "To find the area of a rectangle, you multiply the length by width. Since the length is 8 feet and the width is 6 feet, the answer is 48 square feet because 6x8=48." Notice how you can figure out what the question is based on my solution without even seeing the actual question.
One thing that I tell my students is "If you make it sound like you know what you are talking about, even if you don't, chances are you will impress the reader enough to give you a higher score." They seem to buy into that pretty well.
2. Explain your thinking
This is definitely the hardest part for students to do, but as teachers, you have to coach them on how to do this. Like I stated before, many of them could describe the process of getting an answer verbally, but they just don't get how to do it in writing.
In explaining your thinking, this is where sentence fluency helps. I tell them to just describe their steps in order of how they solved it. For example, "First, I did this. Then I did this. Next I did this." Using those transitional words will really help to organize their thought process.
Just because the student describes the steps in order of how they solved it doesn't mean they understand what they are talking about. I also tell them to describe why they did a certain operation. If they said they added 5, 7, 12, and 3, I would want them to describe why they added these numbers. By doing this, it will solidify that they know the concept.
Sometimes I have students that will tell me they still don't know how to explain their answer. I can see they have a solution, but they don't know how to explain it. I will nonchalantly ask them what they did. I might toss in a "Why did you do that?" After they get done telling me, usually I can see they know what they are talking about. I then tell them, "Everything that you just told me, write that on paper." It's a simple strategy, but usually it works.
After we discuss these ideas, I feel it is important to immediately let them try a constructed response problem on their own. I give them a problem and let them work on what they think a good solution would be based on the ideas we just talked about. After 5-10 minutes, depending on the difficulty of the problem, they share answers. Other students and myself provide constructive criticism on their solutions. Modeling a good solution is also a great idea as the students can see what is expected of them.
Sometimes having a teacher generated response isn't the best idea because the students will downplay the expectations as the math teacher is supposed to be the smartest one in the room. Instead, show student responses that meet your expectations. The Massachusetts Comprehensive Assessment System website may be good resource for this as you can search for questions based on grade level, subject level, and question type. If you toggle the answers on, you can also see sample responses from students.
I spent about a one class period going over these expectations, but I also have them practice periodically throughout the year and continue to model good solutions.
