I am reviewing Binomial Expansion with my support kiddos and I wanted an activity that had them working. I had them break-up into partners and then explained the activity. I had the following chart on the board to help explain.
I printed 6 copies of the pdf attached below and cut up the problems and placed them in the bags above. Problems 1-6 where in Bag A, 7-12 in Bag B, 13-18 in Bag C, 19-64 in Bag D, and 69-100 in Bag E. I increased the point value as the problems increased in difficulty. LEAVE THE QUESTION #S ATTACHED TO EACH SLIP OF PAPER. (Trust me, this will save your sanity) I also need to mention that I did not create the worksheet or answer sheet--I believe as the pdf states, that Steve Blade did. Thank you Steve Blade!
I then let students pick which bag to draw a problem from and I recorded the problem number on my grade sheet in the corresponding Bag letter. The last page of the PDF has all solutions on it. I just looked at the number on the slip and checked it with the corresponding number on the solution page! The advantage of printing multiple sheets and having students draw, this eliminated groups working together or copying off each-other. I did not let students pick another problem till they got their current one correct.
What I liked:
1) Gave students the opportunity to choose what type of problem they complete
2) Limited the number of types of problems the did to 3 of each kind
3) Gave students the flexibility to earn a higher grade and their grade was a true reflection of their effort
1) Encourage students to try all bags--I had students get stuck on the harder problems from Bag E and waste a good bit of time
2) I let my students earn up to a 130 on this assignment
I LOVE when I can bring the life of a mathematician into a lesson. Binomial Theorem/Expansion is a great example of this!
I always introduce Binomial Expansion by first having my student complete an already started copy of Pascal's Triangle. This is one warm-up that every student does without prompting. They see it as a puzzle and not "math" but you may have to encourage students to keep looking for the pattern. When they enter the classroom, I hand them the sheet, wear a beret, and only speak in French. My french is limited and it is easy to see who the French students are on how they respond to my questions. I keep up the French speaking through the warm-up and then I go into the life of Blaise Pascal. (Source: http://en.wikipedia.org/wiki/Blaise_Pascal)
Once that is done I introduce Binomial Expansion and tie that into Pascal's Triangle. I find that this method makes Binomial Expansion a little more exciting. Now, while I find BE very thrilling and life-changing, my students typically do not. I find the French speaking and little history lesson make a somewhat less thrilling topic a little more exciting.
I also recommend teaching your students how to logically expand these problems and not have them memorize the different formulas. This is a concept were students can pick up on the pattern quickly and ignore the formal definition of the formula!
I find when teaching how to write the equations of lines the best progression is as follows:
1st: Graph the function when given the equation
2nd: Match a given graph to its equation
3rd: Write the equation of function given its graph
I feel that this order helps students complete the last task better.
For this matching game, I printed the solution page of the worksheet from kuta(http://www.kutasoftware.com/freeia2.html) and cut the equation and graph on separate index cards for each group. I knew my students would find it easy and it allowed the kiddos to work with one another on a task that was not that long. I planned on using this the opener to my student's review day for their upcoming quiz but then I started to make them. To make one set took me 10 minutes and I was planning on making 10. I made 2. I plan on making the rest to use for next year-I will be making these while watching a movie or getting a student to make them! While we reviewed, I handed out the index cards to students who where done and had them match with the sets I had completed. It worked well to keep those students working with something they find 'fun'!
I also attached the notes I give my students when we first look at the writing the equation of an absolute value function graph. The lesson went well--my students typically find it "easy" and nice break.
I see it as the calm before the storm. Piecewise functions are next.
Absolute Value functions hold a dear place in my heart. I love the "V" shape graph that is produced and I love that the absolute value graph is ALWAYS symmetric.
Once again, the summer math revision team at Fulton County did a great job at providing awesome graphic organizers to use for this topic.
We completed each sheet in class--this was a review lesson of a topic covered in the fall so it went very quickly and throughout the lesson I heard my students say "Ah, it makes sense now." That is always good to hear!
The math Fulton County School summer revision team had this great sheet to use when teaching how to solve absolute value inequalities. I love it! ! It is easy to read, easy to fill out, clear, and a great tool for students to use while learning the different situations when solving absolute value inequalities.
I covered solving absolute value equations with my freshman today. It is a concept that students typically catch on quickly to. The only new part is setting the equation inside the absolute value bars to the same and opposite to the number that the equation is equal to. Once again, for these topics I like to end the class with an interactive activity rather then drill and kill problems. I found the game modeled after "Who Wants to be a Millionaire." I divided my class into 2 groups and then showed the site on my projector and we played! To make things easier on me, I assigned one person in each group to be the official answer. I just listened to that person. The game is great and my students enjoyed it. The one snag...it was easy so once a team got picked they got all the questions right and never switched to the other team. I guess it is a good problem to have--the team that won the coin toss got all the problems right!
1) Will have students play against each other 1 to 1 in the computer lab
2) Will have all students write and work out each problem
Enjoy!I have attached a copy of the notes that I distributed to my students.
Georgia has brought in a good bit of probability and stats into the high school math curriculum. Which I LOVE! There is a new movement (well discussion of a movement) to switch the focus of getting students prepared for statistics as opposed to calculus. The reasoning being that most careers need more stats than calculus. For those careers that are more heavy in calculus it is assumed that those students choosing those paths are stronger in mathematics and can master concepts with less instruction time. I see the value in both. Stats is a little more easy to show students how they will use in the world they live in presently.
This is why I love teaching the multiplication counting principle--it is easy for students to understand and easy to make connections to the real world. After I teach the multiplication counting principle, I have students break-up into groups and create a restaurant to answer the following questions.
1) Name a restaurant you and your group will open
2) Create a menu with at least 2 different food categories
3) Find the total number of combinations available at your restaurant using…
a. the Multiplication Principle of Counting
b.a tree diagram
4) Write and solve a probability problem pertaining to your eatery
This activity also serves as a great refresher of past concepts and reinforcing how each is different but connected at the same time!
Technology has changed how we all receive information. Learning is no exception. While there are some annoying parts of technology-constantly having to tell me students to turn off their cellphones--there are many great teaching strategies to use.
YouTube is my favorite source!
1st: If a student is absent I can send them to a YouTube video to watch to learn the lesson (reserve learning-which I do plan on trying at some point this school year)
2nd: Use it to re-teach a lesson--this is especially beneficial to my support students
3rd: Introduce a topic or make a problem more interactive to support a lesson in class
How I use YouTube in each of those 3 categories...
1st and 2nd: YayMath is produced by an energetic teacher that has enertaining videos on topics covering Algebra, Algebra II and Geometry. I also encourage students who are gone to watch other videos when they missed a day or do not understand an objective and cannot come in for extra help. For my support students, YouTube provides another way to address an objective in a more exciting way then me writing on the board. It provides a 3rd presenter (1st: Math 3 Teacher, 2nd: Math 3 Support Teacher) on a topic.
3rd: I will use YouTube videos to introduce the Quadratic Formula Song, my Barbie Bungee Project, and the Fibonacci Sequence
YouTube is awesome! Just make sure that you watch a video completely before you show it to your students. This source provides a great way to make math a little more interactive and my students enjoy hearing a different voice (and especially when I do not sing for them, they really really appreciate not having to hear me sing!)
During November 2010, I went to the Tennessee Independent Schools Bi-Annual conference held at the Baylor School in Chattanooga, TN. I was impressed with Baylor's picturesque campus, campus dormitories (which I did convince a teacher from Baylor to sneak me into on-way, way larger than my closet of a room at Tech), and their amazing math department who are incredible innovative. My first post about chalking was from one of the teachers from Baylor. I sat through a presentation on how a 7th grade teacher had her Pre-Algebra kiddos create an 3-D animal from paper towel rolls, shoe boxes, and similar material and then find the area and volume of their animal. Her Algebra students where jealous so she had them draw animals on graph paper (using all straight lines) and then find the equations of particular lines. This the part that I borrowed!
I did this project with my 7th graders in Memphis and then my 9th graders in Atlanta. The class subjects are the same so the material was relevant to both. For both classes I asked them to draw an animal on graph paper using only straight lines. I did not tell them what the purpose was. My 7th graders completed this while having a sub one day and my 9th graders completed this for homework the night after a test (100% completion rate!) I also had them go over their final animal in pen. I then collected them and made a photocopy of them. The students got the original back and their copy. I asked them to decorate the copy and use the original to somehow label the lines they defined on a separate sheet of paper. The final version included the original animal, the decorated animal, and then the equation sheet on a poster board with the rubric on the back.
1st: Will do this project again
2nd: Took forever to grade so may consider this a partner project to lessen the grading part
3rd: Will allow more class-time to work on the project
4th: Will use strong student examples from the past in the introduction of this project
5th: May expand theme on animals to something like school spirit
I love the idea of my students having fun in class but I find it hard to develop/find games/activities that are productive to learning or practice. It takes a good bit of trial and error and reflection. For me, I use short games that can be explained, completed, and cleaned-up in less than 15 minutes (it may roll into 20 minutes depending on the day.) I really really want to use JEOPARDY games in my class as a review but I have not been able to successfully pull that off where all students learn/practice/benefit from the game.
The activity I am attaching (I in no way deserve credit, I found it online) is GREAT! Students are in groups of 3. 1 moderator and 2 players. I will assign who-is-who. I usually have the strongest student out of the 3 be the moderator. I have the moderator come up and get the board, instruction sheet with the answers on the reserve side, two dice (or "number cubes" as we call them in Georgia), and a handful of two sided coins. The beauty of this activity is that I have the moderator read the instructions to their group-I rarely have questions, it is pretty self explanatory.
The Game1. Decide who goes first by tossing a die.
2. The first player tosses both dice and locates the corresponding box on the
game board. For example, if the player tosses a 3 and a 4, they may go
to the 3rd row, 4th column, or the 4th row, 3rd column.
3. The player factors the problem and asks the moderator if he/she is correct.
If the solution is correct, the player places his/her marker in that box. If
the solution is incorrect, the other player can steal the box by giving the
4. If a player tosses the dice and the box indicated is already occupied, the
player rolls the dice again.
5. The winner is the player who has four of his/her game markers in a row(row, column, or diagonal).Materials NeededGame Board (I laminated my)Instruction Sheet with copy of answers on the back for moderator Two diceChips of two different colors (Georgia gave all high school teachers a box full of goodies)I also reserved this and made the answer sheet the game board and the game board the answer sheet to have my students play a game when we learned to multiply binomials with FOIL (I know some people dislike FOIL).If one group finished quickly, I will have them switch moderators and play again!Hope your students enjoy it as much as mine did!
Educator who loves math and working with students.