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The following is a copy of the handout given to participants at the 1995 NCTM Regional Conference held in Phoenix, Arizona Presenters: Dan Dillon & Deby Valdez
A FEW WORDS FROM YOUR PRESENTERS:
During a combined total of more than 25 years of teaching we have learned many things. One of the most shocking discoveries we had to face up to was that the majority of students entering our classroom had things more important to them on their minds than doing math. We are all teaching in an ever changing world. We have to compete with technology for the attention of our students. Our students are surrounded by outside stimuli constantly: TV, Movies, Music, Nintendo to name just a few.
Over the years we have tried numerous methods to gain and hold the attention of our students. What we have shared today are several of the best "Engine Starters" we have come across. We all need to remember that anything will become boring to a student if they are exposed to it day after day. We want to encourage you to be creative. Experiment with different ways to start your class. Find some class starters that fit your personality and that your students seem to enjoy, but DON'T OVERDUE any of them.
Attached you will find everything you need to know to enter your classroom on Monday morning and start class a little different than you did this past Friday. There are a lot of resources out there, have fun looking for more exciting ways to start your classes in the future.
If you ever have any questions or concerns please call either of us or feel free to send any information to us at the address below. ............See "About The Instructor"
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WALK ON WATER
Marcia was a Magician by trade. However, her fans were hard pressed to believe she would be able to perform the advertised feat - walking on water. The lake on the edge of town was chosen for the event. At the announced time, Marcia did walk on the surface of the water. How did she do it?
(Answer) The lake was frozen
ENLIGHTENING TAKE
Elsa was very clever. One of her tricks was to turn off the light in her bedroom and get into her bed, which was five feet away from the light switch, before the room was dark. How did she do it?
(Answer) It was still light outside when she went to bed.
TRAIN TUNNEL
Two train tracks run parallel except for a spot where they go through a tunnel. The tunnel is not wide enough to accommodate both tracks, so they become a single track for the distance of the tunnel. one afternoon a train entered the tunnel going in one direction, and another train entered the same tunnel going in the opposite direction. How did they avoid the accident?
(Answer) They entered the tunnel at different times of the day.
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This is a probability activity that can last for a week, a month, a quarter or all year if you want. I randomly select 10 colored marbles to put in the box (I don't even know what is selected) I have a hole punched in one of the corners of the box on the bottom. Each day I will ask four or five students to look in the hole and tell me what color they see. We keep a tally going on the board. They then start making predictions as to what they think is the color combination in the box. This is a really interesting activity because you let them guess and then ask if any student is willing to risk their grade to make a prediction. This doesn't happen for a really long time. (This activity has nothing to do with a students grade in my class)
In the past I have had a combination like 6 whites, 3 blacks and 1 yellow. For the first week or so the yellow marble may never have been seen and then low and behold there it is and it blows the kids away. These are some possible results that could have been obtained.
1st Inspection: W, W, W, B, B
2nd Inspection: W, W, B, B, B
3rd Inspection: W, W, W, W, W - This would probably really confuse
them.
4th Inspection: B, B, B, W, Y - The yellow appears. You may want
to bring up the possibility that there may still be a green marble
in the box. All we know now is that there are at least three different
colors.
Only on a rare occasion will the box ever be opened. After making enough inspections the classes usually come to agreement as to what has to be inside the box. They are very curious at the beginning but feel very confident after around 100 trials or so.
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You tell the students that you have selected one word out of a dictionary that you hold up. They are to find the word by asking questions that can only be answered by saying yes or no. I try to pick a word that has something to do with the lesson for the day. If we are talking about long division my word may be "remainder". Students at first will just start randomly guessing after the first few questions. I will make comments like, "well that is one word down now only 79,999 left to go." After doing this activity several times they will begin to learn that they need to start narrowing down the field. They will start asking questions like, "Does it start with the letters A through M?"
A variation of this activity can be "I AM A FRACTION, WHAT AM I?" This will lead to questions like, are you improper, etc.
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This is a great activity, especially on days when you have about 5 minutes of prep work to do at the beginning of class. Once the students are familiar with this activity they do not need the teacher to help run through it.
The cards are passed out at the beginning of class. I try to make sure that each student has at least two cards. I hold one card back to start with. I would read my card. "I have 24, what is this number divided by 6 then times 8?" The student that has 32 on their card would stand up and say, "I have 32...." then they would read their card.
You can have several decks of cards printed up to cover different topics. This can be used as a great way of reviewing facts. Once square roots are introduced you can include clues like, "What is my number plus the square root of 64?" If you are studying geometry terms you may want to include questions like, "What is my number plus the number of sides of an octagon?" You can make these as easy or as hard as you want.
To make a set of cards it is real important not to repeat an answer. I start with a blank sheet of paper and in a column at the left I write down a number then I start writing a question. Lets say my first number was 4. My question may be, "I have four, what is this number squared?" I now write 16 in my column and write my second question. "I have 16, what is this number divided by 8 then added to the number of sides of a pentagon?" Make sure that the answer to your last question ends up being the first number in your column, in our case 4.
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This is a take off from a game that my father used to play with me when I was growing up. He would take the following 10 cards from a deck of cards: Ace, Two, Three, Four, Five, Six, Seven, Eight, Nine and Ten. He would then select four cards and I would have to try and come up with a problem that would have an answer of 24. The rules were that I could use, Multiplication, Division, Addition and/or Subtraction as many times as I needed to. I must use each of the numbers, but could only use them one time.
SAMPLE PROBLEM: Numbers selected: 3, 7, 9, 4
Possible Solution: (3 x 4) x (9 - 7) = 24
If you have a really sharp student in your class that finishes before any of the other students just ask them, "Now can you find me some other problems, using the same four numbers that have 24 as an answer?"
Variation: You can select one number and then have the students use the numbers 1, 2, 3, & 4 to come up with a problem that equals your selected card. You can also just put a number between 1 and 24 on the board and have them use 1, 2, 3 and 4 to come up with a problem.
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RAINBOW LOGIC (Adapted from "Family Math" by Stenmark, Thompson and Cossey)
BEFORE YOU START It would help to have the following prepared
for your class before beginning the activity. On a blank white
business envelope have two grids drawn. One grid should be a 3
x 3 grid and one should be a 4 by 4 grid. (See below) In the envelope
you should have squares corresponding to the same size of squares
on your grid. You will need four squares of four different colors.
(example: Red, Blue, Yellow and Green)
The WHY of this activity: To practice deductive thinking and spatial reasoning.
The HOW of this activity: Lets first play Rainbow Logic on the 3 x 3 grid even though the rules are basically the same for either grid. The leader must fill their grid with three different colors. He must use three squares of each of the colors and the squares must be arranged in a "legal" manner. To be legal each square must share at least one full side with another square of the same color. For example, the following are legal arrangements.
Players ask for the colors in a row or a column (rows are horizontal, columns are vertical.) The leader gives the colors, but not necessarily in order. The leader should allow time for the players to discuss what they have learned after each guess before giving a new clue. The goal is for the players to be able to give the location of all colors on the grid after as few questions as possible. Each player should use their gird and colored squares to try and keep track of the clues. Clues are continued to be given until someone can correctly identify the arrangement on the leaders grid. When everyone is familiar with the game you can use the 4 x 4 grid. The rules are the same. except you will use four squares of four different colors. Example of some legal arrangements are given below.
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This activity, along with many of the activities that I have found successful in my classroom, come from "Family Math". This activity can range from a very easy version to quite difficult. It is a take off from the "Master Mind" game that many of us have played in the past.
Lets start with an easy version. You pick a four digit number where digits have to be either 1, 2, 3, 4 or 5 and they can not repeat. You place your 4 digit number in the first four squares on the overhead sheet that you prepare (A black line master is provided for you on the next page). The students then try to determine your number. You say PICO for every number they have correct but in the wrong place, you say FERMI for every number they have correct and in the correct place and you say BAGEL for every number that does not belong at all. For example: Lets say your number was 3425 and the following guesses come from your students.
1234 - You would say: PICO, PICO, PICO, BAGEL because they have three numbers correct (the 2, 3 and 4) but all are in the wrong spots and you have one number (1) that doesn't belong at all. [Notice that I did not give the clues in order of the numbers they selected]
2135 - You would say: PICO, PICO, BAGEL, FERMI because the 2 and the 3 are the correct numbers but in the wrong place, the 1 doesn't belong and the five is in the exact right place.
4325 - You would say: PICO, PICO, FERMI, FERMI because the 4 and the 3 are correct but in the wrong place and the 2 and 5 are in the exact right places.
3425 - You would say: FERMI, FERMI, FERMI, FERMI because all four numbers are in the exact right places.
At first students just guess and you will have to help them start using their reasoning skills. After two or three times they will really work hard to come up with the correct answer as soon as possible. I move around the room and let students from each of my 9 groups of four take turns trying to find the answer. Like I said earlier you can make this even more difficult by eventually picking a five digit number made up of any digits, even repeating digits - I have never gotten this hard with my 7th graders. You will probably need to make a different overhead sheet, one which shows more choices.
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I KNOW YOUR NUMBER "Base 2" number puzzle.
This puzzle is based on "Base 2". For most classes you will have to end up telling them how the puzzle works. But keep them guessing for as long as possible. You may be surprised that a student may finally figure it out. Let them stay after class to copy down the numbers if they want to take it home and try to figure it out.
The numbers on the five cards are arranged as follows:
Notice that the first number in the upper left hand corner is a power of 2 (1, 2, 4, 8, 16). In base 2 each place value is represented by a power of 2. Our ones place is still the 1 but our tens place is now 21 or 2, the hundreds place is now 22 or 4, the thousands place is now 23 or 8 and so on. When a person tells you that their number is on a certain card then you know that their number contains the power of 2 that the card represents. I have broken it down a little more below to show you how to determine what numbers go on each card.
NUMBER 20=1 21=2 22=4 23=8 24=16
5 YES NO YES NO NO
8 NO NO NO YES NO
12 NO NO YES YES NO
28 NO NO YES YES YES
30 NO YES YES YES YES
31 YES YES YES YES YES
You may decide that you only want to start with three cards. This would mean the student would have to pick numbers between 1 and 7... numbers 8 and above would require the fourth card. You may even decide to expand your game. What numbers would you place on your 6th card? How high could the number be that your students selected?
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Game #1 - Get the children to decide upon a gatekeeper who will check their "tickets". The tickets are attribute blocks chosen by the children. When somebody approaches the gate they will show their "ticket" to the gatekeeper who will have decided what he will allow to proceed. Anybody who can correctly identify what is being collected will take the place of the gatekeeper. The gatekeeper may only allow "red" through or "circles" or "small", etc.
Game #2 - In this game there are two gatekeepers. Tickets are shown to Number 1 and then to Number 2. All the squares will get past the first gate, but only those that are large will get past the second gate. We have selected the set "Square and Large". It could have been "Round and Small", or "Triangle and Red", etc.
Game #3 - The gatekeeper selects one attribute block or attrilink. Each time a person brings a tickets the gatekeeper will respond either yes or no. This indicates that at least one attribute is contained in their ticket. When a person thinks they have solved the problem they state, "Gatekeeper may I pass with a "Large, Red, Think, Circle"? (Only allow them to make guesses after several tickets have been presented to the gatekeeper) At this the gatekeeper will respond either yes or no - the individual with the ticket does not know which attributes or how many are contained when the response is "no".
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Place a grid on the overhead. This can be a complete coordinate grid containing all four quadrants or just the one positive quadrant. Students have to tell you where to place their X or O. Once they tell you where to place their mark it can not be changed. The first group to have three in a row (You can use four or five in a row if desired) is the winner. This is an amazing way to introduce negative numbers on the number line to students. They can get a feel visually where the numbers are on the number line as they play this game.
* A complete 4 quadrant coordinate graph is on the next page. If only the positive quadrant is desired you can cover up the other three quadrants.
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