Friday, October 17, 2008
Response to Teaching Lesson
I think it is important to teach students as to why rules are such. Simply telling students that you cannot divide by zero is not an effective way of teaching. The lesson plan was effective because it allowed students to link together different concepts learned, possibly in a previous lesson or previous grade. The lesson also incorporated different teaching styles. There was an explanation displayed on the board, this is effective for students that need concrete examples for learning. This form of teaching let students learn through breaking down examples. Furthermore, added to the lesson were the verbal cues provided by the teacher, this will help students who learn better through auditory senses to gain knowledge of the concept. The aspect that I really like was the second form of teaching, graphically. This way of teaching allowed for students who didn’t quite understand from the first analytical style another chance to grasp the same material. Just as displayed in this micro lesson, I think it is vital to provide students with many opportunities to learn, through many different teaching methods. It is important to give students many opportunities to be engaged by math, as not all students learn through the same styles. To extend this lesson I would possibly set it up so students work together to build a story to present to the class about dividing by zero.
Poem
What is zero?
I am zero, but what does this mean?
Am I nothing, irrelevant and empty?
Do you consider me to positive, negative or neither?
Or is zero even a number at all?
I am zero, but what does this mean?
I am the score at the start of every soccer game.
I am the point at which water will freeze.
There is no distance between you and me.
I am zero, but what does this mean?
Divide by me and get no answer
Multiply by me and always get the same answer
I am zero, so many uses you’ll see.
I am zero, but what does this mean?
Am I nothing, irrelevant and empty?
Do you consider me to positive, negative or neither?
Or is zero even a number at all?
I am zero, but what does this mean?
I am the score at the start of every soccer game.
I am the point at which water will freeze.
There is no distance between you and me.
I am zero, but what does this mean?
Divide by me and get no answer
Multiply by me and always get the same answer
I am zero, so many uses you’ll see.
Free writing - Divide and Zero
Divide
When thinking about the word “divide” the first thing that comes to my head is division. I think about splitting things up, as in dividing a PE class into four teams. I’m sure the word divide can be taken into many contexts and now that I think about I’m sure that a form of the word divide is used in everyday of my life. Our classes at UBC are sometimes divided into two or three classes throughout the week. My day is divided in many ways as well, there is the time I spent at home and the time I spend at school, the time I spend travelling between the two, all of those aspects divide up parts of my day. Thus far the way I have talked about the word divide has been a view in which something is taken and split up into smaller pieces, but what about when in school we divide by a number smaller than one we get a larger number.
Zero
When I first think of zero the number zero is what pops into my head. Then I start to think what value does zero have, does zero mean nothing? Why is zero not the freezing point in Fahrenheit degrees with respect to temperature yet it is when using degrees Celsius. Zero is what is used as an initial value in most sports, games typically start with score 0-0. But why zero, and why is it called zero. My whole life I have learned that zero is essentially zero. There has been no explanation really as to what zero is and what zero means. Zero could possibly be seen as the most important number, because it acts as the starting value for so many situations.
When thinking about the word “divide” the first thing that comes to my head is division. I think about splitting things up, as in dividing a PE class into four teams. I’m sure the word divide can be taken into many contexts and now that I think about I’m sure that a form of the word divide is used in everyday of my life. Our classes at UBC are sometimes divided into two or three classes throughout the week. My day is divided in many ways as well, there is the time I spent at home and the time I spend at school, the time I spend travelling between the two, all of those aspects divide up parts of my day. Thus far the way I have talked about the word divide has been a view in which something is taken and split up into smaller pieces, but what about when in school we divide by a number smaller than one we get a larger number.
Zero
When I first think of zero the number zero is what pops into my head. Then I start to think what value does zero have, does zero mean nothing? Why is zero not the freezing point in Fahrenheit degrees with respect to temperature yet it is when using degrees Celsius. Zero is what is used as an initial value in most sports, games typically start with score 0-0. But why zero, and why is it called zero. My whole life I have learned that zero is essentially zero. There has been no explanation really as to what zero is and what zero means. Zero could possibly be seen as the most important number, because it acts as the starting value for so many situations.
Citizenship Article Response
From the article I took that it is important for us as math teachers to teach for learning outside the classroom. Math is essential in everyday life, no matter where you go and what you do there is typically some form of math in our world. It is essential that we teach students that they can apply the knowledge they gain in class and apply it to their everyday lives. From my days in high school, I remember that math was typically viewed as a boring class, based solely on lecture notes. I feel that if we give the students the ability to apply math to their own worlds they will be more easily receptive to math. With this in mind we must also remember that we are still obliged to fulfill prescribed learning outcomes. However, I recall from my interview with a math teacher that he feels that he now has more creative ability with the in the math provincial, as it is now optional. My other subject in education is physical education; here we discuss providing students with skills that will lead to healthy living and providing it in such a way that students will be able to apply these skills for their whole life outside of school. Math must be taken in the same context in my eyes. Math is probably the most prominent subject that can be used daily along with physical education. When we drive we need to know what speed limits mean, we need to know how much change we should receive, we need to be able to tell time. Management of numbers is vital in everyday life and we need to realize this in our society, as I am sure that the other twenty six students in this class know this, but not everyone else sees this.
Friday, October 10, 2008
Lesson Plan
Teaching objectives
To teach ‘equivalent fractions’ in a more ‘engaging’ manner.
Learning Objectives
The students will be able to recognize some fractions that have equivalent values.
Students will be able to add fractions with common denominators.
Students will have an opportunity to consider adding fractions with different denominators by first changing one or both fractions to equivalent fractions.
Bridge
Today we are doing jigsaws. But instead of pictures we are going to be using fractions.
Explain FREEZE including perhaps allowing which ever half of the class wins freeze most often, gets to leave first at the end of class.
Pretest
5 mins
Hand out sheet – 12ths, 6ths, already on. Ask students to complete outlines for 4ths, 3rds & halves and give an example on the whiteboard. They can then colour them in with pencil crayons not markers FREEZE –we would ask students to colour in the new bits that they have drawn on the sheets to make them feel more attached to it but you guys aren’t going to get that chance.
As they are drawing these, hand out the blocks. Put them loose on one table, in bags on another table with instructions not to touch and no blocks on the other tables. FREEZE you will notice that we have put some blocks on the tables. You need to consider very carefully when exactly you want the students to have access to manipulatives. See what’s happened here.
Once most of the students have finished drawing, ask them for their attention. Freeze – it is very hard to stop students doing something part way through so you may want to give both instructions 1 and 2 at the beginning. However, if you are stopping them, you may well want to do something like ask them to turn around to face you and fold their arms to reduce the temptation to carry on drawing while you are talking. If any of you here tonight draw while we’re talking you’ll get your knuckles rapped with a ruler!
Put a few simple fractions on the board and ask students to find some equivalent fractions, using blocks and fraction sheet to help, and ask them to put their hands up to offer their answers.
Activity
10 mins
We are going to do fraction jigsaws. You will each have a jigsaw of your own to complete but you can work together in groups of two or three if you wish. FREEZE - If the teacher continues talking now you will not have the attention of many of the students because they will be figuring out their groups of three. So either, say “You can collaborate in groups of two or three so let’s sort out those groups now and you can move to be close to the others in you group” OR don’t mention groups until you have explained everything else. There are also many ways to arrange groups so you may wish to employ a particular method in this situation in the classroom, but tonight you can just choose yourselves.
Please choose groups of three now and sit with your group.
The finished jigsaw will look like this (overhead of blank completed jigsaw)
Except each white space will have a fraction or a fraction sum on it.
Adjoining pieces must have the same value.
Use the sheet and blocks to help if you wish.
Please finish your drawings and then try to complete the jigsaw. You probably won’t complete it today but you will have time again next lesson (you may wish to number the pieces you have completed before you dismantle it at the end of this lesson)
Hand out jigsaws. Put student’s names on their baggies.
While the students are completing this activity, consider the following
Possible hints:
· Count the number of pieces in the puzzle. What will the dimensions of the finished jigsaw be?
· Some people find it easiest to complete the edges first.
Possible questions:
How did you start with this puzzle?
At what stage did it get hard?
How did you get through that block?
How could it be made harder?
Post test
Ongoing
The post test will be completed during the activity by observing individuals and groups as they are completing the jigsaw.
Resources
Sheet of squared paper with 12ths and 6ths marked on for each student.
15 rulers and pencils
15 sets of blocks in plastic bags (6, 4, 3, 2 cm)
15 jigsaws in plastic bags
Permanent marker.
Overhead projector
Image of blank completed jigsaw
Whiteboard pens
Summary
In addition to completing the jigsaws in the next lesson there are a number of possible extensions.
These include:
Asking students to create jigsaws of their own while considering these questions:
· Would it have been harder if the numbers did not have to be "the right way up"?
· What if the same answer occurred more than once?
· What if there were calculations on the outside edges, rather than grey?
· Can you make a harder (but still possible) puzzle?
To teach ‘equivalent fractions’ in a more ‘engaging’ manner.
Learning Objectives
The students will be able to recognize some fractions that have equivalent values.
Students will be able to add fractions with common denominators.
Students will have an opportunity to consider adding fractions with different denominators by first changing one or both fractions to equivalent fractions.
Bridge
Today we are doing jigsaws. But instead of pictures we are going to be using fractions.
Explain FREEZE including perhaps allowing which ever half of the class wins freeze most often, gets to leave first at the end of class.
Pretest
5 mins
Hand out sheet – 12ths, 6ths, already on. Ask students to complete outlines for 4ths, 3rds & halves and give an example on the whiteboard. They can then colour them in with pencil crayons not markers FREEZE –we would ask students to colour in the new bits that they have drawn on the sheets to make them feel more attached to it but you guys aren’t going to get that chance.
As they are drawing these, hand out the blocks. Put them loose on one table, in bags on another table with instructions not to touch and no blocks on the other tables. FREEZE you will notice that we have put some blocks on the tables. You need to consider very carefully when exactly you want the students to have access to manipulatives. See what’s happened here.
Once most of the students have finished drawing, ask them for their attention. Freeze – it is very hard to stop students doing something part way through so you may want to give both instructions 1 and 2 at the beginning. However, if you are stopping them, you may well want to do something like ask them to turn around to face you and fold their arms to reduce the temptation to carry on drawing while you are talking. If any of you here tonight draw while we’re talking you’ll get your knuckles rapped with a ruler!
Put a few simple fractions on the board and ask students to find some equivalent fractions, using blocks and fraction sheet to help, and ask them to put their hands up to offer their answers.
Activity
10 mins
We are going to do fraction jigsaws. You will each have a jigsaw of your own to complete but you can work together in groups of two or three if you wish. FREEZE - If the teacher continues talking now you will not have the attention of many of the students because they will be figuring out their groups of three. So either, say “You can collaborate in groups of two or three so let’s sort out those groups now and you can move to be close to the others in you group” OR don’t mention groups until you have explained everything else. There are also many ways to arrange groups so you may wish to employ a particular method in this situation in the classroom, but tonight you can just choose yourselves.
Please choose groups of three now and sit with your group.
The finished jigsaw will look like this (overhead of blank completed jigsaw)
Except each white space will have a fraction or a fraction sum on it.
Adjoining pieces must have the same value.
Use the sheet and blocks to help if you wish.
Please finish your drawings and then try to complete the jigsaw. You probably won’t complete it today but you will have time again next lesson (you may wish to number the pieces you have completed before you dismantle it at the end of this lesson)
Hand out jigsaws. Put student’s names on their baggies.
While the students are completing this activity, consider the following
Possible hints:
· Count the number of pieces in the puzzle. What will the dimensions of the finished jigsaw be?
· Some people find it easiest to complete the edges first.
Possible questions:
How did you start with this puzzle?
At what stage did it get hard?
How did you get through that block?
How could it be made harder?
Post test
Ongoing
The post test will be completed during the activity by observing individuals and groups as they are completing the jigsaw.
Resources
Sheet of squared paper with 12ths and 6ths marked on for each student.
15 rulers and pencils
15 sets of blocks in plastic bags (6, 4, 3, 2 cm)
15 jigsaws in plastic bags
Permanent marker.
Overhead projector
Image of blank completed jigsaw
Whiteboard pens
Summary
In addition to completing the jigsaws in the next lesson there are a number of possible extensions.
These include:
Asking students to create jigsaws of their own while considering these questions:
· Would it have been harder if the numbers did not have to be "the right way up"?
· What if the same answer occurred more than once?
· What if there were calculations on the outside edges, rather than grey?
· Can you make a harder (but still possible) puzzle?
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