Week 10 Lesson Plan
This lesson is called Just too Big it is for 3-4 grade. In this activity students create different sized “burgers” using two Cuisenaire Rods of the same color as the bun and one rod of a different color as the burger. In this activity students have the opportunity to describe a geometric pattern, connect a numerical pattern to a geometric pattern and extend and generalize a numerical pattern. Students work in partners to build “just too big burger” using Cuisenaire Rods. The class will make a list of all the just too big burgers they found. As children build “burgers” and compare their constructions, they learn to recognize and extend visual patterns. Some students may notice that for each bun there is only one burger. Another activity students can do is “just too small burgers” and compare the patterns they find to those for the just too big burgers.
Sunday, May 2, 2010
Sunday, April 25, 2010
Week 9
Week 9 Lesson Plan:
Capture The Flag! is a two player game, students take turns placing Cuisenaire Rods on a rectangular gird in an effort to be the one to cover the last empty square. In this activity students have the opportunity to see how rods are related to each other, think in terms of the numerical allure of each rod and develop strategic thinking skills. Once the students have played the game at least three times the class will have a discussion about the game. They will be asked to the kinds of things they thought about when they planned their moves. If the developed a strategy that they think with always work.
Students could play again but reversing the rules: The player who covers the last square loses. They could make up their own rules or limit the colors of rods to be used. As students play Capture the Flag! they engage in logical, numerical and spatial reasoning. In this game, the varied lengths of the rods increase the challenge and so the length of a rod, its orientation and its placement on a rectangular gird must all be considered.
Week 9 Virtual Manipulative:
Number Patterns is found under Number & Operations for 3 – 5. This manipulative helps students in the recognition of simple patterns in number sequences. The patterns are simple enough that there is only one answer the computer accepts. The computer will tell the students when they are correct, which is good that way they can work on their own. Most can be completed by adding a common difference (positive or negative). This is a manipulative that can be used after patterns have been studied in class.
Capture The Flag! is a two player game, students take turns placing Cuisenaire Rods on a rectangular gird in an effort to be the one to cover the last empty square. In this activity students have the opportunity to see how rods are related to each other, think in terms of the numerical allure of each rod and develop strategic thinking skills. Once the students have played the game at least three times the class will have a discussion about the game. They will be asked to the kinds of things they thought about when they planned their moves. If the developed a strategy that they think with always work.
Students could play again but reversing the rules: The player who covers the last square loses. They could make up their own rules or limit the colors of rods to be used. As students play Capture the Flag! they engage in logical, numerical and spatial reasoning. In this game, the varied lengths of the rods increase the challenge and so the length of a rod, its orientation and its placement on a rectangular gird must all be considered.
Week 9 Virtual Manipulative:
Number Patterns is found under Number & Operations for 3 – 5. This manipulative helps students in the recognition of simple patterns in number sequences. The patterns are simple enough that there is only one answer the computer accepts. The computer will tell the students when they are correct, which is good that way they can work on their own. Most can be completed by adding a common difference (positive or negative). This is a manipulative that can be used after patterns have been studied in class.
Sunday, April 11, 2010
Week 8
Week 8 Lesson 1: Add a Clue
Students use their Geoboards to create clues that will complete riddles. In this activity the students have the opportunity to focus on the attributes of geometric figures. Students will use deductive reasoning to refine riddle clues. They will become familiar with the language of geometry. Working in pairs students will each solve a riddle. Once they come up with their own answers to the riddles they will compare answers. Then they each have to add one more clue so that their shape will be the only solution. This activity helps children develop logical reasoning skills.
Week 8 Lesson 2: Shape Puzzles
Students investigate the various ways a particular rectangle can be divided into triangles, rectangles and squares then use their smaller shapes to make and solve shape puzzles. In this activity students have the opportunity to describe shapes using geometric terms. Students also discover some similarities and differences among squares, triangles and rectangles. Working in groups each student uses one rubber band to make a rectangle on a Geoboard. Then they use one more rubber band to divide the rectangle into two or three shapes. Each group copies their shape onto geodot paper which they cut out and place in an envelope. They switch with other groups and solve each others puzzles. This activity develops student’s ability to visualize space and divided geometric shapes in different ways.
Students use their Geoboards to create clues that will complete riddles. In this activity the students have the opportunity to focus on the attributes of geometric figures. Students will use deductive reasoning to refine riddle clues. They will become familiar with the language of geometry. Working in pairs students will each solve a riddle. Once they come up with their own answers to the riddles they will compare answers. Then they each have to add one more clue so that their shape will be the only solution. This activity helps children develop logical reasoning skills.
Week 8 Lesson 2: Shape Puzzles
Students investigate the various ways a particular rectangle can be divided into triangles, rectangles and squares then use their smaller shapes to make and solve shape puzzles. In this activity students have the opportunity to describe shapes using geometric terms. Students also discover some similarities and differences among squares, triangles and rectangles. Working in groups each student uses one rubber band to make a rectangle on a Geoboard. Then they use one more rubber band to divide the rectangle into two or three shapes. Each group copies their shape onto geodot paper which they cut out and place in an envelope. They switch with other groups and solve each others puzzles. This activity develops student’s ability to visualize space and divided geometric shapes in different ways.
Monday, March 29, 2010
Week 7
Week 7 Virtual Manipulative: Diffy
This manipulative is found under Number & Operations (Grades 6 – 8). Diffy is designed to help students practice subtraction. Students have to find the differences of the given number. If their answer is correct they continue till they are done filling in all the answers. If they type in the wrong answer they will not be able to continue on to the smaller squares. Students are able to choose which kind of numbers to use for the difference. Students can pick from whole numbers, integers, fractions, decimals and money. This is a good manipulative to use with students once subtraction has been introduced with one of the five number options.
Week 7 Lesson Plan: From A to Z (Geoboard)
From A to Z is a two player game. Students take turn making secret letters on their Geoboardes and describing them to the other player who tries to make the letters from the information given. In this activity students have the opportunity to identify attributes of lines and communicate specific information. This activity provides students with a way to link mathematics to another important K-2 curriculum area such as language arts.
This manipulative is found under Number & Operations (Grades 6 – 8). Diffy is designed to help students practice subtraction. Students have to find the differences of the given number. If their answer is correct they continue till they are done filling in all the answers. If they type in the wrong answer they will not be able to continue on to the smaller squares. Students are able to choose which kind of numbers to use for the difference. Students can pick from whole numbers, integers, fractions, decimals and money. This is a good manipulative to use with students once subtraction has been introduced with one of the five number options.
Week 7 Lesson Plan: From A to Z (Geoboard)
From A to Z is a two player game. Students take turn making secret letters on their Geoboardes and describing them to the other player who tries to make the letters from the information given. In this activity students have the opportunity to identify attributes of lines and communicate specific information. This activity provides students with a way to link mathematics to another important K-2 curriculum area such as language arts.
Sunday, March 28, 2010
Week 6
Week 6 Virtual Manipulative: Attribute Trains
This manipulative is found under Geometry (Grades 6 – 8). Attribute Trains helps students recognize attributes and the pattern of attributes that appear in the given Train. There are three different attributes to pick from color, number and shape. Students have to recognize which of the three is in the Train and finish it. If a wrong piece is put in it will go back to the pile of pieces. When the train is finished the pattern is given in words. This is a good manipulative to use with students who can solve simple patterns. Since there are three different attributes to pick from it makes it more of a challenge.
Week 6 Private Universe Project:
This week’s Private Universe Workshop 6 – Possibilities of Real Life Problems focused on how students come up with strategies to build their understanding of a real-life calculus problem at a young age. When the problem was first introduced in the video I thought it would be impossible for the students to solve. Then Aquisha came up with a good way to start to solve the problem. The way she went about trying to solve it gives the other students a visual representation of the movement of the cat. Making the scale 50 times bigger was a great idea. With this the students got to see when the cat speed up and how much. One of the things I have likes most about the Private Universe Project is how hand on it is. I think students learn more this way. When they can visual see something it is the best experiences they will get. It is interesting how the students go from thinking the cat was running to thinking he was jumping. They get their ideas from looking a graphs, data and talking to each other. They might not have come up with an exact answer but they all learned something. It was good to hear that they use Math in their everyday life. They take what they learned throughout the years with them forever.
Week 6 Lesson Plan: Counting Colors (Color Tiles)
In Counting Colors students spin a spinner with sectors allocated to the four Color Tiles colors and keep track of how many times each color comes up within a specific number spins. In this activity, children have the opportunity to organize and graph data, determine the probability of the occurrence of unequally likely events. Students will first have to guess which number will have ten spins first. They will take turns spinning and use the color tiles to keep track of the number of times. Once one of the colors reaches ten they will have to stop. And talk about their outcome. Everyone’s findings will be up into a larger class graph. We will talk about their results.
This manipulative is found under Geometry (Grades 6 – 8). Attribute Trains helps students recognize attributes and the pattern of attributes that appear in the given Train. There are three different attributes to pick from color, number and shape. Students have to recognize which of the three is in the Train and finish it. If a wrong piece is put in it will go back to the pile of pieces. When the train is finished the pattern is given in words. This is a good manipulative to use with students who can solve simple patterns. Since there are three different attributes to pick from it makes it more of a challenge.
Week 6 Private Universe Project:
This week’s Private Universe Workshop 6 – Possibilities of Real Life Problems focused on how students come up with strategies to build their understanding of a real-life calculus problem at a young age. When the problem was first introduced in the video I thought it would be impossible for the students to solve. Then Aquisha came up with a good way to start to solve the problem. The way she went about trying to solve it gives the other students a visual representation of the movement of the cat. Making the scale 50 times bigger was a great idea. With this the students got to see when the cat speed up and how much. One of the things I have likes most about the Private Universe Project is how hand on it is. I think students learn more this way. When they can visual see something it is the best experiences they will get. It is interesting how the students go from thinking the cat was running to thinking he was jumping. They get their ideas from looking a graphs, data and talking to each other. They might not have come up with an exact answer but they all learned something. It was good to hear that they use Math in their everyday life. They take what they learned throughout the years with them forever.
Week 6 Lesson Plan: Counting Colors (Color Tiles)
In Counting Colors students spin a spinner with sectors allocated to the four Color Tiles colors and keep track of how many times each color comes up within a specific number spins. In this activity, children have the opportunity to organize and graph data, determine the probability of the occurrence of unequally likely events. Students will first have to guess which number will have ten spins first. They will take turns spinning and use the color tiles to keep track of the number of times. Once one of the colors reaches ten they will have to stop. And talk about their outcome. Everyone’s findings will be up into a larger class graph. We will talk about their results.
Sunday, March 14, 2010
Week 5
Week 5 Virtual Manipulative: Bar Chart
This manipulative is found under Number & Operations Grade Pre-K to 2. This manipulative is a good way to introduce bar chart (bar graph) to students. It could record as many as 12 columns and 20 rows. The students can label the columns whatever they want. I used this manipulative in a kindergarten class. We talked about our favorite colors. Since the colors of the columns are preset I made sure that they were the right colors so that the students did not get confused. After I made the bar chart they each had to copy it on paper. For the younger grades the standard mode would be used which counts the number of filled cells. The percentages mode shows the percentages of the total number that is in each column. This could be used in the upper grades.
Week 5 Private Universe Project:
This week’s Private Universe Workshop 5 – Building on Useful Ideas focused on the teacher’s role in the classroom. As teachers we should always challenge are students. We should get them to think in different ways. Students have to be asked why and how. The teachers in the video asked their students to explain how they got their answer and why they thought it was right. This makes them think more about what they did and how they could change it if needed. The video showed how the students were able to build on what they had learned in the past. It is very important that students are able to recall in the past, not only the day before but years ago. The students recognized how things they learned in the past could be used to solve the new problem.
This manipulative is found under Number & Operations Grade Pre-K to 2. This manipulative is a good way to introduce bar chart (bar graph) to students. It could record as many as 12 columns and 20 rows. The students can label the columns whatever they want. I used this manipulative in a kindergarten class. We talked about our favorite colors. Since the colors of the columns are preset I made sure that they were the right colors so that the students did not get confused. After I made the bar chart they each had to copy it on paper. For the younger grades the standard mode would be used which counts the number of filled cells. The percentages mode shows the percentages of the total number that is in each column. This could be used in the upper grades.
Week 5 Private Universe Project:
This week’s Private Universe Workshop 5 – Building on Useful Ideas focused on the teacher’s role in the classroom. As teachers we should always challenge are students. We should get them to think in different ways. Students have to be asked why and how. The teachers in the video asked their students to explain how they got their answer and why they thought it was right. This makes them think more about what they did and how they could change it if needed. The video showed how the students were able to build on what they had learned in the past. It is very important that students are able to recall in the past, not only the day before but years ago. The students recognized how things they learned in the past could be used to solve the new problem.
Week 4
Week 4 Virtual Manipulative: Number Line Bounce
Number Line Bounce is under Number and Operations grades 3 – 5. This manipulative helps students practice with addition and subtraction of whole numbers. Students work on the number line moving left and right with the given arrows to end up with the given target. Using this manipulative students should be able to understand that there are several different ways to arrive at a given answer. Students first have to put the arrows on the number line and then write the number sentence. What I like about this manipulative is that it does not only use two numbers in the problem but four, it makes it more challenging for the students.
Week 4 Private Universe Project:
This week’s Private Universe Workshop 4 – Thinking Like a Mathematician talked about the Tower of Hanoi Problem which we learned about a few weeks ago in class. The students had to find out how long it would take to solve the puzzle with 100 pieces. The problem was introduced to them by Robert Davis. He showed the students how it might be easier if they simplified the problem. It is important to show students that there are several ways to solve a problem. With this problem the students noticed that there was a pattern involved. The students found that there were many patterns involved. After finding out how many moves they worked together to figure out how long it would take. They came up with the answer of two billion years. In part two of the video it reminds us that we have to let our students figure problems out on their own. We should not always give them the answer right way we should make them think on their own.
Week 4 Lesson Plan: Changing Areas (Color Tiles)
For this week’s lesson I chose Changing Areas. Students will build a Color Tile shape and then find its perimeter. They will have to build other shapes with the same perimeter and then find the area of each of these shapes. In this activity children have the opportunity to measure to find the perimeter of a shape. They will also develop the understanding that figures with the same perimeter can have different areas. What I liked about this lesson is that students are reviewing perimeter and area of shapes. With this lesson students learn that the area and perimeter of shapes are not always consistent with each other.
Number Line Bounce is under Number and Operations grades 3 – 5. This manipulative helps students practice with addition and subtraction of whole numbers. Students work on the number line moving left and right with the given arrows to end up with the given target. Using this manipulative students should be able to understand that there are several different ways to arrive at a given answer. Students first have to put the arrows on the number line and then write the number sentence. What I like about this manipulative is that it does not only use two numbers in the problem but four, it makes it more challenging for the students.
Week 4 Private Universe Project:
This week’s Private Universe Workshop 4 – Thinking Like a Mathematician talked about the Tower of Hanoi Problem which we learned about a few weeks ago in class. The students had to find out how long it would take to solve the puzzle with 100 pieces. The problem was introduced to them by Robert Davis. He showed the students how it might be easier if they simplified the problem. It is important to show students that there are several ways to solve a problem. With this problem the students noticed that there was a pattern involved. The students found that there were many patterns involved. After finding out how many moves they worked together to figure out how long it would take. They came up with the answer of two billion years. In part two of the video it reminds us that we have to let our students figure problems out on their own. We should not always give them the answer right way we should make them think on their own.
Week 4 Lesson Plan: Changing Areas (Color Tiles)
For this week’s lesson I chose Changing Areas. Students will build a Color Tile shape and then find its perimeter. They will have to build other shapes with the same perimeter and then find the area of each of these shapes. In this activity children have the opportunity to measure to find the perimeter of a shape. They will also develop the understanding that figures with the same perimeter can have different areas. What I liked about this lesson is that students are reviewing perimeter and area of shapes. With this lesson students learn that the area and perimeter of shapes are not always consistent with each other.
Sunday, February 21, 2010
Week 3
Week 3: Virtual Manipulative: Fraction - Adding
For this week's Virtual Manipulative I used the Fraction Adding manipulative. This manipulative shows what it means to find a common denominator and combine. Students have to find the common denominator and then add the fractions. Students are able to see what the fractions look like. Being able to see it visually gives them a better understanding of fractions. I like how it lets you add the parts and see what the answer looks like. Also that it tells you when the answer is wrong. The students who have trouble finding common denominator could use the figure to find the common denominator. To find the answer students can drag the representation of each fraction to be added into the blank box on the right. Others could just type in the common denominator and answer.
Week 3: Private Universe Project
For this week’s Private Universe Project I watched Workshop 3: Inventing Notations. When solving math problems we all use different techniques. I think it all has to do with the type of learners we are. I am more of a visual learner that is why when I solved the pizza question in class I made a list. I do not think anyone in our class made a picture but then again we are adults so I do not think any of us would have made pictures. Do you think you would have drawn pictures if this problem was given to you in elementary school?
Students need to be given the freedom to solve a problem how they see fit. Some students will surprise us with the methods they use. It is interesting to see what children can do. They invent their own notations and their own ways of communicating to each other. The fact that they can come up with their own way of solving problems is great but that they can also explain it to their classmates and teachers is even better.
Week 3: Lesson Plan (Pattern Blocks)
Cover The Caterpillar
NJCC Standards:
4.3.2 A. Patterns
Recognize, describe, extend, and create patterns.
4.4.2 A. Data Analysis
Collect, generate, record, and organize data in response to questions, claims, or curiosity.
4.5 B. Communication
Use communication to organize and clarify their mathematical thinking.
Overview:
Children will find combinations of blue and green Pattern Blocks that can be used to cover four yellow hexagons.
Objectives:
With this lesson students will be able to:
· Use patterns to solve a problem
· Work with equivalence in a geometric context
Materials:
· Pattern Blocks, at least 6 yellow, 20 blue and 40 green per pair
· Caterpillar outlines
· Crayons
Teaching:
Introduction:
1. Students will be asked to find a way to cover their yellow Pattern Block using exactly 4 blocks.
2. Students will go over the only combination that works: 2 blue blocks and 2 green blocks.
3. Students will be asked to cover the hexagon using exactly 5 blocks.
4. Students will go over the only solution: 1 blue block and 4 green blocks.
Activity:
1. Students will be asked to pick a partner.
2. Students will be asked to answer the following question: How many different ways can you use only blue and green Pattern Blocks to cover the caterpillar?
3. Students will put 4 yellow blocks together to make their caterpillar.
4. Students will use only blue and green Pattern Blocks to cover their caterpillar.
5. Students will record their solution by coloring the caterpillar outline.
6. Students will keep track of the number of blue and green blocks used and also the total number of blocks used.
7. Students will find as many solutions as possible.
8. Students will look for patterns in their work.
Follow Up Discussion:
1. Students will be asked discuss how they worked on the activity.
2. Students as a class will create a class chart with their findings.
3. Students will be asked some of the following question to prompt class discussion:
a. How many different combinations of blue and green blocks did you find that will cover the caterpillar?
b. What is the greatest number of blocks that anyone used? What it the least?
c. What strategies did you use for solving this problem?
d. Did you notice any patterns that helped you find solutions? If so, describe them.
Grade Level:
2nd Grade
For this week's Virtual Manipulative I used the Fraction Adding manipulative. This manipulative shows what it means to find a common denominator and combine. Students have to find the common denominator and then add the fractions. Students are able to see what the fractions look like. Being able to see it visually gives them a better understanding of fractions. I like how it lets you add the parts and see what the answer looks like. Also that it tells you when the answer is wrong. The students who have trouble finding common denominator could use the figure to find the common denominator. To find the answer students can drag the representation of each fraction to be added into the blank box on the right. Others could just type in the common denominator and answer.
Week 3: Private Universe Project
For this week’s Private Universe Project I watched Workshop 3: Inventing Notations. When solving math problems we all use different techniques. I think it all has to do with the type of learners we are. I am more of a visual learner that is why when I solved the pizza question in class I made a list. I do not think anyone in our class made a picture but then again we are adults so I do not think any of us would have made pictures. Do you think you would have drawn pictures if this problem was given to you in elementary school?
Students need to be given the freedom to solve a problem how they see fit. Some students will surprise us with the methods they use. It is interesting to see what children can do. They invent their own notations and their own ways of communicating to each other. The fact that they can come up with their own way of solving problems is great but that they can also explain it to their classmates and teachers is even better.
Week 3: Lesson Plan (Pattern Blocks)
Cover The Caterpillar
NJCC Standards:
4.3.2 A. Patterns
Recognize, describe, extend, and create patterns.
4.4.2 A. Data Analysis
Collect, generate, record, and organize data in response to questions, claims, or curiosity.
4.5 B. Communication
Use communication to organize and clarify their mathematical thinking.
Overview:
Children will find combinations of blue and green Pattern Blocks that can be used to cover four yellow hexagons.
Objectives:
With this lesson students will be able to:
· Use patterns to solve a problem
· Work with equivalence in a geometric context
Materials:
· Pattern Blocks, at least 6 yellow, 20 blue and 40 green per pair
· Caterpillar outlines
· Crayons
Teaching:
Introduction:
1. Students will be asked to find a way to cover their yellow Pattern Block using exactly 4 blocks.
2. Students will go over the only combination that works: 2 blue blocks and 2 green blocks.
3. Students will be asked to cover the hexagon using exactly 5 blocks.
4. Students will go over the only solution: 1 blue block and 4 green blocks.
Activity:
1. Students will be asked to pick a partner.
2. Students will be asked to answer the following question: How many different ways can you use only blue and green Pattern Blocks to cover the caterpillar?
3. Students will put 4 yellow blocks together to make their caterpillar.
4. Students will use only blue and green Pattern Blocks to cover their caterpillar.
5. Students will record their solution by coloring the caterpillar outline.
6. Students will keep track of the number of blue and green blocks used and also the total number of blocks used.
7. Students will find as many solutions as possible.
8. Students will look for patterns in their work.
Follow Up Discussion:
1. Students will be asked discuss how they worked on the activity.
2. Students as a class will create a class chart with their findings.
3. Students will be asked some of the following question to prompt class discussion:
a. How many different combinations of blue and green blocks did you find that will cover the caterpillar?
b. What is the greatest number of blocks that anyone used? What it the least?
c. What strategies did you use for solving this problem?
d. Did you notice any patterns that helped you find solutions? If so, describe them.
Grade Level:
2nd Grade
Sunday, February 7, 2010
Week 2
Week 2: Virtual Manipulatives – Peg Puzzle & Towers of Hanoi
For this week’s virtual manipulative I asked my Dad to doing it. I first started my giving him the directions. I explained that he could not move backwards or jump over more than one. I explained that the goal is to switch the pegs on the left with the pegs on the right by moving one at a time. He started off with two pegs; he got that one right away. When it came to do four pegs it took him a little longer; he got it after three tries. As he was trying to do the four pegs he told me he did not like doing these kinds of activities. He said that there must be a pattern but that he could not see it. I asked him to go back to the two pegs and then the four pegs and see if he could find the pattern. He still could not find the pattern. When it came to the six pegs he tried four times and could not finish. So I solved it as he watched. I told him to try to find the pattern. I did it slowly so that he would be able to clearly see what I was doing. After the second time I did it he noticed that the empty spot was always between pegs of the same color. Once he noticed this I told asked him to try the six pegs again. He did it twice and could not finish so I helped him with the first three steps and after that he was on his own. We did that twice and on the third time he finished the puzzle. He noticed that all the reds were moved to the right first then the blues to the left and then back to the reds. The eight pegs we did together.
The Towers of Hanoi were much harder for him to complete. I explained that he could only move one disk at a time and that a larger disk could not be stacked on top of a smaller disk. I explained that the goal of the Towers of Hanoi is to move a stack of disks from one peg to another in as few moves as possible. He completed two disks without a problem. When he completed the three disks he completed the stack in the middle peg and the computer accepted the stack in the middle peg; I was surprised when this happened. The stack of four took a little longer then the stack three for him to finish. I guided him through the stack of four. He stopped at the stack of four. I went back and tried to get the stack of four to end up in the middle peg. After a few tries I figured it could end up in the middle peg but it would take more moves and that would defeat the purpose of the game.
Week 2: Private Universe Project
For this week’s Private Universe Project journal I watched Workshop 2: Are you convinced? I always ask my students why the answer is the answer. Most of the time they answer “Because it is.” I try to get them thinking about the problem. When I am working on word problems I try to find out why the answer makes sense. I cannot always explain it to other people but to me it makes sense. It is important to know why an answer is the answer. These students were put to the challenge of finding an answer and then try to explain why it is the answer. It is interesting to see how they each explain why they know the answer is right. The students and the one group of teachers noticed the same pattern; added two towers for each one from the previous pattern. The teachers and students found similar patterns but explained them differently. Students should always be challenged to explain why the answer is correct. Get them thinking beyond the problem given. Like we did in class not only did we have to solve the peg puzzle but also explain how we did it. Mathematics is full of Whys.
Week 2: Lesson Plan (Pattern Blocks)
How Many Seats?
NJCC Standards:
4.3.2 A. Patterns
Recognize, describe, extend, and create patterns.
Overview:
Children use Pattern Blocks to model a problem involving the number of tables needed to seat a given number of guests.
Objectives:
With this lesson students will be able to:
· solve an open-ended problem
· explore concepts of multiplication, division and remainders
· explore patterns that allow them to count more efficiently
Materials:
· Pattern Blocks, 13 squares and 13 trapezoids per pair
· Pattern Block triangle paper
Introduction:
1. Students will be shown a square and a trapezoid on the chalkboard.
2. Students will be asked to pretend that each of the blocks is a table: The orange square seats four people and the red trapezoid seats five.
3. Students will be asked to come up and draw a picture that shows how many people could be seated if two square tables were used.
4. Students will be asked to do the same thing for two trapezoids. (Making sure drawings show that if the long sides of the trapezoids are put together, the answer is 6 seats; if short sides are put together, the answer is 8 seats.)
Activity:
1. Students will be asked to pick a partner.
2. Students will be asked to imagine they are in charge of arranging the tables for a special school lunch party. How could they set up the tables so there are enough seats for everyone?
3. Students will use 2 kinds of Pattern Blocks- orange squares and red trapezoids- as tables.
4. Students are to arrange the 2 kinds of tables to seat 23 students, themselves, their teacher and the principal.
5. Students will be asked to come up with different arrangements that work.
6. Students will record each solution on triangle paper and will be ready to tell the class which they think works best and why.
Follow Up Discussion:
1. Students will be asked to come to the chalkboard and show one of their solutions, and explain how it works.
2. Students will be asked some of the following question to prompt class discussion:
a. How did you count the number of seats?
b. Did you notice any patterns when you were counting?
c. Why did you think one of your solutions was the best?
d. Which solutions have the exact number of seats that are needed? Which have extra seats?
.
Grade Level:
1st Grade
For this week’s virtual manipulative I asked my Dad to doing it. I first started my giving him the directions. I explained that he could not move backwards or jump over more than one. I explained that the goal is to switch the pegs on the left with the pegs on the right by moving one at a time. He started off with two pegs; he got that one right away. When it came to do four pegs it took him a little longer; he got it after three tries. As he was trying to do the four pegs he told me he did not like doing these kinds of activities. He said that there must be a pattern but that he could not see it. I asked him to go back to the two pegs and then the four pegs and see if he could find the pattern. He still could not find the pattern. When it came to the six pegs he tried four times and could not finish. So I solved it as he watched. I told him to try to find the pattern. I did it slowly so that he would be able to clearly see what I was doing. After the second time I did it he noticed that the empty spot was always between pegs of the same color. Once he noticed this I told asked him to try the six pegs again. He did it twice and could not finish so I helped him with the first three steps and after that he was on his own. We did that twice and on the third time he finished the puzzle. He noticed that all the reds were moved to the right first then the blues to the left and then back to the reds. The eight pegs we did together.
The Towers of Hanoi were much harder for him to complete. I explained that he could only move one disk at a time and that a larger disk could not be stacked on top of a smaller disk. I explained that the goal of the Towers of Hanoi is to move a stack of disks from one peg to another in as few moves as possible. He completed two disks without a problem. When he completed the three disks he completed the stack in the middle peg and the computer accepted the stack in the middle peg; I was surprised when this happened. The stack of four took a little longer then the stack three for him to finish. I guided him through the stack of four. He stopped at the stack of four. I went back and tried to get the stack of four to end up in the middle peg. After a few tries I figured it could end up in the middle peg but it would take more moves and that would defeat the purpose of the game.
Week 2: Private Universe Project
For this week’s Private Universe Project journal I watched Workshop 2: Are you convinced? I always ask my students why the answer is the answer. Most of the time they answer “Because it is.” I try to get them thinking about the problem. When I am working on word problems I try to find out why the answer makes sense. I cannot always explain it to other people but to me it makes sense. It is important to know why an answer is the answer. These students were put to the challenge of finding an answer and then try to explain why it is the answer. It is interesting to see how they each explain why they know the answer is right. The students and the one group of teachers noticed the same pattern; added two towers for each one from the previous pattern. The teachers and students found similar patterns but explained them differently. Students should always be challenged to explain why the answer is correct. Get them thinking beyond the problem given. Like we did in class not only did we have to solve the peg puzzle but also explain how we did it. Mathematics is full of Whys.
Week 2: Lesson Plan (Pattern Blocks)
How Many Seats?
NJCC Standards:
4.3.2 A. Patterns
Recognize, describe, extend, and create patterns.
Overview:
Children use Pattern Blocks to model a problem involving the number of tables needed to seat a given number of guests.
Objectives:
With this lesson students will be able to:
· solve an open-ended problem
· explore concepts of multiplication, division and remainders
· explore patterns that allow them to count more efficiently
Materials:
· Pattern Blocks, 13 squares and 13 trapezoids per pair
· Pattern Block triangle paper
Introduction:
1. Students will be shown a square and a trapezoid on the chalkboard.
2. Students will be asked to pretend that each of the blocks is a table: The orange square seats four people and the red trapezoid seats five.
3. Students will be asked to come up and draw a picture that shows how many people could be seated if two square tables were used.
4. Students will be asked to do the same thing for two trapezoids. (Making sure drawings show that if the long sides of the trapezoids are put together, the answer is 6 seats; if short sides are put together, the answer is 8 seats.)
Activity:
1. Students will be asked to pick a partner.
2. Students will be asked to imagine they are in charge of arranging the tables for a special school lunch party. How could they set up the tables so there are enough seats for everyone?
3. Students will use 2 kinds of Pattern Blocks- orange squares and red trapezoids- as tables.
4. Students are to arrange the 2 kinds of tables to seat 23 students, themselves, their teacher and the principal.
5. Students will be asked to come up with different arrangements that work.
6. Students will record each solution on triangle paper and will be ready to tell the class which they think works best and why.
Follow Up Discussion:
1. Students will be asked to come to the chalkboard and show one of their solutions, and explain how it works.
2. Students will be asked some of the following question to prompt class discussion:
a. How did you count the number of seats?
b. Did you notice any patterns when you were counting?
c. Why did you think one of your solutions was the best?
d. Which solutions have the exact number of seats that are needed? Which have extra seats?
.
Grade Level:
1st Grade
Sunday, January 31, 2010
Week 1
Week 1: Four-Block Tower Problem
I asked my sister and Dad to help me with Unifix Cube four-block tower problem. I started off by explaining that they had to make a pattern using four blocks. My sister looked at me puzzled and said it was not possible. According to her using only four blocks is not considered a pattern. My Dad started with the all red tower, one blue three red and worked his way to all blue. While my sister started with two blues and two reds. She made different patterns and then found the opposites. As they were working I noticed that they had repeated some of the patterns so I told them to look over their patterns and make sure none were repeated. I asked them to explain to each other what they had done. Once they each thought they were done my sister asked me if they had to use all of the blocks. I told her as many as they thought they needed. Once they said they were done I asked them how they knew they were done my Dad answered that there were no more possibilities. I reminded them that this assignment was for a Mathematics class so to think let a Mathematic for their answer. Once I said that my Dad said 4 x 4. He explained to me four colors four blocks high.
Unifix Cubes are a good manipulative to use in class. With the Unifix Cubes the students are able to visually see Math problems. Another way that the Unifix Cubes could be use is in multiplication problems. The students could see multiplication is related to addition. I am sure there are many more ways that Unifix Cubes could be used.
Week 1: Virtual Manipulatives
For this week’s Virtual Manipulative journal I used the manipulative called Factor Tree. I am currently teaching about factor trees and prime factorization. This manipulative would be great to incorporate into my lesson for the students that are struggling. I would have liked if it let the student put in both factors instead of the computer giving the other one. I do like that it tells when the factor is wrong. Overall I would definitely use it in the classroom. It is a good tool for students to use.
Week 1: Private Universe Project
For this week’s Private Universe Project journal I watched Workshop 1: Following Children's Ideas in Mathematics. When it was talking about how even Kindergarteners use Math during their free play time I started to think about the Kindergarten class I work with. Thinking back at what they do during the time they are waiting to start a new assignment. They are playing with their pencils or whatever they have in their hands and are making shapes. For example when they have their notebooks they build squares. They use their notebooks as the walls and the top. Sometimes they make triangles too.
It would be great to know how we each developed our mathematics skills. Being Mathematics major I would have loved to see myself develop my mathematics skills, to see when I “fell in love with Mathematics”. Being able to look back at the videos gives teachers an insight to the minds of students. Lets them see how the students develop their skills. This could help with lesson planning and curriculum changes. I am curious to see how the second graders I work with would solve the three shirts and two jeans problem. As I watched this video I thought of how I would solve a similar problem maybe just a little harder. Come to think of it it is similar to the pizza problem we did in class.
I have always said that students learn best when they are involved the learning process. Students get more involved when it is hands on. They do not think of it as work but as something fun. The students in the video remember things they learned in second grade but cannot remember what they learned in the 10th grade. The more involved the student is the better.
I asked my sister and Dad to help me with Unifix Cube four-block tower problem. I started off by explaining that they had to make a pattern using four blocks. My sister looked at me puzzled and said it was not possible. According to her using only four blocks is not considered a pattern. My Dad started with the all red tower, one blue three red and worked his way to all blue. While my sister started with two blues and two reds. She made different patterns and then found the opposites. As they were working I noticed that they had repeated some of the patterns so I told them to look over their patterns and make sure none were repeated. I asked them to explain to each other what they had done. Once they each thought they were done my sister asked me if they had to use all of the blocks. I told her as many as they thought they needed. Once they said they were done I asked them how they knew they were done my Dad answered that there were no more possibilities. I reminded them that this assignment was for a Mathematics class so to think let a Mathematic for their answer. Once I said that my Dad said 4 x 4. He explained to me four colors four blocks high.
Unifix Cubes are a good manipulative to use in class. With the Unifix Cubes the students are able to visually see Math problems. Another way that the Unifix Cubes could be use is in multiplication problems. The students could see multiplication is related to addition. I am sure there are many more ways that Unifix Cubes could be used.
Week 1: Virtual Manipulatives
For this week’s Virtual Manipulative journal I used the manipulative called Factor Tree. I am currently teaching about factor trees and prime factorization. This manipulative would be great to incorporate into my lesson for the students that are struggling. I would have liked if it let the student put in both factors instead of the computer giving the other one. I do like that it tells when the factor is wrong. Overall I would definitely use it in the classroom. It is a good tool for students to use.
Week 1: Private Universe Project
For this week’s Private Universe Project journal I watched Workshop 1: Following Children's Ideas in Mathematics. When it was talking about how even Kindergarteners use Math during their free play time I started to think about the Kindergarten class I work with. Thinking back at what they do during the time they are waiting to start a new assignment. They are playing with their pencils or whatever they have in their hands and are making shapes. For example when they have their notebooks they build squares. They use their notebooks as the walls and the top. Sometimes they make triangles too.
It would be great to know how we each developed our mathematics skills. Being Mathematics major I would have loved to see myself develop my mathematics skills, to see when I “fell in love with Mathematics”. Being able to look back at the videos gives teachers an insight to the minds of students. Lets them see how the students develop their skills. This could help with lesson planning and curriculum changes. I am curious to see how the second graders I work with would solve the three shirts and two jeans problem. As I watched this video I thought of how I would solve a similar problem maybe just a little harder. Come to think of it it is similar to the pizza problem we did in class.
I have always said that students learn best when they are involved the learning process. Students get more involved when it is hands on. They do not think of it as work but as something fun. The students in the video remember things they learned in second grade but cannot remember what they learned in the 10th grade. The more involved the student is the better.
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