Here are links to five educational blogs that I had found that are truly resourceful and I have found great ideas and have come to a better understanding of how big and wonderful the world of education is!
Blog #1: http://coolcatteacher.blogspot.com/
Blog #2: http://www.learningismessy.com/
Blog #3: http://thankyoubrain.blogspot.com/
Blog #4: https://organizedclassroom.com/classroom-management/
Blog #5: http://www.teachjunkie.com/blog/
Monday, April 9, 2018
Word Problems got you down? Well, Poyla is here to save the day!
Word problems for lots of students can be frustrating and hard to understand. Some word problems have lots of information that is being thrown at you and you want to know what you actually need to use to solve it and what formulas and steps you need to take to get the answer without too much crying. George Poyla helped shed some bright and amazing light on this terrible dilemma with his effective four-step formula.
Step 1: Understanding the problem:
Givens: (What do you know in the problem?)
Goal: (What are you trying to find in the problem?)
Conjecture: Prediction (This should be numerical and in words. Give an estimate you know is too low and an estimate that you know is too high.)
After you first read the word problem you go back to the word problem and highlight and write down the answers to all of those questions to get you started.
Step 2: Devise a Plan:
Strategy: Toolbox (You can choose from the ones listed or write in your own.)
- Draw model/visual
- Make use of structure
- Look for repeated reasoning
- Create an equation/expression
- Guess & check
- Work backward
- Formula
This is just a short list of many strategies that you could work with and this is where students can feel the most comfortable because they can choose and use multiple strategies to figure out the problem.
Step 3: Carry out the plan:
Solution: (show all work, label, be precise)
Final answer (written in a complete sentence with units)
I really like the final answer being written in a complete sentence because that gives you time to look back at the original problem and make sure you did everything correctly.
Step 4: Looking Back:
Verification- Check that your answer is mathematically correct. Is your answer reasonable? (This should be written in words and mathematically calculated.)
Looking back can give you the extra emphasis you need to feel confident and truly make sure that everything makes sense and it completes the original problem and answers what it precisely asked.
I would definitely use this in my future classroom because it gives the foundation and the exact format you need to solve an easy and a hard word problem!!
Helpful Link: http://www.mathgametime.com/subject/problem-solving
(This link is here for students to practice problem-solving with fun games and videos and worksheets for grades K-7.)
Here is the Polya formula used in action! (Link to the example on this website: http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut8_probsol.htm)
Step 1: Understanding the problem:
Givens: (What do you know in the problem?)
Goal: (What are you trying to find in the problem?)
Conjecture: Prediction (This should be numerical and in words. Give an estimate you know is too low and an estimate that you know is too high.)
After you first read the word problem you go back to the word problem and highlight and write down the answers to all of those questions to get you started.
Step 2: Devise a Plan:
Strategy: Toolbox (You can choose from the ones listed or write in your own.)
- Draw model/visual
- Make use of structure
- Look for repeated reasoning
- Create an equation/expression
- Guess & check
- Work backward
- Formula
This is just a short list of many strategies that you could work with and this is where students can feel the most comfortable because they can choose and use multiple strategies to figure out the problem.
Step 3: Carry out the plan:
Solution: (show all work, label, be precise)
Final answer (written in a complete sentence with units)
I really like the final answer being written in a complete sentence because that gives you time to look back at the original problem and make sure you did everything correctly.
Step 4: Looking Back:
Verification- Check that your answer is mathematically correct. Is your answer reasonable? (This should be written in words and mathematically calculated.)
Looking back can give you the extra emphasis you need to feel confident and truly make sure that everything makes sense and it completes the original problem and answers what it precisely asked.
I would definitely use this in my future classroom because it gives the foundation and the exact format you need to solve an easy and a hard word problem!!
Helpful Link: http://www.mathgametime.com/subject/problem-solving
(This link is here for students to practice problem-solving with fun games and videos and worksheets for grades K-7.)
Here is the Polya formula used in action! (Link to the example on this website: http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut8_probsol.htm)
A math class has 30 students. Approximately 70% passed their last math test. How many students passed the last math test?
|
Step 1: Understand the problem.
|
Make sure that you read the question carefully several times.
We are looking for how many students passed the last math test, we will let
x = number of students
|
Step 2: Devise a plan (translate).
|
 |
Step 3: Carry out the plan (solve).
|
 | *Multiply |
Step 4: Look back (check and interpret).
|
21 is 70% of 30.
FINAL ANSWER: 21 students passed the last math test.
|
Saturday, April 7, 2018
Gum Drops, and Toothpicks, and Polyhedra OH MY!
In class this past week we learned of what geometric solids and polyhedra are by going through 6 different stations that included hands-on activities electronically (I-pads) and on paper. With each individual activity, the overall common goal was to find and look for the relationship between vertices, faces, and edges. One of the stations that was in the rotation was the Gumdrop Polyhedra. I will explain what and how to do the activity in a lesson plan type format to be able to use in my future class.
Materials needed:
-Bags of gumdrops
-Toothpicks
-Colored paper of instructions (picture below)
-Blue fact cards (picture below)
Instructions:
- Using gumdrops and toothpicks and the picture below, create and build different models of polyhedra.
- While you are building the polyhedra be sure to fill out the fact cards.
-Fact cards: blue pieces of paper, fill out the shapes name, draw a picture of the shape, count the number of vertices, faces, and edges and record each and also draw the shape of the faces.
- The gumdrops as the representing a vertice and the toothpicks are representing an edge.
- Construct each polyhedron on the piece of paper which include: Cube, triangular pyramid (tetrahedron), square pyramid, triangular prism, pentagonal prism
- After you create each polyhedron fill out the fact cards using those models to get a better visual and also try to look for a relationship between vertices, faces, and edges.
- Discuss the relationship between vertices, faces, and edges
The finished product
This activity and the rest of the activities were so hands-on and truly helped me understand and truly visual polyhedra and how they connect to each other and the real world. I think that this gumdrop activity is perfect for any age because it can be easily manipulated into something less complex or even more difficult. I truly enjoyed this activity and I know that I will be able to use it in my future classroom.
Helpful link: https://illuminations.nctm.org/activity.aspx?id=3521
This link takes you to a website that students can interact virtually with geometric solids and polyhedrons.
Materials needed:
-Bags of gumdrops
-Toothpicks
-Colored paper of instructions (picture below)
-Blue fact cards (picture below)
Instructions:
- Using gumdrops and toothpicks and the picture below, create and build different models of polyhedra.
- While you are building the polyhedra be sure to fill out the fact cards.
-Fact cards: blue pieces of paper, fill out the shapes name, draw a picture of the shape, count the number of vertices, faces, and edges and record each and also draw the shape of the faces.
- The gumdrops as the representing a vertice and the toothpicks are representing an edge.
- Construct each polyhedron on the piece of paper which include: Cube, triangular pyramid (tetrahedron), square pyramid, triangular prism, pentagonal prism
- After you create each polyhedron fill out the fact cards using those models to get a better visual and also try to look for a relationship between vertices, faces, and edges.
- Discuss the relationship between vertices, faces, and edges
The finished product
This activity and the rest of the activities were so hands-on and truly helped me understand and truly visual polyhedra and how they connect to each other and the real world. I think that this gumdrop activity is perfect for any age because it can be easily manipulated into something less complex or even more difficult. I truly enjoyed this activity and I know that I will be able to use it in my future classroom.
Helpful link: https://illuminations.nctm.org/activity.aspx?id=3521
This link takes you to a website that students can interact virtually with geometric solids and polyhedrons.
Wednesday, April 4, 2018
Symmetry, Symmetry, Symmetry!!
Yesterday in class, we learned about shapes and the how symmetry is in the vocabulary bank for defining every shape. So, there are two definitions one is line symmetry and the other is rotational symmetry. Line symmetry is when a figure divides a figure into two congruent halves. To help truly illustrate this definition in class we each got a strip of white paper with a triangle, a square, a pentagon and a hexagon on it. With a ruler, we were supposed to draw all of the possibilities of a line of symmetry in each shape. (picture at the bottom of the post) I discovered after checking my work with everyone else's and the sample I forgot so many different lines! Then I learned that each line of symmetry can be drawn from every possible vertice within a shape and that changed my whole perspective and understanding of symmetry.
Next was rotational symmetry. A figure has rotational symmetry when it is rotated 0° and 360° the resulting figure coincides with the original. The number of times you get an identical figure is called the order. So to truly understand this concept we were given a colored piece of paper with three yellow shapes (square, parallelogram, and trapezoid) and three brads. (finished product below) As we cut out each shape we were instructed to poke a hole through the shape and then poke the brad and the shape through the colored paper and close it so we could glue it in our notebooks. Because of the brads, we were able to see the rotations that each shape could do. The square has rotational symmetry and can be turned in the order of 4. The parallelogram also has rotational symmetry and can be turned in the order of 2. And then the trapezoid has no rational symmetry as you could physically tell when you tried to move it, it would not rotate.
This activity truly helped me get a solid foundation and start to understanding symmetry which is also a foundation for understanding each individual shape we use in geometry. Also being able to physically touch and move things around helped me and also could help my future kinesthetic learners truly understand this concept on a whole other level.
Helpful link: https://www.topmarks.co.uk/symmetry/symmetry-matching
This is an interactive website geared towards 4-8-year-olds and learning about symmetry with colorful pictures and games.
(Line symmetry activity)
(Rotational Symmetry Activity)
Next was rotational symmetry. A figure has rotational symmetry when it is rotated 0° and 360° the resulting figure coincides with the original. The number of times you get an identical figure is called the order. So to truly understand this concept we were given a colored piece of paper with three yellow shapes (square, parallelogram, and trapezoid) and three brads. (finished product below) As we cut out each shape we were instructed to poke a hole through the shape and then poke the brad and the shape through the colored paper and close it so we could glue it in our notebooks. Because of the brads, we were able to see the rotations that each shape could do. The square has rotational symmetry and can be turned in the order of 4. The parallelogram also has rotational symmetry and can be turned in the order of 2. And then the trapezoid has no rational symmetry as you could physically tell when you tried to move it, it would not rotate.
This activity truly helped me get a solid foundation and start to understanding symmetry which is also a foundation for understanding each individual shape we use in geometry. Also being able to physically touch and move things around helped me and also could help my future kinesthetic learners truly understand this concept on a whole other level.
Helpful link: https://www.topmarks.co.uk/symmetry/symmetry-matching
This is an interactive website geared towards 4-8-year-olds and learning about symmetry with colorful pictures and games.
(Rotational Symmetry Activity)
Saturday, March 31, 2018
The Mystery of the Nameless Triangle
In class on Tuesday this week we got to explore the complex but fascinating world of triangles. The first activity consisted of us all getting a colored piece of paper and ruler and could draw any big triangle we wanted to and then we needed to classify what kind of triangle it was. But we had no words or even their definitions of what to classify the triangle we couldn't just leave it nameless! So, with the mystery needing to be solved, we needed clues and definitions so next came the foldable that was going to solve our dilemma of the nameless triangle.
The "classifying triangles" foldable (picture at the bottom) consisted of the categories angles and sides. First, we addressed the angles side which is put into three separate categories the first being acute, then right, then obtuse. Acute triangles are defined as having all angles measure to less than 90°. Right triangles are defined as having exactly 1 90° angle within the triangle. And lastly, obtuse triangles are defined as having one angle greater than 90° and less than 180°. So with these definitions, we could now define what kind of triangle it was by its angles! But, we still needed the sides to get the full picture and completely define what kind of triangle we had next to us laying on the table waiting to be labeled and to be solved. The sides were put into three categories just like the angles and the categories were equilateral, isosceles, and scalene. An equilateral triangle is defined as all of the sides having the same length. An isosceles triangle is defined as at least 2 sides having the same length. And a scalene triangle is defined as all of the sides have different lengths. After sides and angles were defined, there were extra boxes within the foldable that we were able to draw close to accurate pictures of what each triangle would look like to get a visual aspect and understanding of classifying triangles.
Now we could FINALLY solve the mystery of what we could name our different triangles. Using our newly gained knowledge, and angle finders and protractors, we were able to solve it and name our triangles! My official name for my triangle was an acute scalene triangle.
This lesson was interactive and I could truly apply what I learned automatically and if I still didn't understand I could ask for clarification in class from my fellow peers and professor. I would definitely use a hands-on activity like this in my future classroom because it truly helps you visually see what types of triangles there are and finding the way that works for you to understand and remember the definitions of each classification of a triangle.
Helpful link:
http://www.sheppardsoftware.com/mathgames/geometry/shapeshoot/triangles_shoot.htm
-This link gets you to an interactive math game called triangles shoot which will give students a better understanding of triangles and their angles and sides.
(The foldable in its full glory.)
(What the foldable looks on the outside)
(The triangle that was finally named!)
The "classifying triangles" foldable (picture at the bottom) consisted of the categories angles and sides. First, we addressed the angles side which is put into three separate categories the first being acute, then right, then obtuse. Acute triangles are defined as having all angles measure to less than 90°. Right triangles are defined as having exactly 1 90° angle within the triangle. And lastly, obtuse triangles are defined as having one angle greater than 90° and less than 180°. So with these definitions, we could now define what kind of triangle it was by its angles! But, we still needed the sides to get the full picture and completely define what kind of triangle we had next to us laying on the table waiting to be labeled and to be solved. The sides were put into three categories just like the angles and the categories were equilateral, isosceles, and scalene. An equilateral triangle is defined as all of the sides having the same length. An isosceles triangle is defined as at least 2 sides having the same length. And a scalene triangle is defined as all of the sides have different lengths. After sides and angles were defined, there were extra boxes within the foldable that we were able to draw close to accurate pictures of what each triangle would look like to get a visual aspect and understanding of classifying triangles.
Now we could FINALLY solve the mystery of what we could name our different triangles. Using our newly gained knowledge, and angle finders and protractors, we were able to solve it and name our triangles! My official name for my triangle was an acute scalene triangle.
This lesson was interactive and I could truly apply what I learned automatically and if I still didn't understand I could ask for clarification in class from my fellow peers and professor. I would definitely use a hands-on activity like this in my future classroom because it truly helps you visually see what types of triangles there are and finding the way that works for you to understand and remember the definitions of each classification of a triangle.
Helpful link:
http://www.sheppardsoftware.com/mathgames/geometry/shapeshoot/triangles_shoot.htm
-This link gets you to an interactive math game called triangles shoot which will give students a better understanding of triangles and their angles and sides.
(The triangle that was finally named!)
Monday, March 26, 2018
Goldfish and Probability
At the beginning of the semester in this course, we learned about the topic of probability and all of its aspects and effects on the world through using it in things like experiments and studies. To get a better understanding of how probabilities are determined, their properties, the definitions of mutually exclusive and non-mutually exclusive events, and experimental probabilities vs theoretical probabilities we did the healthy fish activity.
So, with this experiment, we each needed a bag of colored goldfish, and a gold worksheet (pics of both below). The fish in the sample represented healthy and sick fish. The green fish were sick, and all of the other colored fish were healthy. We all opened our bags and started to separate them into groups by color to answer the questions in the worksheet. On a side note, it was really interesting to see how people decided to organize their fish as some people were very nit-picky as others didn't truly care how things were organized and that just truly shows how diverse every student is. And as a future teacher knowing how each individual student learns determines how you are going to set up your curriculum and teach and guide your students.
Part A of the worksheet addressed the counting and recording of the healthy fish, the sick fish, and the total number of the fish.
Part B is computing the probability of healthy and sick fish in the sample through using the numbers from Part A. Part A was very foundational because of the totals of the fish help you to create possibilities and put things together and start to make and discover predictions and possibilities.
Part C addresses computing the probability of something NOT occurring and asks how both questions relate to each other.
And finally, Part D and Part E put the activity into the context of a word problem or a real-life situation which brings back material and certain subjects from 256 which is proportions and word problems.
This activity truly reached all of the objectives and I came to a better understanding of how probability works. It also was a great activity opener to understanding the vocabulary and how to apply probability to the real world and even how to use this activity in my future classroom.
Helpful link: http://www.mathgametime.com/subject/probability
This link takes you to a website that has games on probability, videos explaining probability, and lesson plans for probability and for grades K-7.
(Healthy Fish Activity Worksheet)
(Type of goldfish to buy for the activity)
So, with this experiment, we each needed a bag of colored goldfish, and a gold worksheet (pics of both below). The fish in the sample represented healthy and sick fish. The green fish were sick, and all of the other colored fish were healthy. We all opened our bags and started to separate them into groups by color to answer the questions in the worksheet. On a side note, it was really interesting to see how people decided to organize their fish as some people were very nit-picky as others didn't truly care how things were organized and that just truly shows how diverse every student is. And as a future teacher knowing how each individual student learns determines how you are going to set up your curriculum and teach and guide your students.
Part A of the worksheet addressed the counting and recording of the healthy fish, the sick fish, and the total number of the fish.
Part B is computing the probability of healthy and sick fish in the sample through using the numbers from Part A. Part A was very foundational because of the totals of the fish help you to create possibilities and put things together and start to make and discover predictions and possibilities.
Part C addresses computing the probability of something NOT occurring and asks how both questions relate to each other.
And finally, Part D and Part E put the activity into the context of a word problem or a real-life situation which brings back material and certain subjects from 256 which is proportions and word problems.
This activity truly reached all of the objectives and I came to a better understanding of how probability works. It also was a great activity opener to understanding the vocabulary and how to apply probability to the real world and even how to use this activity in my future classroom.
Helpful link: http://www.mathgametime.com/subject/probability
This link takes you to a website that has games on probability, videos explaining probability, and lesson plans for probability and for grades K-7.
(Type of goldfish to buy for the activity)
Thursday, March 22, 2018
Crash Course: How to Use a Protractor
Today in class we learned how to correctly and effectively use a protractor. I had used a protractor before when I was taking a geometry class in high school but I never truly understood why we would use it and how to use it correctly until today. We were all given a protractor and a piece of paper with written instructions on how to use the protractor also we were provided with a worksheet to practice measuring angles. The two worksheets are displayed to the left at the bottom. So here are the instructions on how to use a protractor put into the terms that I understood them throughout the lesson today.
Step 1: Place the center point of the protractor on the angle's vertex.
- There is an open hole at the bottom of the protractor and that is where you place the protractor onto the paper. The angle's vertex is where the two ray's meet.
Step 2: Align the protractor with the bottom ray.
- Make sure that the bottom of the protractor lines up with the bottom line (ray)
Step 3: Read the angle's measure by finding where the top ray crosses the protractor.
- It is not always going to be extremely accurate but if you are above or below the actual degree by 2 it is still going to be accurate. Follow the top of the arrow and see what line on the protractor is the most directly pointed towards.
After learning how to properly use a protractor, we were given the opportunity to practice using the worksheet to try it out on our own and then going over the answers at the ending. After learning how to appropriately use a protractor I got a better sense of how they can help measure angles and I came to a better understanding of what acute and obtuse angles look like and how I can measure them! I would definitely apply this lesson to my future classroom because learning about the different angles by using a tool will give students a true visual and be able to physically discover on their own how angles work and how to measure them. I truly enjoyed learning about protractors in class and now feel more confident in my abilities to use it on my own and also share it and teach it to others.
Helpful link: https://www.mathplayground.com/measuringangles.html
This link will take you to a game using an online and interactive protractor to find, measure, and name an angle.
Step 1: Place the center point of the protractor on the angle's vertex.
- There is an open hole at the bottom of the protractor and that is where you place the protractor onto the paper. The angle's vertex is where the two ray's meet.
Step 2: Align the protractor with the bottom ray.
- Make sure that the bottom of the protractor lines up with the bottom line (ray)
Step 3: Read the angle's measure by finding where the top ray crosses the protractor.
- It is not always going to be extremely accurate but if you are above or below the actual degree by 2 it is still going to be accurate. Follow the top of the arrow and see what line on the protractor is the most directly pointed towards.
After learning how to properly use a protractor, we were given the opportunity to practice using the worksheet to try it out on our own and then going over the answers at the ending. After learning how to appropriately use a protractor I got a better sense of how they can help measure angles and I came to a better understanding of what acute and obtuse angles look like and how I can measure them! I would definitely apply this lesson to my future classroom because learning about the different angles by using a tool will give students a true visual and be able to physically discover on their own how angles work and how to measure them. I truly enjoyed learning about protractors in class and now feel more confident in my abilities to use it on my own and also share it and teach it to others.
Helpful link: https://www.mathplayground.com/measuringangles.html
This link will take you to a game using an online and interactive protractor to find, measure, and name an angle.
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In class this past week we learned of what geometric solids and polyhedra are by going through 6 different stations that included hands-on a... -
Here are links to five educational blogs that I had found that are truly resourceful and I have found great ideas and have come to a better ...