What's the Big Idea???
Data from the results of an experiment can be used to predict the theoretical probability of an event and to compare and interpret.
PROBABILITY PROJECTS
Learning Goals
These goals are a combination of Big Ideas, Curricular Competencies, Content, and the Core Competencies.
• Use reasoning, logic, play, and inquiry to design and conduct an experiment about probability.
• Create graphical representations to demonstrate understanding of probability concepts.
• Use visual, textual, and oral communication strategies to share and reflect on mathematical thinking and design processes. • Generate, develop, and test ideas while creating an original game.
• Use text and oral language to convey both information (how to play a game) and a narrative story.
• Work collaboratively and with perseverance throughout a creative process.
These goals are a combination of Big Ideas, Curricular Competencies, Content, and the Core Competencies.
• Use reasoning, logic, play, and inquiry to design and conduct an experiment about probability.
• Create graphical representations to demonstrate understanding of probability concepts.
• Use visual, textual, and oral communication strategies to share and reflect on mathematical thinking and design processes. • Generate, develop, and test ideas while creating an original game.
• Use text and oral language to convey both information (how to play a game) and a narrative story.
• Work collaboratively and with perseverance throughout a creative process.
Activity 1: What’s in the Bag
• To begin, I divided students into pairs and gave each pair a paper bag containing the same combination of 10 coloured square tiles and told the students that each bag contained the same combination of 10 tiles.
• Then I challenged the students to think about how they could determine what the colours of each of the tiles were if they are only allowed to draw one tile at a time from the bag. We brainstormed solutions.
• We agreed that we could use tallies and then make a bar graph with the results, or we could even record the results straight onto a bar graph.
• Students can use their graphs to make predictions about how many tiles of each colour are in their bag.
• When all the groups had made predictions and were ready, we compiled the results from each group and compared their results with the results from the whole class.
• As a whole group we re-visited the question "Which is more likely to be closer to the true result?"
• We wanted to get at the idea that the more trials we do, the more statistically likely we will be to get the true result.
• To begin, I divided students into pairs and gave each pair a paper bag containing the same combination of 10 coloured square tiles and told the students that each bag contained the same combination of 10 tiles.
• Then I challenged the students to think about how they could determine what the colours of each of the tiles were if they are only allowed to draw one tile at a time from the bag. We brainstormed solutions.
• We agreed that we could use tallies and then make a bar graph with the results, or we could even record the results straight onto a bar graph.
• Students can use their graphs to make predictions about how many tiles of each colour are in their bag.
• When all the groups had made predictions and were ready, we compiled the results from each group and compared their results with the results from the whole class.
• As a whole group we re-visited the question "Which is more likely to be closer to the true result?"
• We wanted to get at the idea that the more trials we do, the more statistically likely we will be to get the true result.
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Reflection: Probability Games
In a reflection you will describe…
In a reflection you will describe…
- the “what?” (What did you do?)
- the “so what?” (What did you learn?)
- and the “now what?” (What will you do with this new learning?
We were pulling out the little colored card there was a red one and a blue and a green and a yellow and a orange.
~Heather Ford
I learned that is more red in the papers bags.
~Kaltee Baker
Pull out a piece of paper and we had to mark down the colour and i learned about the math i did to make 10 pieces while my partner was doing nothing and myself and maxine were doing a little bit of math because heather was not helping at all and what i would do with the stuff i learned it would be helping me do math
~Shalako Wallace
I will use this learning to make my arcade game with probability so everyone can play and have fun winning so no one gets sad and quits. I also know that graph paper really helps you get the results you need so now I know to use graph paper for another project in the future.
~Lindsey Jones
I learnt that probability games are fun and you can multitask by learning how to count by only pulling one out at a time and learning how to graph. I also learnt that it is fun to work in groups with a person or many people that you don’t usually talk to.
~Talise Chapelle
I learned what the word probability meant and I learned what the meaning meant.
Activity 2: Blind Boxes
• We started this activity with a story about toys in blind boxes. If there are six different toys that could come in a blind box, and you want to collect them all, how many boxes would you have to buy (on average)?
• We wondered what experiment the students could design to answer this question?
• As a class when we discussed experiment options we discovered that we could use a 6 sided dice
• Students rolled a six-sided die and recorded which number they got with each roll, keeping track of how many times they had to roll to get all six numbers. They repeated this several times for accuracy.
• After students had done this activity for a little while, I asked them to stop rolling the die and draw some conclusions about their own data.
• Again we drew conclusions based on our own data and on data from the class as a whole.
• As a class we realized that it was important to understand that more experiments lead to more accurate predictions.
• We started this activity with a story about toys in blind boxes. If there are six different toys that could come in a blind box, and you want to collect them all, how many boxes would you have to buy (on average)?
• We wondered what experiment the students could design to answer this question?
• As a class when we discussed experiment options we discovered that we could use a 6 sided dice
• Students rolled a six-sided die and recorded which number they got with each roll, keeping track of how many times they had to roll to get all six numbers. They repeated this several times for accuracy.
• After students had done this activity for a little while, I asked them to stop rolling the die and draw some conclusions about their own data.
• Again we drew conclusions based on our own data and on data from the class as a whole.
• As a class we realized that it was important to understand that more experiments lead to more accurate predictions.
Activity 3: Martha Blah Blah
- We began this activity by reading a story of Martha the dog, from the book Martha Blah Blah, by Susan Meddaugh. “There is a dog named Martha who is able to speak when she eats the letters in alphabet soup. The letters Martha eats are the letters she can use to speak. One day, the soup company’s owner removes some letters from the soup to save money. Martha has difficulty speaking because certain letters are missing from her soup and therefore she can no longer use those letters to form words.”
- After reading the story we asked ourselves which letters should the company remove to have the least effect on Martha’s speech, and which letters will have the greatest effect on Martha’s speech?
- We wondered how we could design an experiment to answer these questions?
- The students concluded that they would need to gather data about the frequency with which each letter is used in the English language.
- To do this, we used comic books.
- Students recorded how many times each letter appeared directly onto a bar graph, or onto a tally sheet.
- When the students were done, we gathered and I asked them to draw conclusions from their results.
- We began this activity by reading a story of Martha the dog, from the book Martha Blah Blah, by Susan Meddaugh. “There is a dog named Martha who is able to speak when she eats the letters in alphabet soup. The letters Martha eats are the letters she can use to speak. One day, the soup company’s owner removes some letters from the soup to save money. Martha has difficulty speaking because certain letters are missing from her soup and therefore she can no longer use those letters to form words.”
- After reading the story we asked ourselves which letters should the company remove to have the least effect on Martha’s speech, and which letters will have the greatest effect on Martha’s speech?
- We wondered how we could design an experiment to answer these questions?
- The students concluded that they would need to gather data about the frequency with which each letter is used in the English language.
- To do this, we used comic books.
- Students recorded how many times each letter appeared directly onto a bar graph, or onto a tally sheet.
- When the students were done, we gathered and I asked them to draw conclusions from their results.
Activity 4: M&Ms Odds
Probability Game Projects
#WIP
Student explanations of their project
"In our game you will need either a small chip or a marble to drop down the game and we only have three rules
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"After we tell you the rules you can start to drop the marble the way you win the game and get a prize is you have to get 250 points to get any prize the prizes would either be rainbow loom bracelets or little plastic toys etc. we have no identified vocabulary word to said if you win the game."
~Lindsey |
"I need cardboard to make the ball Roll different directions through the obstacles And then I need a spring to Hot glue cardboard On Spring And then you pull the spring back And it launches the ball And then I painted it different colors."
~ Lowell |
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Interpreting Data Sets |
Curricular competencies: Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving
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Penny stacking activity
- We began this activity with me passing out some play money and us discussing the approximate value that each student had.
- After discussing the concept of average, the students were put into small teams and were given a large pile of pennies. Each team was challenged to stack their pennies as high as they could until the stack fell over. The pennies were counted and recorded.
- Each team had 4 rounds and 4 data points. We ended up with 16 data points in all.
- When all teams had completed 4 rounds we gathered and briefly discussed four different mathematical ways that researchers use to interpret data: mean, median, mode, and range.
- To finish up our activity, as a group we added all of our data points together and divided them by the number of data points we collected (16) to end up with our class mean.
- We began this activity with me passing out some play money and us discussing the approximate value that each student had.
- After discussing the concept of average, the students were put into small teams and were given a large pile of pennies. Each team was challenged to stack their pennies as high as they could until the stack fell over. The pennies were counted and recorded.
- Each team had 4 rounds and 4 data points. We ended up with 16 data points in all.
- When all teams had completed 4 rounds we gathered and briefly discussed four different mathematical ways that researchers use to interpret data: mean, median, mode, and range.
- To finish up our activity, as a group we added all of our data points together and divided them by the number of data points we collected (16) to end up with our class mean.
AveragesCardGame (1) by K-m Lowe on Scribd
What's the Big Idea???
Computational fluency and flexibility with numbers extend to operations with larger and multi-digit numbers.
FAIR SHARES
Learning Goals
These goals are a combination of Big Ideas, Curricular Competencies, Content, and the Core Competencies.
- Multiplication and division up to three digits, including division with remainders
- Multiplication and division facts to 100 (emerging computational fluency)
- Model mathematics in contextualized experiences
- Develop mental math strategies and abilities to make sense of quantities
- Represent mathematical ideas in concrete, pictorial, and symbolic forms
These goals are a combination of Big Ideas, Curricular Competencies, Content, and the Core Competencies.
- Multiplication and division up to three digits, including division with remainders
- Multiplication and division facts to 100 (emerging computational fluency)
- Model mathematics in contextualized experiences
- Develop mental math strategies and abilities to make sense of quantities
- Represent mathematical ideas in concrete, pictorial, and symbolic forms