Core Curriculum Objective(s)
Describe all possible outcomes of an event or experiment that is based on chance using informal language (certain to happen, equally likely, more likely, not likely to happen, impossible (1SP2-2; South Carolina Standard- VI.A);
Overview:
In these lessons, children learn how to use probability terminology to describe all possible outcomes of certain events. The teacher uses transparency or magnetic manipulatives (such as colored counters, shapes, coins, colored bear counters) to create a pretend "purse" of objects. The teacher models how to use the terms certain, impossible, more likely, not likely, and equally likely given a variety of situations using the manipulatives. The students are given several opportunities to create their own probability drawings and to practice describing the drawings using the appropriate probability terms. Also, the students are given a chance to play a probability game, using student created M&M designs, with a partner and to share their creations with their classmates. In the culminating assessment, students must describe all possible probability outcomes given four different bags of gummi bears.
Focus/Essential Question(s):
When you are given a group of objects, what words can you use to tell what chance you have of selecting a certain object from that group?
Time Frame: Six 45 minute- 1hour lessons
Resources/Materials:
Period 1
For the teacher:
- Dry-erase board or chalkboard
- Dry-erase markers or chalk
- Overhead projector, transparency sheets, overhead pens (optional)
- Transparency counters or Comprehensive School Mathematics Program (CSMP) mini-computer magnets (10 red, yellow, green, blue, etc...)
For each student:
- Construction paper
- Pencils
- Crayons or markers
Period 2
For the teacher:
- Dry-erase board or chalkboard
- Dry-erase markers or chalk
- Overhead projector, transparency sheets, overhead pens (optional)
- Transparency counters or CSMP mini-computer magnets (20 red, yellow, green, blue, etc...)
For each student:
- Construction paper
- Pencils
- Crayons or markers
Period 3
For the teacher:
- Dry-erase board or chalkboard
- Dry-erase marker or chalk
- Overhead projector, transparency sheets, and overhead pen (optional)
- Transparency counters or CSMP mini-computer magnets (10-20 red, yellow, green, blue, etc...)
- Digital camera
- Computer disks (3 1/2 inches)
For each group:
- 1/2 lb. Bag of M&Ms
- Glue
- Construction paper (8-10 pieces)
- Pencils
Period 4
For the teacher:
- Dry-erase board or chalkboard
- Dry-erase markers or chalk
- Destination computer with remote control
- Computer disks with pictures of student designed M&M probability designs
- CSMP A-block shapes (magnetic) or overhead shapes
For each student:
- Construction paper
- Pencils
- Crayons or markers
- Coin cut-outs of pennies, nickels, dimes
- Scissors
- Glue
Period 5
For the teacher:
- Dry-erase board or chalkboard
- Dry-erase markers or chalk
- Overhead projector, transparency sheets, and overhead pens (optional)
- CSMP A-block shapes or overhead shapes
For each student:
- Coin cut-outs of pennies, nickels, dimes
- Glue
- Construction paper
- Scissors
- Crayons or markers
- Pencils
Period 6
For the teacher:
- Dry-erase board or chalkboard
- Dry-erase makers or chalk
- Overhead projector, transparency sheets, and overhead pens (optional)
- CSMP A-block shapes, colored counters, magnetic coins, and/or colored bear counters (or transparency materials for any of these items)
For each student:
- Four Ziploc bags: Bag 1 should contain 20 red and 20 green gummi bears, Bag 2 should contain 10 green gummi bears, Bag 3 should contain 20 yellow and 2 orange gummi bears, and Bag 4 should contain 1 clear and 30 orange gummi bears.
- 1 plate
- Paper
- Pencils
- Crayons or markers
Culminating Assessment:
The students will be given four bags of gummi bears. For each bag, the students will describe all possible outcomes for each bag by using the probability terms certain, impossible, more likely, not likely, and/or equally likely. The rubric below will be used to assess describing all possible outcomes of an event based on chance using informal language such as certain, impossible, more likely, not likely, and/or equally likely.
- The student correctly describes two different probability statements that correspond with Bag 1 = 2 points
- The student correctly describes two different probability statements that correspond with Bag 2 = 2 points
- The student correctly describes three different probability statements that correspond with Bag 3 = 3 points
- The student correctly describes three different probability statements that correspond with Bag 4 = 3 points
TOTAL = 10 points so that
10/10 points to 9/10 points = +
8/10 points = a check
Below 8/10 points = a dot
Instructional Activities:
Period 1
- The teacher will tell the students that they will be learning about a new concept called probability. The teacher will tell the students that probability is based on chance.
- Then, the teacher will read aloud as he/she writes the following probability terms on the board: certain, impossible, more likely, not likely, and equally likely. The teacher will tell the children that they will be learning the meaning of these probability words, and they will be learning which of these words to use given a certain situation based on chance.
- The teacher will draw on the board/transparency a circle with a handle at the top to make a "pretend" purse. Then, he/she will tell the children that this is his/her purse or bag and that inside the purse, he/she has candy. Then, the teacher will show the children the "pretend" candy by placing either 10 red transparency counters or red CSMP mini-computer magnets on the overhead projector or board.
- Then, the teacher will tell the children that he/she will pull out only one piece of candy from the purse without looking. The teacher will ask the students what color candy they think he/she could pull out of the purse. The teacher will ask the students if they think that he/she will pull out the red candy EVERY time. Once the children agree that the teacher will pull out a red candy every time he/she tries to pull out just one candy, the teacher will explain that, in this situation, the students should use the word CERTAIN. The teacher will explain that the word certain means that something will definitely happen (something will happen all the time, 100% of the time). The teacher will model the appropriate use of the word by saying, "It is CERTAIN that I will pull out a red candy because I have only red candy in my purse. So, I will pull out red every single time."
- Then, the teacher will repeat steps 3-4 using just yellow "candies," just green "candies," etc... until the children understand the meaning of the word CERTAIN.
- Next, the teacher will tell the children that they will be drawing a circle or "purse/bag" on a piece of paper and that inside the purse/bag, they will need to choose one color to draw their pieces of candy. Then, at the bottom of the paper, the students will need to write the following probability statement to match their picture: "It is CERTAIN that I will pull out a __________ (child's chosen color) candy." The teacher will ask the students if they have any questions, and then he/she will pass out construction paper, crayons, and a pencil to each child.
- After students have completed their drawings and written their sentences, they will share their pictures with the group by showing their picture and calling on a student to guess what probability statement is written below the picture.
- Then, to introduce the word IMPOSSIBLE, the teacher will place 10 green transparency counters or green CSMP magnets inside the drawn circle. The teacher will ask the children what they think that he/she will pull out. The teacher will ask the students if they think that he/she will pull out the green candy EVERY time. Once the children agree that the teacher will pull out a green candy every time he/she tries to pull out just on candy, the teacher will remind the children that, in this situation, the students should use the word CERTAIN when talking about pulling out the green candy.
- The teacher will ask, "So, can I pull out a blue candy?" Once the students agree that the teacher cannot pull out a blue candy because there are not blue candies in the purse/bag, then the teacher will explain that, in this situation, the children could also use the word IMPOSSIBLE. The teacher will explain that the word impossible means that something will never, ever, ever happen. The teacher will model the appropriate use of the word by saying, "It is IMPOSSIBLE that I will pull out a blue candy because I have no blue candy in my purse. So, I have no chance of pulling out a blue candy in this situation. It will never happen."
- The teacher will repeat steps 7-8 using other colored candies until the children understand the meaning of the word IMPOSSIBLE.
- Then, the teacher will tell the children that they will be drawing a circle or "purse/bag" on a piece of paper and that inside the purse/bag, they will need to choose one color to draw their pieces of candy. Then, at the bottom of the paper, the students will need to write the following probability statement to match their picture: "It is CERTAIN that I will pull out a __________ (child's chosen color) candy." Also, the children will write the following probability statement, "It is IMPOSSIBLE that I will pull out a ___________ (any other color NOT drawn in the circle) candy. The teacher will ask the students if they have any questions, and then he/she will pass out construction paper, crayons, and a pencil to each child.
- After students have completed their drawings and written their sentences, they will share their pictures with the group by showing their picture and calling on a student to guess what probability statements are written below the picture.
- Then, the teacher will review the terms certain and impossible by asking the students to explain when they might use these terms.
Period 2
- The teacher will review the terms certain and impossible by showing some similar examples from the previous day and asking the children to provide certain and impossible probability statements.
- Then, to introduce the probability phrases "more than likely" and "not likely," the teacher will place 20 green and 2 yellow transparency counters or green CSMP magnets inside the drawn circle. The teacher will ask the children what they think that he/she will pull out. The teacher will ask the students if they think that he/she will pull out the green candy EVERY time or a yellow candy EVERY time. The teacher will ask which color he/she has MORE of in the purse/bag. Once the children agree that the teacher has MORE of the green candy, the teacher will tell the children that, in this situation, the students could use the following two probability phrases "more than likely" and "not likely." The teacher will see if the students know how they can use these two phrases in this situation. The teacher should make sure that the students understand that it is MORE LIKELY that the teacher will pull out a green candy because there are a lot of green candies in the purse and only two yellow candies. Also, the teacher should explain that because there are only two little yellow candies that it is NOT LIKELY that the teacher will pull out a yellow candy.
- The teacher will repeat step 2 using other colored candies until the children understand the meaning of the phrases "MORE THAN LIKELY" and "NOT LIKELY."
- Then, the teacher will tell the children that they will be drawing a circle or "purse/bag" on a piece of paper and that inside the purse/bag, they will need to choose one color to draw a lot of pieces of candy, and they will choose a second color to draw one or two pieces of candy. Then, at the bottom of the paper, the students will need to write the following probability statement to match their picture: "It is MORE LIKELY that I will pull out a __________ (the color that the child chose the most of) candy." Also, the children will write the following probability statement, "It is NOT LIKELY that I will pull out a ___________ (the second color with only one or two candies) candy. The teacher will ask the students if they have any questions, and then he/she will pass out construction paper, crayons, and a pencil to each child.
- After students have completed their drawings and written their sentences, they will share their pictures with the group by showing their picture and calling on a student to guess what probability statements are written below the picture.
- Then, to introduce the probability phrase "equally likely," the teacher will place 10 red and 10 yellow transparency counters or green CSMP magnets inside the drawn circle. The teacher will ask the children what they think that he/she will pull out. The teacher will ask the students if they think that he/she will pull out the red candy EVERY time or a yellow candy EVERY time. The teacher will ask which color he/she has MORE of in the purse/bag. Once the children agree that the teacher has the SAME amount of red and yellow candies, the teacher will tell the children that, in this situation, the students should use the following probability phrase "equally likely." The teacher should make sure that the students understand that it is EQUALLY LIKELY that the teacher will pull out a red candy or yellow candy. Also, the teacher should explain that the children can remember the term equally likely by remembering that the word EQUAL means SAME AS and that they should use the term equally likely when they are given an event or situation which has the same amount of each color or item.
- The teacher will repeat step 6 using other colored candies until the children understand the meaning of the phrase "EQUALLY LIKELY."
- Then, the teacher will tell the children that they will be drawing a circle or "purse/bag" on a piece of paper and that inside the purse/bag, they will need to choose one color to draw some pieces of candy, and they will choose a second color to draw the same amount of candy as they did with their first color. Then, at the bottom of the paper, the students will need to write the following probability statement to match their picture: "It is EQUALLY LIKELY that I will pull out a __________ (the first color) candy or a __________ (the second color) candy. The teacher will ask the students if they have any questions, and then he/she will pass out construction paper, crayons, and a pencil to each child.
- After students have completed their drawings and written their sentences, they will share their pictures with the group by showing their picture and calling on a student to guess what probability statement is written below the picture.
- Then, the teacher will review the terms "more likely," "not likely," and "equally likely" by asking the children to describe situations in which they would use each of the terms.
Period 3
- The teacher will review all the probability terms from Periods 1 and 2 by designing a "purse" on the overhead projector or board and filling the "purse with either all one color or a combination of two colors (either with equal amounts of the two colors or a lot of one color and only one or two of a second color). The teacher will use either transparency counters or CSMP mini-computer magnets to "fill" the purse. Then, the teacher will model how to look at each of the probability terms (certain, impossible, more likely, not likely, and equally likely) and see which terms can be used with the given situation or if the term cannot be used at all when writing a probability statement.
- After modeling a couple of examples and modeling how to look at each of the terms to see if the terms apply to the given situations, the teacher will call on children to come to the board or overhead projector to design their own "purse" of candy and to call on a classmate to provide an example of a probability statement that applies to the child's purse design.
- After this activity, the teacher will divide the children into groups of two. Each child will design two "purses" or bags filled with M&M candy. Each "purse" will be designed on a separate sheet of construction paper. Inside each purse, the children can choose to fill the purse with either all one color or a combination of two colors of M&Ms (either with equal amounts of the two colors or a lot of one color and only one or two of a second color). The children will glue the M&Ms on the piece of construction paper inside their drawn circle. After each child finishes a design, he/she will write an answer key to go with the design. The answer key will include all possible probability statements about the design. The teacher should keep the probability terms on the board and remind the children to test out each probability term to see if the term will work with their designs.
- The teacher will pass out a 1/2 pound bag of M&Ms, 8 pieces of construction paper, glue, and pencils to each group.
- As the partners finish their designs, they will exchange designs, one at a time, and partners should try to think of all the probability statements that his/her partner wrote on his/her answer key for that design. For each statement that the partner gets correct, he/she earns one point. If the partner thinks of a probability statement that the designer did not include on the answer key, then the two partners should discuss the statement to determine if the statement matches the design. If this statement matches the design and it was not included in the answer key, then the child earns 2 points for thinking of a statement that his/her partner did not think of when designing the answer key.
- After one partner looks at a design, then the other partner should look at partner one's design and repeat the same above procedure. This game will continue, with partners keeping score of how many correct probability statements they describe, until two designs have been analyzed by each partner. Then, the partners will add up their earned points to determine which partner earned the most points.
- As the children engage in this partner game, the teacher will circulate and provide feedback to the children.
The teacher will review the probability terms one last time via a few examples on the board or overhead
projector
***** On this day, the teacher should use the digital camera to take pictures of the children's M&M designs to use for the next day.
Period 4
- The teacher will review all the probability terms by using the Destination computer to access the picture files of children's M&M designs.
- The teacher will open one of the student's picture files, and the teacher will call on children to look at the list of probability words on the board and to examine each word to determine if that word can be used with the M&M design shown. The teacher will continue calling on children until the class has found all the possible probability statements or outcomes. The teacher will open several other picture files for further practice with describing probability outcomes.
- Then, the teacher will repeat the procedures outlined in steps 3-13 in Period 1in order to reinforce and review the probability terms CERTAIN and IMPOSSIBLE. Instead of using colored counters, the teacher should use CSMP A-block shapes.
**** Note: If children finish their drawing assignments early, they can use coin cut-outs (pennies, nickels, dimes) to design purses containing all of one type of coin. The children will glue their chosen coins onto the construction paper. Also, the child must include the appropriate probability statements.
Period 5
- The teacher will review the terms CERTAIN and IMPOSSIBLE by creating several purse examples using CSMP shapes or overhead projector shapes. The teacher will call on students to describe the "purse" using the words CERTAIN and IMPOSSIBLE.
- The teacher will repeat steps 2-10 in Period 2 in order reinforce and review the probability terms MORE LIKELY, NOT LIKELY, and EQUALLY LIKELY. Again, instead of using colored counters, the teacher should use CSMP A-block shapes.
**** Note: If children finish their drawing assignments early, they can use coin cut-outs (pennies, nickels, dimes) to design purses containing either all one type of coin or a combination of two types of coins (either with equal amounts of the two coins or a lot of one coin and only one or two of a second coin). The children will glue their chosen coins onto the construction paper. Also, the child must include the appropriate probability statements.
Period 6
- The teacher will use the CSMP shapes, colored counters, magnetic coins, or colored bear counters (or transparency materials for any of these items) to provide several "purse" examples for the children. Again, the teacher will call on the students to provide appropriate probability statements.
- Then, the teacher will tell the students that now they will have a chance to show the teacher how much they have learned about probability.
- The teacher will tell the class that each child will receive four Ziploc bags of Gummi Bears. In Bag 1, every child will receive 20 red gummi bears and 20 green gummi bears. In Bag 2, every child will receive 10 green gummi bears. In Bag 3, every child will receive 20 yellow gummi bears and 2 orange gummi bears. In Bag 4, every child will receive 30 orange gummi bears and 1 clear gummi bear. The teacher will explain that, for Bag 1, the children must empty their bag onto a plate and then look at what colored bears they have on their plate and how many they have of each colored bear. Then, the children must look at the probability terms (certain, impossible, more likely, not likely, and equally likely) and decide which two probability terms can be used with Bag 1. For Bag 1, the children must write at least 2 correct probability statements by using 2 different probability terms (student description should include at least 1 equally likely statement and 1 impossible statement). For Bag 2, the children must write at least 2 correct probability statements by using 2 different probability terms (student description should include at least 1 impossible statement and 1 certain statement). For Bag 3, the children must write at least 3 correct probability statements by using 3 different probability terms (student description should include at least 1 impossible statement, 1 more likely statement, and 1 not likely statement). For Bag 4, the children must write at least 3 correct probability statements by using 3 different probability terms (student description should include at least 1 impossible statement, 1 more likely statement, and 1 not likely statement). At this time, the teacher will explain the rubric.
- Then, the teacher will pass out Ziploc bags, paper, and pencils to each child for the assessment.
- If children finish their assessment early, then they may make original probability designs by using objects other than colored "candies," shapes, or coins.
- Once all children have finished the assessment and the teacher has collected all papers and materials, the teacher will use transparency or magnetic bear counters to design each of the four bags on the board. The teacher will call on students to share the probability statements that they recorded on their assessment papers until all statements have been discovered for all four bags.
- Then, the teacher will ask the students what they have learned about probability, and he/she will record the knowledge on the board.
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