UNIT PLAN OVERVIEW
Unit Topic: Probability with Data Analysis
GUIDING GOALS:Students will be able to:∑ Make sense of the concepts never, sometimes, and always ∑ Connect the concepts of never, sometimes and always to real life situations∑ Predict the chance of an event happening using the terms never, sometimes and always∑ Collect, organize and analyze data based on first hand info∑ Compare data using appropriate language including quantitative terms∑ Use what they have learned to create activities with probable outcomes
RATIONALE:∑ The British Columbia IRP clearly states that basic probability skills are required at the Kindergarten and Grade one level.∑ Because of today's advanced technological world, statistical information is very common. It is important; therefore, for students to have a solid base for building on probability skills.∑ Probability helps students learn critical thinking skills.∑ These students have already learned some basic graphing skills, and probability allows them to build and improve their data analysis skills by graphing and analyzing their results in this unit.∑ Probability activities can be very hands-on and engaging for students.∑ Because children have a real sense of what is fair, probability can help them when they are playing games with dice and chance. This can also give them some real life connections.∑ The visual representation of graphing their data can help many students better understand the concepts of probability.∑ Working in groups can help students learn different strategies and points of views from their classmates.∑ Probability is used everyday to help make decisions.
PRIOR KNOWLEDGE:∑ We are assuming they have no prior knowledge of probability, but we will assess this by asking questions about sometimes, never, and always during the opening lesson.∑ Students will have basic data analysis skills from a previous unit. They will know how to collect data and record it on a graph.∑ Depending on the level of the students, pictures can be substituted for writing in most of the activities.
Subject: Math Unit: Probability Topic: Launching the unit
Objectives: ∑ Students will be introduced to probability as a part of mathematics∑ Students will explore the notions of probability that are part of their everyday lives∑ Students will be introduced to some language used in probability and will be able to use it appropriately (never, sometimes, and always)
Introduction: ∑ Read John Patrick Norman McHennessy -The boy who was always late! by John Burningham-- this story has many events that would never occur in real life∑ Ask question about the possibility of some of these events occurring. Use language such as what are the chances of, the probability of, the likelihood of.∑ When answering the questions stress words used such as never, sometimes and always
Teacher Activity Student Activity
∑ Display chart paper labeled "Probability Words" add the words sometimes, never and always and inform the class that they had been discussing a math concept called probability∑ Ask students if they can tell you what probability is or where they've heard it being used∑ Explain that probability is the chance of something happening -- it has something to do with making predictions and that we use probability in our lives everyday to make decisions -- ie) in weather probability is often used when discussing the possibility of rain etc∑ Point out the words that you have added to the chart paper and explain how these terms are often used to describe the probability of some events happening∑ Initiate discussion about probability of events in their own lives. Ask questions such as: What is the chance that you have recess every school day? What is the probability that you wake up every morning? What is the likelihood that you have dinner with a dragon. . .etc(use probability, likelihood and the chance of so the students get familiar with the language∑ Ask students if they heard any other words they think should be added onto the word chart∑ Go over new vocabulary∑ Pass out the envelopes of statements to each pair of students, explain that they have a statement which they have to decide where it would go under the headings never, sometimes, always∑ Ask a students to think of their own statement to fit into the three categories -- ask for some students to share∑ Hand out the probability folders with journals inside -- explain its purpose ∑ Students volunteer information by raising hands∑ Students are answering the questions using the language provided from the chart paper -- or may be introducing other language used in probability∑ Students add to word chart with suggestions of words they heard∑ Students decide together where they think their statement should go, read it aloud and Velcro it under the heading as they are called up∑ Other students have a chance to agree or disagree -- if they disagree there is a discussion to see other's points of view∑ A few volunteers share with the class their statements∑ Each student will title it "probability folder" and add their name
Lesson Topic Specific Lesson Objectives Activity/Task to meet objectives Ongoing Assessment
Lesson #2 -Students will become familiar with more language used throughout the unit: likely, unlikely-Students will be able to use this new vocabulary in sentences that are connected to their experiences -Class will review vocabulary on chart and will begin by discussing the concept of sometimes -- teacher will initiate conversation about likelihood, introducing terms likely and unlikely-in pairs students will brainstorm events that are likely or unlikely and write out at least one sentence for each (sentences should not include the words likely or unlikely so others can guess where they belong)-Students will add their statements to chart divided by headings, unlikely and likely -Have a checklist for each student reflecting their understanding of the language (do their statements fit into the right column)-Take notes to keep track of students' abilities, difficulties and progress.(These forms of assessment will be ongoing throughout the unit)
Lesson#3 -Students will collect, organize and analyze data based on first hand information-Students will be able to explain why two outcomes may not be equally likely because of uneven number of chances of each -Students will be given one bag of coloured chips to share between two or three students. There will be 2 green chips and 6 blue chips in each bag.-Students will pick a chip from the bag and record its colour, then return it to the bag. They will repeat this for a total of 15 draws.-Students will graph their outcomes (students are experienced in graphing) so they will have a visual representation of what happened - Students are asked to empty the contents of their bags and record in their journal how many green and blue chips there are-Teacher tallies up whole class outcomes and initiates conversation about why blue was more likely to be picked-Introduce the concept of something being very likely when the chances are very great -Students will write in their journal sentences explaining what the graph represents as well as why the outcome occurred the way it did-By the end of the discussion, students should be able to see that there were many more chances of picking blue chips than green chips because of the number of chips per colour
Lesson#4 -Students will use information they have learned from the previous lesson and will be able to make a prediction of the outcome-Students will understand that when chances are more equal, the outcome is more equal -Begin lesson by discussing prediction/predicting -- add these words to the probability word chart-Discuss with students how probability has something to do with making predictions, and that we use probability in our lives everyday to make decisions. Ie) what makes you bring an umbrella to school today?-Students will discuss the chance of rain etc-Teacher and students will discuss how weather forecasters need data/information to make predictions (add term data to vocabulary list)-In the same groups as the day before, students will be given a bag with 4 green chips and 5 blue ones-Students are asked to empty contents and record their data and make a prediction of what their outcome/graph may look like after 15 picks-Students graph the outcomes of the 15 picks and will write a sentence explaining if their findings confirm or disconfirm their prediction. They will also write a sentence as to why they think the outcome was different than the previous day -Students' prediction will determine if they understand that when the chances are more equal, the outcome is more equal-Students' explanations of why today's outcome was different from the previous lesson's outcome will show if they understand how the number of chances affects the outcome
Lesson#5 -Students will be able to transfer the concepts they have learned about chances and outcomes to a different probability situation (the spinner)-Students will learn that equal chances constitutes fairness -In same groups of two students are given a spinner -- The spinner has an unequal chance of landing one colour more than the other.-Students are each assigned to one of the colours on the spinner, they spin 10 times each and record the outcome-The question is the spinner fair? Why or why not? is on the board. -the students write their answers in their journals-When they finish this question -- ask them how would you make this fair- See Tank's book, pg 175 for directions to make spinner -journal is assessed for understanding of concepts -- this will be reflected in their answers
Lesson #6 -Students will learn that the it is equally likely for each outcome to occur because there is an equal number of chances-Students will make a reasonable prediction based on knowledge accumulated over the unit - In pairs, students are given one die one acts as recorder, the other tosses the die (they can switch roles after 10 rolls)- Students will make a prediction in their journal of what they think their outcome will be (explain that we will tally up whole class' results) -- students at this time have been experienced with tallying from previous lessons (if they are not -- take a few minutes to show/remind them how) -Students will record the number they roll by tallying their result on a chart (modeled by teacher)Roll one die 1 2 3 4 5 6 -When all students have completed rolling and recording have pairs get into small groups and tally their results up and discuss- Ask the students to share their ideas about what the data shows them-Initiate a conversation showing students how there is one chance out of six to get a one, one chance out of six to get a two etc. All of the numbers have one chance out of six-Ask students to compare the result to their predictions -- Record in their journal -Their journal entry will reflect their understanding of the concept -- look for a reasonable prediction as well as an explanation of why or why not their prediction was a reasonable one- Depending on the ability of the students, they may not meet the learning objectives set in this lesson -- this activity would serve as an introduction/ experience for this statistical concept
Subject: Math Unit: Probability with Graphing Topic: Preparation for Probability Party
∑ Students will draw on skills learned in this unit to be able to create and explain a probability activity.
∑ By creating a spinner or a pull from bag probability activity, students will demonstrate that they understand that the more there is of a specific colour, the greater the probability of picking/spinning that colour.
∑ Coloured classroom objects for "pull from bag" activity.
∑ Felt pens for spinner.
∑ Cardboard paper
∑ 1 piece plastic straw
∑ 1 piece of spinner face (round cardboard piece)
∑ Coffee and juice for parents.
∑ "How many of you like to celebrate when you accomplish something big?" "Well we've done a lot of learning in this probability unit, and I think we really deserve a celebration party!"
∑ Tell students they will be creating their own probability activity to share their learning with their parents at a "Probability Party".
Teacher Activity Student Activity
-Tell students they can choose to make either a spinner or a pull from bag probability activity.-If they choose to make a pull from bag activity they will choose from objects in the classroom (coloured cubes, beads, buttons. . .) If they decide to make a spinner, they will choose two coloured felt pens to colour it with.-Set out criteria that students should make it very likely, likely or just as likely to choose/spin one colour over another.-Give examples of different probability scenarios on chart paper, and how to explain them. Prompt students "If you want to make the activity very likely that a red object is pulled over a blue one, you might want to use 3 blue objects and ? red."-Once students have a good idea of how to set up their game and explain the outcome, have them pick up their materials.-Teacher will circulate and help students create their activities.-Teacher will take notes on how well students are able to explain their activity and its outcomes. -Students will give suggestions for their activities. -Students will decide which activity they would like to create and collect their materials.-Students will make their activity and explain its outcomes to the teacher.
Closure: ∑ Have students write one or two sentences in their probability journal explaining their activity.∑ Have them write one thing they are looking forward to at the Probability Party.
Assessment:∑ How well can students verbally explain their activity? Did they grasp the concept that the more of one colour means it is more likely to choose that colour? ∑ Were they able to express this concept in writing in their journal?
Culminating Activity-Celebration of Learning
Students will be able to:
∑ Explain how their activity works to parents, teacher and classmates.
∑ Feel successful and proud of their learning over this unit.
∑ Parents will be invited in to take part in the class' "Probability Party". Each will be asked to bring a snack to share with the class.
∑ Desks will be arranged in a horseshoe shape so parents can wander around and see all students' work.
∑ Students will have their completed probability activity and their probability folder displayed to show to the visitors.
∑ Parents will circulate and half the students will show and explain how their activity works. (Is one colour much more likely, a little more likely, or just as likely as another to be picked/spun?)
∑ The other half of the students will also circulate and try their classmates' activities.
∑ Students will switch so the other half of the class is able to show their activities to their classmates. Parents can continue to circulate or have coffee or juice.
∑ Once everyone is done viewing the activities, students and parents can enjoy some snacks.
∑ To wrap up, students will be presented with probability and data analysis certificates to honour their hard work and learning over the course of this unit.
Final Assessment∑ Teacher will collect Probability Portfolios, journals and graphs. Check for completion and progression of learning.∑ Review teacher checklists and observations kept during the unit.∑ Was the student able to effectively create a probability activity and explain how it worked? Can they recognize the different situations where something is most likely, likely, just as likely?∑ Was the student able to effectively collect, organize and analyze their data using graphs?
Resources:Burns, Marilyn. "About Teaching Mathematics" Probability and Statistics. Bereska, Carolyn, Bolster, Carey L., Bolster, Cyrilla H., Schaeffer, Richard. Exploring Statistics in the Elementary Grades K-6. Dale Seymour Publications: New York.Integrated Resource Package. Mathematics K-7.Jones, Graham A. and Thornton, Carol A. Data, Chance and Probability: Grades 1-3 Activity Book. Learning Resources Inc.: Illinois. 1992.Lutz, Val and Elspeth, Anjos. Statistics and Probability: Data Analysis Chance and Uncertainty . Resource Package. 1996. Tank, Bonnie. Math, By All Means: Probability, Grades 1-2. Math Solutions Publications: New York. 1996.