p174-218_Gr3BC-Patterns-Unit2-Probability

Unit 2: Probability Lesson Content Page Probability Introduction 174 176 1 Read Aloud: Pigs at Odds: First Reading 182 2 Pigs at Odds: Second Reading 188 3 and 4 Using Probability Language 189 3 Describing Probability 192 4 Comparing Probability of Possible Events 195 5 to 10 Investigating Probability with Simulations 197 5 Investigating Probability with Coins 200 6 Is It Fair or Not Fair? (Investigating Equal Likelihood) 204 7 Investigating Probability with Dice 206 8 Investigating Probability with Spinners 210 9 Investigating Equal and Unequal Probabilities 214 10 Creating a Fair Game 217 11 Reinforcement Activities

Probability Introduction Introduction to Probability Probability “is the study of measures of likelihood for various events or situations” (Small, 2009, p. 544). Van de Walle and Lovin state that the most important big idea at the primary level is that “not all events occur with equal likelihood” (Van de Walle & Lovin, 2006, p. 332). Even if we know the likelihood of an event, it may not occur as predicted. Probability makes sense for young students when it is discussed within the context of everyday events occurring in their lives. This involves acquiring the appropriate language to describe probability. As Marian Small explains, “you can never be sure what will happen on a particular occasion, unless the event is either impossible or certain” (Small, 2009, p. 544). For example, even though math class may be scheduled for 11:00 every day, it is not certain because there could be an assembly or a fire drill that could interfere with the planned event. When an event is certain, it is impossible for it not to occur, so the event will happen. The term ‘possible’ means that it is neither certain nor impossible and that an element of randomness or chance can affect the outcome. Throughout the discussions, students can use other terms such as ‘less likely,’ ‘more likely,’ and ‘equally likely’ to describe ‘possible’ in more comparative terms. Students also need to understand that probability affects the decisions that we make in our lives. For example, a high probability of rain affects the activities we plan and the clothes that we wear. Many people have misconceptions about probability. For example, some people think that if the number 5 is rolled on a die six times in a row, there is less chance that a 5 will be rolled a seventh time. In reality, the probability that a 5 will be rolled is 1 in 6, which is the same probability each time the die is rolled. Each outcome is an independent event and is not affected by previous outcomes. Students enjoy testing out the likelihood of events by carrying out simulations with dice, spinners, and coins. They can predict what is going to happen depending on the possible outcomes. From their results, they can also predict whether they will get the same outcomes if the simulation is repeated or is carried out on another population. Through such simulations, students learn about the element of change. For example, if one outcome has a very likely probability of happening, it does not guarantee that it will occur since chance plays a role. 174 Patterns & Relations/Data & Probability

Lesson Topic Page 1 Read Aloud: Pigs at Odds: First Reading 176 182 2 Pigs at Odds: Second Reading 188 189 3 and 4 Using Probability Language 192 195 3 Describing Probability 197 200 4 Comparing Probability of Possible Events 204 206 5 to 10 Investigating Probability with Simulations 210 214 5 Investigating Probability with Coins 217 6 Is It Fair or Not Fair? (Investigating Equal Likelihood) 7 Investigating Probability with Dice 8 Investigating Probability with Spinners 9 Investigating Equal and Unequal Probabilities 10 Creating a Fair Game 11 Reinforcement Activities Probability 175

1Lesson Pigs at Odds: First Reading English Introduction to the Read Aloud Language Arts Learning Standards The Read Aloud introduces math concepts in a meaningful context that allows students to make connections to their everyday lives. During the first reading Arts of Pigs at Odds, students apply their literacy strategies, such as inferring, using Learning prior knowledge, and making predictions, to understand the context and Standards progression of the story. (See the Literacy and Mathematics Links chart in the Overview Guide for more on comprehension strategies.) During the second reading, students act as mathematicians and apply the curricular competencies to discover and explore the math concepts embedded in the story. Both readings are also valuable for assessing where students are, what some of their misconceptions might be, what concepts need greater emphasis, and what differentiation may be necessary. Curricular Competencies • Comprehend and connect (reading, listening, viewing): Use sources of information and prior knowledge to make meaning; engage actively as listeners, viewers, and readers, as appropriate, to develop understanding of self, identity, and community; use personal experience and knowledge to connect to text and make meaning Content • Story/text: elements of story; text features Curricular Competencies • Exploring and creating: Create artistic works collaboratively and as an individual, using ideas inspired by imagination, inquiry, experimentation, and purposeful play Content • Elements in the arts: drama: character, time, place, plot, tension Assessment Opportunities Observations: Note each student’s ability to: – Make connections to the text, using prior knowledge – Make predictions based on text features and visual cues – Solve word meanings using illustrations and context – Make inferences and demonstrate understanding by engaging in discussions and follow-up activities 176 Patterns & Relations/Data & Probability

Materials: Read Aloud: Pigs at Odds Written by Amy Axelrod Summary: During the first reading of Pigs at Odds, students apply their literacy Illustrated by Sharon strategies, such as inferring, using prior knowledge, making connections, and McGinley-Nally synthesizing information, to understand the context of a family trip to a county Text Type: Fiction: fair. There are many opportunities to examine elements of style, such as word Narrative – Adventure choice, and how they enhance the story and help readers understand the text. Time: 20–30 Mr. and Mrs. Pig also use many interesting expressions that are plays on words. minutes NOTE: Pick and choose the prompts that are most suitable for your students. Before Reading Inferring/predicting Activating and Building On Prior Knowledge Building on prior • Show students the front cover and ask what they see. Read the title and the knowledge names of the author and illustrator. Have students predict what the book might be about and explain their reasoning. • Ask students what they think ‘at odds’ means and if they have heard that expression before. Ask what they think ‘odd’ means. • Have students make predictions of what they think the expression ‘at odds’ means. Check back with students’ predictions after reading the story. • Ask students if this is a fiction or non-fiction story and why they think so. • Ask students if they have ever been to an amusement park or a fair. Have students share what they did while they were there (e.g., rides, games, ate, etc.). Ask what kinds of rides, games, and food they tried. • Setting a Purpose: Explain that there are several interesting expressions and words to investigate in this story. Start with the expression ‘at odds’ and begin an anchor chart of each expression/word as you read the story. Have students make predictions about what they think these words mean and/or offer synonyms for each. Encourage them to suggest interesting expressions to add as they arise in the story. • Tell students, “Now that we have made our predictions, let’s keep reading to see if our predictions are correct.” Probability 177

During Reading Page spread Expressions Page spread Words book cover at odds page spread (“The Pigs tumbled tumbled…”) steered dipped page spread (“Mr. Pig and raring to go page spread (“‘Kids,’ colossal asked Mr. Pig…”) grinned the piglets…”) hold your horses page spread (“Let’s rock let’s rock and roll page spread (“The Pigs wobbled and roll…”) wobbled…”) page spread (“‘Kids,’ not for the faint of heart page spread (“‘C’mon, grew tired asked Mr. Pig…”) dear,’…”) page spread (“But after I don’t think the odds are Mr. Pig…”) in your favor I think we’ve got a better chance of seeing a two- headed snake page spread (“Mrs. Pig I should have quit while and the piglets…”) I was ahead page spread that’s more up your alley (“‘Sweetie’…”) page spread (“‘I’m down down to my bottom dollar to my’…”) I have a hunch Using text features/ • Read the page spread (“Mr. Pig and the piglets…”) aloud. Ask students why they inferring think Mr. Pig and the piglets are ‘raring to go’ and what that expression means. Analyzing/inferring (e.g., in a hurry) Ask what visual cues help to understand that expression. Analyzing/ • Ask what Mrs. Pig means when she says, “Hold your horses,” and why she using text features says this? (e.g., The piglets want to go on the rides, but Mr. Pig wants to play games.) Ask whether the piglets actually have horses. Discuss the difference between the literal and figurative meanings of certain expressions. • Explain that in this situation, the “piglets and Mr. Pig are at odds.” Ask what they think ‘at odds’ means. (e.g., they have different ideas, they disagree) • Read the page spread (“‘No problem,’ said Mr. Pig…”). Ask how the pigs settle the argument about where to go first. (e.g., Mr. Pig tossed a coin.) • Ask who won the coin toss and how they know. (e.g., The piglets, because they say “All right!”) • Ask where they think the family will visit first and why they think so. (e.g., the rides, the piglets’ choice) • Read the page spread (“Let’s rock and roll…”). Ask students what they think the expression ‘Let’s rock and roll’ means. (e.g., Let’s dance to rock and roll music; let’s get moving.) 178 Patterns & Relations/Data & Probability

Inferring • Ask how the picture helps to understand the meaning. Ask if there is actually Making connections/ inferring/visualizing/ rock and roll music playing. Ask how the organization of the words helps to understand what’s happening. Talk about the literal and figurative meanings using text features of the expression. Making connections/ • Read the page spread (“The Pigs tumbled…”). Ask students if they have ever inferring/visualizing/ been on a fair/amusement park slide and how it is different from the slide on using text features a playground. Using text features/ • Ask why they think the author uses the word ‘tumbled’ rather than ‘went’ to visualizing/analyzing describe how the pigs came down the slide. Have students close their eyes and Using text features/ imagine these two sentences: analyzing – The pigs went down the slide. – The pigs tumbled down the slide. • Ask students which sentence creates a better picture of the action. • Begin creating an anchor chart of rich words such as ‘tumbled’ and add in student suggestions for synonyms. (See other words to add to the chart above.) • Repeat this process with the words ‘steered’ and ‘dipped,’ and add them to the chart along with some synonyms. • Read the first page of the page spread (“‘Kids,’ asked Mr. Pig…”). Ask students if they have been on a roller coaster and how they liked it. • Highlight that the one in the story is called the “Colossal Coaster.” Ask what they think ‘colossal’ means (e.g., big, huge, etc.). Add this word to the anchor chart. Ask for some synonyms. • Ask why Colossal Coaster is a good name. (e.g., It sounds more impressive; both words start with a ‘C’ so it sounds catchy, etc.) Explain that it is known as alliteration when two or more words start with the same letter. • Read the second page of the page spread (“‘Kids,’ asked Mr. Pig…”). Ask students how they know that the piglets may not be able to go on the ride. Ask what the exception says. (e.g., If the parents ride with them, they can go on.) Ask why the piglets “grinned,” and what it means. Add this word to the anchor chart. • On the same page of the book, direct students’ attention to the sign that says, “Not for the faint of heart.” Ask what they think this expression means. (e.g., If you’re scared, don’t go on this ride.) Add this expression to the list. • Before reading the page spread (“The Pigs wobbled…”), ask students what they notice about the pigs on the Colossal Coaster. (e.g., They’re upside down.) Ask whether they think the pigs are enjoying the coaster and why they think so. (e.g., They’re smiling; they have their hands in the air, etc.) • Read the right-hand page and highlight that the author uses the word ‘wobbled’ to describe how the pigs get to the games. Ask what they think this means (e.g., walked while wobbling back and forth). Have students visualize ‘walked’ versus ‘wobbled.’ Discuss which word creates a better picture. Add this word to the anchor chart. • Read the page spread that shows all the carnival stands and signs. Ask students what they find interesting in the illustration. Ask what they notice about how the signs are designed. (e.g., They are usually in capital letters; they use different kinds of fonts; sometimes the letters are in different directions; Probability 179

Using text features/ they all have at least two colours; they have a border; sometimes they have inferring/making a picture; the contrast of colours and large letters gets our attention, etc.) connections • Ask whether there are any other names that use alliteration (e.g., Cotton Using text features/ inferring Candy, Basketball Bounce). Using text features/ • Read the page spread (“‘C’mon, dear,’…”). Ask what the name of the tattoo inferring shop is (e.g., Temporary Tattoos). Ask what the word ‘temporary’ means and Inferring/analyzing/ what it means in terms of a tattoo. Ask what the opposite of a temporary making connections tattoo would be. Making connections/ • Highlight the phrase ‘the pigs grew tired.’ Ask what they think it means and analyzing/inferring whether the pigs actually ‘grew.’ Ask how else the author could have conveyed this idea. Add this expression to the anchor chart. • Read the page spread (“But after Mr. Pig…”). Highlight that Mrs. Pig says, “I don’t think the odds are in your favor” when Mr. Pig is not doing very well at the Basketball Bounce game. Ask what Mrs. Pig means. (e.g., His luck has run out; he’s not doing so well.) • Ask what Mrs. Pig means when she says, “I think we’ve got a better chance of seeing a two-headed snake.” Ask whether she is referring to an actual two- headed snake. Discuss the literal and figurative meanings of this expression. Add the expression to the anchor chart. • Read the page spread (“Mrs. Pig and the piglets…”). Reread the phrase about how Mrs. Pig ‘dragged’ Mr. Pig down the midway. Ask what she means. (e.g., She forced him to leave the Basketball Bounce to do something else.) • Ask why Mrs. Pig wanted Mr. Pig to leave (e.g., he was losing too much money). Add ‘dragged’ to the anchor chart. • Direct students’ attention to the right-hand page of the spread. Ask what game Mr. Pig is playing now (strength game with a mallet). Ask what words are on the scale (e.g., wimp, weakling, chump, champ) and what they think they mean. • Ask what other words could be added to this game. • Read the page spread (“‘Sweetie’…”). Ask why Mrs. Pig suggests that Mr. Pig try bowling. (e.g., because he didn’t do so well at basketball or the strength game) • Ask why Mr. Pig says, “No, you go ahead. That’s more up your alley,” and what it means. (e.g., It means that she is better at bowling.) • Ask students if they have bowled before and what ‘alley’ means in reference to this game. • Explain the double meaning of ‘That’s more up your alley’ and add it to the anchor chart. • Turn to the page spread (“‘I’m down to my’…”). Ask students if they have played the water gun/balloon game at a fair/carnival. • Read the signs on the left-hand page of the spread. Ask students what they can win (e.g., toys or 4 tickets for the Colossal Coaster). • Read the right-hand page of the spread. Mr. Pig says, “I’m down to my bottom dollar.” Ask what this expression means and whether he is really using the bottom bill of a stack of dollars. (e.g., He only has one dollar left.) Ask why Mr. Pig only has one dollar left. (e.g., He spent too much money on Basketball Bounce.) 180 Patterns & Relations/Data & Probability

Inferring/ • Mrs. Pig says, “I have a hunch you’re going to win this time.” Ask what this using text features means (e.g., she thinks/she has a feeling that he’s going to win). Add the word ‘hunch’ to the anchor chart. • Have students predict whether Mr. Pig is going to win and why they think so. • Turn to the page spread (“Mr. and Mrs. Pig gripped…”). Ask students if Mr. Pig won and how they know. (e.g., The whole family is on the Colossal Coaster.) Synthesizing After Reading Visualizing/inferring • Have students study the anchor chart of the expressions and words from the story. They can choose one to write a refection about in their journals. • Ask students how the interesting vocabulary helped them visualize what was happening in the story. Refer to this chart at other times throughout the year and add new words as they arise in class. Materials: Further Practice BLM 37: Expressions! • Drama: Divide the class into small groups of three to four students each. BLM 37: Expressions! Provide each group with one of the expressions from BLM 37: Expressions! Raring to go! I think we’ve got a better Have students recreate a scene from the story OR create one of their own, chance of seeing where they incorporate the expression, showing that they understand what it means by its context in the scene. a two-headed snake! • Writing: Refer to the anchor chart to help students improve their writing and Hold your horses! I should have quit while I was ahead! make it more descriptive. Let’s rock and roll! That’s more up • Media Literacy: Use the examples of signs at the fair from the book your alley! (particularly on pages 14–15) to highlight the conventions and techniques of Not for the faint I’m down to my sign-making. If there is an event happening at the school, have students apply of heart! bottom dollar! some of these features in their own sign-making to create a poster for the event. I don’t think the odds I have a hunch you’re are in your favour! going to win this time! 58 © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 Scholastic Canada GR3 BC Patterns & Relations 4th Pass Reproducibles November 9, 2021 Probability 181

2Lesson Pigs at Odds: Second Reading Math Curricular Competencies Learning Standards • Reasoning and analyzing: Use reasoning to explore and make connections; Teacher estimate reasonably; develop mental math strategies and abilities to Look-Fors make sense of quantities; use technology to explore mathematics; model mathematics in contextualized experiences • Understanding and solving: Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving; visualize to explore mathematical concepts • Communicating and representing: Communicate mathematical thinking in many ways; use mathematical vocabulary and language to contribute to mathematical discussions; explain and justify mathematical ideas and decisions • Connecting and reflecting: Reflect on mathematical thinking; connect mathematical concepts to each other and to other areas and personal interests Content • Likelihood of simulated events, using comparative language Possible Learning Goals • Reflects on the importance of probability in real-life contexts • Predicts and describes probability using mathematical language • Relates fairness to outcomes that are equally likely • Explains what probability is within the context of the story • Identifies possible outcomes in situations (e.g., ways to win at games) • Identifies when the likelihood of winning a game is equally likely, thereby making it a fair game About the This story explores the concept of probability in terms of the likelihood of events occurring during the Pig Family’s adventure to the fair. As different events unfold, the Pig Family discovers that sometimes what is expected to happen because it is more likely, doesn’t always occur. This helps students recognize the role that chance plays in all events that are neither impossible nor certain. Throughout the text, students can predict the likelihood of events occurring based on an analysis of possible outcomes. 182 Patterns & Relations/Data & Probability

Moiulmldieankdpsetcshoseli,shrVlctisokaohioebicandllanye,,,bc,lmieeukc,qloeeapurlrryetray,oal:lulbiiynkna,elbilkiyle,itlyy,, It should be noted that although the word ‘odds’ is informally used to likely describe probability in the story, odds and probability in mathematical terms are different. Probability can be represented by the fraction of the desired outcome versus all possible outcomes, while odds can be represented by the fraction of the likelihood that an event will occur versus the likelihood that it will not occur. For example, the probability of getting heads when flipping a coin is ½ or 1:2, while the odds are 1/1 or 1:1 (probability of getting heads is 1 and probability of not getting heads is 1). It is best to use the term ‘probability’ throughout the unit and in all discussions. About the Lesson Within the lesson plan, there are more prompts than are feasible to use in one session. Some options for delivering the lesson are: • focus on some, rather than all of the book’s pages; • carry out the second reading over two or three days, reading a few pages each day; • revisit some of the pages on other days to explore the Further Investigations that may pertain to specific concepts. Materials: Assessment Opportunities Pigs at Odds Observations: Throughout the reading, the related problem-solving tasks, Time: 20–30 and discussions, note which concepts are too difficult or too easy for students minutes so next steps can be planned and lessons can be differentiated to meet individual needs. Note each student’s ability to: – Recognize probable or likely events – Compare events that are more or less likely to occur – Explain why something is likely, less likely, or more likely to occur – Connect ideas in the story to events in their lives Before Reading Activating and Building On Prior Math Knowledge • Ask students why the name of the book is Pigs at Odds: Fun with Math and Games. Ask students what the word ‘odds’ means within the context of the story. Explain that it is a play on words to refer to the likelihood of events happening, and the term more commonly used in math class is probability. Ask what probability has to do with math and games. Students can turn and talk to a partner before sharing ideas as a class. • Setting a Purpose: Tell students, “We are going to revisit the story as math investigators and learn about probability and what it has to do with games.” Probability 183

During Reading Connecting and NOTE: Use any of the prompts below as needed to explore the math in the story. reflecting Select the number and types of prompts to use based on your learning goal and the needs and interests of your students. Reasoning and Throughout the lesson, add probability vocabulary to an anchor chart. analyzing • After reading page spreads (“Mr. Pig and the piglets…”) and (“‘No problem,’ Understanding and solving said Mr. Pig…”), ask students why Mr. Pig is flipping a coin. Connecting and • Ask if students have ever flipped a coin to make a decision. reflecting • Ask what the possible outcomes are if you flip a coin (heads, tails). Ask which Connecting and reflecting/ possibility has a greater probability of happening. Introduce the term ‘equally communicating and likely.’ representing • Ask students whether they think flipping a coin is a fair way of making a decision. Connecting and • Partner Investigation: Have students predict the outcome of flipping a reflecting/reasoning coin 10 times. They can test out their predictions by flipping the coin and and analyzing recording their outcomes. Understanding and • Discuss whether what they predicted occurred. Ask why the outcome may not solving have turned out the way they had predicted. Introduce the concept of ‘chance’ Connecting and and how it plays a role in all events that are not impossible or certain, but reflecting possible. • After reading page spreads (“‘No problem,’ said Mr. Pig…”) and (“Let’s rock and roll…”), ask students, what side the coin landed on and explain how they know. (e.g., They went on the rides, so the coin must have landed on tails.) • Partner Investigation: Have students talk with a partner about how flipping a coin can be useful in other situations in their lives. • Before reading the page spread (“‘C’mon, dear,’…”), ask students if they have ever played a similar game and whether they won. • Ask what the options are that Mr. and Mrs. Pig can choose. Ask whether they think it is likely that Mr. and Mrs. Pig will win and why they think so. • After reading the left-hand page of the spread, discuss whether the probability of winning this game is greater or less than flipping a coin. Explain that there are 12 options that are equally likely to win, but unlikely that you would choose the correct month. Add ‘likely’ and ‘unlikely’ to the anchor chart. • Partner Investigation: Students work in partners. They each think of a different month and then find out if they picked the same month. They can repeat this game 10 times. Discuss whether they ever picked the same month and whether this happening frequently is likely or unlikely. • After reading the page spread (“But after Mr. Pig…”), ask students what happened to Mr. Pig. • Discuss what it means when Mrs. Pig says, “I don’t think the odds are in your favor.” • Ask what the outcomes are in this game (e.g., the ball goes in or it doesn’t go in). Ask which outcome is more likely and why they think so. 184 Patterns & Relations/Data & Probability

Understanding • Partner Investigation: Have students set up a bucket a certain distance away and solving and take turns trying to throw a crumpled piece of paper into it. They can Reasoning and repeat this activity five times each and record their results. analyzing • Discuss whether it was more probable for the paper to go into the bucket or Communicating and representing not. Have them explain their reasoning. Ask whether they think chance or skill plays a role in the game. • After reading page spread (“Mrs. Pig and the piglets…”), discuss why they think Mr. Pig did not win. Ask what role they think skill played and what role chance played. Ask whether another person could do better than Mr. Pig and why they think so. • After reading page spread (“‘Sweetie’…”), ask students how many opportunities Mrs. Pig had to win. • Ask whether chance or skill had a greater impact on the outcome and why they think so. • After reading page spreads (“‘I’m down to my’…”) and (“Mr. and Mrs. Pig gripped…”), ask students what they think the likelihood is of Mr. Pig winning the game. Have them explain how they knew they were correct. Connecting and After Reading reflecting • Discuss whether playing games at a fair is a good idea. Ask what rules you might follow to make sure that you do not lose too much money. • Have students reflect on what they think probability means. Create a definition and add it to the anchor chart. Further Practice • Discuss the games that students play that involve probability. Ask which ones involve skill and which ones involve chance and why they think so. • Reflecting in Math Journals. Have students explain in their own words what they think probability means. Have them include examples of probability in their lives. Materials: Math Talk: “Take Your Chances!” Math Focus: Exploring ideas about probability and chance (page 18 in the Patterns, Relations, Let’s Talk Data, and Probability big book and little • Show the big book page “Take Your Chances!” What do you see on this page books), dice and what do all of the pictures have in common? What does the title mean? Turn and talk to your partner. • What do you think? Discuss some of the students’ responses. continued on next page Probability 185

Teaching Tip •C oLient’s look at both sides of the coin. How can you describe the coin? People often Integrate the math talk talk about the two sides as being either heads or tails. What do you think this moves (see page 8) means and which side is which? throughout Math Talks to maximize student • Why did Mr. Pig flip a coin in the story? How can it help to make decisions? participation and active listening. If you wanted to choose between four colours, would a coin be a good way to select one? Why? What kinds of decisions can the coin help you with? (e.g., yes/ no answers or decisions that only have two possibilities) •5 Six-Sided Dice about dice? One is called a die and more than one are known What do you know as dice. When have you used dice before? • How many numbers are there on the five dice in the picture? How many numbers are displayed? Why is the cube a good shape for displaying six numbers? (e.g., It has six faces.) • What is a decision that could be made using one die? (e.g., choosing from six colours) Would it be a fair decision? Why? • Have you ever played the game called Yahtzee? In the game, you score a ‘Yahtzee’ by rolling five dice and getting the same number on all of the dice. You get three rolls. After each roll, you only have to roll the dice that you don’t like. Do you think it is very likely to get a ‘Yahtzee’? Why? Let’s try it together. What strategies might you use with your three rolls to increase your chances of getting a Yahtzee? •P aHrtanveerstIundveensttsiwgaortkioinn partners and try several times to get a Yahtzee. They can record the number of trials and the number of Yahtzees they rolled. • Compile the class results to determine how many trials took place and how many Yahtzees were rolled. •O tHheowr Dice dice different from the six-sided dice? If there are more sides on are these one die and one of each number, how does this affect the probability of rolling a certain number? For example, if a die has 12 sides with the numbers 1 to 12, is it more or less likely to roll a 6? Why? •S pWinhnaetrdo you notice about this spinner? Which colour has the greatest probability of being spun? What do you think it means that it is equally likely to land on green or blue? • Since green and blue are the most likely colours to be spun, does this guarantee that they will be spun? Why? • What other colours are equally likely to be spun? • What colour is unlikely to be spun? Why? • What colour is impossible to spin? Why? 186 Patterns & Relations/Data & Probability

P• aProtnseetrhIenfvoellsotwiginagtipornoblem: What combination of colours would be as equally likely as spinning blue? How many different combinations can you find? •P aIpmeargiBnae gthwe siqthuaSreqsuoanrtehse outside of the bag are actually inside the two bags. Look at Bag 1. How can you compare the likelihood of certain colours being chosen if one object is pulled out of the bag? Does this guarantee that our predictions are true? Why? • How can you compare the likelihood of certain colours being chosen for Bag 2? • Which bag would you want to have if your goal is to pull out a blue square? Why? Which bag would you want if your goal is to pull out a red square? Why? • Is it certain that you will get a specific colour? Why? • What would be impossible to pull out of either bag? P• aHrtanveerstIundveensttsicgraetaitoenone bag with the shown combinations of coloured tiles. They can take turns pulling out a tile 10 times and record their results. Ensure that students replace the chosen square after every trial. They can repeat the experiment and determine whether they get the same results. B• oWtthleereTohsavse you seen a game like this before? Which game in Pigs at Odds is similar? How do you think you play the game? • What do you think the probability of winning is? Will it be the same for every person who plays? Why? (e.g., No, because some people may be better at throwing than other people.) • Do you think that most people would be able to knock down the bottles? Why? (e.g., No, because the owners of the game would have to give away a lot of prizes and they wouldn’t make any money.) • How is this game different from some of the other examples of probability on this page? (e.g., Skill plays a part in the game.) •F oWllohwat-UmporTeahlakv:e you learned about probability? • What do you think chance is? What things do you do in your lives that involve chance? Probability 187

3 4Lessonsand Using Probability Language Math Curricular Competencies Learning Standards • Reasoning and analyzing: Use reasoning to explore and make connections; Previous Experience model mathematics in contextualized experiences with Concepts: Students have had • Understanding and solving: Develop, demonstrate, and apply mathematical experience describing and comparing the probability understanding through play, inquiry, and problem solving of everyday events. • Communicating and representing: Communicate mathematical thinking in many ways; use mathematical vocabulary and language to contribute to mathematical discussions; explain and justify mathematical ideas and decisions • Connecting and reflecting: Reflect on mathematical thinking; connect mathematical concepts to each other and to other areas and personal interests Content • Likelihood of simulated events, using comparative language Mppullirioankkosetcebhsellayyir,,bVbtpllaioeelriicot,nsyabs,c,baeuilubmirnktlillaeapiitkrlioynyyes,,:llisyen,ieqbmuleao,lrley About the Students can first learn about events that are impossible, certain, or probable to happen. They can refine their understanding of ‘probable’ by using comparative terms such as less likely, equally likely, or more likely. Van de Walle suggests that students “in the primary grades need to develop an intuitive concept of chance: the idea that some events, when compared to others, have a better or worse likelihood or an approximately equal likelihood of happening” (Van de Walle, 2001, p. 354). Giving them a variety of opportunities to compare the probability of events occurring and describe them using mathematical language (e.g., more likely, equally likely, less likely) will help with this development. Another helpful way to develop the language of probability is to use a probability line. Marian Small describes the probability line as “a pictorial model that shows relative probabilities, making it a useful tool for helping students describe and compare the likelihood of events” (Small, 2017, p. 629). Students can apply their knowledge of the number line to help them interpret the probability line since they both increase from left to right. The probability line not only helps develop the vocabulary students need but offers a visual image for comparing the likelihood of certain events occurring. About the Lessons In the two following lessons, students review probability concepts learned in previous grades and further develop the mathematical language needed to compare the probability of events occurring. 188 Patterns & Relations/Data & Probability

3Lesson Describing Probability Teacher Possible Learning Goals Look-Fors • Identifies and describes the probability of events using mathematical language • Uses simulations of events to represent different probabilities Materials: paper bags; variety • Describes the probability of events using mathematical language (e.g., less of coloured, concrete materials (e.g., colour likely, equally likely, more likely, impossible, certain, uncertain) tiles, bears, pattern blocks, connecting • Explains their reasoning for predicting certain probabilities cubes) • Simulates events that are less likely, more likely, equally likely, impossible, and Time: 50 minutes possible using concrete materials Minds On (15 minutes) • Show students a paper bag. As they watch, place 3 blue tiles, 5 yellow tiles, and 2 green tiles inside the bag. Ask how many tiles are in the bag. • Shake up the bag and ask the students the following prompts. After each prompt, have a student pull out a tile to test their prediction. Have students replace the tile each time. Possible prompts include: – Do you think it is possible to pull out a yellow tile from the bag? Why? (e.g., Yes, you put yellow tiles in there.) Let’s pull a tile out and see what happens. Do you still think that ‘possible’ is a good description? Why? – Could we pull out a green tile? (e.g., Yes, there is one green tile in the bag.) Let’s pull a tile out. – Is it less likely or more likely to pull out a green tile? (e.g., less likely because there is only one) Let’s pull out a tile and see. Why might we not have pulled out what we predicted? – Do you think we can pull out a red tile? (e.g., No that’s impossible because there are no red tiles.) Let’s try. • Add the words that were used in the discussion to an anchor chart of probability vocabulary (e.g., possible, likely, more likely, less likely). Discuss the meaning of each word in relation to the tiles in the bag. • Ask students what you would need to have in the bag so it is certain that you will pull out a yellow tile. • Remove the tiles and have them watch as you put in 5 blue tiles, 2 yellow tiles, and 3 red tiles. Record the following questions on chart paper and have students discuss them in pairs. – What is possible to pull out of the bag? – What is impossible? – What is less likely? Probability 189

– What is more likely? – What is certain? • Discuss students’ answers and record them. • Have a student pull out a tile and discuss whether the outcome matches what was expected. Replace the tile and have another student pull out a tile. Repeat this process 10 times. Discuss why the results may not be what students expected. Explain that chance plays a role in all events unless they are certain or impossible. For this reason, we can never be sure what will happen. Working On It (15 minutes) • Explain to students they are going to create their own paper bag with a partner. Their task is to create a bag with the following criteria: – something is less likely to be pulled out – something is more likely to be pulled out – something is impossible to be pulled out • They can choose any type of concrete materials to put in the bag. • After they have created their bag, have them create statements that describe the possibilities of pulling different items out of the bag. They can record their statements on chart paper. Differentiation • For students who need language support, complete the Working On It section in a small group to help consolidate the key words. Show students different examples relating to each word and have them create their own personal dictionary. Refer to the words on the anchor chart each time you use them. Use gestures (e.g., thumbs up for possible, thumbs down for impossible) to help students as they learn the new words. • For students who need more of a challenge, have them create another scenario that represents an event that is equally likely to occur. Assessment Opportunities Observations: Pay attention to how accurately students are using the correct mathematical language to describe the probability of the event occurring. Conversations: As students are creating their own probability bags, use the following prompts to check in with different pairs. – What are all the possible outcomes that could occur if you pull something out of your bag? Explain how you know they are possible. – What do you know that is likely about your probability bag? Explain how you know it is likely. Is it more likely or less likely? – What do you know that is less likely? Why it is less likely? Is it very unlikely or just a little unlikely? – What do you know that is impossible? What else is impossible? Why are these outcomes impossible? 190 Patterns & Relations/Data & Probability

First Peoples Consolidation (20 minutes) Principles of Learning • Group pairs together and have them share their probability bags and sentences with each other. Encourage them to discuss whether they agree with the statements or not, giving reasons for their thinking. • Meet as a group. Discuss any examples that students found confusing. Ensure all students understand the math language. Review what needs to be in a bag in order for an outcome to be certain to occur. • Building Growth Mindsets: Ask students how they feel about all of the new vocabulary that has been introduced in this lesson. Explain that it is normal to feel overwhelmed or frustrated at this early stage in a unit. Learning math words is like learning a new language. Discuss what they have to do when learning a new language. Emphasize that it takes time and patience. Practice also plays an important role. The more you use the language, the better you become at speaking and understanding it. Tell students that over the next few days, they will play some games that will help them use the words in the word wall and better understand their meaning. Ask students what they can do when they feel overwhelmed or confused in math class (e.g., take a break, do some stretching, ask a friend, look at an anchor chart). It is important for students to develop a repertoire of strategies to help them cope in stressful situations so they do not develop math anxiety. This supports the First Peoples Principles of Learning that learning is holistic, reflexive, reflective, experiential, and relational (focused on connectedness, on reciprocal relationships, and a sense of place); and that learning involves patience and time. Further Practice • Reflecting in Math Journals: Have students use pictures, numbers, and/ or words to give an example of each of the key words used in the lesson (e.g., possible, impossible, likely, unlikely). Probability 191

4Lesson Comparing Probability of Possible Events Teacher Possible Learning Goals Look-Fors • Identifies and describes the probability of events using mathematical language • Compares the probability of different events using a probability line • Identifies whether events are impossible, certain, or probable • Describes probable events using mathematical language (e.g., more likely, less likely, equally likely) • Simulates events that are more likely and less likely to occur • Understands how to use a probability line to compare and order probabilities Materials: Minds On (20 minutes) © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1“Take Your Chances!” • Draw a line on chart paper and label it “Probability Line.” Ask what they (page 18 in Patterns, Relations, Data, and think the line is for. Explain that students can compare probability of events Probability big book and happening by ordering them along a line, much like they order numbers on little books); paper bags; a number line. variety of coloured, concrete objects (e.g., • Ask what word they could put on the far left end of the line if it is supposed to bears, pattern blocks, connecting cubes), describe an event that cannot happen. Print the word ‘Impossible’ under the BLM 38: Probability Line line. Ask what they think should go at the other end and why. (e.g., ‘Certain,’ because it is the opposite of impossible and it means that the event will Time: 60 minutes definitely happen.) BLM 38: Probability Line • Ask what the line in between impossible and certain represents (e.g., events Scholastic Canada GR3 BC Patterns & Relations Unlikely Likely that are possible to happen). Ask what they think could go halfway between Reproducibles impossible and certain. Discuss why less likely and more likely are not November 9, 2021 appropriate. Introduce the term, ‘equally likely.’ Have students turn and talk to a partner about events that are equally likely to occur. They can think about Impossible Equally Likely Certain different colours of tiles in a bag as a context. 4th Pass • Discuss students’ responses (e.g., there are 5 red tiles and 5 blue tiles in a bag). • Show students the “Take Your Chances!” page in the big book and draw 59 attention to Bag 1. Ask what events are possible if one tile is pulled from the bag (e.g., a red tile, a blue tile, a yellow tile). • Ask how they would order these possibilities on the probability line. They can discuss this with their partner. • Discuss students’ responses. Put the colours on the line with descriptive words (e.g., less likely, more likely). • Ask what they would need to do to the bag to create an event that is equally likely (e.g., remove one red tile so there is one red tile and one blue tile; add 192 Patterns & Relations/Data & Probability

a blue tile so there are 2 red and 2 blue tiles; add 2 red tiles so there are 4 red tiles and 4 yellow tiles, etc.). Discuss why there are so many possibilities. Working On It (15 minutes) • Students work in pairs. • Explain that they are going to create their own probability bag of items. They put objects in the bag that represent more likely, less likely, and equally likely events. They can create statements that describe events that are more likely, less likely, and equally likely when pulling a tile from the bag. • Students create a probability line on chart paper and place possible outcomes for pulling out a tile on the line. Differentiation • For students who need language support, ensure they understand the probability line and how to use it. Compare it to a number line. Use events in their lives as examples for the various possibilities. • If students struggle with creating their own probability line, have them use BLM 38: Probability Line. Assessment Opportunities Observations: Pay attention to how students interpret the correct mathematical language to describe the possibility of events: – Do they understand what equally likely means? – Can they differentiate between equally likely and likely events? – Can they order likely events in relation to each other? Conversations: As students are creating their own probability bags, use the following prompts to check for understanding: – Why is this event equally likely? Is there another way that you could make an equally likely event? Why do both ways represent equally likely? – You have said that these two events are both less likely to occur. Which is less likely? Why? – What is impossible for me to pull out of the bag? Why is it impossible? What other events are impossible? What do all of the impossible events have in common? (e.g., There is nothing in the bag to represent them.) Consolidation (25 minutes) • Students meet with another pair and take turns sharing their probability lines and statements. Have them discuss whether they agree or disagree and why. They can also pull some items out of the bag, one at a time, replacing them after every draw, to see if their predictions matched what actually happened. • Meet as a class. Discuss how they ordered the events on their probability line. • Show one of the bags with the probability statements. Ask what would need to be in the bag to have an event that is certain. Probability 193

Materials: • Have 10 students take turns pulling out an item from the bag and then replacing Digital Slide 52: Probability Bags it. Record what gets pulled from the bag. Ask whether the 10 outcomes match the statements. Discuss why what actually happens doesn’t always match the Bag 1 Bag 2 predictions and that chance plays a role in any possible events. Scholastic Canada GR3 BC Patterns & Relations Slide 3rd Pass • Add any new terms to the anchor chart and to the word wall (e.g., more likely, Digital Slides November 9, 2021 52: equally likely, very unlikely). Digital Math Talk: Probability Bags, Math Focus: Using a probability line to compare the probability of events occurring probability line drawn Let’s Talk on chart paper • Display a probability line with the terms ‘impossible,’ ‘certain,’ and ‘equally Teaching Tip likely’ printed on it. Integrate the math talk moves (see page 8) • Show students Digital Slide 52: Probability Bags. Look at the two bags. Can we throughout Math Talks to maximize student compare the probability of pulling items out of the bags? Why? (e.g., There are participation and active the same number of items in each bag.) listening. • Which bag would be better to use if you want to pull out a green apple? Where would you put this event on the probability line? (e.g., on the likely side) • Look at the bags again. What bag should we use if we want to pull out a yellow apple? (e.g., it doesn’t matter) Why doesn’t it matter? (e.g., both bags have the same number of yellow apples) Where would you put that on the probability line? (e.g., in the middle—where it says equally likely) How could you change the apples in one of the bags to make another equally likely event? Turn and talk to your partner. • What did you find? What is important when you create an equally likely event? (e.g., There must be an equal number of items in each bag.) • What bag could we use if we wanted it to be less likely to pull out a green apple? Where would we put this event on the probability line? • Do we know for sure that our predictions will actually happen when we pull out an apple from the bag? Why? Further Practice • Create a class probability line (e.g., on a bulletin board). Each day, describe two or more events that could occur and have students discuss where they could be placed on the probability line. 194 Patterns & Relations/Data & Probability

5 10Lessonsto Investigating Probability with Simulations Math Curricular Competencies Learning Standards • Reasoning and analyzing: Use reasoning to explore and make connections; Previous Experience model mathematics in contextualized experiences with Concepts: Students have • Understanding and solving: Develop, demonstrate, and apply mathematical investigated probability and described possible understanding through play, inquiry, and problem solving; visualize to explore events using comparative mathematical concepts; develop and use multiple strategies to engage in mathematical language. problem solving • Communicating and representing: Communicate mathematical thinking in many ways; use mathematical vocabulary and language to contribute to mathematical discussions; explain and justify mathematical ideas and decisions; represent mathematical ideas in concrete, pictorial, and symbolic forms • Connecting and reflecting: Reflect on mathematical thinking; connect mathematical concepts to each other and to other areas and personal interests Content • Likelihood of simulated events, using comparative language About the Participating in simple games, simulations, and experiments allows students to predict a particular outcome based on what theoretically should happen, and then test out their predictions to see what actually occurs. In this way, students can experience the role that chance plays in many events in their lives. Part of testing probability is first establishing all possible outcomes. For example, when tossing a 6-sided number cube, there are 6 possible outcomes, 1, 2, 3, 4, 5, or 6, all of which are equally likely. Students can describe what they think will happen using comparative language, carry out the test, and then compare the results with their predictions. They can also predict whether the results will be the same if the experiment is repeated. Students and some adults often develop misconceptions about probability, such as believing that they can somehow influence the next result or that the previous results will affect future ones (Small, 2009, p. 557). For example, people may think that a 3 is more likely to be rolled on a die if it has not been rolled for a long time. As Van de Walle and Lovin aptly continued on next page Probability 195

Math Vocabulary: explain “[c]hance has no memory” (Van de Walle & Lovin, 2006, p. 331). cpgmeusoraqnpoiomnucibrnseaeean,lrsbllethyi,iakrlei,leeitinakydxly,,depi,eislpemyl,,eo,rdipstscmaiosseciesilrebsltnsi,ka,iltieibistnlly,ye,,,, It is also important for students to realize that when they are testing out outcome, results a prediction, the goal is not about one person or event winning or losing. They are being mathematicians testing out ideas and learning more about how probability works in their lives. About the Lessons In the following lessons, students predict what they think will happen in simulations and experiments based on determining possible outcomes, and then carry out the game or experiment to find out what actually happens. They also further explore the concept of equally likely as they determine whether games are fair or not. Students also design their own fair game. 196 Patterns & Relations/Data & Probability

5Lesson Investigating Probability with Coins Teacher Possible Learning Goals Look-Fors • Describes and predicts the probability that an event will occur • Compares the predicted results with the actual results and explains why they Materials: may not be the same Digital Slide 54: Heads or Tails Tally Digital Slide 53: Coins • Names all of the possible outcomes of tossing a coin using mathematical Tails Heads language (e.g., heads and tails are equally likely) Photo: © asafta/iStockphotoa • Predicts a result based on the possible outcomes (e.g., If I toss a coin 50 times, Scholastic Canada GR3 BC Patterns & Relations 3rd Pass I could get heads 25 times) Digital Slides November 9, 2021 • Consistently carries out an experiment • Uses mathematical language to compare a prediction with the actual results Photos: © asafta/iStockphoto • Explains why predictions don’t always match actual results Digital Scholastic Canada GR3 BC Patterns & Relations 53: 3rd Pass Minds On (15 minutes) Digital Slides November 9, 2021 Coins, • Project Digital Slide 53: Coins. Ask what coins are in the images and clarify Slide what the different sides of the coins are called. Digital Slide 54: Heads • Ask students if they have seen someone flipping a coin to make a decision or Tails Tally, BLM 39: such as who will go first in a game. Ask students why Mr. Pig flipped a coin in the story Pigs at Odds. Ask whether they think flipping a coin is a fair way to Coin Toss Experiment, make a decision and why they think so. a variety of plastic or • Explain to students that they are going to carry out experiments to learn more real coins about probability, just like mathematicians do. Time: 55 minutes • Ask how many times they think heads will come up if they toss a coin 60 © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 BLM 39: Coin Toss Experiment 20 times. They can turn and talk to a partner. Record their predictions. Scholastic Canada GR3 BC Patterns & Relations If we toss a coin 20 times, how many times will it land on “Tails”? • Project Digital Slide 54: Heads or Tails Tally and use the tally table to record tosses. Reproducibles Perform the experiment 3 times and make note of any changes you make in how • Review the results of the experiment by posing the following questions: November 9, 2021 you do the experiment . – How many times did we toss heads? Tails? Experiment 1 Experiment 2 Experiment 3 – Do you think we would get the same result if we were to do the Prediction: times Prediction: times Prediction: times experiment again? Would you change your prediction? Tails Heads Tails Heads Tails Heads • Ask students how this experiment has helped them better understand the 4th Pass problem. Working On It (20 minutes) • Students work with a partner and carry out the same experiment as in the Minds On. They can predict what they think will happen, perform the Probability 197

experiment three times, and record their results on a copy of BLM 39: Coin Toss Experiment. • Review the instructions on the BLM. Ask students what it means to make note of any changes they make to the experiment. • Explain to students that they can carry out the experiment in any way they choose (e.g., taking turns tossing the coin; each person tossing the coin ten times in a row; shaking the coin in a cup before dumping it out). Differentiation • Provide counters to keep count of each toss if students have difficulty keeping track of their total number of tallies. • For students who may need a challenge, provide them with a different coin to test, to see if their results are similar or different. Assessment Opportunities Observations: Pay attention to students’ ability to: – Accurately record their results using a tally table – Describe results using the language of probability (e.g., equally likely, more likely, less likely, heads, tails, etc.) – Consistently carry out their experiments Conversations: Pose some of the following prompts to check for understanding: – Is your prediction looking likely so far? – Did you and your partner have the same prediction? – If not, which of your two predictions is looking more likely so far? – If you could change your prediction, what would you change it to? Why? – What will/did you change from the last experiment to this one? Did it change your results? 198 Consolidation (20 minutes) • Meet as a class. Ask whether students changed their predictions from experiment to experiment. Discuss why they changed them. Ask whether it made a difference as to whether the predictions matched the results. • Discuss whether they made any changes to the way in which they carried out their experiment and why they made those changes. • Create a T-table with ‘heads’ as one heading and ‘tails’ as the other heading. • Have each pair share the number of times heads came up and the number of times tails came up in their experiments, while you record the results. Together, total the results for each column using mental math strategies or a calculator. • Ask what they think the probability is for getting heads or tails when flipping a coin. Ask whether they think the two possible outcomes are equally likely and whether it is a fair way to make a decision. Discuss the role that chance plays in flipping a coin. Patterns & Relations/Data & Probability

First Peoples • Ask whether they think they are more likely to get ‘heads’ if ‘tails’ came up six Principles of Learning times in a row. Explain that chance has no memory when flipping a coin and previous flips do not affect the next flips. • Building Growth Mindsets: Discuss how carrying out experiments is not about one person winning or losing. It is also not about ‘hoping’ that a desired outcome will occur and then changing conditions so it will happen. Explain that they are mathematicians testing out ideas and they need to be very careful to carry out each trial in a consistent manner so the results cannot be affected by other factors. Make a list of ways in which partners can interact so they are working as mathematicians and not as competitors in a game. Post the list in the room and refer to it if students start getting competitive about the actual experiment. This supports the First Peoples Principles of Learning that learning ultimately supports the well-being of the self, the family, the community, the land, the spirits, and the ancestors. Further Practice • Have students try either a different coin or a different partner to test the same experiment. • Independent Problem Solving in Math Journals: Whenever they need to decide something at Masha’s house, her dad pulls out a coin and says, “Heads I win, tails you lose.” Do you think that this is a fair way to decide? Explain. Probability 199

6Lesson Is It Fair or Not Fair? (Investigating Equal Likelihood) Math Curricular Competencies Learning Standards • Reasoning and analyzing: Use reasoning to explore and make connections; Teacher model mathematics in contextualized experiences Look-Fors • Understanding and solving: Develop, demonstrate, and apply mathematical Previous Experience with Concepts: understanding through play, inquiry, and problem solving; visualize to explore Students have investigated mathematical concepts; develop and use multiple strategies to engage in what makes outcomes problem solving less likely, more likely, or equally likely. • Communicating and representing: Communicate mathematical thinking in many ways; use mathematical vocabulary and language to contribute to mathematical discussions; explain and justify mathematical ideas and decisions • Connecting and reflecting: Reflect on mathematical thinking; connect mathematical concepts to each other and to other areas and personal interests Content • Likelihood of simulated events, using comparative language Possible Learning Goals • Identifies and describes events as fair or unfair in terms of equally likely or not equally likely outcomes • Explains how to change an unfair game into a fair game by making outcomes equally likely • Identifies events as equally likely or not equally likely • Describes a fair game as equally likely for any player to win • Sorts spinners according to whether their outcomes are equally likely or not equally likely • Explains how to change an unfair game into a fair game About the Students may find it difficult understanding the concept of fairness in games, sometimes interpreting fair as meaning they have a better chance of winning than their opponent. They need to understand that in a fair game, it must be equally likely for all players to win. If skill is also involved in the game (e.g., throwing balls into a basketball hoop), 200 Patterns & Relations/Data & Probability

Mflaikaier,tlhyu,nVufoancilrik,aeeblquyulaarllyy:likely, they need to understand that chance may not be the only factor that determines the winner. As students play games, they can reflect on whether the game is fair or not and determine whether chance or skill or both are involved in determining a winner. They can also think of ways to make an unfair game a fair game by ensuring that all players are equally likely to win. About the Lessons In this lesson students further investigate the concept of fairness and what equally likely means by analyzing and playing games. Materials: Minds On (15 minutes) Digital Slide 55: Dice • Show students Digital Slide 55: Dice and ask them what they see (6-sided die, Photos ©: (10-sided die) PixelSquid3d/Shutterstock; (6-sided die) malerapaso/iStockphoto 10-sided die). Show students the actual dice and pass them around. Ask how the dice are the same and how they are different, especially in terms of the Scholastic Canada GR3 BC Patterns & Relations 3rd Pass number of faces that they have. Digital Slides November 9, 2021 pencils, • Explain to students that they are going to play a game with you using the dice. paper clips, If they win, they get 10 minutes of free-choice time and if they lose, they do not. 6-sided die, 10-sided • You will play with the 10-sided die, while the class will play with the 6-sided die, Digital Slide 55: die. Both teams take turns rolling the die for 10 turns, continually adding up the numbers after each turn. The team with the higher total wins. Dice, BLM 40: Spinners, • Ask students who they think will win and why they think so. BLM 41: Fill It Up! • Play the game and record the numbers that each team rolls. • Discuss the results. Ask whether they think the same team will win if they Time: 55–60 minutes play the game again. Ask if they think this is a fair game and explain their BLM 40: Spinners continued reasons. Have students turn and talk to a partner about what fair means. After discussing their responses, emphasize that fair means all players have 3 4 BLM 40: Spinners an equally likely chance to win. 2 1 • Ask whether it is possible for the 6-sided die to ever win the game against the 1 2Yellow Red Red 4 3 Blue 10-sided die. (e.g., Yes, because the 10-sided die could show 10 ones in a row, Yellow while the 6-sided die could show 10 sixes in a row.) Green Blue Red Green • Ask how they could make the game fair. © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 14 BLM 41: Fill It Up! • Tell students that you will still give them 10 minutes of free-choice time later 2 cInhsotorsuectoionnlysO1: CNhEocoosleouar .cSoploinuBrthl(uoeressphianpneero . rEnaucmhRbtiemerde) othneysopuirnsnpeirnlnaenrd. sEaocnhypoluaryceor lcoaunr, on because the game wasn’t fair. 1 you get to fill2in one of your squares . The person who fills in their squares first wins! Scholastic Canada GR3 BC Patterns & Relations Red Working On It (25–30 minutes) Reproducibles 41 November 9, 2021 • Pre-cut the eight spinner cards from BLM 40: Spinners. Use one set of cards Player One Blue per student pair. In partners, ask students to sort the spinners as to whether Yellow they are fair or unfair (e.g., each player has an equally likely chance of winning if they each choose one colour). Player Two 62 © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 • Partners choose a fair spinner and an unfair spinner from their cards and Scholastic Canada GR3 BC Patterns & Relations 4th Pass use them to play two games of “Fill It Up!” Show students the “Fill It Up!” Reproducibles © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 November 9, 2021 Probability 201 4th Pass 61 Scholastic Canada GR3 BC Patterns & Relations 4th Pass Reproducibles 63 November 9, 2021

game on BLM 41. Together, review the rules and answer students’ questions. If necessary, have two students model how to play the game. They play one game using the fair spinner and one game using the unfair spinner. • Show students how to use a pencil and paper clip to make the spinner. Differentiation • For students who need language support, ensure they understand the concept of fair and unfair in terms of outcomes being equally likely or not being equally likely. Analyze a couple of spinners together. • For students who need a challenge, have them create their own fair and unfair spinners to use to play the game. Assessment Opportunities Observations: Pay attention to how students are classifying the spinners: – How are they determining what is fair or unfair? – Do they understand that fair means that all outcomes are equally likely? – Can they give reasons for their choices or are they guessing? Conversations: As students are sorting the spinners and playing the game, use some the following prompts to check in on students’ understanding of fairness: – Explain why you think this spinner is fair. – Explain why you think this spinner is unfair. – What happens when you play with the (fair/unfair) spinner? Who is going to win? Why do you think that? How do you know? Consolidation (15 minutes) • Meet as a class and discuss what happened when they played the “Fill It Up!” game with the fair and the unfair spinners. • Discuss what a fair spinner looks like in terms of possible outcomes. • Select one or two unfair spinners to discuss (e.g., three-fourths of the spinner is blue and one-fourth is red). Propose the idea that two people are playing, with one person winning if the spinner lands on blue and the other person winning if it lands on red. Ask whether this guarantees that the person with the advantage (blue) will win. Explain that chance plays a role so red could win the game. • Have students discuss how they could make the unfair spinner fair. Reinforce the idea that fair means that all outcomes are equally likely. 202 Patterns & Relations/Data & Probability

Materials: Math Talk: “Is It Fair?” (page 20 Math Focus: Understanding the concept of fairness in games in Patterns, Relations, Data, and Probability Let’s Talk big book and little books) Select the prompts that best meet the needs of your students: Teaching Tip • What is the title of this page? What does fair mean when you are playing a game? Integrate the math talk What is an example of a fair game? An unfair game? moves (see page 8) throughout Math Talks • Look at this first picture. What game are the two children playing? (Snakes and to maximize student participation and active Ladders) Have you ever played this game? How do you play it? listening. • What are the children using to determine how far they can move on the board? Do you think the way the children are playing the game is fair? Turn and talk to a partner. • What do you think? (e.g., It is not fair because one child has one die, and the other child has two dice.) How does this make the game unfair? • Which child do you think is more likely to win? Why? Is it certain that the child with two dice will win? Why? How could the child with one die win? (e.g., The child with two dice goes down a big snake near the end of the game, and the child with one die doesn’t go down any snakes.) What else is affecting the outcome besides the dice? (e.g., chance) • How could we make this game fair so each child has an equal probability of winning? (e.g., Give both children the same number of dice.) • Continue with this line of questioning for the other two images on page 20 of the big book. Further Practice • Reflecting in Math Journals: Have students use pictures, numbers, and/or words to give examples of fair and unfair. Probability 203

7Lesson Investigating Probability with Dice Teacher Possible Learning Goals Look-Fors • Identifies and describes all of the possible outcomes in a probability experiment involving dice • Predicts how many times a certain outcome will happen when rolling a die a certain number of times • Compares the predicted results with the actual results using mathematical language • Identifies the possible outcomes of rolling a die using mathematical language • Predicts a result based on the possible outcomes • Consistently carries out the experiment • Accurately records and totals the results • Uses mathematical language to compare predictions with the actual results • Explains the role of chance in the probability experiment Materials: Day 1 Digital Slide 56: Ladybug Game Minds On (15 minutes) How many times will we need to roll a die to make sure each ladybug has 5 spots? • Show students a standard six-sided die. Ask what all of the possible outcomes Which ladybug will have 5 spots first? 123 are. They can turn and talk to a partner. Share their ideas. 456 • Explain to students that they are going to design a game that uses a die to total number of rolls investigate the probability of how often the different numbers are rolled. Scholastic Canada GR3 BC Patterns & Relations 3rd Pass • Project Digital Slide 56: Ladybug Game. Discuss what they see. Explain that Digital Slides November 9, 2021 56: Ladybug this game is a simulation, or experiment, to learn more about probability. Explain the rules of the game: Digital Slide Game, 6-sided die Time: 50 minutes – The object of this game is to get exactly 5 spots on each ladybug. – Each time you roll the die, you give a spot to the ladybug that has the same number above its back. If you roll a number that matches the number above the ladybug, but that ladybug already has 5 dots, the roll counts as a turn, but you don’t add any more dots. • Students predict how many total rolls they think it will take to complete the game. They can turn and talk to a partner. • Students can share their predictions. (e.g., We think 30 rolls, because each ladybug needs 5 spots and 6 groups of 5 OR 5 × 6 is 30.) Ask whether they think they can complete the game in less than 30 rolls and why they think so. Have students predict which ladybug will have its 5 spots first. Record their predictions using tallies. Working On It (whole class – 20 minutes) • Perform the experiment as class, having students share rolling the die. Have one student keep track of the number of rolls, while other students add the dots. 204 Patterns & Relations/Data & Probability

Materials: Consolidation (15 minutes) BLM 42: Ladybug • When finished, review the results using any of the following prompts to lead Game, 6-sided dice, chart paper the discussion: – What do you notice about our class results? Time: 55 minutes – Which number ladybug had 5 spots first? Second? Last? etc. – What was our total number of rolls of the die? BLM 42: Ladybug Game 3 – Was your prediction correct? Were you close? How many times will we need to roll a die to make sure each – What do you predict will happen if we repeated the same experiment? ladybug has 5 spots? Which ladybug will have 5 spots first? Day 2 12 Minds On (10 minutes) 456 • Review the ladybug experiment that was carried out on Day 1. Ask students to total number of rolls predict what will happen if the game was played again. 64 © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 Working On It (25 minutes) Scholastic Canada GR3 BC Patterns & Relations 4th Pass • Students work in pairs. They predict what will happen if they play the game again. Reproducibles • Pairs of students play the game using BLM 42: Ladybug Game and record their November 9, 2021 results. Differentiation • If students are having difficulty playing the game independently, meet with them as a small group. After each turn, reinforce how they record their results. Assessment Opportunities Observations and Conversations • Listen to students’ conversations as they play the game. Do they think that the game is fair or unfair? Can they explain why a different number might win in their game than the number that won in the game played by the class? Consolidation (20 minutes) • Create a six-column chart with the numbers 1 to 6 as the headings. Have each pair share which ladybug won their game. Put an X in the appropriate column to represent each response. • Ask students whether they think the game is fair or not. Have students turn and talk to their partner as they analyze the results in order to answer the question. • Discuss students’ responses. Ask students why the results may be different. Discuss whether they think one number is more likely than the other numbers to be rolled most frequently on a die. Reinforce the idea that each number has an equally likely chance of winning the game. Probability 205

8Lesson Investigating Probability with Spinners Teacher Possible Learning Goals Look-Fors • Identifies and describes the possible outcomes on a spinner • Predicts how many times a certain outcome will happen when using the spinner Materials: • Plays a game to gather actual results and compares them to their predictions Pigs at Odds (“‘C’mon, • Identifies and describes all of the possible outcomes on a spinner using dear,’…”), document camera, paper clip, mathematical language rulers, Digital Slide 57: The Birthday Game, • Predicts a result based on the possible outcomes BLM 43: Birthday Game • Consistently carries out a game to investigate probability Wheel • Accurately records results of the game • Compares the actual results to their predictions Time: 40 minutes Day 1 BLM 43: Birthday Game Wheel Minds On (10 minutes) Digital Slide 57: The Birthday Game • Show students the page spread (“‘C’mon, dear,’…”) in the book Pigs at Odds. November December Ask what game Mr. Pig played at the fair and what the rules are. November • Explain to students that they are going to create a spinner game and December October determine whether it is fair or not. They will also predict the outcomes and September then play the game to see if their predictions are correct. October • Tell students that they are going to investigate the Birthday Game first to learn September more about how to create a game. August JanuarAyugust January July July February Working On It (whole class – 20 minutes) February • Project Digital Slide 57: The Birthday Game and remind students of the Birthday March April Game from page spread (“‘C’mon, dear,’…”) in the book Pigs at Odds. Pose some of the following prompts: March April – What do you notice about the birthday game? (e.g., There is a board June and players put their money on one of the months of the year; the man May spins a wheel to determine which month is the winner; if you place your money on the same month, you win the game.) June May – What do you notice about the spaces on the wheel? (e.g., There are 12 sections; they are all the same size; the name of each month is in one Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec of the sections; each month name appears once.) Scholastic Canada GR3 BC Patterns & Relations 3rd Pass – Do you think this game is fair? Discuss with a partner. (e.g., Yes, the spaces are Digital Slides the same size; each month is equally likely to be spun as any other month.) November 9, 2021 65 © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 Scholastic Canada GR3 BC Patterns & Relations 4th Pass Reproducibles November 9, 2021 206 Patterns & Relations/Data & Probability

Materials: – Why do you think Mr. Pig isn’t very successful at this game? (e.g., because there are 11 other possible outcomes; his month is only 1 of 12 possible BLM 44: Create Your outcomes) Own Spinner • Have students predict how many times the spinner will land on ‘September’ Time: 55 minutes if it is spun 12 times. Have students share their ideas with a partner and then BLM 44: Create Your Own Spinner continued with the class. (e.g., 1 time, because there are 12 outcomes; we should spin The possible outcomes with our spinner are: each month once; maybe 0 times because the spinner might land on another month twice, etc.) If we spin our spinner times, we predict that weBwLillMlan4d4o:n Create Your Own Spinner , times . • Place a copy of BLM 43: Birthday Game Wheel so all students can see it or We think this because . project it with a document camera. After spinning our spinner times, we landed on • Make a spinner out of the birthday game wheel BLM using a paper clip. Have , times . students take turns spinning the birthday wheel spinner a total of 12 times. One student records the results using tallies. Another student records the experimental Our prediction was . results with tallies on the birthday game table at the bottom of Digital Slide 57. Our result was . Consolidation (10 minutes) Compare your prediction with your result . • When the simulation/experiment is complete, discuss the results as a group. © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 67 Pose some of the following prompts: – What are the possible outcomes of our experiment? Scholastic Canada GR3 BC Patterns & Relations 4th Pass – What were some of our predictions? How do they compare to the actual Reproducibles 66 © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 results? November 9, 2021 – What do you predict would happen if we repeated the game 12 more times? Why? Scholastic Canada GR3 BC Patterns & Relations 4th Pass Reproducibles Day 2 November 9, 2021 Minds On (10 minutes) • Review the results from yesterday’s experiment about the Birthday Game. Ask whether each month was equally likely to be spun. • Discuss whether it is likely or unlikely to win if you choose your birthday month, even though each month is equally likely to be spun. Working On It (25 minutes) • Provide each pair of students with a copy of BLM 44: Create Your Own Spinner. • Tell students that they are going to create their own spinner with a theme of their choice (e.g., colours, seasons, animals, numbers, etc.). • Students can divide their spinner into as many sections as they wish. They can use a ruler to help them and make sure that each pie section points to the centre of the circle. • When students have created their spinners, they can decide on how many spins they will perform and create a tally chart to record their results. • They make a prediction about the outcome of their experiment. They can complete the questions on the second page of BLM 44. Review all of the questions with students before they begin. • Students carry out their experiment, record the results, and compare them to their predictions. Probability 207

Differentiation • If students are finding it difficult to think of a theme, suggest that they use something simple like colours, numbers, or shapes. • Have student pairs check in with you once they have created their spinner to ensure that it is workable for the task. • For students who need language support, ensure that they understand the sentence starters on the second page of BLM 44: Create Your Own Spinner. You may wish to create a completed version of a spinner using the Birthday Game as an example. • For students who need more of a challenge, have them design another spinner that is not fair, predict the outcome, play the game, and then compare their results to their predictions. Assessment Opportunities Observations: Pay attention to how students are completing their activity: – Can they identify the possible outcomes? – Can they make a prediction about their experiment based on the number of spins they will perform? – Can they use mathematical language to describe their prediction? – Are they accurately recording their results? – Can they compare their actual results to their prediction? Conversations: Ask any of the following prompts to probe students’ thinking: – How many different possible outcomes do you have on your spinner? – Are all of your outcomes equally likely? Is one more likely than another? Why? – How many spins did you decide to do? – What was your prediction? Why did you think that? – What were your results? – How do your results compare with your prediction? – What could be the reason for your results? Consolidation (20 minutes) • Have students meet with another pair to describe their game and predictions. They can exchange games and try them out. They can compare their actual results to the other groups’ results and predictions. • Meet as a class. Discuss what they needed to do with their spinners to ensure that all outcomes were equally likely. Ask what other factors might have affected the results. • Discuss whether they would do anything differently if they were going to design a spinner game again. 208 Patterns & Relations/Data & Probability

Materials: Further Practice BLM 45: Which Spinner? • Reflecting in Math Journals: Have students reflect on previous situations BLM 45: Which Spinner? when they have used a spinner. Students can describe the situation and Jamil spun a spinner . The chart below shows his results . whether the spinner was fair or not. 30 15 15 • Independent Problem Solving in Math Journals: Provide students with Spinner A Spinner B Spinner C a copy of BLM 45: Which Spinner? Have them complete the activity in their math journals, using math vocabulary to justify their choice of spinner. Which spinner did Jamil most likely use? Explain your answer in your math journal. Students can make a second prediction using a different number of spins and/ or a different outcome and conduct the experiment with their partner. 68 © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 Scholastic Canada GR3 BC Patterns & Relations 4th Pass Reproducibles November 9, 2021 Probability 209

9Lesson Investigating Equal and Unequal Probabilities Teacher Possible Learning Goals Look-Fors • Plays a game to figure out total possible outcomes and whether all outcomes have an equal probability of occurring • Explains findings by comparing probability of outcomes, using mathematical language • Follows the rules to play a game • Accurately records results in a frequency table • Describes possible outcomes for a game • Determines whether some outcomes are more probable of occurring and explains their reasoning. • Explains strategies for playing a game. Materials: Day 1 BLM 46: Crossing Minds On (20 minutes) the River 1, counters, 6-sided die with NOTE: A visual example of a 12-space game board set-up is shown in the Day 2 numbers 1–6 (one die Minds On section below. per pair of students), BLM 48: Frequency • Give each student a copy of BLM 46: Crossing the River 1 game board and six Table 1 counters, which represent their six boats. Explain that the object of the game Time: 55 minutes is to move all six boats across the river to the same-numbered dock on the other side. Scholastic Canada GR3 BC Patterns & Relations © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 BLM 46: Crossing the River 1Scholastic Canada GR3 BC Patterns & Relations© 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-16 Reproducibles Reproducibles • Students put their six counters on any of the lower docks that are numbered 1 to November 9, 2021 BLM 48: Frequency Table 1November 9, 2021 Crossing the River Board Game 6. They can put more than one counter on a lower dock, and they can leave lower 1 2 3 4 Frequenc5y of Numbe6rs Rolled docks (numbers) blank. Students cannot change the location of their boats on the lower side of the game board to other numbers once the game is in play. 12345 River • Roll one die and read out the number. Record the number from each roll on 123456 a master sheet so the totals of the winner can be checked against the master sheet at the end of the game. 4th Pass • If students have a counter on the dock that equals the rolled number, they can 69 4th Pass move the boat across the river to the matching numbered dock on the other 71 side of the river (top of the game board). If there is more than one counter on that dock, only one boat can be moved across the river on that turn. • The first person to get all boats across the river wins. 210 Working On It (20 minutes) • Have students play the game again in partners. They record the numbers that were rolled. They predict whether the results will be the same if they play the game again. Patterns & Relations/Data & Probability

Scholastic Canada GR3 BC Patterns & Relations 70 © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1Materials:Scholastic Canada GR3 BC Patterns & Relations 72 © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 • Students can play several times, trying different strategies for placing their Reproducibles Reproducibles November 9, 2021 “Crossing the River” November 9, 2021 boats at the docks on the bottom side of the game board. (page 19 in Patterns, Relations, Data, and • They can use BLM 48: Frequency Table 1 to keep track of the numbers that Probability big book and little books), BLM 47: were rolled in a game. Have them keep track of the numbers that were rolled Crossing the River 2, for each game using a new copy of the BLM. counters, BLM 49: Frequency Table 2, Differentiation 6-sided dice with numbers 1–6 (two dice • Some students may only get through the game one time. per pair of students), • Some students may benefit from only recording their numbers for one of the chart paper Time: 60 minutes games so they can concentrate on playing for the rest of the games. BLM 47: Crossing the River 2 Assessment Opportunities BLM 49: Frequency Table 2 Observations: This is an excellent opportunity to observe without Crossing the River Board Game interrupting students’ thinking. Pay attention to how they change their 1 2 3 4 5 6 7 8Frequ9ency 1o0f Sum11s Ro1l2led strategies for placing the boats from game to game. 1 2 3 4 5 6 7 8 9 10 11 12 Consolidation (15 minutes) River • As a whole group, discuss the strategies that students used for placing their boats. 1 2 3 4 5 6 7 8 9 10 11 12 • Ask if they noticed any patterns in the numbers that were rolled or whether 4th Pass some numbers were rolled more often than others. Have them check with their frequency table to prove their thinking. 4th Pass • Discuss whether the outcomes were the same from game to game. • Ask students what they think the probability is of the number 4 being rolled compared to the other numbers. Discuss why each number is equally likely to be rolled. Day 2 Minds On (20 minutes) Example Game Board Set-Up 1 2 3 4 5 6 7 8 9 10 11 12 River 1 2 3 4 5 6 7 8 9 10 11 12 • Show students page 19 “Crossing the River” in the Patterns, Relations, Data, and Probability big book. Ask how it is different from the game they played in the previous lesson (Day 1). Ask how they think the rules for the game may be different in this new version of the game. Have students turn and talk to a partner. They can share the little book versions of the big book to get a closer look at the book page. Probability 211

• Explain to students that they are going to play another version of Crossing the River. This time, each game board has 12 docks. Two dice will be rolled for each turn, and the sum of the two numbers will indicate the dock number from which a boat can be moved. • Play the game as a class, with groups of three students sharing a little book as you play. Keep track of the sums so they can be used to check the moves of the winners. Working On It (20 minutes) • Have students play the game in triads using copies of BLM 47: Crossing the River 2 and 12 counters. • They can keep track of their sums using BLM 49: Frequency Table 2. Have them predict whether the results will be the same if they play the game again. • If there is time, they can play the game several times, keeping track of their sums separately for each game. Assessment Opportunities Observations: Note whether students change their strategies from the ones they used while playing the first version of Crossing the River (6 docks) to the version of the game they just played that has 12 docks. 212 Consolidation (20 minutes) • Meet as a class. Ask what strategies they used to place their boats while playing the second version of the game. • Discuss whether there were any docks that they didn’t put their boats on (e.g., we didn’t put our boats on dock 1 because it is impossible to roll a sum of 1; we didn’t put boats on 12 very often because we didn’t roll 12 too many times). • Ask what docks they preferred using and why. • Have students check their frequency tables to discover whether any sums were rolled more often than others. Ask why they think certain sums were more common than others. • Together, make a chart with 12 columns with headings 1 to 12 on chart paper. Ask students what math facts add up to the various amounts. Print the number addition facts under the appropriate sum. • Have students analyze the completed chart. Discuss why certain sums are more probable than others. Ask which sums are most likely to be rolled, and which sums are least likely. Ask if any sums are impossible to get (1) and why. • Discuss how this information could affect the strategies they use to place their boats. Ask whether their new strategies (e.g., putting more boats on 7) guarantees that they will win. Discuss the role that chance plays in the game. Further Practice • Students love this game and will play it often when given the opportunity. Set it up as a centre. It also offers good practice for students to learn their addition facts. Patterns & Relations/Data & Probability

Materials: • Change the rules of the game. Use dice that have a different number of faces Online story The Snowsnake Game, and numbers. Alternatively, use two spinners with the numbers 1–9. Create spruce sticks a new game board on chart paper with docks from 1–18. (optional) Math Talk: Teaching Tip The Snowsnake Game Integrate the math talk Math Focus: Investigating probability in games moves (see page 8) NOTE: This is a link to The Snowsnake Game story (link functions as of this writing): throughout Math Talks http://rrs.yukonschools.ca/uploads/6/7/0/1/67017833/snowsnake_pp.pdf to maximize student You may also find a link to the Snowsnake Game story in the Grade 3 BC math participation and active curriculum: see the elaboration section for the Content bullet point: likelihood of listening. simulated events, using comparative language. Let’s Talk • Today, we are going to read a story called The Snowsnake Game. What do you think it might be about? What do you think a snowsnake is? What time of year do you think people play this game? Let’s read the book and find out. • Stop reading from time to time and pose some of the following prompts: – What do you think the goal of the game is? – Why was this game played in the past? – Do you think that this is a game of chance or a game of skill? Why? – Why do you think that a spruce branch is used to represent a ‘snowsnake’? – What is important when making a snowsnake? Why? – What are the rules to follow when you play the game? – Why do you think running up to the starting line is important? – Do you think that it is equally likely that the girls will throw the snowsnake about the same distance? Why? – How does playing the game make the girls feel? How does playing the game help them connect to and understand the past? – What is important to remember when throwing a snowsnake so it goes a far distance? – How do you think the girls could increase their chances of winning at this game? (e.g., they can practise more) What other games do you know that require practise in order to win? – After reading the book, do you think that chance or skill plays a greater role in winning? Why? Further Investigation • If possible, take students outside on a wintry day and play the snowsnake game. Ask students how they feel after playing the game. Ask how they would change or improve their technique, so they have a greater chance of winning. Probability 213

10Lesson Creating a Fair Game Teacher Possible Learning Goal Look-Fors • Creates a fair game by designing the rules of how to play Materials: • Understands and explains what ‘fair’ means in the context of playing a game • Clearly articulates (either verbally or in writing) how the game is played “What Are the Rules?” • Explains and justifies why the rules of the game are fair (page 17 in Patterns, • Plays the game in order to prove that the game is fair Relations, Data, and Probability big book Minds On (15 minutes) and little books) Time: 60 minutes • Explain to students that they are going to create their own games so that they are fair for all of the players. • Show students the “What Are the Rules?” page in the big book. Have students turn and talk to their partner about what they see. Discuss their responses. • Discuss some options for creating their games. They can use any of these ideas to get started or decide on a variation of their own. • Make an anchor chart of the criteria that must be included in the game. – Explain how you win the game. – Decide what to use to determine how far each player moves. – Create rules for how the game is played. – Make a prediction and test it out yourselves. – Record the results from playing your game. – Determine whether it is a fair game. Working On It (25 minutes) • Students work in pairs or triads to create their game. They can use the “What Are the Rules?” pages in the little book versions of the big book. • Students can record their game rules on chart paper. Differentiation • If it is too challenging for some students to design a different game, have them repeat the Ladybug Game from Lesson 7, but change some of the rules. Assessment Opportunities Observations: Pay attention to students’ conversations as they discuss the design and execution of their game: – Are they making it a fair game? – Can it be easily repeated? 214 Patterns & Relations/Data & Probability

First Peoples – Can they predict a possible outcome? Principles of – Can they accurately tally and total their results? Learning – Can they make comparisons of the actual results to their predictions? Conversations: Pose any of the following prompts in order to clarify students’ thinking: – What is the name of your game? – How do you win your game? – What prediction did you make before testing out your game? – Have you tested out your game? If so, what were your results? – How did your results compare with your prediction? – Do you think that your game is fair? Why or why not? – Are you rolling some numbers more than others? Which ones? Consolidation (20 minutes) • Have each group meet with another group to describe and explain the game that they created. Groups can exchange games and play each other’s games. • Meet as a class. Ask students about their experience creating and testing out their game. Pose some of the following prompts: – What did you choose to determine how far people can move? Do you think it is fair? Why? – Do you think the rules of your game are fair? Why? – What was the most challenging part of creating your own game? – Was the game fair when you first tried to play it? What adjustments did you need to make? – What would you do differently if you had to redesign your game? Why? • Discuss why it is important to design fair games. • Building Growth Mindsets: Discuss what was challenging about making their game. Ask how they solved any problems that arose while they were working. Ask what they learned from the mistakes that they made. Explain that it can take a long time to design a real game, especially to determine whether it is fair so that it is equally likely that all players can win the game. Discuss some of the games they play and whether skill or chance are involved in order to win. This supports the First Peoples Principles of Learning that learning involves recognizing the consequences of one’s actions. Further Practice • Make copies of the rules of each of the games students created and set up centres so students can play each other’s games. Building Growth Mindsets: Have students reflect back on the lessons in the Probability unit. Ask which activities they enjoyed the most and why. Ask what they learned about probability that was most interesting. Ask what they Probability 215

First Peoples still wonder about and make a list of their ideas. On some of the days over the Principles of next few weeks, address one of their queries. Discuss how they could do an Learning experiment or find some information that will help to answer their questions. Set up centres of games that involve chance. After students have had an opportunity to play them, discuss what they learned from playing the game. Students may also wonder about the probability of events happening during the school day. Choose an event and have students make predictions about how often it will occur over the next week. Keep track of what happens and compare the results to your predictions. In this way, students realize that probability continues to play a role in their lives, even when the unit in class is completed. This supports the First Peoples Principles of Learning that learning is holistic, reflexive, reflective, experiential, and relational (focused on connectedness, on reciprocal relationships, and a sense of place); and that learning involves patience and time. 216 Patterns & Relations/Data & Probability

11Lesson Reinforcement Activities Math • All Math Learning Standards identified in this unit Learning Possible Learning Goal Standards • Applies understanding of probability to carry out related activities Teacher • Describes probability of events using mathematical language Look-Fors • Consistently carries out simulations, experiments, and games and makes Previous Experience predictions based on probability of outcomes with Concepts: Students have had several • Explains how different options change the probability of events opportunities to describe the probability of different About the Lesson events, to investigate experimental probability. The following activities can be carried out by the whole class, in small groups, or as centres that students can rotate through. They can also Math Vocabulary: be used throughout the unit any time you decide to offer guided math piclmlioiekkspreetsollayiysb,i,nsisol,iipbtumyiltn,econ,poreloemikrs,elesiekliybqe,llueyua,,nlllleiyksesly, lessons, as extra practice for students, or for early finishers. Differentiation: For students who need language support, explain all activities to ensure students understand the instructions and the vocabulary involved at the centres. Materials: Centre 1: Paper Bag Games paper bags, colour I•n sPtlarucectthioenfsollowing objects in three different bags: tiles or connecting cubes – Bag 1: 3 red cubes, 7 blue cubes – Bag 2: 8 blue cubes, 2 red cubes – Bag 3: 5 blue cubes, 5 red cubes • Tell students that there are 10 cubes of different colours inside but they cannot look inside the bag. • Students take turns pulling out 1 cube from the first bag. After each removal, they record their results and then replace the cube before the next person pulls out a cube. They repeat this process until they have pulled out a total of 10 cubes. • They repeat this process for the other two bags. • Students predict what they think is in the bags. Probability 217

© 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1Materials: Differentiation paper, pencil, paper • Students who need a challenge can create their own bags with similar criteria. clips, BLM 50: Spin and Win Centre 2: Spin and Win BLM 50: Spin and Win •In sStturudcentitos ncrseate two different spinners using the spinner templates found on Scholastic Canada GR3 BC Patterns & Relations BLM 50: Spin and Win. One spinner should show a situation that is equally Reproducibles likely, and the second spinner should show a situation that is not equally likely. November 9, 2021 • With their partner, they spin their spinners 10 times and keep track of who 4th Pass wins. They compare results to see if they align with the way in which the spinners were designed. 73 Materials: Centre 3: Which Would You Want? pre-cut cards from I•n sSthrouwctsitoundsents the instructions for the Fill It Up game described on BLM 41. BLM 40: Spinners, • Students analyze the spinner cards from BLM 40 and decide which spinner BLM 41: Fill It Up! they want to use for the Fill It Up game. BLM 40: Spinners continued • Students play the game with a partner and determine who the winner is. 3 4 BLM 40: Spinners • They can repeat the game and play with a different spinner. 2 1 1 2 Red Red 4 Yellow Blue Yellow 3 Green Blue © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 14 BLM 41: Fill It Up! 2 Instructions:1Choose a colour (or shape or number) on your spinner. Each player can choose otonlfyillO2inNoEnecoolof uyro .uSrpsiqnButahlureeess p. Tinhneerp . eErascohnRtwimehedo tfhilles spinner lands on your colour, Scholastic Canada GR3 BC Patterns & Relations 1 you get in their squares first wins! Reproducibles November 9, 2021 41 Red Red Green Player One Blue Yellow Player Two 62 © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 4th Pass Scholastic Canada GR3 BC Patterns & Relations 4th Pass Reproducibles © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 November 9, 2021 61 63 Scholastic Canada GR3 BC Patterns & Relations 4th Pass Reproducibles November 9, 2021 Materials: Centre 4: Play a Game! Is It Fair? a variety of •In sHtarvuecativoanrisety of popular games (e.g., board games) at the centre. Ensure students commercial games understand the rules. Students can play the games and determine whether they are fair or not (e.g., whether it is equally likely for all players to win). 218 Patterns & Relations/Data & Probability

References Beatty, R. (2014). Exploring the Power of Growing Patterns. What Works? Research into Practice. Ontario Ministry of Education. Online: www.edu.gov. on.ca/eng/literacynumeracy/inspire/research/WhatWorks.html Beatty, R., & Blair, D. (2015). Indigenous pedagogy for early mathematics: Algonquin looming in a grade 2 math classroom. The International Journal of Holistic Early Learning and Development, 1, 3–24. Beatty, R., & Bruce, C. (2012). From patterns to algebra: Lessons for exploring linear relationships. Toronto, ON: Nelson Education Ltd. British Columbia Ministry of Education. (2015). Aboriginal worldviews and perspectives in the classroom. Victoria, BC: Queen’s Printer for British Columbia. Chapin, S.H., O’Connor, C., & Canavan Anderson, N. (2009). Classroom discussions: Using math talk to help students learn, K–6, Second Edition. Sausalito, CA: Math Solutions. Clements, D.H., & Sarama, J. (2009). Learning and teaching early math: The learning trajectories approach. New York, NY: Routledge. Newcombe, N.S. (2013). Seeing relationships: Using spatial thinking to teach science, mathematics, and social studies. American Educator: Spring 2013. Newcombe, N.S. (2010). Picture this: Increasing math and science learning by improving spatial thinking. American Educator: Summer 2010, pp. 29–43. Small, M. (2017). Making math meaningful to Canadian students, K–8, Third Edition. Toronto, ON: Nelson Education Ltd. Small, M. (2014). Uncomplicating algebra to meet common core standards in math, K–8. Toronto, ON: Nelson Education Ltd. Small, M. (2013). Making math meaningful to Canadian students, K–8, Second Edition. Toronto, ON: Nelson Education Ltd. Small, M. (2010). Big ideas from Dr. Small: Creating a comfort zone for teaching mathematics, grades K–3. Toronto, ON: Nelson Education Ltd. Small, M. (2009). Making math meaningful to Canadian students, K–8. Toronto, ON: Nelson Education Ltd. Van de Walle, J.A. (2001). Elementary and middle school mathematics: Teaching developmentally, Fourth Edition. Toronto, ON: Pearson Education, Inc. Van de Walle, J.A., & Lovin, L.H., (2006). Teaching student-centered mathematics grades K–3, Volume One. Boston, MA: Pearson. References 219

Patterns & Relations/Data & Probability Teacher’s Guide Part of Math Place Grade 3 Lead Author: Diane Stang, National Math Consultant for Scholastic Education Math Reviewers: Katie McCormack, Kamloops/Thompson School District #73 Indigenous Consultant: Diane Jubinville, Delta School District #37 Director of Publishing: Molly Falconer Project Manager: Jenny Armstrong Editor: James Gladstone Proofreader: Danielle Arbuckle Art Director: Kimberly Kimpton Designer: Pronk Media, Inc. Production Specialist: Pauline Galkowski-Zileff Copyright © 2022 Scholastic Canada Ltd. 175 Hillmount Road, Markham, Ontario, Canada, L6C 1Z7 ISBN: 978-1-4430-5410-2 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, scanning, recording or otherwise, without the prior written consent of the publisher or a license from The Canadian Copyright Licensing Agency (Access Copyright). For an Access Copyright license, call toll free to 1-800-893-5777.