p106-173_Gr3BC-Patterns-Unit1-Data

Unit 1: Data Lesson Content Page 1 Getting Started with Data and Probability 106 2 Inviting Data and Probability into the Classroom 107 3 Data Introduction 109 4 Read Aloud: The Great Graph Contest: First Reading 111 5 to 8 The Great Graph Contest: Second Reading 115 5 Graphing in Our Lives 120 6 Sorting and Classifying Using Various Attributes 124 7 Displaying Data in Various Ways 127 8 Displaying Data: Concrete Graphs to Pictographs 129 9 to 12 Displaying Data: Bar Graphs 132 9 Displaying Data in Vertical and Horizontal Bar Graphs 135 10 Using Features of Graphs to Ask and Answer Questions 138 11 Analyzing Data 141 12 Analyzing Data in Different Displays 143 13 Describing Data 146 14 to 17 Interpreting Data 149 14 Drawing Conclusions from Data 152 15 Guided Lesson: Reinforcing Data Concepts and Skills 155 16 Applying Data Concepts and Skills 164 17 Analyzing Survey Questions 166 Collecting and Organizing Data 168 Displaying Data: Creating Graphs 170 Analyzing and Interpreting Data 172

Getting Started with Data and Probability The order of the Data and Probability lessons follows a general developmental trajectory of how students tend to acquire knowledge and skills. Below is an overview of the included units and instructional suggestions. Unit Description 1 Data 2 Probability 106 • Each unit includes a series of BLMs and Digital Slides to support the visual nature of data and probability concepts. The Digital Slides are developmental in their complexity. • Each unit includes Math Talks, group discussions, and activities that target the curricular competencies (reasoning and analyzing, understanding and solving, communicating and representing, and connecting and reflecting) to support and develop student understanding. • Each unit includes activities to develop and build habits of mind, growth mindsets, and positive attitudes toward math in the classroom. • Making connections between data and probability and other areas of math or curricula will maximize student learning and support flexibility in their thinking. Teachers often collaborate with partners and use their professional judgment when planning out their math schedule for the year, taking into account how the strands may support each other. It may be beneficial to offer them in close succession. When developing your long-range plans, consider the following: – As students sort and classify sets of objects in order to organize and graph them, they apply their understanding of attributes and shapes that are also investigated in both Patterning and Spatial Sense. – Students can apply their knowledge of collecting and displaying data when working with data related to other curriculum areas. – As students read and analyze data, they are applying many of the concepts and skills that deal with counting and number relationships in the Number strand. – Students can apply their ability to analyze information in order to draw conclusions from the data, which is at the heart of reflecting on any inquiry topic students might explore in Science or Social Studies. – Data concepts and skills can be applied to inquiry questions or themes presented in other curriculum areas (e.g., students’ favourite artist; keeping a tally table of everyday classroom events—students absent, recognizing a classmate for a good deed, etc.). Many of the data and probability concepts explored in grade three expand on students’ previous experiences and offer more complexity and incorporate a greater variety of ways to present the data. Students also expand their vocabulary to describe the probability of certain events or outcomes occurring. Patterns & Relations/Data & Probability

Inviting Data and Probability into the Classroom Since math plays an integral part in our lives, it makes sense to take advantage of its role in everyday routines at school. Whether it is using a simple T-table to record how many students are present or absent, or a chart of assigned jobs for the week, bringing math experiences into real-life contexts will deepen understanding of concepts in a meaningful way. There are many ways to embed data and probability concepts into your daily routines. These activities can be 5–10 minutes that can be carried out while the class waits in line to go somewhere, when there is five minutes at the end of a period, or when students need a quick break. Several ideas are described below. Sorting and Classifying Students need to be able to sort and classify in order to organize and graph data in a meaningful way. Take every opportunity to have students sort and classify objects and themselves. • When you are transitioning from one activity to another, use a series of questions related to what students are wearing, how they are feeling, etc. on any given day. – If you are wearing a blue shirt (glasses, running shoes, jeans, shorts), clap once. – If you are feeling tired today (excited, happy, grumpy, silly), clap twice. • If you have a bin of classroom materials that is messy, take the opportunity to have a quick math talk about how you might sort and organize the materials. Then do it and talk about it. • When lining up for an activity, have students sort and re-sort themselves based on a variety of criteria/categories. By doing so, they are creating concrete graphs that can be used to make comparisons. – Sort yourselves into two groups: names that start with a consonant and names that start with a vowel; names that have six letters or less and names that have more than six letters; shoes with laces and shoes without laces; etc. – Sort yourself into three groups: I prefer apples/oranges/bananas; I prefer red/blue/green; I prefer cats/dogs/hamsters, etc. • Use the four corners strategy to help students group themselves for any activity. Choose four pictures related to the activity you are doing (e.g., four types of forces, four communities in colonial Canada, four DPA activities, etc.) and ask students a question about the options to help them sort themselves. (e.g., Choose the DPA activity that you like the least and go to that corner. Have a discussion with the people in the group to explain why you chose that corner.) Data 107

• When beginning any unit of study, use individual cards/sticky notes/photos of the ideas you will be studying (e.g., types of structures, natural elements in various regions, etc.) and have small groups of students sort the ideas and name the categories they chose. Have them explain/share with the group how they sorted and classified each group. Create a graph with the results. Start of the Day (Greetings/Attendance) When you are meeting with students to start the day (e.g., taking attendance) pose a survey question to find out how students are feeling. • Say, “When I call your name, I want you to answer this survey question: How are you feeling this morning? Awake! A bit tired! Excited!” Options for recording survey results: – have one student add the answer options to a posted tally table template and keep track of the tallies; – add the answer options to the bottom of a posted vertical or horizontal bar graph template and have a student add colour in bars as students answer the survey question; – have labelled containers where students can vote for themselves by adding a stone or stick to the appropriate container. 108 First Peoples Perspectives An Indigenous perspective of gathering is to all come together in a circle. A circle is where everyone is equal: there is no one person more important than another, everyone supports one another and the circle is a symbol of unity. You can begin to go around the circle with a survey question such as “How are you feeling this morning?” and everyone can answer in sequence. If someone does not want to answer right away or at all, continue in the circle and come back to them. This offers a safe space in case someone does not want to participate and offers them the patience and time needed during this activity. • Have students keep individual graphs of any of the activities they do throughout the year: – minutes of sustained silent reading – number of jumping jacks in a minute – number of books read • Have students make predictions about the probability of everyday events (e.g., the weather) using mathematical language learned throughout the unit (e.g., likely, more likely, possible). • Play a quick game using materials that have multiple outcomes (e.g., dice, spinners, coins) and have students predict a certain result with 10 tries and then compare their result to their prediction. • When playing any kind of game to review concepts studied in other subject areas, use dice or a spinner to choose categories or determine how many points a team gets on each turn. • When reading a story aloud, have students predict the likelihood of a certain event in the story. • When conducting a scientific investigation, have students discuss the possible results and the likelihood of each result. Patterns & Relations/Data & Probability

Data Introduction Introducing Data About the The use of data plays an integral role in our lives. We see, use, and analyze data in advertisements, on television, and on the Internet. Students need to be critical thinkers and be able to discern whether the information is being fairly represented in the graphs, tables, and charts so they can make educated decisions. Students need to realize that we collect data to answer questions. This can be accomplished by giving them authentic tasks that are relevant to their lives. These can often begin with an inquiry that requires more data. Students can develop meaningful survey questions, and then collect, sort, and organize the data using various charts and organizers. They can then learn to display the data in various visual forms. Grade three students focus on using bar graphs and pictographs that involve one-to- one correspondence. Once they have displayed the data, students can interpret the information in order to answer their inquiry questions. Marian Small discusses the many ways we want students to use the data. “You want students to be able to read specific pieces of information or facts from a graph and also work with multiple facts, for example to make comparisons. Eventually, you want them to make inferences about what they see on the graph with appropriate justification” (Small, 2017, p. 617). Students need a variety of experiences to analyze the data as a group so they can discuss and compare each other’s observations and conclusions. Data 109

Lesson Topic Page 1 Read Aloud: The Great Graph Contest: First Reading 111 2 The Great Graph Contest: Second Reading 115 3 Graphing in Our Lives 120 4 Sorting and Classifying Using Various Attributes 124 5 to 8 Displaying Data in Various Ways 127 5 Displaying Data: Concrete Graphs to Pictographs 129 6 Displaying Data: Bar Graphs 132 7 Displaying Data in Vertical and Horizontal Bar Graphs 135 8 Using Features of Graphs to Ask and Answer Questions 138 9 to 12 Analyzing Data 141 9 Analyzing Data in Different Displays 143 10 Describing Data 146 11 Interpreting Data 149 12 Drawing Conclusions from Data 152 13 Guided Lesson: Reinforcing Data Concepts and Skills 155 14 to 17 Applying Data Concepts and Skills 164 14 Analyzing Survey Questions 166 15 Collecting and Organizing Data 168 16 Displaying Data: Creating Graphs 170 17 Analyzing and Interpreting Data 172 110 Patterns & Relations/Data & Probability

1Lesson The Great Graph Contest: First Reading English Introduction to the Read Aloud Language Arts Learning Standards The Read Aloud text introduces math concepts in a meaningful context that allows students to make connections to their everyday lives. During the first reading of The Great Graph Contest students apply their literacy strategies, such as inferring, using prior knowledge, and making predictions, to understand the context and 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 Materials: Assessment Opportunities Observations: Note each student’s ability to: – Use visual cues to make and support predictions – Make inferences and demonstrate understanding by engaging in discussions and follow-up activities Written by Loreen Leedy Read Aloud: The Great Graph Contest Text Type: Fiction: Summary: The Great Graph Contest is about three amphibian friends that love Narrative – Adventure to display and discuss data. They decide to hold a graphing contest to see who can create the best graph. Time: 15–20 Chester the Snail is chosen to judge the graphs of Beezy the Newt and Gonk the minutes Frog. While Beezy and Gonk try to think of new and better ideas for graphs, many new characters join them in some not-so-typical amphibian settings. Loreen Leedy uses several text features within her creative illustrations to help students understand the storyline, the dialogue, and the feelings of the characters. Data 111

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. Read the title and the author’s name. Ask them knowledge to predict what they think the book might be about (e.g., some fun animals, a contest) and have them explain their reasoning (e.g., title is The Great Graph Contest, a frog and a newt are holding up a graph). Ask students if they think this is a fiction or non-fiction story and how they know. • Ask students if they have participated in a contest. Ask why they think we have contests (e.g., people like to win, sometimes there’s a prize for the winner). Keep track of their answers on chart paper. • Setting a Purpose: Tell the students, “Now that we have made our predictions, let’s read the story together to see what this story is all about.” Using text features/ During Reading inferring • Page 3: Before reading page 3, ask students what they notice in the picture. Using text features/ (e.g., a newt, a snail, a flowerpot, a ladybug, leaves, etc.) analyzing • After reading page 3, ask students who the newt (Beezy) is talking to (Gonk) Using text features and why they think so. (e.g., He says “Hello? Gonk? Are you home?”) • Ask where Gonk lives (e.g., inside the flowerpot) and how they know (e.g., there is a mailbox beside it with his name on it, etc.). Ask students if they have a mailbox like this one or how they get their mail delivered. • Have students compare the speech bubbles above Chester (snail) and Beezy (newt) (i.e., one has circles, one has a point). Ask students what they think the difference is (i.e., the one with circles is a thought bubble; the one with a point is a speech bubble). Ask why it is important for readers to know what the bubbles represent. • Pages 4–5: After reading pages 4–5, ask students what Gonk is doing (i.e., he’s making a graph). Ask what the graph is about (which of Gonk’s friends like mud) and how they know (e.g., question, title). • On page 5, point out Beezy’s speech bubble, “More of us do like mud!” Ask students what they notice about the word ‘do’ (larger font) and why it is written differently than the other text (it tells us to read that word with emphasis). Have students read the text aloud, first without the emphasis and then with the emphasis. Discuss how it changes the meaning of the text. • Ask what they notice in the bottom corner of page 5 (an outline cartoon of Gonk, holding hands with Beezy and Chester). Ask why the author wanted to include this in the story (to give us more information, to add a fun drawing). • Pages 6–7: After reading pages 6–7, ask students what they notice about the bubble above Chester’s head and what it tells them. (e.g., It’s a thought bubble with circles.) Ask what Chester is thinking. (e.g., He doesn’t like cherry pie. “Yuck!”) • Ask how the larger text in the speech bubble (e.g., best, not, so, correct math, creativity, neatness) helps the reader better understand the text. (e.g., We know 112 Patterns & Relations/Data & Probability

Inferring to read these words with more emphasis.) Students can read the text, paying attention to the text features. Predicting Using text features/ • Ask why some text (e.g., WHOA) is capitalized and how it helps the reader. analyzing (e.g., We know to read these words louder and with more expression.) Students can read the text aloud. Inferring Making connections • Ask what Chester suggests for Gonk and Beezy (i.e., to have a graph-making Inferring contest). Direct students’ attention to the blue outline cartoon at the bottom Using text features of page 7. Have students infer what Gonk and Beezy are thinking. Ask how Chester might be feeling right now. Predicting Inferring • Ask students what topics Gonk and Beezy might choose for their graphs. Have Using text features them predict who they think will win and why they think so. Analyzing/making connections • Pages 8–9: After reading pages 8–9, ask why Beezy says “That sounds really Using text features Analyzing hard. Hee! Hee!” and why ‘hard’ is in larger font. Ask why Beezy laughs after Analyzing making this comment (e.g., because the graph might be hard, as in not easy, but rocks are hard, too, as in not soft). Ask students to think of other words that might have two meanings (e.g., add/add; glass/glass, etc.). Begin an anchor chart with words that have two or more meanings. Students can add to it throughout the year. • Ask what Gonk is thinking but does not say aloud. • Pages 10–11: After reading pages 10–11, ask students if they have ever had a picnic. Ask what clues indicate there is a picnic happening. • Ask what Beezy is thinking about when he plans his graph, and why he doesn’t say it aloud. • Pages 12–13: After reading pages 12–13, ask how the reader knows that the juice is cold. • Ask students where the characters are going next and how they know. • Ask students to predict what they think Suitmart is (e.g., store that sells men’s suits, bathing suits, etc.). • Pages 14–15: Before reading pages 14–15, check students’ predictions about what kind of store Suitmart is (e.g., bathing suit store). • Ask what kind of bathing suit the snake may have in the bag and why they think so. • Pages 16–17: After reading pages 16–17, have students note some of the text features they have been focusing on throughout the story and why they have been included in the text on this page. • Ask what they think the word ‘overlap’ means. • Pages 18–20: After reading pages 18–20, ask students why the word ‘orange’ is in larger font (e.g., because it’s the most common colour of butterfly). • Ask what they wonder about butterflies and what investigation they would find interesting to do. • Page 21: After reading page 21, ask students what is different about the word ‘eggsellent’ and why it is spelled this way (e.g., it sounds like ‘excellent’ but it has the word ‘egg’ in it; the word ‘egg’ makes it funny, because it’s not what we expect). Data 113

Predicting • Have students predict what animals may hatch from the eggs in the Inferring/activating illustration and why they think so. prior knowledge • Pages 22–23: After reading pages 22–23, ask what they think the differences Predicting Using text features are between reptiles and birds. Have them compare their features, highlighting which are the same and which are different. Making connections/ activating prior knowledge • Ask students where the characters are going next and how they know? • Pages 24–25: Ask why the words in the signs are spelled a bit differently Inferring/ making connections (e.g., to get our attention). Ask if they have seen words spelled differently (e.g., Toys R Us). Predicting • Ask students what needs plants and animals share. Ask how they depend on Analyzing each other in the environment. Inferring • Pages 26–27: Ask how they think Chester is feeling now and why they think so. Ask whether students have ever had to make a choice between two friends. • Ask students who they think will win now. Ask if their predictions have changed since the beginning of the story and why. • Pages 28–29: After reading pages 28–29, have students discuss how Gonk and Beezy are feeling now. Ask how Chester is feeling. • Ask how they think that Beezy and Gonk would have felt if they had won or lost. After Reading Synthesizing • Ask students what they think the author’s message is and why they think so. • Building Growth Mindsets: Materials: Digital Slide 37: How – Have students think of a time when they did or didn’t win a contest and Should We Read the how they felt. Ask how the other people in the contest felt. Discuss how Words? it is important to view situations like these from different perspectives so they can understand why people may be reacting or feeling the way they Digital Slide 37: How Should We Read the Words? do. Discuss how they can be good winners and good losers. I don’t like bananas. – Discuss why it is important to not always say what you may be thinking. Have students create a one-page scene with at least two characters, one of I don’t like bananas. I don’t like bananas. which says something in a speech bubble, and another that only thinks about something in a thought bubble. Encourage students to think of a I don’t like bananas. I don’t like bananas. situation when a character might think something without wanting to say it out loud. For example, students can illustrate a social situation with friends ?I don’t like bananas I DON’T LIKE BANANAS! on the playground, with one friend saying, “Let’s pick teams for our game,” and the other student thinking “I hope I get picked for A’s team!” Students Scholastic Canada GR3 BC Patterns & Relations 3rd Pass can also incorporate larger letters and/or capitalized letters for effect. Digital Slides November 9, 2021 Further Practice • Dramatic Arts: Project Digital Slide 37: How Should We Read the Words? Review how font size, style, and punctuation affect the way in which we read aloud or imagine how the words would be spoken. Have students practise with the given samples. They can work in small groups and create their own scene, using sentences and text features that indicate how the text can be read to create different meanings. 114 Patterns & Relations/Data & Probability

2Lesson The Great Graph Contest: Second Reading 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 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 • One-to-one correspondence with bar graphs, pictographs, charts, and tables Possible Learning Goals • Reflects on the importance of data in real-life situations • Identifies the features of various types of graphs and organizers and explains how they contribute to understanding the data • Describes and interprets data within a realistic context • Identifies the features of various graphs (e.g., labels, title) • Explains how to use a Venn diagram to sort sets • Explains what each symbol in a pictograph represents • Describes the meaning of displayed data within the realistic context About the Throughout the story, the characters collect data to answer their questions. The characters expose the reader to the various stages of data collection, including creating a survey question with possible responses, collecting and organizing the data, and then displaying the data so they can be easily understood and comparisons can be made. All of these stages require critical thinking in order to carry out an accurate survey. continued on next page Data 115

Throughout the process, students can analyze various types of graphs and organizers and their features, as well as compare their effectiveness. They can also critically analyze the choice of scale and realize how this can affect the way the graphs portray the data and how the information is interpreted. Eventually, we want students to independently decide which graph best depicts their data. 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 pages; • carry out the second reading over two or three days, reading a few pages each day, followed by one of the Further Investigation activities; • revisit some of the pages on other days to explore the Further Investigations that may pertain to specific concepts (e.g., creating a Venn diagram, discussing scale). Materials: Assessment Opportunities The Great Graph Contest Observations: Throughout the reading, the related problem solving, and Time: 15–20 minutes discussions, note which concepts are too difficult or too easy for students so per session next steps can be planned and lessons can be differentiated to meet individual needs. Note each student’s ability to: – Describe the elements of different representations of data – Read and describe the data represented in different forms (e.g., bar graph, pictograph, tables, Venn diagrams) – Connect ideas in the story to further investigations Before Reading Activating and Building On Prior Math Knowledge • Review what happens in The Great Graph Contest. Have students discuss how you would win a graph contest and what the judge would be looking for. Have them share what they already know about graphs. Record their ideas in a KWL chart that can be filled out as you read the book. • Setting a Purpose: Tell students, “We are going to revisit the story as math detectives, and learn about how we can ask questions, keep track of mathematical information, and how to display the information in a graph to help us understand it.” 116 Patterns & Relations/Data & Probability

Connecting and During Reading reflecting • Pages 4–5: Ask what they notice about Gonk’s graph (e.g., pictograph, Reasoning and categories are yes and no). Ask students what each mud stain represents. analyzing • Ask how many friends took part in the survey. Communicating and • Say, “Beezy says ‘More of us do like mud!’ Do you agree with Beezy?” Have representing/connecting students turn and talk to a partner first before sharing some answers as a and reflecting/ whole class. Discuss the importance of knowing how many more friends like reasoning and analyzing mud when making conclusions. Connecting and reflecting/ • Pages 6–7: Have students identify the different graphs (e.g., circle graph, communicating and representing Venn diagram, picture/bar graph). Understanding and • Ask what information each graph reveals and how they know. Discuss the solving/reasoning and analyzing importance of having a title that describes the data. Connecting and • Discuss how they can interpret numbers from each of the graphs (e.g., count reflecting the number of wedges in the circle graph). Ask what comparisons they can Connecting and make within one of the graphs. reflecting/reasoning • Pages 8–9: Ask students what the organizer might be called (T-table, sorting and analyzing mat). Ask what the animals did to create this representation (sorted the rocks Understanding and depending on if they are smooth or rough). solving/communicating • Ask students whether they think there are more smooth or rough rocks and and representing why they think so. Ask how else the animals could have sorted the rocks Connecting and reflecting/ (e.g., size, colour). reasoning and analyzing • Ask whether they think they would find the same results in another environment. • Pages 10–11: Ask whether stacking up the cookies would be a fair way to compare the number of cookies by looking at how high each stack is (e.g., the cookies would need to be the same thickness). • Pages 12–13: Ask what kind of graph Beezy made (e.g., concrete graph). • Have students compare the heights of the towers at 5 cookies. Discuss why they are not the same height. Ask what they need to do to compare the number of cookies (e.g., count them). • Have students make some comparisons. Encourage observations such as there are more than double the number of chocolate chip cookies and oatmeal cookies. • Partner Investigation: As a class, take a survey of the students’ favourite type of cookies. Partners can create a concrete graph or pictograph to show the results. Have a class gallery walk and look for similarities and differences between the different concrete graphs. • Pages 16–17: Ask students what Gonk is doing to organize the bathing suits (sorting). • Ask why a Venn diagram is a good choice for this sort. Ask what the middle section represents. • Ask what conclusions they can make from looking at the Venn diagram. Data 117

Reasoning and analyzing/ • Have students prove there are more bathing suits with bugs than flowers in communicating and representing this image. Reasoning and analyzing/ • Ask where a plain-coloured suit with no flowers or bugs would go on the communicating and representing Venn diagram (outside both circles). Connecting and reflecting/ • Ask what other ways they could sort the bathing suits. reasoning and analyzing • Pages 20–21: Ask students what type of graph Beezy made (circle graph). • Ask what conclusions they can make from the circle graph. Ask how many Reasoning and analyzing/ communicating and butterflies were counted and how they know. representing • Ask what other type of graph could show this information. Communicating and • Partner Investigation: Have students create another graph that represents representing the same information. Compare students’ graphs and discuss the features that are included on each. Highlight the connections among the graphs. Discuss which graph is the easiest to understand and why they think so. • Pages 22–23: Ask what types of displays are shown (tally table, pictograph). • Draw attention to the tally table on page 22. Ask how they would record another turtle using tallies. Discuss why tallies are made in groups of 5. • Ask whether the two graphs represent the same information and why students think so. (e.g., Yes, because there are the same number of animals represented in each graph.) • Ask what Gonk had to do to the data to make the second graph (created new categories, which grouped some of the animals together). • Pages 24–27: Ask what type of graph is used to show the data (e.g., picture/ bar graph). Discuss the various features of the graph and how they help to understand the information. • Ask how many shoppers took part in the survey. Ask whether they would get the same results if they surveyed a different group of shoppers and why they think so. • Partner Investigation: Have students represent the same data in a different way. • Pages 28–29: Have students compare and contrast the different representations of data. • Draw attention to Chester’s score sheet. Discuss what the numbers 1, 2, and 3 represent at the top. Ask whether they think this is a good way to judge the graphs. • Ask whether they think the categories are fair and whether they should all be equally important. • Further Investigation: Have students choose one of the representations and use the data in it to create a different type of graph. After Reading • Building Growth Mindsets: Revisit the KWL chart created before reading the story. Discuss what students learned and what they still wonder about. Add these ideas to the chart. Tell students that they are going to learn even more about graphing in the upcoming lessons. Regularly revisit the chart so you can 118 Patterns & Relations/Data & Probability

First Peoples add new learning and understanding. In this way, students can see the progress Principles of they are making throughout the unit and how new questions may arise as they Learning learn more and more. This supports the First Peoples Principles of Learning that learning involves patience and time. Further Practice • As a class, determine a survey question or observation that you could do over the course of a school week (e.g., count absent students, cans of food collected for the food bank, loonies collected for a school-based fundraiser, etc.). Co‑create a tally table and a vertical bar graph to represent the data. Discuss how this information is valuable for making decisions. • Reflecting in Math Journals: Pose the following prompt: After reading the story The Great Graph Contest, choose one of the representations and explain how it helps you to understand data. Data 119

3Lesson Graphing in Our Lives 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 understanding through play, inquiry, and problem solving; visualize to explore mathematical concepts • Communicating and representing: Communicate mathematical thinking in many ways; 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 • One-to-one correspondence with bar graphs, pictographs, charts, and tables Possible Learning Goals • Interprets graphs by comparing and analyzing their features • Analyzes what the graphical information means in realistic contexts • Identifies various features of graphs, such as the title, labels, and scale, and what the bars and/or pictures represent • Uses features of graphs to interpret what the graphical information means • Compares different graphs by analyzing their features • Explains what the data mean in terms of a realistic scenario • Hypothesizes about what questions could be answered by having the graphical information About the In the primary grades, it is not only important for students to learn how to collect, organize, and display data, but also to critically analyze what the information means. Van de Walle and Lovin emphasize that “the focus of explorations at this and every grade level should be on using data and graphs to answer questions. This means that the emphasis should be on ways to present data and to interpret data in the context of real questions” (Van de Walle & Lovin, 2006, p. 310). In the primary grades, teachers support students to analyze the data in three ways: • reading the data (finding explicit information); • reading between the data (finding relationships and comparing data points); • reading beyond the data (making inferences about information that is not explicit). 120 Patterns & Relations/Data & Probability

About the Lesson This lesson is comprised of several Math Talks based on the four graphs and one tally table in “Tell Me About...” (pages 14–15 in the big book). The different displays of data allow students to compare graphs, analyze their features, and pose/answer questions. Related discussions can evoke further inquiry about the presentation of data and how it relates to students’ lives. Each graph or tally table can support a stand-alone Math Talk and/or investigation. You can use the suggested prompts in each section that follows to develop your own Math Talk. The Math Talks that you develop can be used on progressive days, introducing one or two of the graphs (or the tally table) each day. Through discussion, new investigations may emerge that are more pertinent to students’ lives. You may decide to intersperse your Math Talks throughout the unit to introduce or reinforce concepts that are covered in the actual lesson. For each graph (or the one tally table) shown on pages 14–15 of the big book there are: • several possible prompts from which to pick and choose, depending on your learning goal; • possible inquiries for students to explore. Integrate the math talk moves on page 8. For example, continually encourage students to expand upon their responses and explain their reasoning. Have students respectfully react and respond to what other students are saying so they become active listeners. Have students repeat or paraphrase what their peers have said. Ask questions such as “Do you agree?” or “Can anyone add on to what she said?” Have students turn and talk to a partner before sharing with the group. Provide wait time so students can reflect what is being asked. NOTE: Select the prompts that best meet the needs of your students. Materials: •F aWvohuartitdeo Seasons of Students in Our Class—Tally Table similar to this we call this type of display? Have you seen something “Tell Me About…” before? When would you use a tally table? (pages 14–15 in • What is the title of the tally table? What does it tell us about the information? Patterns, Relations, • Which season would you choose as your favourite? Data, and Probability big • Would it make sense to add ‘other’ to the list of options in this chart? Why or book and little books) why not? Time: 10–20 minutes • What do you think the survey question was? Why do you think that? per day • How many people do you think took this survey? How do you know? • How many people prefer spring? Summer? Fall? Winter? • How did you use the tally marks to help you determine the totals for each season? • Why might this be an important survey to do? How might the information be used? Data 121

•PaHratvneesrtuIndveenststiegxaptloiorenthe data and make some conclusions. Give students some prompts to help them get started: – What seems to be the favourite season? How do you know? – Why might you want to find out what people’s favourite season is? •E yHeaCveolyoouursseeonf Students in Our Class—Pictograph it? What kind of graph is it? a graph like this before? Where have you seen • When might you use a pictograph? How is it helpful for showing data? • What is this pictograph about? • What symbol is used to represent the data? • What comparisons can you make by studying this graph? • How many people took part in this survey? •F uCrtahrreyr Investigation colour in the class using a tally table. Have students out a survey of eye work in partners to create a pictograph of the data. • As a class, compare the class pictograph to the pictograph in the big book. •H eDigohytosuoref cSotgundizeentthsisignraOpuhr? Class—Picture/Bar Graph What is it called? Where have you seen it before? • What do you think this bar graph is about? What do you think is being compared? What does each square represent? • What do the numbered categories at the bottom of this diagram tell us? How do you know? Why do you think the different heights of students were grouped into various intervals of centimetres? • How many students took part in this survey? • Why do you think the class wanted to collect this data? • How do you think the information was collected? •F uHrtahveerpIanirvseosftsigtuadteiontns measure each other’s height. Co-create a class version of this bar graph to see if all class members would fit into the categories represented in the big book. • Compare the class data to the data presented in the big book. •B iWrthhdaat ykinMdoonftghrsapohf Students in Our Class—Bar Graph for understanding data? is this? When might we use it? How is it helpful • How is this graph similar to the graph about heights of students? How is it different? • What is this graph about? How do you know? • What question was asked to collect the data? Why do you think that? • How many students are in this class? How might we figure this out? • What comparisons can you make? What do you find interesting? • What numbers are missing on the vertical axis? 122 Patterns & Relations/Data & Probability

• Why do you think there are horizontal lines going all the way across the graph? How do they help to read the graph? • How many people took part in this survey? • Why do you think the class wanted to collect this information? • How do you think the class collected this information? Is there more than one way? F• uTrothgeetrheInr,vceasrrtyigoauttiaosnurvey and create a bar graph of students’ birthday months. • Have students compare their graph to the one in the big book. S• hWoehaSt itzyepse of Students in Our Class—Bar Graph When do we use bar of graph is this? Have you seen one before? graphs? How are they helpful? • What is this bar graph about? How do you know? Why are titles important to include on a graph? • What information do the bars on the graph give? Why do you think the bars have different colours? • How can we use the bar graph to figure out how many people wear each shoe size? • How can we use the bar graph to figure out how many people took this survey? • How is a bar graph similar to a pictograph? How is it different from a pictograph? • What numbers are missing on the horizontal axis? What would be the highest number represented on the bar graph? What is the lowest number on the bar graph? •P aHrtanveerstIundveensttsicgoamtipoanre the “Birthday Months of Students in Our Class” bar graph to the “Shoe Sizes of Students in Our Class” bar graph. Pose some of the following prompts: How are the two graphs similar? How are they different? Which type of graph would you rather use to display information? Why? Do you think the information came from the same class? Why? Consolidation (10 minutes) • Building Growth Mindsets: Strategically choose some of the students’ findings or solutions to discuss. Focus on how the collection and display of data relate to their lives and how data can impact the decisions that people make. Discuss how the purpose of collecting data is to answer questions and make decisions. Ask why it is important to think critically about the meaning of data since there can be many interpretations. • Discuss how students feel about math and what they find interesting or confusing about it. Ask how they feel when they are given a math problem to solve and how they deal with those feelings. Assure students that they have time to learn math and if it feels frustrating at first, they can find strategies and ways to practise so it is more understandable. • Ask students what they wonder about math. By making connections and sparking curiosity throughout the discussion, students can develop a positive attitude toward math and be motivated to engage in and persevere at problem solving. Data 123

4Lesson Sorting and Classifying Using Various Attributes 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 Previous Experience with Concepts: • Understanding and solving: Develop, demonstrate, and apply mathematical Students have had experiences sorting and understanding through play, inquiry, and problem solving; visualize to explore classifying objects using mathematical concepts; develop and use multiple strategies to engage in one attribute. problem solving • Communicating and representing: Communicate mathematical thinking in many ways; explain and justify mathematical ideas and decisions; represent mathematical ideas in concrete, pictorial, and symbolic forms • Connecting and reflecting: Reflect on mathematical thinking Content • One-to-one correspondence with bar graphs, pictographs, charts, and tables Possible Learning Goals • Describes attributes that can be used for sorting and how they can be categorized • Sorts and classifies objects in different ways, using various attributes • Explains and justifies sorting rules and how the objects have been classified • Displays results of sorted objects in an appropriate graph • Describes attributes of objects and how the attributes can vary by their characteristics (e.g., attribute is colour and they can be red, yellow, or green) • Sorts and classifies materials using one or more attributes and correctly labels the different categories • Sorts a set of objects in more than one way • Explains and justifies how they sorted materials by stating the rule • Creates a graph that represents the results of their sort. 124 Patterns & Relations/Data & Probability

Math Vocabulary: About the srguorlaretp,, hac,ltatprsiicbstiuoftyge,r,sacoporhtn,incrgete bar graph The ability to sort and classify sets of objects lays the foundation for learning how to collect and organize data. Before beginning to sort, students need to identify attributes of objects and recognize how they can vary. This allows them to sort (e.g., moving items that belong together into groups) and classify (e.g., giving names to the categories they have created). Students also need to realize the items can be sorted in different ways according to other criteria. Teachers can support the development of students’ sorting skills by having them sort and classify the same set of objects in many ways and then ask questions that evoke reflection and critical thinking. Through discussion, students learn to more clearly explain their sorts and justify their sorting rules. About the Lesson In the following lesson, students sort and classify various sets of objects in different ways. They learn how to display the results of their sort using different types of graphs. Materials: Minds On (20 minutes) loose materials, two • Meet as a class. Secretly choose a way to sort your students (e.g., types of hoops or strings that can be shaped into shoes, colour of t-shirt). circles to create a Venn diagram (or sorting • Sort four or five students and have them move into the appropriate groups circles) without disclosing the sorting rule. Time: 60 minutes • Select a student and have the rest of the class predict where the student should be placed. Have them justify their reasoning. • Continue sorting some more students and ask whether they have changed their prediction of the sorting rule. • Once all students are sorted, disclose the sorting rule. Ask students what helped them figure out how they were sorted. • Ask what the word ‘attribute’ means. Students can turn and talk to a partner. As a group, define attribute (e.g., a characteristic of a shape or object) and add it to an anchor chart. Have students think of examples to support the definition. Ask how the attributes can vary. Discuss how the variations allow us to sort and classify objects in many ways. • Discuss other ways that students could have been sorted. Working On It (15 minutes) • Students can work in small groups. Give each group a bucket of loose materials to sort. Encourage them to sort the materials in various ways. You may decide to have groups work in pairs and then have the others in the group guess their sorting rule. Data 125

• Once students have sorted their materials in various ways, have them sort the objects in one way, without identifying the sorting rule. Differentiation • Select the loose objects that are most appropriate for your students’ needs. Assessment Opportunities Observations: This is a good opportunity to observe how students sort and whether they can justify their sorting rules: – Can they consistently sort one or most of the objects according to their rule? – Are there objects that won’t fit into their sort? How do students deal with that? – Can students articulate and justify their sorts? – Can they identify the attributes they are using and how they differ? – Can they flexibly group the items in another way? – Are they sorting by one or more attributes? – How do they organize their sort? Consolidation (25 minutes) • Have a gallery walk. As a class, move to each of the sorts completed by the groups in the Working On It section. Have students analyze the sorted objects and guess the rule. Have them justify their reasoning. Identify the attributes used to sort and how the attributes can differ. • Select one of the students’ sorts. Together, create a concrete graph that represents the results of the sort. Ask what labels they would give to the various categories and what title would be appropriate for the graph. • Ask how they could represent the concrete graph in another graph that could be displayed on chart paper. Together, create a pictograph or bar graph, complete with labels and a title. Make connections between the two representations. • Discuss why graphs on paper can be more practical than concrete graphs. 126 Patterns & Relations/Data & Probability

5 8LessonstoDisplaying Data in Various Ways Math Curricular Competencies Learning Standards • Reasoning and analyzing: Use reasoning to explore and make connections; Previous Experience estimate reasonably; develop mental math strategies and abilities to with Concepts: make sense of quantities; use technology to explore mathematics; model Students have had mathematics in contextualized experiences some experience with representing data in • Understanding and solving: Develop, demonstrate, and apply mathematical concrete graphs and pictorial versions of understanding through play, inquiry, and problem solving; visualize to explore concrete graphs. mathematical concepts; develop and use multiple strategies to engage in problem solving • Communicating and representing: Communicate mathematical thinking in many ways; explain and justify mathematical ideas and decisions; represent mathematical ideas in concrete, pictorial, and symbolic forms • Connecting and reflecting: Reflect on mathematical thinking Content • One-to-one correspondence with bar graphs, pictographs, charts, and tables About the According to Marian Small, students should first gain some experience with concrete graphs that are created with real objects, before they progress to making graphs from concrete models that represent the real objects, which is more of an abstract representation of the data (Small, 2013, p. 520). Helping students to display their data in various graphical representations will allow them to make connections between each model and to see that different types of representations tell different things about the same data (Van de Walle, 2001, p. 367). Furthermore, these visual displays of data encourage spatial thinking (Newcombe, 2013, p. 31). When the data presented has been collected and represented as the result of a student-generated question, it is more relevant for students and they will be more personally invested in what it has to say. Eventually, we want students to choose their own way to display collected data. Marian Small points out the importance of choosing a format that suits the data, as well as including clear titles and labels to guide the reader in interpreting it (Small, 2013, p. 518). When students can represent and compare data using different models, and explore how the elements of those representations appear, they can make choices about continued on next page Data 127

Mstvvaaueaexlrrltrivytstheiic,tcyVaaal,abolld,blcaeaheax,tolbai,bsru,ita,zilptorahlinergocytrtr:aaoizlpgo,rhna,tpahl , which model best displays their data. Whichever model they choose, data collection should always be for a purpose, to answer questions, and preferably about topics that are of interest to students (Van de Walle, 2001, p. 361). About the Lessons In these lessons, students learn how to represent data in tally tables, pictographs, and bar graphs. They learn about the features of the various displays and how to use them to read the data. They also make connections and comparisons between the various displays. 128 Patterns & Relations/Data & Probability

5Lesson Displaying Data: Concrete Graphs to Pictographs Teacher Possible Learning Goals Look-Fors • Creates concrete graphs to represent a set of data • Creates a pictograph to represent a set of data represented in a concrete graph Materials: • Makes connections between concrete graphs and pictographs and explains Our Favourite Digital Slide 40: Graph Topics how they can represent the same data Digital Slide 39: Concrete Graph (2) • Describes the difference between the pictograph and a concrete graph Digital SOluidreF3a8v:oCuroitnecrete Graph (1) • Explains why they would use a pictograph • Collects data using a tally table Tally Table Pictograph • Creates a pictograph with data they have collected Scholastic Canada GR3 BC Patterns & Relations 3rd Pass Minds On (15–20 minutes) Digital Slides November 9, 2021 3rd Pass • Create a concrete graph, modelled after Digital Slide 38: Concrete Graph (1) 3rd Pass Scholastic Canada GR3 BC Patterns & Relations without showing the slide. Ask what kind of graph students see (concrete graph). Digital Slides November 9, 2021 • Say, “What do you think the categories in this graph might be?” (e.g., triangle/ Scholastic Canada GR3 BC Patterns & Relations rhombus/square/trapezoid; green/blue/yellow/red) Using small pieces of paper Digital Slides or cardboard, add the categories that the class determines (e.g., colour, shape) November 9, 2021 to name each row. Digital Slides 38 and • Ask, “Could we mark our categories by the number of sides each shape has? 39: Concrete Graph (1 and 2), Digital Slide 40: (e.g., 3, 4, 4, 4) No, because if we had three rows for the same category, that Graph Topics, a variety would actually be one category.” of pattern blocks, BLM 28: Tally Table/ • Ask, “What do you think the title might be?” (e.g., Our Pattern Block Shapes; Pictograph Template, “What’s My Data?” Our Pattern Block Colours) Add the title that the class determines to the (pages 12–13 in the template. Ensure that it matches the categories you identified earlier. Patterns, Relations, • Ask, “What would happen if I wanted to create this graph, but I didn’t have Data, and Probability big book), clipboards, sticky any actual pattern blocks? Visualize what that graph might look like. What notes could I do?” (e.g., You could draw them!) Time: 55–60 minutes • Say, “Great idea!” Project Digital Slide 39: Concrete Graph (2) and ask students BLM 28: Tally Table/Pictograph Template to compare it to the first concrete graph with these prompts: Our Favourite – What is the same? What is different? What do we need to add? – This kind of graph with pictures to represent concrete things is called Tally Table a pictograph. Our Favourite • Project “What’s My Data?” on pages 12–13 of the Patterns, Relations, Data, Pictograph 44 © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 and Probability big book. Have students look at the pictograph “Pets of Students in Our Class” on page 12 and ask: Scholastic Canada GR3 BC Patterns & Relations 4th Pass Reproducibles – What kind of graph is this? How do you know? What are the categories? November 9, 2021 Data 129

Teaching Tip What is the title? (e.g., pictograph; it has categories and pictures for how many of each; dog/cat/bird/fish/no pets) What does each picture Ask students to visualize represent? How do you know? This is known as the key. what picture/symbol – Why might we choose to do a pictograph instead of a concrete graph they will use for each sometimes? (e.g., It’s too hard to have live animals; the real things are too category when they big; it’s easier to draw them.) get to the pictograph, to ensure that it is Working On It (20 minutes) something they can draw. This might affect • Tell students that today they are going to work with a partner to gather some the options they choose for their categories. data from some of their classmates and represent it in a pictograph. • Project Digital Slide 40: Graph Topics. – Say, “With your partner, you are going to decide on a topic. What might be some ideas for topics for a pictograph? Remember that you will need to draw the categories.” Brainstorm a list of possible topics for pairs to consider (e.g., favourite colour, season, vegetable, fruit, sport, etc.). • You may wish to model an example using Digital Slide 40. (e.g., Fill in the tally table title with “shape” and write four categories in the column on the left [e.g., circle, square, triangle, star].) • Ask for one partner to get a copy of BLM 28: Tally Table/Pictograph Template, a clipboard, and a pencil. Partners work together to decide on a topic and four categories to add to their tally table. • Once pairs have determined that part of their tally table, divide the class into two groups and have them sit, with their partner, in one of the two groups. Smaller groups will make the data collection simpler as there will be approximately five pairs (i.e., five surveys) in each half of the class. • Say, “One pair at a time, you are going to read out your topic and ask the question ‘What is your favourite _________ ?’ Share the four categories you chose. Then, each student in the group needs to decide which category is their favourite choice. Repeat the four categories, one at a time, and count the votes from the group. Fill in the tally table with the number of votes.” • Once all pairs have completed their tally table, they can represent this information in a pictograph on BLM 28. Remind them that they can copy the names of the categories in the left-hand column. Have them add the pictures to their pictograph so that it matches the tallies in their tally table. Differentiation • If a group is having difficulty choosing a topic, suggest one. Consider the complexity of the symbol/picture they will need to draw when doing so. • If students are struggling to get started, engage them in small-group instruction to help them do so. • For students who may struggle with representing data visually, provide them with stickers, stamps, and/or the use of a computer to copy and paste multiple images using a simple table. 130 Patterns & Relations/Data & Probability

Assessment Opportunities Observations: • Pay attention to ensure that each student is only voting once per survey. • Pay attention to accuracy when students are tallying their count. Conversations: • What are your categories? • How many do you have for each category? In total? • What picture will you use to represent each category? Consolidation (20 minutes) • Building Growth Mindsets: One at a time, pose the following reflection questions and have foursomes share ideas. Have students look at both their tally tables and pictographs: – Which is the most interesting? Why? – Which is the easiest to know the count/how many? Why? – Which is the easiest to complete? Why? – When would you choose a tally table? – When would you choose a pictograph? • Have each pair sit with another pair with their completed tally table and pictograph. • Have students display their completed tally table and pictograph. Give each pair of students enough sticky notes for one per pair. Together, as pairs visit peers’ work, they write one star and one wish based on the success criteria (e.g., the tally matches the picture count, the categories are clear, etc.). • As a class, review the important features of a pictograph, including the title, labels, and the key. Further Practice • Reflecting in Math Journals: Have students explain what they have learned about tally tables and pictographs. Data 131

6Lesson Displaying Data: Bar Graphs Teacher Possible Learning Goals Look-Fors • Creates a bar graph to represent a set of data • Understands the features of bar graphs and explains how they help to read the data • Describes features of a bar graph • Collects data using an appropriate organizer • Explains or shows why they would use a bar graph • Creates a bar graph using their collected data • Uses features of a bar graph to read the data Materials: Minds On (20 minutes) • Draw a horizontal axis on a piece of chart paper to create the base for a bar graph. – Add the title “Number of Pets in Our Homes.” – Number each tick mark on the bottom with the numbers 0, 1, 2, 3, 4. “What’s My Data?” – Give each student a small sticky note. Have them draw a large “X” on (pages 12–13 in the their sticky note. Ask the survey question, “How many pets do you have Patterns, Relations, at home?” Data, and Probability big book), Digital Slide 41: • One at a time, invite students to come up to the chart paper and add their Bar Graph Template, BLM 29: Bar Graph sticky note above the correct number of pets at home. Template, sticky notes, markers, chart paper • Once the concrete graph is complete, ask the following questions: Time: 45 minutes – How many pets at home is the most common? The least common? How do you know? BLM 29: Bar Graph Template • Project “What’s My Data?” (pages 12–13 from the Patterns, Relations, Data, and Probability big book). Ask the following questions: – Do you remember some of these graphs? Digital Slide 41: Bar Graph Template – Is there one that looks like the graph that we just created? • Students should see that the example at the top of page 12 (“Countries Students in Our Class Have Visited”) is similar. Ask: Scholastic Canada GR3 BC Patterns & Relations 3rd Pass – What is the same? (e.g., There is a line across the bottom; there are ticks Digital Slides on the line for each of the choices; the choices are written down under the November 9, 2021 45 ticks; there is a title.) © 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 – What is different? (e.g., There are X’s instead of sticky notes; the topic is different; the title is different; the choices are places not numbers.) – Why might it be important for us to use X’s to show our choices instead of sticky notes? (e.g., We might not have sticky notes; the sticky notes could fall off and we would lose some data; writing down an X is easy to do and it won’t fall off the line plot.) 132 Patterns & Relations/Data & Probability

• Project Digital Slide 41 onto the whiteboard. Add the following categories under the five bars, “Water, Milk, Juice, Lemonade, Hot Chocolate.” Use the following prompts: – Let’s try making another type of graph. This is called a bar graph. Why do you think we call it a bar graph? (e.g., It looks like bars.) – Looking at the categories, what do you think the survey question might be? (e.g., What’s your favourite drink?) – What do you think our title might be? Is a title a question? How might we change our question just a little to make it a title? (e.g., Favourite Drinks of Students in Our Classroom) Does the title include the source of the data, or where it is from? (yes) – Raise your hand if water is your favourite drink. Count the votes and shade in the appropriate number of boxes. Repeat the process for milk, juice, lemonade, and hot chocolate to add the other votes to the bar graph. Remind students they can only select one choice. • Once the bar graph is complete, ask the following questions: – Which drink do we like the most? The least? How do you know? (Count the boxes.) • Inform students that they are going to take a survey of what their favourite sport is. Ask students what categories they would like to include. Set up a tally table that includes the chosen categories. Carry out a class survey, having students indicate their favourite sport by adding a tally to the tally table. • Project “What’s My Data?” once more and ask students if they can see an example of a graph that looks like the bar graph you just made together. (“Favourite Sports of Students in Our Class” on page 13) Ask: – What is the same? (e.g., It has a title that also tells us the source of the data; there are categories across the bottom; there are bars to show how many votes for each category.) – What is different? (e.g., There are lines across the graph instead of blocks; there are numbers on the left to show us how many; it’s in colour, etc.) – Why do you think we leave spaces between the bars? (e.g., So we can see and read the data more clearly.) Working On It (15 minutes) • Leave the co-created bar graph up for student reference. Say, “Today, you are going to make a bar graph from the data we just collected about our favourite sports.” • Provide copies of BLM 29: Bar Graph Template for students to choose. Remind them to refer to the co-created examples that are posted to create the new graph. Differentiation • If students are unsure of how to start, engage them in small-group instruction to help them do so. Data 133

Assessment Opportunities Observations: • Pay attention to see that students are transferring the data correctly from the tally table to the bar graph. • Pay attention to check that students are including all elements of a bar graph. Conversations: • How do you know where to add a box on your bar graph? • How do you know that you’ve included all of the information from the tally table? • Have you included all of the necessary information? (e.g., title, categories, numbers of each item) Consolidation (10 minutes) B• uAilsdkinsgtudGernotws twhhMatitnhdesyentost:iced about the bar graph they created and the tally table. Ask how they are the same and how they are different. • Ask any of the following questions to help students reflect on their work: – What was the easiest part of making your graph? – What was the hardest part of making your graph? – Which display is easier to count how many people chose each answer? Why? – Why do you think bar graphs are used so frequently to display data? Further Practice • Have students prepare a bar graph using a survey question of their own. • Reflecting in Math Journals: Have students explain what they have learned about bar graphs. 134 Patterns & Relations/Data & Probability

7Lesson Displaying Data in Vertical and Horizontal Bar Graphs Teacher Possible Learning Goals Look-Fors • Conducts a survey to collect data • Organizes data using a tally table Materials: • Creates vertical and horizontal bar graphs to represent data “Tell Me About…” • Conducts a survey and accurately collects and records data in tally table (pages 14–15 in • Accurately represents data in both vertical and horizontal bar graphs Patterns, Relations, • Uses titles and labels accurately, as needed, on vertical and horizontal bar graphs Data, and Probability big • Compares a vertical and a horizontal bar graph book and little books), BLM 29: Bar Graph Minds On (20 minutes) Template, Digital Slide 41: Bar Graph Template, • Project Digital Slide 42: Tally Table Template. Tell students that they are going Digital Slide 42: Tally Table Template to do a class survey and display the collected data in various ways. Time: 50 minutes • Pose the following prompts: BLM 29: Bar Graph Template – The survey question we are all going to answer is “What is your favourite season?” Digital Slide 42: Tally Table Template – What are the possible answers for this question? (winter, spring, summer, fall) Digital Slide 41: Bar Graph Template – Look at the tally table template. Is there enough room for our data? How © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTEDSRcigNhiotSalalAsStNliicdDeCsaRnEaLdAa TIGORN3SB/CDAPaTtAterAnsN&DRPeRlaOtioBnAs BILITY ISBN 978-1-4430-7299-1 45 3rd Pass do you know? (e.g., Yes, because there are only four seasons and there is November 9, 2021 3rd Pass enough room in the table for four categories) – What if my survey question had more options? (e.g., then you might need Scholastic Canada GR3 BC Patterns & Relations 4th Pass to add some rows) Reproducibles November 9, 2021 Scholastic Canada GR3 BC Patterns & Relations • Add in the categories top to bottom in the tally table. Digital Slides • Conduct the survey by counting hands. As students tell you what to do, fill in November 9, 2021 the tally table. • Ask students how they can make a vertical bar graph of the class results using the grid on Digital Slide 41: Bar Graph Template. • As students explain, create the vertical bar graph. Ask questions to ensure all titles and labels are also included. • Repeat the process for the horizontal bar graph using another blank version of Digital Slide 41. Data 135

Teaching Tip • Discuss the similarities and differences between the two representations. Fill in the templates and – Similar: data, title, subtitles, spaces between bars, etc. verbalize your ideas as – Different: location of subtitles is switched, direction of the bars you collect the data from students (rather than • Continue to project the two class models for students to reference. ahead of time) to model the process. Working On It (20 minutes) • Students work in small groups and share a copy of the little book versions of the big book. • Students use the data in the tally table about favourite seasons displayed on page 15 of the big book. They represent the data in a vertical bar graph and in a horizontal bar graph using copies of BLM 29: Bar Graph Template. • As a group, they make comparisons between the class data and the data in the big book and draw some conclusions. Ask what decisions can be made from knowing this information. Differentiation • Some students may only have time to complete one of the bar graphs, which still allows them to make comparisons. • For students who need more or a challenge, have them also represent the data in a pictograph. Assessment Opportunities Observations: Pay attention to how students are including the features of the graph into each representation: – Do they see the connections between the two bar graphs? – Can they flexibly transfer the information from one graph to another or do they need to reference the model for each? Conversations: Pose some of the following prompts to help students create complete graphs: – Compare your graphs to the ones we made in the Minds On. Are you missing any features? – What is the title of your graph? What are the subtitles on your graph? Where are they on the two graphs? – Have you left a space between the first bar and the axis? Have you left a space between bars? Why is this important? – Have you checked to make sure that the data represented is the same in all four charts/graphs? Is it the same? How do you know? 136 Patterns & Relations/Data & Probability

Consolidation (10 minutes) • Meet as a class and pose some of the following reflection questions: – Which bar graph did you prefer to create (vertical/horizontal)? Why? – Which bar graph is the easiest to read? Why? • Discuss the comparisons and conclusions that students made by comparing the two graphs. Further Practice • Reflecting in Math Journals: Have students describe the characteristics of both vertical and horizontal bar graphs and state which they prefer and why. Data 137

8Lesson Using Features of Graphs to Ask and Answer Questions Teacher Possible Learning Goals Look-Fors • Reads data in a variety of graphs, using mathematical language • Asks and answers questions about class-generated data in a variety of graphs Materials: • Generates questions about different graphs “What’s My Data?” • Answers questions about graphs using information they read from the graph (pages 12–13 in the • Describes the similarities and differences between different representations Patterns, Relations, Data, and Probability big of the same data book), two colours of sticky notes Minds On (20 minutes) Time: 50 minutes • Project “What’s My Data?” (pages 12–13 from the Patterns, Relations, Data, and Probability big book) on the whiteboard. • Have students work in partners. Hand out one coloured sticky note to each pair of students. • Say, “You and your partner are going to write one thing on your sticky note. Write something you know about one of the graphs.” (e.g., Four people have fish as a pet.) Write this example on the first colour of sticky note and post it on the whiteboard beside the graph that you used to create it. • When students have written down one thing that they know about one of the graphs, have each pair read out their ‘fact’ and have the other students guess which graph it comes from. NOTE: There are two representations of each set of data. • Hand out a second colour of sticky notes to each pair of students. On the second colour of sticky note, ask a question about one of the graphs. (e.g., How many people have never visited another country?) Write this example on the second colour of sticky note and post it on the whiteboard beside the graph that you used to create it. • When students have written down one question that they can ask about one of the graphs, have each pair read out their question and have another student guess which graph it comes from and answer the question. • Support students through the activity with prompts as needed. 138 Patterns & Relations/Data & Probability

Working On It (20 minutes) • Leave up the questions and observations that students wrote on sticky notes during the Minds On as an anchor. • Students work in small groups, sharing the little book versions of the big books. • Give two different coloured sticky notes to each student: one for an observation and one for a question as modelled in the Minds On. Ask students to write their name on both. • Have students post their sticky notes beside the graph that they used to create each one. • When all sticky notes have been posted, have students choose one with a question from another student and answer it below the note and sign their name. Differentiation • Provide a simpler or a more complex question about a graph if the ones available are not suited to the student. Assessment Opportunities •O bPsaeyrvaattteionntiso:n to the information students share and if it includes mathematical language. • Pay attention to students’ ability to match their observations and questions with the appropriate graph. • Pay attention to students’ ability to correctly answer the question they chose. Conversations: If students are struggling to generate questions from graphs, choose a simple student-generated graph and use the following prompts to support their learning: – Which graph are you looking at? – What information are you trying to describe? – What information are you trying to ask a question about? – What is the question asking you? Where do you think you can find that information in the graph? Consolidation (10 minutes) • Gather students back to reflect on this activity. – Which graph was the easiest to work with for this activity? Why? – What kind of observation did you make about some data? – What question did you ask? – What question did you answer? – What was the hardest part of this activity? Making an observation? Asking a question? Answering a question? Why? – Why do you think we graph information instead of just describing it in words? Data 139

First Peoples • Building Growth Mindsets: As a whole group, discuss some of the following Principles of Learning prompts: – What was challenging about our learning today? – How do we know we learned something today? – Did we make mistakes today? – What did it feel like when we made a mistake? What about when we worked through our mistake? • Remind students that learning can be HARD WORK and sometimes we make mistakes, but these mistakes are what help us learn new things and help our brains grow. It is very important that when something is hard we keep trying, because we might not get it YET but we will get better at it the more we try. This supports the First Peoples Principles of Learning that learning involves patience and time; and that learning involves recognizing the consequences of one’s action. 140 Patterns & Relations/Data & Probability

9 12Lessonsto Analyzing Data Math Curricular Competencies Learning Standards • Reasoning and analyzing: Use reasoning to explore and make connections • Understanding and solving: Develop, demonstrate, and apply mathematical Previous Experience with Concepts: understanding through play, inquiry, and problem solving; visualize to explore Students have had mathematical concepts; develop and use multiple strategies to engage in experience with data problem solving presented in concrete graphs, pictographs, bar • Communicating and representing: Communicate mathematical thinking graphs, and tally tables. in many ways; explain and justify mathematical ideas and decisions; represent mathematical ideas in concrete, pictorial, and symbolic forms • Connecting and reflecting: Connect mathematical concepts to each other and to other areas and personal interests Content • One-to-one correspondence with bar graphs, pictographs, charts, and tables About the The ability to analyze and interpret information presented in data displays (e.g., graphs/tally tables) is important so students understand what the data mean and how the information can be used to make decisions. In early primary grades, there are three ways in which students learn to read and analyze data. • Level 1: Students read what is directly on a data display (e.g., graph) without having to interpret the data (e.g., six people like dogs). • Level 2: Students make comparisons among the data (e.g., more people like dogs than cats; ordering pets from greatest to least frequency). They also may use various operations and calculations to make their comparisons (e.g., four more people like dogs than cats). • Level 3: Students read the data to make inferences, taking into account the information about the population and the situation. For quantitative data, students consider the distribution of the data as a whole, or the shape of the data, and make general conclusions because they can see the relationships between pieces of data and the whole (e.g., dogs are the most popular, with the other pets having about half as many votes). continued on next page Data 141

Math Vocabulary: As students are introduced to other types of data displays (e.g., pictographs, sgbvluaraaearxbrrvpitesegihc,lyrs,aa,l,eplpd,taihacihst,ttlotoeat,r,ag,imzrlhcloayooonpnrstthiactza,,borle,lnette,al horizontal and vertical bar graphs), they learn about the features of each representation and how they are useful for interpreting the data. They more, less can also make connections among the representations by analyzing how the same data can be displayed in different ways. As students build their repertoire of data displays, they can eventually select the ones that are best suited for the type of data. About the Lessons The lessons in this section provide students with opportunities to analyze a variety of data representations (e.g., pictographs, horizontal and vertical bar graphs, tally tables, etc.) about familiar topics (e.g., height, shoe size). Throughout the discussions, students can analyze the data and pose and answer questions. They can also interpret the data and draw conclusions. 142 Patterns & Relations/Data & Probability

9Lesson Analyzing Data in Different Displays Teacher Possible Learning Goals Look-Fors • Identifies features of a variety of displays of data (e.g., graphs, tally table) and explains their purpose • Asks and answers questions about data presented in a variety of displays of data • Reads and analyzes data presented in various displays of data, including vertical and horizontal bar graphs • Recognizes and describes the features of different types of displays of data (e.g., graphs and tally table) • Explains why the features are important for understanding the data • Explains what the data mean within a context • Generates questions about different displays of data • Answers questions about data and supports their responses using information from the displays of data (e.g., graph, tally table) Materials: Minds On (20 minutes) BLM 30: Exploring • Project Digital Slide 43: Types of Pets of Students in Our Class. Displays of Data, • Using BLM 30: Exploring Displays of Data as a reference, ask students about BLM 31: Tell Me About, Digital Slide 43: Types the features of the graph shown on Digital Slide 43 and how those features of Pets of Students in help us to understand the data. Our Class, two different colours of sticky notes What is the title of this display of data? Types of Pets of Students in Our Class Time: 60 minutes What was the survey question? What kind of pets do you have? BLM 31: Tell Me About What type of display of data is it? Bar Graph Is the display of data vertical or horizontal? Horizontal Favourite Seasons of Students in Our Class How is the information recorded? Bars BLM 30: Exploring Displays of Data (e.g., pictures, symbols, tallies, bars, etc.) What are the answer choices? Dog, Cat, Bird, Hamster Spring What is the title of this display How many answer choices in total? 4 Summer of data? Are there labels on the axes? If so, what Yes. Type of pet/Number are they? of students Fall What was the survey question? Winter Digital Slide 43: Types oWfhPatettyspeooffSditsupdlaeynotfsdaitna iOs iut?r Class Type of Pet Dog Is the display of data vertical or Cat horizontal? Bird How is the information recorded? (e .g ., pictures, symbols, tallies, bars, etc.) What are the answer choices? How many answer choices in total? Hamster Are there labels on the axes? If so, what are they? 0 2© 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 47 4 6 Number of Students Scholastic Canada GR3 BC Patterns & Relations 4th Pass Reproducibles November 9, 2021 46 © 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 Scholastic Canada GR3 BC Patterns & Relations 3rd Pass Digital Slides November 9, 2021 Data 143

Teaching Tip • Inform students that they are going to study the graph on Digital Slide 43 to Students will be using determine what the data tell us. BLM 30: Exploring Displays of Data as a • Hand out one sticky note to each pair of students and have them write down template to explore the features of different data one thing that they know about the data. (e.g., 2 people have birds) displays (e.g., graphs, tally table). You may wish • Collect the notes and randomly redistribute them to different pairs. Provide to create an anchor chart of the BLM and record pairs with a different colour of sticky note. Students determine the question answers for students to that this data fact would answer. (e.g., How many people have birds?) reference later. • Have students share the data point that they had and the question they created to match. Post the pairs of sticky notes alongside the projected bar graph. Working On It (20 minutes) • Post the graph, observations, and questions developed in the Minds On, so students can reference them if necessary. • Pair off students and give each pair a copy of one of the first five pages of BLM 31: Tell Me About (two student pairs work on each display of data). Also give student pairs a copy of BLM 30: Exploring Displays of Data to record their answers and observations, as well as two different coloured sticky notes per student. • Students study the display of data (graph or tally table) they have been given and complete BLM 30 together. Each student records an observation on one sticky note and the related question on the other sticky note. Differentiation • Provide a sentence starter for students who may struggle with determining what they know about their display of data. (e.g., The category with the highest number is     ;       (category e.g., cats) has       (number) votes; the least popular       (e.g., pet) is      , etc.) • For students who may need support with the language, ensure that they understand the language in BLM 30, and in their particular display of data, to support them in making an observation. • Provide an anchor chart of question starters that might be asked about the data. (e.g., How many votes/people…? Which category of       has the most/least/highest/lowest…? etc.) • For students who need more of a challenge, have them create more observations and questions. Assessment Opportunities Observations: Pay attention to the information students derive from their display of data (graph or tally table): – Can they correctly read the data using the features of the display of data? – Is the information based on part of the data (e.g., How many people have birds?) or the data as a whole (e.g., Which pet is the most popular?)? – Do students use mathematical and comparative language to describe the data? – Do the questions match the chosen information? 144 Patterns & Relations/Data & Probability

Materials: Conversations: Pose some of the following prompts if students are having difficulty: BLM 31: Tell Me About (sixth page) – Which display of data are you looking at? – Do you have any questions about the features of this display of data? 52 © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 BLM 31: Tell Me About continued – Do you have any questions about the data represented in this display Scholastic Canada GR3 BC Patterns & Relations Favourite Seasons of Students in Our Class Eye Colours of Students in Our Class Heights of Students in Our Class of data? Reproducibles Spring – What information are you trying to describe? November 9, 2021 Summer blue – What information are you trying to ask a question about? Fall – Have you tried asking your question out loud to your partner? Does it Winter green make sense? Did your partner answer your question with the observation brown that you made? If not, how might you rephrase your question? hazel Consolidation (20 minutes) grey 110–114 115–119 120–124 125–129 130–135 • Have students meet with the other students who worked on the same display Height (cm) of data. They can take turns posing their questions and having the rest of the Legend: = 1 student 1 square = 1 student group answer them. • Meet as a class. Post copies of each display of data, with students’ completed BLM 30 and observation and question sticky notes. • Have each group present their display of data, explain its features, and ask one or two questions for the rest of the class to answer. • Ask what features all the displays of data have. Have students compare one or two of the displays of data. Discuss how the features on these data displays are the same and how they are different. • Ask which display of data students find the easiest to read and why they think so. Further Practice • Independent Problem Solving in Math Journals: Provide a copy of the sixth page of BLM 31: Tell Me About and one student’s observation sticky note from today’s activity. In their math journals, have students determine which display of data the student’s observation is about, how they know, and have them ask the question that would give them the answer they were given. Shoe Sizes of Students in Our Class Birthday Months of Students in Our Class 5 4 Shoe Size3 4 Students 2 2 4th Pass 1 03 9 Students January February March April May June July August September October November December Month Data 145

10Lesson Describing Data Teacher Possible Learning Goals Look-Fors • Describes data using comparative language (e.g., more, less) • Compares different parts of the data to make statements (e.g., there are two Materials: more people who prefer spring to fall) “Tell Me About...” (pages 14–15 in • Uses the features of the display of data (graphs and tally table) to understand Patterns, Relations, Data, and Probability big the data book and little books), Digital Slide 44: Heights • Describes some of the data in the display of data and explains what the of Students in Our Class, BLM 32: Heights of information means within a context Students in Our Class, measuring tapes or • Compares data using mathematical language (e.g., more, less) metre sticks, chart • Explains what they know from looking at the data as a whole paper, markers Minds On (15 minutes) Time: 45 minutes • Project big book pages 14–15 and draw students’ attention to the graph BLM 31: Tell Me About continued Heights of Students in Our Class entitled “Shoe Sizes of Students in Our Class.” Have students turn and talk to a partner about what they know from analyzing this graph. They can use the Digital Slide 44: Heights of Students in Our Class little book versions of the big book to get a closer look. Heights of Students in Our Class Describe this Data • Discuss some of their findings. (e.g., 3 people wear size 5; 10 people wear size 1. What is one data fact that you can state 110–114 115–119 120–124 125–129 130–135 4; no one wears size 1, etc.) Height (cm) about this data? • Explain to students that sometimes we can learn more about our data by 1 square = 1 student 2. What is one comparison can you make between data? considering two or more pieces of data at the same time and comparing them. Ask what words we might use to make comparisons (e.g., more than, 3. What is one thing that you can say less than, as many, etc.) and write these words on chart paper for students to about the shape of the data? reference. 110–114 115–119 120–124 125–129 130–135 • Have students work with their partners to make some comparisons. Height (cm) • Share some of the students’ observations. Below are some possibilities: 1 square = 1 student – There are 7 more people that wear size 4 than size 5. – There are 2 less people that wear size 2 than size 3. © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIOSNcSh/oDlaAstTicACAanNaDdaPRGORB3ABBCILPIaTttYernsIS&BRNel9a7ti8on-1s-4430-7299-1 49 3rd Pass – There are as many people that wear both sizes 2 and 3 as people that wear Digital Slides November 9, 2021 size 4. (10 = 4 + 6) Scholastic Canada GR3 BC Patterns & Relations 4th Pass • Ask what observations and statements students can make by looking at the Reproducibles November 9, 2021 information in the graph as a whole. Working On It (15 minutes) • Distribute one copy of BLM 32: Heights of Students in Our Class to each pair and project Digital Slide 44, which is the same as the BLM. • Ask students what they notice about this graph. (e.g., there are 5 categories of height; there are people represented in each category, etc.) 146 Patterns & Relations/Data & Probability

• Review the three questions under the heading ‘Describe this Data’ and use the examples identified in the Minds On section to model how to answer each of these questions. An example of each is given below for the graph ‘Shoe Sizes of Students in Our Class’ on page 15 of the big book: – Reading one data point: “No one wears size 1.” – Comparing more than one data point: “There are 7 more people who wear size 4 than size 5.” – Describing the whole data: “Most people wear sizes 3 and 4.” Differentiation • Provide sentence starters as needed for each question or scribe students’ responses. • For students who need language support, ensure that they understand the mathematical vocabulary necessary to make comparisons. Assessment Opportunities Observations: Pay attention to the observations that students make: – Do they use mathematical language to describe the data? – Can they make both qualitative and quantitative observations? – Which parts of the graph are students using to interpret data? – Can they interpret the whole data in terms of the context? Conversations: Pose some of the following prompts to help students make more detailed observations: – What observation did you make? Which part of the graph did you use to make that observation? – Which parts of the data did you compare to make this observation? Show me on the graph. – You said that there was more in this category than the other one? How many more? – How can the title help you interpret the meaning of the information as a whole? What could you conclude about the people who took this survey? Consolidation (15 minutes) • Meet as a class to share and discuss students’ observations. See below for sample responses: – Reading one data point: “6 people are between 120 and 124 cm tall.” – Comparing more than one data point: “There are two or three people that are the shortest or tallest height.” – Describing the whole data: “Every height group has some people. The most common height is 125–129 cm.” Data 147

First Peoples • Encourage other observations, such as the number of people who took part in Principles of Learning the study. Materials: • Discuss why someone would want to collect this information and what the BLM 32: Heights of results could be used for. Students in Our Class • Building Growth Mindsets: © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 BLM 32: Heights of Students in Our Class – Ask students to reflect on which of the three questions was the easiest and Scholastic Canada GR3 BC Patterns & Relations Heights of Students in Our Class Describe this Data which was the most challenging to answer. Reproducibles 1. What is one fact that you can state about November 9, 2021 – Discuss what other information they would like to know in order to make the data? this graph more meaningful. (e.g., Who took this survey and how old are 2. What is one comparison that you can make they? Why did the person want to collect this data? Would the results be between data? similar if it was done with another group of the same age? When was this study done? How were the measurements taken? Were they accurate?) 110–114 115–119 120–124 125–129 130–135 3. What is one thing that you can say about the This supports the First Peoples Principles of Learning that learning Height (cm) data as a whole? ultimately supports the well-being of the self, the family, the community, the land, the spirits, and the ancestors. 1 square = 1 student – Discuss why it is important to know a lot about the data before making 4th Pass conclusions and that data could be misleading without knowing all of the facts. Further Practice • Use the ‘Describe this Data’ questions on the right-hand side of BLM 32 to help students describe the data in the other displays of data (graphs and one tally table) shown on pages 14–15 of the big book. • Have students reflect in their math journals about which kind of display of data (graphs or tally table) they find the easiest to describe and why. • Collect class data on either shoe size or height and compare the results to the two graphs used in today’s lesson. 53 148 Patterns & Relations/Data & Probability

11Lesson Interpreting Data Teacher Possible Learning Goals Look-Fors • Makes inferences from data • Uses data as evidence to support inferences Materials: • Describes the whole data and explains what the information means within Digital Slide 45: How Much Sleep Did We Get Last Night? a context Fewer than 8 8 9 10 11 12 More than 12 • Explains or shows where they get information in tables/graphs Hours of Sleep • Compares information in tables and graphs to make inferences • Asks questions about other students’ inferences using data to support their Adapted from A Guide to Effective Instruction in Mathematics: DMP, 2007 questions Scholastic Canada GR3 BC Patterns & Relations Slide 3rd Pass Digital Slides • Answers peers’ questions about their own inferences using data to support November 9, 2021 45: How their answers Digital Minds On (15 minutes) Much Sleep Did We Get • Project Digital Slide 45: How Much Sleep Did We Get Last Night? Ask students Last Night?, BLM 33: how much sleep they got last night based on hourly intervals displayed in Hours of Sleep the graph. Model how you can figure out the number of hours of sleep by counting on your fingers from when you went to bed to when you woke up. Time: 45 minutes • Have students share their answers and record them on the graph by drawing BLM 33: Hours of Sleep an X in the appropriate column. Recommended Hours of Sleep per Night • Once the graph has been completed, ask students what they know about the Hours of Sleep20 18 data. Include the following concepts to frame the discussion: 16 2–3 3–5 5–12 13–18 More than – reading a single data point 14 years years years years 18 years – comparing more than one data point 12 – describing the whole data and making inferences 10 • Ask students what they don’t know from looking at the data and what they 8 6 may still wonder about. They can turn and talk to a partner. 4 2 • Have students share what they discussed. (e.g., We don’t know WHY some 0 people got more sleep than others; we don’t know how much sleep we should get; Less than is the amount of sleep we got good or bad; was last night just a bad/good night 1 year for sleep; was someone sick or was there a lot of noise during their sleep, etc.) 54 © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 • Collect students’ ideas on what we can ‘infer’ as likely from a graph and what Scholastic Canada GR3 BC Patterns & Relations 4th Pass we don’t really know unless we ask the people who were surveyed or have Reproducibles some other data to make comparisons. (e.g., maybe we could survey another November 9, 2021 class; maybe we could ask an expert; maybe we need to ask people to keep track of their sleep for a week, etc.) Data 149

Working On It (15 minutes) • Continue to project Digital Slide 45 with the co-created graph. Provide each triad of students with a copy of BLM 33: Hours of Sleep. • Tell students that, in their triads, they are going to consider the class data along with the displayed bar graph to see what they can interpret about the class data. Remind them that when they make inferences, they need to consider the data as a whole as well as individual points. They also need to use information from the data to explain and support their conclusions. Differentiation • For students who need language support, ensure that they understand the topic of the bar graph on the BLM, “Recommended Hours of Sleep per Night,” and the meaning of the word “recommended.” • Provide sentence starters as needed to support drawing conclusions from the data: We believe that        . We believe this because the data tell us that . Assessment Opportunities •O bWsehrivcahtpioanrtss:of the graph are students using to describe the data? • Which pieces of data are students comparing to make inferences? Are they choosing data that make sense to compare? • Are students considering individual data points when necessary? Are they considering the data as a whole when necessary? Conversations: Pose some of the following prompts to guide students in making more detailed descriptions: – What is the title of the graph? – What do the labels and numbers on the graph mean? – What does the graph tell us? – Which has the most? The least? Why do you think so? – Which are more (fewer) than    ? Why? – Are there more     or    ? – How many     and     are there altogether? – Is there anything about the data that surprises you? – Does this graph provide us with all the information we want to know? – Which parts of the graph did you use to make that inference? 150 Patterns & Relations/Data & Probability

Materials: Consolidation (15 minutes) BLM 33: Hours • Pair up triads to share their inferences and to show/explain the data that they of Sleep used to support them. BLM 33: Hours of Sleep • Encourage students to ask questions of each other to ensure that they Recommended Hours of Sleep per Night understand the inferences. Hours of Sleep20 18 • Meet as a class. Discuss the following questions: 16 2–3 3–5 5–12 13–18 More than 14 years years years years 18 years – Did you understand the inference of the other group? 12 – Did the data they used make sense to you? 10 – Did you have a similar inference? – Did the other group’s questions help you to better explain your inference? 8 6 • Some possible inferences could include: 4 2 – We believe that our class gets a good amount of sleep. Most people 0 in our class are 8 years old and sleep 10 hours per night, which is the recommended amount of sleep for that age. Less than 1 year – We don’t get enough sleep. Most people in our class sleep less than 9 hours per night. The recommended amount of sleep for us is 10 hours per night. Further Practice • Have students collect data from another class in the school to answer the same question. As a class, use BLM 33 to make additional inferences and to compare them with their own class data. • Reflecting in Math Journals: Have students reflect in their math journals about a question they had about the class data (How Many Hours of Sleep Did You Get Last Night?) and what survey question they could use to collect information to answer their question. 54 © 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 Data 151

12Lesson Drawing Conclusions from Data Teacher Possible Learning Goals Look-Fors • Distinguishes between different types of graphs and tables that represent the Materials: same data and describes how the data are represented in each “Describe This!” • Compares different parts of the data to make inferences and draw simple (page 16 in the Patterns, Relations, Data, and conclusions Probability big book), “What’s My Data?” • Identifies features of different graphs and tables and what they reveal about (page 12–13 in the Patterns, Relations, Data, the data and Probability big book), Digital Slide 46: Data • Identifies information in graphs that help answer questions Detectives, BLM 34: • Explains or shows where they read the information in the graph Data Detectives • Makes conclusions by comparing information they read on the graph Time: 45–50 minutes Minds On (15–20 minutes) © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 Detective 1: BLM 34: Data Detectives • Project “Describe This!” (page 16 in the Patterns, Relations, Data, and Detective 2: Scholastic Canada GR3 BC Patterns & Relations Digital Slide 46: Data Detectives Probability big book) on the whiteboard. Reproducibles November 9, 2021 • Ask any of the following prompts: 4th Pass Clue 1: Clue 2: Clue 2: – What do you notice? What do you wonder? Our conclusion: Clue 1: – What is the title? What survey question was probably asked to collect Our conclusion: 55 this data? Does the title tell us the source of the data? – What type of graph or table is each one? (pictograph, tally table, bar graph) Scholastic Canada GR3 BC Patterns & Relations 3rd Pass – How does the data look different in each of these graphs or tables? What Digital Slides November 9, 2021 do you notice? – Which representation do you think represents the data best? Why? – What data can you compare in these displays of data? Which one makes the data the clearest/easiest to read? Why? – Which way of getting to school received the most votes? (e.g., 10 people ride the bus to school) Working On It (15 minutes) • Tell students that today they are going to be data detectives. All good detectives work with a partner so that they don’t miss any clues. Their job as a data detective is to ‘Draw a Conclusion’ from the data. Ask, “What do you think draw a conclusion means?” Explain to them that it really means they are going to have to be good detectives to make a really good observation about the data. • Project “What’s My Data?” (pages 12–13 in the Patterns, Relations, Data, and Probability big book). Say, “Look at the ‘Pets of Students in Our Class’ pictograph on page 12. Think of an observation you can make about the data.” 152 Patterns & Relations/Data & Probability

• Bring two student volunteers up to model this. Ask them each for an observation about the data. If they are having difficulty coming up with something, use the example here to model the process. – Say, “Let’s say that Lauren (Detective #1) observes that ‘Three people have birds.’” Project Digital Slide 46 and add Detective #1’s observations. – Say, “Now let’s say that Ben (Detective #2) observes that ‘Six people have dogs.’” Project Digital Slide 46 and add Detective #2’s observations. – Say, “Now, your job as detectives is to work together to compare the two observations that you just made. What might be your conclusion from these two observations?” (e.g., Less people have birds than dogs; more people have dogs than birds; three more people have dogs than birds; three less people have birds than dogs; there are twice as many people that have dogs than birds; etc.) – Decide on a conclusion and add it to the box at the bottom of Digital Slide 46. • Distribute one copy of BLM 34: Data Detectives to each pair, and have them work through this activity together, using the data from the Minds On about going to school. Project “Describe This!” (page 16 from the Patterns, Relations, Data, and Probability big book). Students can also share the little book versions of the big book. Differentiation • Have students work with one set of data only, their favourite, to draw simple conclusions. • Provide a visual anchor chart for students who need language support to reinforce their understanding of comparative terms (e.g., more than, less than). • Provide sentence stems for students who need support in writing conclusions about their graphs. Assessment Opportunities Observations: Pay attention to the mathematical language that students are using to make their observations. Conversations: Use the following prompts: – What observations did you make? – How does your observation compare to your detective partner’s observation? – How are they the same? How are they different? – Which category has the greatest number? Which category has the least number? – How many more/less does this category have than the other one? Data 153

Materials: Consolidation (15 minutes) BLM 34: Data • Gallery Walk: Have students leave out their completed Data Detective work Detectives and do a gallery walk of each other’s conclusions. © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 Detective 1: BLM 34: Data Detectives – Provide each pair of students with enough small sticky notes to add one Detective 2: to each sheet to give them feedback. – Post this chart to help guide their feedback: Scholastic Canada GR3 BC Patterns & Relations Reproducibles We understand your conclusion. November 9, 2021 ! We like your conclusion. ? We have a question about your conclusion. – Visit each group’s conclusions, and leave them some feedback about their work. – Bring the group back together to share their favourite conclusion by another group. Further Practice • Use BLM 34: Data Detectives to make observations and draw conclusions from other data. • Reflecting in Math Journals: Have students reflect in their journals about which kind of graph they find the easiest to read and why. Clue 1: Clue 2: Our conclusion: 4th Pass 55 154 Patterns & Relations/Data & Probability