p132-184_Unit1_BC1-Data-pass2

Unit 1: Data Lesson Content Page Getting Started with Data and Probability 132 Inviting Data and Probability into the Classroom 133 Introducing Data 135 1 Read Aloud: Tally O’Malley: First Reading 137 2 Tally O’Malley: Second Reading 141 3 to 5 Let’s Sort! 145 3 Sorting Items 147 4 Classifying Items 150 5 Let’s Sort and Classify! 154 6 to 8 Collecting, Organizing, and Displaying Data 156 6 Collecting and Organizing Data: Concrete Graphs 158 7 Collecting and Organizing Data: Tally Tables 162 8 Displaying Data: Concrete Graphs 165 9 and 10 Describing and Analyzing Data 169 9 Describing Data and Asking Questions 170 10 Analyzing Data 172 11 Guided Math Lesson: Reinforcing Data Concepts and Skills 175

Getting Started with Data and Probability There are two units in Data and Probability as shown below. Unit Description 1 Data 2 Probability 132 • Each unit includes a series of Blackline Masters (BLMs) with co-ordinating Digital Slides to support the visual nature of data and probability concepts. • Each unit includes Math Talks, group discussions, and activities that target the curricular competencies (reasoning and analyzing, understanding and solving, communicating and representing, connecting and reflecting). • Each unit includes activities to develop and build habits of mind, growth mindsets, and positive attitudes toward math. • Making connections between data and probability, and other math and subject areas, will maximize students’ 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: – Sorting and classifying data includes attributes of familiar shapes that are also investigated in the Spatial Sense strand and the Patterning lessons. – Collecting loose parts relates to other curriculum areas (e.g., samples of different materials and their properties, or types of animals in science), and having students organize these objects according to categories and/ or attributes supports concepts integral to sorting and classifying. – S tudents apply many counting skills and their understanding of number relationships as they analyze data. – T opics that students use to collect, organize, and display data can be related to inquiry questions or themes presented in other curriculum areas (e.g., students’ favourite artist; comparing the needs and characteristics of two living things using a Venn diagram, graphing daily and seasonal changes in the weather, making predictions about the likelihood of a certain type of weather the next day, keeping track (T-table) of any everyday classroom event such as students absent, etc.). – M any of the probability ideas explored in grade one are related to the likelihood of an event happening. Surveying students to familiarize them with this vocabulary (e.g., never, sometimes, always, more likely, less likely) throughout the year will support their learning and progression through the Probability lessons when they begin to use these words to describe the likelihood of events occurring. Patterns & Relations/Data & Probability

Inviting Data and Probability into the Classroom Since math plays an integral part of our lives, it makes sense to take advantage of its role in everyday routines at school. For example, you can use a concrete graph to record how many students are present or absent, or use a jobs chart to assign responsibilities to group members. There are many ways to embed data and probability concepts into your daily routines. These activities can be 5–10 minutes long and be carried out while the class waits in line to go somewhere, when there is a bit of time left 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 objects in order to organize data and create concrete graphs. Take every opportunity to have students sort and classify objects or 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. For example: – If you are wearing (e.g., a blue shirt, glasses, running shoes, jeans, shorts), stand up. – If you are feeling (e.g., tired, excited, happy, grumpy, silly) today, clap twice. • If you have a messy bin of classroom materials, take the opportunity to have a quick Math Talk about how you might sort and organize the materials. Have students carry out the task and highlight what they were thinking as they did it. • When lining up for an activity, have students sort and re-sort themselves based on a variety of criteria/categories. You can integrate different subject areas. For example: 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 – Those wearing shoes with laces and those wearing shoes without laces; etc. Sort yourselves into three groups: – I prefer apples/oranges/bananas – I prefer red/blue/green – I prefer cats/dogs/hamsters Getting Started with Data and Probability 133

• Use the Four Corners strategy to group students for any activity. Choose four pictures related to the activity you are doing (e.g., four animals, four simple machines, four Daily Physical Activities [DPAs]). Give students a prompt about the options to help them sort themselves. (e.g., Say, “Choose the DPA 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.”) • When beginning any unit of study, use individual cards/sticky notes/photos of the ideas you will be studying 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. Start of the Day (Greetings/Attendance) • When starting the day with routines, pose a question pertinent to the upcoming day and do a quick survey to find out how students are feeling or what they prefer. For example: – 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!” – Have one student add the options to a posted tally table template and keep track of the tallies. – Have labelled containers where students can vote for themselves by adding a stone or stick to the appropriate container. – Once students choose their answer, have them line up in a pattern of their choices. • On a community walk, have students use a tally table to keep track of the number of times they see a specific item (e.g., the number 2, a bird, a red flower). • Have students periodically create concrete 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. • When playing any kind of game, use dice or a spinner to choose categories or to determine how many points a team gets on each turn. • When reading a story aloud, have students predict the likelihood of a certain event occurring in the story. • When conducting a scientific investigation, have students predict the possible results and the likelihood of each result. 134 Patterns & Relations/Data & Probability

Introducing Data About the Interpreting the data around us plays an integral role in our lives, whether we are exposed through advertising, graphs displayed in the media, or statistics used to record and interpret sports. Students need to develop critical thinking skills when they analyze data so they understand what the information represents and how it can help to answer questions. Van de Walle and Lovin emphasize that “data collection should be for a purpose, to answer a question, just as in the real world” and that “the analysis of data should have the agenda of adding information about some aspects of our world” (Van de Walle & Lovin, 2006, p. 310). In order to collect and analyze data, students need to know how to sort and classify. They initially learn how to sort and count objects, but do not necessarily classify the information. They need experiences identifying various attributes of objects, and how they can differ, before they can create meaningful categories (Clements & Sarama, 2009, p. 199). Grade one students use the sorted objects to create a concrete graph by lining them up side by side and matching them using one-to-one correspondence. They need to include necessary titles and labels so other people can make sense of their data displays. An important skill is being able to read and analyze the data. At first, students can recognize which categories have the most or the least by comparing the heights of the various categories in their concrete graphs. With prompting, they can start to make quantitative comparisons, such as ordering the categories from greatest to least frequency, or realizing that three more people chose red as their favourite colour than chose blue. This requires students to apply their understanding of number concepts, including counting quantities and comparing them through addition and subtraction. It is best if students analyze and interpret data within the context of answering a question. For example, after surveying the class about favourite colours, students may conclude that the teacher will need to order more red paper than blue paper, since it is the most popular with students in the class. In this way, students realize that data collection and interpretation serve a meaningful purpose. Data 135

Lesson Topic Page 1 Read Aloud: Tally O’Malley: First Reading 137 2 Tally O’Malley: Second Reading 141 3 to 5 Let’s Sort! 145 3 Sorting Items 147 4 Classifying Items 150 5 Let’s Sort and Classify! 154 6 to 8 Collecting, Organizing, and Displaying Data 156 6 Collecting and Organizing Data: Concrete Graphs 158 7 Collecting and Organizing Data: Tally Tables 162 8 Displaying Data: Concrete Graphs 165 9 and 10 Describing and Analyzing Data 169 9 Describing Data and Asking Questions 170 10 Analyzing Data 172 11 Guided Math Lesson: Reinforcing Data Concepts and Skills 175 136 Patterns & Relations/Data & Probability

1Lesson Tally O’Malley: 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 Materials: reading of Tally O’Malley, students apply their literacy strategies, such as inferring, using prior knowledge, and making predictions, to understand the context Written by and progression of the story. During the second reading, students become Stuart J. Murphy mathematicians and apply the curricular competencies to discover and explore the Illustrated by math concepts embedded in the story. Both readings are also valuable for assessing Cynthia Jabar where students are, what some of their misconceptions might be, what concepts Text Type: Fiction: need greater emphasis, and what differentiation may be necessary. Narrative—Adventure Time: 15–20 minutes Curricular Competencies • C omprehend and connect: 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 stories and other texts to make meaning 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 – Make connections between the ideas and situations presented in the story, and concepts they are studying in science and social studies Read Aloud: Tally O’Malley Summary: The O’Malley family is packing up for a road-trip vacation. To pass the time in the car, Mom suggests that the three children play a tally game, noting the colour of a particular item en route and keeping tallies to determine a winner. Along the way, the family passes a variety of settings, stopping occasionally to take a break. NOTE: Select the prompts that best suit your students. There are not prompts for all pages, as some are dedicated to math concepts and so will be addressed in the second reading. Data 137

Before Reading Inferring/predicting Activating and Building On Prior Knowledge Building on prior knowledge • Show students the front cover and ask them what they see. Read the title and the names of the author and illustrator. Ask students to predict what they think the book might be about (e.g., making tallies; a visit to the beach) and have them explain their reasoning. (e.g., title is Tally O’Malley and the girl is holding a tally; there is a beach and a sailboat) Ask students if they think this is a fiction or non-fiction story and how they know. • Have students say the title out loud. Ask what they notice about the title. (e.g., It rhymes.) Have students make a rhyming title using their last or first name. (e.g., Clark Park, Ryan Lion) • Ask if anyone has visited a beach. If so, have them share what they saw, what they did, and what they liked the most. • Setting a Purpose: Say, “Now that we have thought about the cover and made some predictions, let’s read together to find out what this story is about.” During Reading Using text features • Show the spread with a yellow background. Draw attention to the family Inferring/predicting Using text features picture in the middle, and note the family members’ names. Ask students who they think wrote this page and how they know. (e.g., by “Nell, that’s me, Nell”) Inferring/predicting Making connections • Show pages 4–5 and ask students what they notice about the picture. (e.g., Dad is packing the trunk of the car; Mom is checking off a list.) Ask what clues the picture gives us about what is happening. • Read pages 4–5 aloud. Ask students what words they hear that give clues about what is happening. (e.g., vacation, pack, beach towels, lock the back door, sunglasses, Hurry up) Ask if these fit with students’ predictions about what the book may be about. • Show pages 6–7. Ask students what they know about where the O’Malley family is in the picture. (e.g., by a farm) Ask how they know. (e.g., because there is corn, sheep, cows, barn, etc.) Ask if they have ever visited a farm, and what kind of farm it was. Ask why farms are important. (e.g., They grow food we eat; they raise animals that produce food such as milk and eggs.) • Read pages 6–7 aloud. Ask students how the children are feeling on the car trip. Ask what clues they see. (e.g., kids are frowning and looking sad) Ask what clues they heard. (e.g., Eric grumbled; Bridget is bothered that Shamrock the dog is breathing on her; Nell is upset that she can’t find her baseball hat.) • Ask students why they think Mom suggests playing a tally game. (e.g., so the children have something fun to do) • Ask students if they have ever been on a long car ride or trip. Ask what activities they did to pass the time. 138 Patterns & Relations/Data & Probability

Using text features/ • Show pages 8–9, and ask students what they notice in the background. (e.g., making connections birds, flowers, countryside) Ask if they think this is a rural or an urban Predicting setting, and why. Ask what kinds of natural and built features they see. Using text features/ making connections • Read pages 8–9 aloud. Ask students what the first thing they are going to Analyzing/ count is. Ask why Eric laughs when Nell picks the colour red. using text features Making connections • Ask students to predict what they think will happen next. Record their Using text features/ predictions. Do not read page 10; it will be discussed during the second reading. inferring • Show pages 12–13. Ask students what they notice in the background. Ask if Analyzing/predicting Using text features/ they think this is an urban or rural setting and why they think so. analyzing • Read pages 12–13 aloud. Using text features • Read pages 14–15. Ask students how they think Eric is feeling right now and Predicting why. Ask how they think Bridget and Nell are feeling and why they think so. Using text features/ • Ask how the family is meeting their basic needs in this scene. (e.g., They are predicting/analyzing Using text features/ stopping for lunch; Dad is taking Shamrock the dog for a walk.) making connections • Show pages 16–17. Ask students how they think Bridget, Nell, and Eric are feeling. Ask what body language clues does the artist give us. (e.g., The girls aren’t smiling and have their hands on their hips; Eric is smiling and holding his hands in the air.) • Read pages 16–17. • Show page 18 and read it aloud. Ask students why they think Dad suggests another tally game. Ask students to predict what Dad will suggest as a topic. Record their predictions. • Show pages 20–21, and ask students what they notice about the scene. Review students’ predictions for the next tally topic and add to the list if new ones are suggested. Ask students who they think will win this round. • Read pages 20–23 and check students’ predictions. • Show pages 24–25, and discuss what students notice in the picture. If it isn’t mentioned, draw attention to the train in the background. • Ask students whether they think there might be one more tally game. Ask who hasn’t won yet. Ask what they think the topic for the next game will be. • Read page 24 aloud and check students’ predictions about the tally game topic. Ask students who they think might win this one and why. (e.g., Eric, because most train cars are black.) • Show page 26. Ask students who they think will win the tally game now, and why. (e.g., Nell, because there are mostly red cars.) • Read pages 26–29 aloud and check students’ predictions. • Show pages 30–31. Ask students what they notice about the picture that might explain why Nell won. (e.g., The sign says “travel the RED line.”) Ask students what they think that means. (e.g., The train is a special one that is mostly red.) • Read pages 30–31 aloud. Ask students why they think Eric says, “that’s not fair”? Ask if they think it is fair and why. Data 139

After Reading Synthesizing • Check back to confirm predictions that students made earlier during the story. Making connections • Ask students what other things the family might have used to make tallies on their road trip. (e.g., animals, number of people in the cars, buildings) • Have students look around the classroom to find things they could use to play a tally game (e.g., markers, crayons, connecting cubes). Further Practice • Students work in groups of three. Have each group recreate the three tally game scenes, using voice and facial expressions to show how the children in the story feel before and after checking their tallies. 140 Patterns & Relations/Data & Probability

2Lesson Tally O’Malley: 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 • C ommunicating and representing: Communicate mathematical thinking in many ways; use mathematical vocabulary and language to contribute to mathematical discussions; explain and justify mathematical ideas and decisions; represent mathematical ideas in concrete, pictorial, and symbolic forms • Connecting and reflecting: Connect mathematical concepts to each other and to other areas and personal interests Content • C oncrete graphs, using one-to-one correspondence • Likelihood of familiar life events, using comparative language • N umber concepts to 20 Possible Learning Goals • Reflects on the importance of math in real-life contexts • Demonstrates an understanding of how to collect data using tallies • Uses tallies to record data • E xplains or shows that one tally set means there are five things • C ounts by 5s when counting tally sets • U ses tallies recorded to help them answer questions About the Before students can collect data, they need to identify the attributes of different objects and how they can vary. This helps them to select categories for organizing the information. They also need to use an effective way to track and record their data. continued on next page Data 141

Math Vocabulary: Tallies are beneficial because they are recorded in groups of five. toarlglya,nciozeu,ndt,actaollect, Students can immediately identify which category has the greatest frequency just by looking at the tally table. By analyzing the overall tally table, they can also list categories from greatest to least frequency. Students can also count the individual tallies to make more refined comparisons, and to discover how much more often one category occurred than another. Tally tables also help students create concrete graphs once they have collected the desired information. 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. Materials: Assessment Opportunities Tally O’Malley 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 differentiated to meet individual needs. Note each student’s ability to: – Collect data using tallies – Recognize that each completed tally set counts as five – Predict answers to questions posed throughout the story, based on information in the story – Count by 5s when counting tally sets – Connect ideas in the story to Further Investigations Before Reading 142 Activating and Building On Prior Math Knowledge • Ask students why the title of the book is Tally O’Malley. Ask if they recognize any words in the title of this book, and if there is anything on the cover that might offer a clue. • Show the yellow page that has many tallies to the left of the title page. Ask students what they think all the marks are and what they mean. Explain that they are called ‘tally marks.’ Ask how some of the tally marks are grouped. (e.g., in 5s) Ask why groups of 5 can be helpful. Patterns & Relations/Data & Probability

• Setting a Purpose: Tell students, “We are going to revisit the story as math detectives, and learn all about some ways we can keep track of data.” During Reading Communicating and • U se any of the prompts below as needed to explore the math in the story. Choose representing which prompts and how many you use according to the needs of your students Connecting and and the curricular competencies that you are targeting (understanding and reflecting/communicating solving, reasoning and analyzing, connecting and reflecting, communicating and representing). and representing Connecting and • R ead pages 4–5. Ask students how many people are going on this trip. Ask how reflecting many people have sunglasses. Understanding and solving • R ead pages 6–9. Ask students what they think a tally game is. Ask why the Communicating and children in the story have to pick something to count. Ask what the children are representing/reasoning collecting data on in their first game. Ask students whether they ever have played a tally game. and analyzing Understanding and • R ead pages 10–11 and ask students what one tally mark represents. Ask what solving/reasoning three tally marks and what five tally marks would look like. Focus on how a and analyzing group of five tally marks is represented by four tallies and a fifth tally drawn Connecting and horizontally through them. reflecting • A fter reading pages 12–13, have students create tallies for the colours of cars Reasoning and shown in the illustration. Ask what needs to be included on their tally table. analyzing/communicating Reinforce the idea that they need titles and labels. and representing • B ased on the fact that Nell chose red, Eric chose silver, and Bridget chose blue, Understanding and ask who is winning the game at this point, who is in second place, and who is in solving third place. Have students explain and justify their reasoning. Connecting and reflecting • R ead page 14, and have students study the tallies in the illustration. Ask who won the game, who came in second, and who came in third. Ask students whether they had to actually count the tallies to determine the winner. Ask how many more tallies the winner had than the person who came in second. • A fter reading page 15, ask students whether they think the same person would win if the children counted the cars at another time or place. Ask students whether they would get the same results as the characters if they counted the same number of cars that passed by the school. • A fter reading pages 16–21, ask students what data the children are collecting in this game. Have students predict who is going to win this game by analyzing the illustration. They can explain and justify their predictions. • H ave students analyze the tallies on page 22. Ask who won the game and how they know. Ask how many more tallies Bridget had than Eric and how many more tallies Eric had than Nell. Ask whether Eric and Nell could win if they combined their tallies. • A fter reading page 23, have students reflect on whether they were correct. Ask whether they think they would get the same results if they repeated the game that the children played. Data 143

Connecting and reflecting/ • After reading pages 24–25, ask students what data the O’Malleys are communicating and representing collecting in this game. Ask why Eric doesn’t think red is a good choice for the colour of train cars. Reasoning and analyzing/ communicating and representing • A fter reading pages 26–27, have students look at the picture and predict who is Understanding and going to win the game. Have them explain and justify their predictions. solving • Show page 28 and have students look at the tallies. Ask who won the game. Ask Connecting and reflecting/reasoning students if they had to actually count the tallies to know. Ask how many more tallies Nell had than Eric and how many more than Bridget. and analyzing • R ead pages 28–29. Ask students if they think Nell would win when the next train goes by and why they think so. Ask whether they would get the same results if they counted the same number of train cars on a train track nearby and why they think so. • R ead pages 30–31. Ask why Nell won and whether she has a better chance at winning the next time a train goes by on that track. Ask if she would win when counting the cars on trains at other locations. After Reading Connecting and reflecting • Ask students for examples of where they saw math in this story. Communicating and • Ask students to explain what a tally is. Have them explain why tallies are representing/reasoning helpful, and to give examples of situations in which they could use them. and analyzing Discuss how tallies help organize information that is being collected. • Ask students how they could use the tallies to create a concrete graph. Select one of the tally tables and build a concrete graph together, using concrete materials. Have students analyze the graph and explain what they can learn from it. Further Practice • Play a tracking game to give students practice making tally marks. As a class, choose something to track, such as how many hats are in the class each day. Have students work independently and practise making tallies. • Choose something to count and record that comes in different colours, such as a collection of crayons. Have students each choose a colour. As a class, pull out the crayons one at a time. Students can use tallies to track the number of crayons in their chosen colour. • Have a daily survey question for students to answer. Collect the information using tally tables. Reinforce that the tally table requires a title, labels, and the source of the information. • Go for a community walk and have students choose something they want to track before you leave. They record a tally each time they see the (object/ colour) during the walk. Ask whether they would get the same results if they took the same walk next week and why they think so. 144 Patterns & Relations/Data & Probability

to3 5Lessons Let’s Sort! Math Curricular Competencies Learning Standards • R easoning and analyzing: Use reasoning to explore and make connections • U nderstanding and solving: Visualize to explore mathematical concepts; Previous Experience with Concepts: develop and use multiple strategies to engage in problem solving Students have had experience sorting and • Communicating and representing: Communicate mathematical thinking comparing two- dimensional shapes and in many ways; use mathematical vocabulary and language to contribute three-dimensional objects to mathematical discussions; explain and justify mathematical ideas and using one attribute. decisions • Connecting and reflecting: Reflect on mathematical thinking; connect mathematical concepts to each other and to other areas and personal interests Content • Concrete graphs, using one-to-one correspondence • Repeating patterns with multiple elements and attributes: Identifying sorting rules • C omparison of 2D shapes and 3D objects: Sorting 3D objects and 2D shapes using one attribute, and explaining the sorting rule About the In order to collect, organize, and display data, students need to be able to sort and classify. In grade one, students sort objects according to one attribute and describe the sorting rules. Marian Small explains that while sorting is the hands-on grouping of objects based on what they look like, classifying happens when students give a name or a category to the items that have been sorted (Small, 2010, p. 114). Students need many opportunities to sort a variety of objects (e.g., loose parts, concrete objects, natural items), in many ways, as well as to find different ways to categorize and classify the sorted objects. Understanding how students learn to sort, classify, and interpret sorting rules helps to identify what students need to move their learning forward. Copley explains how students progress through various levels of sorting (Copley, 2000). Initially, they sort by a common characteristic such as removing all of the blue cars from a container of toy cars. Next, they begin to sort groups of items by one attribute, such as sorting all the cars into different colour categories. Students then move on to sorting items by more than one attribute (e.g., sort cars by colour and size) and explain how they sorted the objects. They also sort objects according to given rules or rules that they have created using their own rules or those they are given. continued on next page Data 145

About the Lessons The following three lessons offer students a variety of experiences to help them develop sorting and classifying skills. The activities included in the lessons will take students through the different levels of sorting to review and strengthen previously learned concepts and help them move forward in their abilities to classify objects using attributes. 146 Patterns & Relations/Data & Probability

3Lesson Sorting Items Teacher Possible Learning Goals Look-Fors • Sorts and categorizes a set of objects in various ways and explains the sorting rule • Identifies and explains the rule for a sorted set of objects • S orts materials using different attributes • D escribes the different characteristics that attributes can have • E xplains or shows how they have sorted materials • E xplains or shows how they can sort materials in different ways • I dentifies and explains the rule for a set of objects that has been sorted Math Vocabulary: Minds On (15 minutes) sorting, attribute • Tell students that they are going to play a guessing game. Explain that, in Materials: buckets containing a your mind, you have picked a mystery object in the classroom. To find out variety of concrete what the mystery object is, they can only ask you questions that can be materials (e.g., toy cars, answered by “yes” or “no.” Give them examples of questions they might ask, blocks, loose parts, such as “Is it a toy? Do we write with it?” pencils, markers) Time: 45 minutes • Keep track of the number of questions students ask using tally marks. • R eview the attributes of the mystery object, such as colour, shape, or size, and how each attribute can differ (e.g., colours can be red, yellow, or blue). Discuss how they can use this knowledge to ask good questions about a mystery object. • Play the game again. Highlight the attributes of the object that were identified in the questions. Working On It (15 minutes) • S tudents work in small groups. Give each group a bucket of concrete materials to sort. Students can choose their sorting rule and do not need to sort all of the items in the bucket. • After all groups have sorted their objects, go on a gallery walk as a class. At each stop, have students guess the sorting rule and give reasons for their responses. Ask them to identify other ways that the objects could have been sorted. • Students can return to their small groups and sort the objects in a different way. Differentiation • For students who need language support, model how to sort a set of objects to ensure they understand the word ‘sort.’ Data 147

• F or students who need more of a challenge, have them sort their objects in several different ways, and then select one to have their classmates guess the sorting rule for. Assessment Opportunities Observations: • Pay attention to how students are sorting. Are they sorting by a specific characteristic, or by an attribute (e.g., pulling out only blue objects versus sorting by colour)? • Are students able to determine how the other groups sorted their objects? • Were students able to sort objects in different ways? Conversations: If students are struggling to sort the objects or determine a sorting rule, use some of the following questions to prompt their thinking: – How are these objects in the bucket alike? How are they different? – Why is this object here? Why is this object not here? – What name could you give this group of objects? What would you name the other group? – How else might we sort the objects? Consolidation (15 minutes ) • Meet as a class. Make a list of all the ways the groups sorted the objects. • Explain to students that they sorted the objects based on attributes. Define ‘attribute’ (e.g., a characteristic of a shape or object, such as colour, size, shape). Discuss how the attributes can vary. Add some examples to the list of attributes. • On the Math Word Wall, add terms used in the lesson, such as ‘sort’ and ‘attribute.’ Include visuals to help with meaning. Over the next few days, draw attention to the words whenever you use them in class. Play word games. For example, you can give a definition and have the class identify it on the Math Word Wall. Further Practice • Guess My Rule (adapted from Van de Walle, 2001, p. 365): Secretly choose an attribute you notice on your students’ attire (e.g., jeans, shoes, colour of shirt) and sort the students accordingly, without telling them the rule. After sorting some of the students, draw attention to one student and have the class predict the group in which the student belongs. Continue sorting until students can identify and explain the rule. • Set up a centre with buckets of items for students to practise sorting. Students can draw their sort in their Math Journals and label each group with a name. 148 Patterns & Relations/Data & Probability

Materials: Math Talk: Math Focus: Sorting objects using one attribute Let’s Talk Select the prompts that best meet the needs of your students. “Let’s Organize!” (pages • D isplay “Let’s Organize!” (pages 10–11 in the Patterns, Relations, Data, and 10–11 in the Patterns, Probability big book). What do you see on this page? (e.g., many different items, Relations, Data, and grouped items, foods, school supplies, living and non-living things, etc.) Let’s Probability big book and little books), BLM 26: read the title of the page together: “Let’s Organize!” Based on the title, what do you Let’s Organize! think we should do with all of these items? (e.g., We can sort them!) Teaching Tip • tLheet’ys’rloeoakllaltivtihnegfothoidnigtse.m) Hs.oHwowareartehethyedyifafelirkeen?t?(e(.eg..g,.S, osommeecaorloeufrrus iatrse, stohme seaamree; Integrate the math talk vegetables, different colours) How could we sort them? (e.g., by type, by colour) moves (see page 7) throughout Math Talks • L et’s sort them by colour. What colours should we use? (e.g., green, red, white, to maximize student yellow, and other) Create a T-table on the board and have students tell you in participation and active which group (category) each object belongs. Ask what titles and labels to listening. include, as well as the source of the information. Partner Investigation • Provide partners with the Patterns, Relations, Data, and Probability little book and BLM 26: Let’s Organize! Have students choose one of the other groups of objects on pages 10–11 to sort and classify. They can circle their sorted items on BLM 26. • If students find sorting the objects too difficult because they can’t move the pictures, they can identify as many attributes and categories they can that could be used for sorting. Follow-Up Talk • Discuss the sorted sets students created. Have students identify the attributes and the related categories. • A dd any new attributes to the class list. Data 149

4Lesson Classifying Items Teacher Possible Learning Goals Look-Fors • Describes items by their attributes and creates sorting categories • Sorts and classifies items in a variety of ways and explains their sorting rules • D escribes different attributes of objects and how they can vary • C reates categories for their sorts based on the various characteristics or attributes • S orts and classifies objects by their attributes • E xplains or shows how they classified their objects Math Vocabulary: Minds On (15 minutes) sorting, attribute, classify • Show Digital Slide 42: Attributes. Alternatively, show students a hexagon Materials: from a set of pattern blocks. Ask students to describe the object in as many ways as possible. (e.g., six sides, yellow, thick) Digital Slides 42–44: Attributes, BLM 27: • Ask what an attribute is. Refer to the anchor chart made previously, if Sorting Cards, chart paper, small paper strips, necessary. For each way students described the shape on Digital Slide 42, ask glue them to name the attribute and then give an example of how that attribute Time: 50 minutes can vary. (e.g., Yellow describes colour and another colour is red; six sides describes number of sides and other shapes could have four sides; thick describes thickness and the opposite would be thin.) • Show Digital Slide 43: Attributes. Tell students that the items have already been sorted. Have students turn and talk to a partner about what attribute was used for sorting and what category name they would give to each sorted group. (e.g., They are sorted by shape, and the categories are circles, triangles, and squares.) • Show Digital Slide 44: Attributes. Explain that the items have been sorted a different way. Ask what attribute was used in the sort and what are the categories. (e.g., They sorted by colour, and the categories are red, yellow, and blue.) Ask whether any more categories are needed for this sort. • Explain to students that they are classifying when they give a name to the groups of sorted materials. Working On It (15 minutes) • Students work in small groups or pairs. Provide each group or pair with a set of cards from BLM 27: Sorting Cards. • Students decide how to sort and classify the items. They can sort the items in many ways, decide on the sort they like best, and then glue their sorts on chart paper. Have them make labels for their categories on small strips of paper, but keep them turned over so they can’t be read by others. 150 Patterns & Relations/Data & Probability

Materials: • G roups or pairs meet with another group or pair and guess each other’s sorting variety of concrete materials rule and the names of the categories. After the guess, the creators can reveal the names they put on the labels, and then turn them over again. Differentiation • For students who need language support, discuss the items on their sorting cards to ensure they have the related vocabulary. • You may need to scribe for some students if they have difficulty labelling their categories. • For students who need a challenge, give them another set of cards from BLM 27, and ask them to sort and classify the same items in a different way. Assessment Opportunities Observations: Pay attention to how students are classifying objects. Are they able to name the attribute and the ways in which it can vary? Do they think of enough categories so all of the items can be included in the sort? Conversations: If students are struggling to classify the objects, use some of the following prompts: – How are the objects in this picture the same? How are they different? – How would you describe the objects in Group 1? What about the objects in Group 2? – What name could you give this group of objects? What would you name the other group? Consolidation (20 minutes ) • Go on a gallery walk as a class. At each stop, have students guess the sorting rule and the names of the categories. Reinforce the vocabulary that students are using or model any missing terms. Ask what the title and the source could be for each sort. • After the gallery walk, add any new attributes to the class list. For each attribute, include the various categories that students identified (e.g., attribute is number of legs and categories are 3 and 4). • Discuss how students decided how many categories they needed. Ask what they did with items that didn’t belong in the categories they first created. Further Practice • Classify This: Provide pairs with a variety of concrete materials. One partner sorts the objects into categories, and the other partner guesses the sorting rule and names the categories. Partners then switch roles. • Take students on a nature walk, and have them classify what they see into living and non-living things. Students can also classify the living things into plants and animals. Data 151

First Peoples Perspectives • Sorting from a First Peoples perspective happens in practices such as beading, which involves the sorting and ordering of beads by colour and size; sorting shells by type, size, or colour. For weaving, weavers would be sorting inner cedar bark strips; sorting longleaf pine needles; sorting porcupine quills; and sorting dyed wools. Check with your local First Peoples community or with your school district’s Indigenous education department to see which natural materials are more commonly used in your area. This could be extended into a place-based activity where you also collect the resources, and have students sort and classify the items. Materials: Math Talk: Math Focus: Sorting, classifying, and organizing data Let’s Talk Select the prompts that best meet the needs of your students. “Looking at Data” (pages Colours of Apples in Our Class—Tally Table 12−13 in the Patterns, Relations, Data, and • S how students “Looking at Data” (pages 12−13 in the Patterns, Relations, Data, Probability big book and and Probability big book). Have you seen a table like this before? Where have little books) you seen it? Do you know what we call this kind of table? Teaching Tip • When do you use a tally table? How is it helpful? Integrate the math talk • cWolhleacttiins gthinisfotarmllyattaiobnleaabboouuttp? eHopowle’sdfoavyoouuriktneoawp?plHeso?w(ei.sgt.,hTishdisifftearbelnettferlolsmus moves (see page 7) throughout Math Talks how many of each colour of apple is actually in the class, which is not the to maximize student same as what people’s favourite apples are.) participation and active listening. • What are the small lines called? (tallies) What do they tell us? What does one tally represent? Why does one of the tallies go across the other tallies? Why do you think we write tallies in groups of five? • How would you order the colours of apples from the most to the least? Did you need to actually count the tallies? Why? • How can a tally table help us create a concrete graph? Writing Tools in the Green Bin—T-Table • D o you recognize this kind of table? Where have you seen it before? • W hy is this helpful? When might we use them? (e.g., sorting items) • What do the titles and labels on this table tell us? • W hat do you know about pencils from looking at this table? How do you know? • W hat do you know about markers from looking at this table? How do you know? • W hat do you think we could compare about pencils and markers? 152 Patterns & Relations/Data & Probability

Partner Investigation • H ave students think of a different way to sort the pencils and markers. Ask, “If I put all these pencils and markers back together in a box and gave it to you to sort, how else could you sort them?” Some Living Things in the Environment—T-Table • W hat has been sorted? • What does the title tell us? Does this sort include all living things in the environment? How do you know? • What do the labels tell us? • What do all of the plants have in common? What do all of the animals have in common? • How are plants and animals the same? How are they different? • W hat other living things could you add to each of the categories? • W hy is it helpful to sort items? • How could you use this information to make a concrete graph? How might the graph be more helpful for making comparisons than the way the information is organized now? Partner Investigation • H ave students think of a different way to further sort the animals and the plants, separately (e.g., sort animals by size, where they live, pets and wild animals). Data 153

5Lesson Let’s Sort and Classify! Teacher Possible Learning Goals Look-Fors • Sorts and classifies objects in a variety of ways • Identifies and describes the sorting rule, attribute, and various categories created to classify objects • S orts and classifies materials using different attributes • C reates categories so all items in a set can be sorted • E xplains or shows how they have sorted materials Math Vocabulary: Minds On (10 minutes) scohratrinagc,teartitsrtiibcute, • Show students Digital Slide 45: What Doesn’t Belong? Ask them what they Materials: see. Digital Slide 45: What Doesn’t Belong?, various • Explain that they are going to work with a partner to determine which image concrete materials, BLM 28: Let’s Sort!, doesn’t belong with the other three. Tell them there is more than one correct camera answer, so they will have to explain their thinking and justify their answer. Time: 40–50 minutes Students can put up their thumbs when they have an answer. • Discuss students’ choices and their reasoning (e.g., the blue circle, because it’s the only blue shape; the rectangle, because the others are all circles). Working On It (20–30 minutes) • P repare centres with different selections of items to sort. Include various concrete materials, such as pattern blocks, loose parts, toy cars, blocks, pencils, markers, and cups of various sizes, as well as pre-cut cards from BLM 28: Let’s Sort! • Students visit the centres in small groups. At each centre, students sort in pairs or individually. Once all students at a centre have finished sorting, students at that centre guess each other’s sorting rules and the categories used. Photograph completed sorts. • Y ou may decide to have students visit more than one centre. Differentiation • For students who need a challenge, have them sort and classify the items in more than one way. 154 Patterns & Relations/Data & Probability

Materials: Assessment Opportunities centres from Working On It Observations: Pay attention to how students are sorting. – Are they sorting by a characteristic, or by an attribute (e.g., pulling out all the blue or sorting by all colours in the set)? – Can students determine how other group members sorted? – Can they sort objects in different ways using different attributes? – Can they name the various categories they have created? – Do they create enough categories for all of the objects in the set? Conversations: • If students are struggling with sorting the objects or determining a sorting rule, use some of the following prompts: – How are these items alike? How are they different? – Why is this item over here? Why is this item not here? – What name could you give this group of items? What would you name the other group? – How else might we sort the items? What attributes other than colour can we use to sort? • As students are working, check in with each group and have them explain and show how they classified their items. Consolidation (10 minutes ) • Project photographs of some of the sorts that students produced. You can choose photographs of sorts from the same centre to highlight how students sorted the same items in different ways. • Have the class guess the sorting rules and justify their reasoning. They can also name the sorting attribute and the categories that were created. • Discuss whether there were enough categories so all objects in the set could be sorted. Ask what other types of items with the same attribute could be added to the set, and whether they would need another category to accommodate all of them. • Add any new attributes and related categories to the chart started in previous lessons. Further Practice • Have students visit the centres again to find other ways to sort the items. They can refer to the list of attributes to help them think of other ways to sort. Data 155

6 8Lessonsto Collecting, Organizing, and Displaying Data Math Curricular Competencies Learning Standards • Reasoning and analyzing: Use reasoning to explore and make connections; Previous Experience model mathematics in contextualized experiences with Concepts: Students have explored • U nderstanding and solving: Visualize to explore mathematical concepts; collecting and organizing data using tally tables and develop and use multiple strategies to engage in problem solving concrete graphs. • C ommunicating 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: Connect mathematical concepts to each other and to other areas and personal interests Content • Create concrete graphs, using one-to-one correspondence • Likelihood of familiar life events, using comparative language MscuoarntvcheryeV,tdoeacgtaarba, upchlaa,tretyag:lolyryt,able, About the title Data are collected to answer questions. Students can learn more about themselves, their classmates, and their families by asking questions of the type “What’s your favourite (pet, sport, game, season, etc.)?” Students typically like to be represented in the data themselves, since this makes the information and outcomes more relevant to them. Other areas of interest may arise when discussing topics in different subject areas (e.g., in science: daily weather for two weeks). In grade one, collecting, organizing, and displaying data can be carried out in concrete ways such as having each person add a craft stick to a category container. This helps students see the one-to-one correspondence in one craft stick representing one person. Many of the ways to collect information can simultaneously serve as a means of organizing the data. For example, students can line up the collected materials, creating a concrete graph. 156 Patterns & Relations/Data & Probability

Teaching Tip Collecting data as a class can provide the support necessary for students to eventually collect and organize data individually or in small groups. It is Keep the samples of important to discuss what happens in the planning and initiation stages, class-generated data and such as how students might word a survey question, collect the their representations information, and organize the data (e.g., using tally tables, graphing mat, from these lessons so or concrete materials). students can analyze the data in later lessons. About the Lessons In Lesson 6, students collect, organize, and display data using concrete graphs. In Lesson 7, they use tally tables to collect and organize data, and then display the results in a concrete graph. In Lesson 8, students select a survey question and appropriate responses, collect data, and then display the information in a concrete graph. The lesson progression moves from asking a simple survey question to collecting and displaying the data in concrete graphs. In the subsequent lessons, students analyze and reflect on their data, draw conclusions, and possibly make decisions based on their findings. Data 157

6Lesson Collecting and Organizing Data: Concrete Graphs Teacher Possible Learning Goals Look-Fors • Explains that people collect data to answer questions and make decisions • Collects and organizes data to answer a question • Creates a simple survey question to collect data • I dentifies categories to organize data • A ccurately keeps track of data using one-to-one correspondence • O rganizes data using a variety of concrete organizers • D escribes ways that we can collect data Materials: About the When collecting and organizing data, it can be challenging to find ways to ensure that each person is surveyed only one time and can select only one of the response categories. Young students benefit from using concrete materials to represent each response. For example, if each person in the surveyed population gets exactly one concrete object to represent their answer, they cannot ‘vote’ more than once or in more than one category. This also helps students see themselves represented in the data, since they can identify with the concrete object that they contributed. Digital Slide 46: Which Is Minds On (10 minutes) Our Favourite?, selection of various concrete • Say, “I was thinking about our healthy snack bin and I wonder what kinds of materials appropriate for students’ data collection, apples would be good to have in there. So, I thought that we might do a class camera, graphing mat survey to find out.” (optional) Time: 50 minutes • Ask students what question they could ask to find out and who should be asked. • Project Digital Slide 46: Which Is Our Favourite? and ask students to think about this question: What is our favourite kind of apple? Ask what the 158 Patterns & Relations/Data & Probability

choices are. Ask whether other categories could have been included. Explain that the categories in the image are the ones they will use today. • Make a label for each category and display them in the class. Have students choose their favourite apple, and then stand or sit in a line in front of the appropriate label (or use a graphing mat, if you have one). You could also use actual apples rather than labels. • Ask students which kind of apple they think the class likes the best. Ask how they could check to be sure. (e.g., count how many people are in each line) Together, count the number of people in each line. • Say, “We’ve just lined ourselves up according to our favourite apple to answer our question. What can we learn from this information?” • Ask how they could collect the information without having everyone line up. Choose a method students suggest, or one of the following, to collect the same information (favourite apple) in a second way: – Label three small cups and have students place one craft stick in the appropriate cup. – Label three bowls and have students place one counter in the appropriate bowl. – Have each student choose one red, yellow, or green connecting cube, and then place the cube in one of three piles, according to colour. – Draw and label three sorting circles and have students place a slip of paper with their name on it in the appropriate circle. – Hang a strip of each of three colours of construction paper (red, yellow, green) and have students attach a clothespin to the appropriate strip. – Label three columns on ledger paper and have students mark their choice in the appropriate column using a red, green, or yellow sticker, or bingo dabber. Working On It (20 minutes) • Students work in pairs. Remind them how they collected the same information in two different ways in Minds On. • Explain that now they will work with their partners to find another way to collect the same information. • Provide a collection of classroom materials students can choose from, such as small containers, craft sticks, connecting cubes, colour tiles, counters, clothespins, construction paper, sticky notes, sorting circles or mats, stickers, rubber stamps, and bingo dabbers. Remind students that their method must ensure that everyone in class responds, and that each person responds only one time. • When they have designed a plan, students can share it with another pair to practise how they will explain their idea in the Consolidation. • Have students save their work, and/or photograph it, to refer to in later lessons. Data 159

Differentiation • If pairs are struggling to come up with a method to collect the data, engage them in small-group discussion to help them do so. • If a pair has a unique idea that requires some other classroom materials, some of the prompts from Assessment Opportunities can help to clarify and support their ideas. Assessment Opportunities Observations: • Pay attention to the communication between students. Are they collaborating to problem solve and to support each other’s ideas? Are they working as a team, and does everyone have a role to play when it is their turn to share their method? • Pay attention to how students plan to describe their method to the class. Conversations: It may be necessary to take some students back to other parts of the problem-solving process, such as understanding the problem, or analyzing the situation. Use some the following prompts in this process: – Does your survey question ask what you want to know in your inquiry? – What materials did you choose for collecting data? Do they represent the categories you chose? – How are you going to organize your materials to be able to collect the answers to your survey question? – How will you know which of your materials will represent each kind of apple? – How will you be sure that each student has given an answer to the survey? – How will you know how many students will like each kind of apple? Consolidation (20 minutes) • Have pairs take turns explaining or showing their collection and organization strategies. Discuss how they know that each person has been included in the data and how they could check. • Select one or two methods, and carry them out as a class. Tell students that the class can use their other collection methods in surveys that they do in future lessons. • Discuss and compare the various collection strategies. Ask which methods are easiest for collecting, counting, and comparing the information. Ask whether they might change their original idea after hearing their peers’ ideas. • Ask whether they would get the same results if they took the survey in another classroom with the same number of students and why they think so. 160 Patterns & Relations/Data & Probability

• B uilding Growth Mindsets: Use the following prompts to initiate discussion: – What did you learn today about collecting data? (e.g., There is more than one way to collect data; you need to have a way to check that everyone voted; etc.) – If you could change anything about your collection tool, what would it be? Why? – If you could try using any of the other collection tools, what might they be? Why? – How can we support each other as we are collecting data? – How can we make sure everyone gets a turn in our groups? – How can we respectfully help a group member who needs help with the activity? Further Practice • R eflecting in Math Journals: Have students draw a picture of their favourite data collection method from today’s lesson. • Have students conduct today’s survey question with family members at home, and share what they learned with the class the next day. • Have students think of a “What’s your favourite...?” survey question to ask their classmates in an upcoming lesson. Data 161

7Lesson Collecting and Organizing Data: Tally Tables Teacher Possible Learning Goals Look-Fors • Collects and organizes data using a tally table • Accurately counts the data in order to make comparisons • Describes the characteristics of tally tables • Uses a template to collect and organize data in a tally table • R ecords tally marks in groups of five • C ounts by 5s when describing data • A ccurately records data with tally marks using one-to-one correspondence • D escribes data and makes comparisons using the tally table • C ompares the features of tally tables Materials: About the One of the simplest ways to collect and organize data is in a tally table. Tally tables can be used to efficiently collect data, without the need for concrete materials. The transition to collecting data in a tally table is important, because it allows students to represent data using tally marks grouped in 5s and so be able to quickly count the numbers in each category (Small, 2009, p. 472). Counting by 5s is a learning standard in grade one Number and Operations. Students can then use the results in the tally table to create concrete graphs. Tally O’Malley, concrete Minds On (10 minutes) materials, Digital Slide 47: Tally Table, BLM 29: Tally • Remind students of the book Tally O’Malley. Show a page with tally tables Table Template Time: 50 minutes (e.g., pages 14, 22, or 28). Ask students what they remember about making tally marks. (e.g., You make a line each time; when you get to five, you make a bundle.) Ask what each tally mark represents. (e.g., one of something you counted) Ask why we make bundles of five. (e.g., to make tally marks easier to count; to count by 5s; when they’re all just lines, it’s easy to lose track of your count) 162 Patterns & Relations/Data & Probability

• Project Digital Slide 47: Tally Table and ask “What is this?” Ask students what the survey question might have been and why it may have been asked. Ask why they think the person doing the survey decided on the choices in the table. Discuss what the person can learn from the data collected in the tally table. Ask what conclusions the person doing the survey might make, and what decisions could be made based on this information. • Tell students that they are going to do a class survey about favourite playground equipment. Ask what answer choices they will have, based on what is available in their school or local park. Create labels for some of their choices and have students line up in front of their favourite playground equipment. Reinforce the idea that they have created a concrete graph, with each of them representing what they voted for. Ask how they could create a tally table as another way to collect the data. Create the tally table together. • Ask students one by one for their response to the survey question “What is your favourite playground equipment?” Student volunteers can add tally marks for the various choices, or students can add their own tally marks when they give their responses. Title this tally table “Favourite Playground Equipment of Students in Our Class.” Ask students how they could use the information in the tally table to create a concrete graph. Use concrete materials, such as connecting cubes, to create the graph. Ask what each cube represents, highlighting the one-to-one correspondence. Ask why it might be easier to represent the graph with cubes rather than with their bodies. (e.g., It can be more permanent.) • Ask students how they can check the data to ensure that every person is included once and only once in the tally table. Working On It (20 minutes) • Students work in pairs to design and conduct a survey by collecting data using a tally table. • Pairs of students develop a new “What’s your favourite...?” survey question. Then they add the appropriate title and choices to BLM 29: Tally Table Template. You can scribe for students who need assistance. • Students record their classmates’ responses on their table using tally marks. Have the class use the ‘stay and stray’ method to collect their data. One partner stays at a spot, asks visitors the survey question, and collects the data. The other partner circulates to other groups and answers their survey questions. Partners then switch roles. • Have students create a concrete graph from their tally tables, using materials of their choice. Differentiation • If students are finding it challenging to ask the question and record their data, suggest that one of them do the recording and that the other ask the question. • Students who need more of a challenge can ask a question of a type different from “What’s your favourite...?” Data 163

Materials: Assessment Opportunities BLM 30: Tally This Observations: Pay attention to whether students can appropriately collect and record the data. • Do they ask everyone in the class and have a way to remember who they have already polled? • Do they ensure that all students select only one answer choice? • Can they correctly make the tally marks? Conversations: If students are having difficulty knowing whether they have polled everyone in the class, pose some of the following prompts: – Have you asked everyone in the class? How could you check? – We have 20 people in our class. How does that compare to the number of tally marks you have made? – Why might you be two people short? Did you and your partner vote? Do you think it would be a good idea to include your information? Why? Consolidation (20 minutes) • As a class, have a gallery walk to look at the various graphs and tally tables. At one or two of the stops, ask students how the tally table and the concrete graph represent the same information. Reinforce how each tally/concrete object represents one person. • D iscuss how the tally table made it easier to collect the information, instead of carrying around concrete materials as they asked their survey question. • Together, analyze one of the concrete graphs. Ask students what they can learn from the information. Further Practice • Provide students with BLM 30: Tally This. Students complete the tally tables, crossing off items on the BLM to track their count. 164 Patterns & Relations/Data & Probability

8Lesson Displaying Data: Concrete Graphs Teacher Possible Learning Goals Look-Fors • Asks a simple survey question with appropriate answer choices • Collects and organizes data in an appropriate way • Displays data using concrete graphs • Creates a simple survey question with a few appropriate answer choices • Collects, organizes, and displays data using concrete materials to create a concrete graph, using one-to-one correspondence • Explains what the concrete materials represent, and makes some observations about the data Materials: About the “Let’s Organize!” (pages Designing an effective survey question can be quite challenging. As 10–11 in the Patterns, Marian Small explains, “a good survey question has a limited number of Relations, Data, and answer choices, yet enough to accommodate everyone (one of the answer Probability big book), choices may be ‘Other’)” (Small, 2009, p. 530). Small also points out that BLM 31: Survey Template students need to define their answer choices clearly to ensure none of and Digital Slide 48: the categories overlap (e.g., for “What’s your favourite type of animal?”, Survey Template, providing both ‘snakes’ and ‘reptiles’ as options). selection of various Students also need to think about who will be in their survey concrete materials population, since this will affect the types of questions that pertain to appropriate for students’ the group and the types of answers that they anticipate. data collection Time: 45 minutes Day 1 Minds On (15 minutes) • Refer back to one of the examples to remind students how they created concrete graphs in the previous lesson. Review what each object represents and how it is important to include titles and labels. • Ask students what class favourite they would like to find out about. Ask what question they could use to survey the class. Discuss what answers they could include for classmates to choose, and what pictures could be used to represent them. You can show “Let’s Organize!” from pages 10–11 in the Patterns, Relations, Data, and Probability big book to help students generate ideas (e.g., What is your favourite fruit? vegetable? toy? community helper?). Data 165

Teaching Tip • Review the collection and organization methods that students used in the Retain students’ previous lesson. Discuss the importance of making sure that every person completed surveys can take part, can vote only once, and can choose only one answer. and concrete data collections for use on Working On It (20 minutes) Day 2 and in later lessons. • Students work in pairs. Explain that they have four tasks over the next two days. Create an anchor chart of these tasks: – Choose a survey question that is appropriate for your inquiry. – Select your answer choices based on what you know about the population you are going to include in your survey. – Collect and organize your data by deciding on what representation, tools, and strategies you will use to build your model (the survey). – Make a concrete graph. • Provide pairs with BLM 31: Survey Template. Project Digital Slide 48: Survey Template and ask how they might fill in the template. Explain that they can use the category of ‘other’ as one of the answer choices. • Provide a selection of materials students can use to collect their data, such as small containers, craft sticks, connecting cubes, colour tiles, counters, clothespins, construction paper, sticky notes, sorting circles or mats, stickers, rubber stamps, and bingo dabbers. Remind students that their method must ensure that everyone in class responds and that each person responds only once. • Once students develop their questions and answer choices, they decide how they will collect their data. Explain that all pairs will ‘stay and stray’ to ask and answer the survey questions. One partner stays at a spot, asks visitors the survey question, and collects the data, while the other partner circulates to other pairs and answers their survey questions. Partners then switch roles. Differentiation • If students are struggling to get started, take them back to other steps in the problem-solving process, such as understanding the problem or analyzing the situation. Engage them in small-group instruction to help them choose a survey question, answer choices, and a data collection method. • Help students who need language support as needed to understand the answer choices of other groups, and to make their personal selections. • Some students may need to have their questions and choices scribed. Assessment Opportunities Observations: Pay attention to how students formulate their questions and answers and how they collect the data. – Are answer choices clear with no overlaps? – Are all students participating in all surveys and providing only one answer to each? – Are students accurately collecting students’ responses? 166 Patterns & Relations/Data & Probability

Conversations: You may need to revisit other components in the steps in the problem-solving process. Use some of the following prompts to help determine students’ abilities to create survey questions and choices: – What is the topic of your survey? – What are your choices? How did you choose them? – Did you use ‘other’ as a choice? Why or why not? Materials: Consolidation (10 minutes) students’ completed surveys and collected • Meet as a class and discuss how their collection strategy worked and whether data from Day 1, camera Time: 45 minutes students had any challenges. Ask what they might do differently to collect their data if they were to do the survey again. Day 2 Minds On (5 minutes) • Review what students did on Day 1 to create a survey question, develop choices for responses, and then collect data. • Refer to the anchor chart of tasks they are to fulfill and ask what they still need to complete. Working On It (20 minutes) • Students work in the same pairs as for Day 1 to create their concrete graphs. • Ask students what decisions they will need to make to create their concrete graphs. Discuss what information needs to be included on the concrete graphs (e.g., title, labels). • Students create concrete graphs to represent the data they collected. Differentiation • Meet with a small group if students are having difficulty creating their concrete graphs and establishing one-to-one correspondence between the objects and what they represent. Assessment Opportunities Observations and Conversations: Check to see if students are aligning the objects in the different categories so they are easier to compare. Pose prompts to find out whether they know what each object represents, and how they know that each person in the class is represented. Consolidation (20 minutes) • Display students’ concrete graphs. Have a gallery walk and visit the concrete graphs as a group. Stop at some of them and ask the class what they think the Data 167

survey question is and whether the graphs reflect the choices. Ask whether the titles and labels help them to understand the graph. • Ask students what kind of results they would likely get if they carried out their surveys in another grade one class that has the same number of students. Discuss whether the frequencies of the categories would be the same or different and why they think so. Ask whether the frequencies would be the same if they carried out their survey in a grade six class that has the same number of students. • After the gallery walk, discuss what is important to remember when creating a concrete graph. Make an anchor chart of students’ ideas. Take a picture of each concrete graph so they can be used in the next lesson. • Ask students whether they think their concrete graphs accurately represent the data they wanted to collect and whether they think it will help to answer their questions. • Building Growth Mindsets: Ask students what they found most challenging about creating a survey question, selecting answer choices, collecting the data, and then making a concrete graph. Ask how they overcame the challenge and/or solved the problem. Ask what they would do differently if they were to ask another survey question. Explain that it is worthwhile to reflect on how they did the task and learn from mistakes that they may have made in order to improve the next time they do a similar task. Without thinking about our mistakes, it is hard for us to get better at something. 168 Patterns & Relations/Data & Probability

and9 10Lessons Describing and Analyzing Data Math Curricular Competencies Learning Standards • Reasoning and analyzing: Use reasoning to explore and make connections; Previous Experience model mathematics in contextualized experiences with Concepts: Students have had • U nderstanding and solving: Develop, demonstrate, and apply mathematical experience in answering questions about data understanding through play, inquiry, and problem solving; visualize to explore presented in concrete mathematical concepts graphs. • 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: Connect mathematical concepts to each other and to other areas and personal interests Content • Concrete graphs, using one-to-one correspondence Msctmuaoarbnotvlchseerty,e,V,ttmoidetcaloegatr,rabeal,u,epcllaheaas,srttyest,a:glolyry, About the As students analyze data, there are three levels of graph comprehension that they need to learn: • Level 1: Students can read what is directly on the graph, which requires no interpretation (e.g., the number of people who prefer dogs). • L evel 2: Students read the data to make comparisons. For example, they may order the data from greatest to least frequency or find how many more people like dogs than like cats by finding the difference between the two categories using addition or subtraction. • Level 3: Students read the data to make inferences. They need to consider the context of the data and the population, as well as apply any background information they may have. As students analyze data, it is important that they are thinking within the context of why the survey question was asked in the first place, especially if it was carried out to make a decision. Analyzing the data may also provoke more questions of interest, which can lead to further surveys or investigations. About the Lessons The following two lessons provide students with opportunities to work with the data collected and presented in the previous block of lessons Students analyze the data, pose and answer questions, and reflect on the effectiveness of the display method. Data 169

9Lesson Describing Data and Asking Questions Teacher Possible Learning Goals Look-Fors • Describes, compares, and analyzes data presented in concrete graphs Materials: • Asks and answers questions about collected data pictures of concrete graphs students • Identifies features of concrete graphs and describes what they represent created in Lesson 8 • G enerates questions about data in concrete graphs Time: 50 minutes • A nswers questions using information from the graphs as proof Minds On (15 minutes) • Show students a picture of one of the concrete graphs that they created in the previous lesson. Have them turn and talk to their partners to discuss what information the graph gives. • Discuss students’ responses. Pose prompts that will provoke deeper thinking. For example, ask students what comparisons they can make between the different categories. Ask what they can infer from the information in the graph or what questions might be answered by looking at the data. Working On It (15 minutes) • Give pairs of students a picture of the concrete graph that they created the previous day. • Partners take turns visiting each other’s concrete graphs. The visitors pose questions about the graph and the creators answer them. Differentiation • For students who are struggling to understand the data in the graph, you may need to revisit some other steps in the problem-solving process, such as understanding the problem (e.g., What might the survey question be? Who do you think took part in this survey? How do you know?). • You may decide to have students visit two graphs each if time permits. 170 Patterns & Relations/Data & Probability

Assessment Opportunities Observations: Pay attention to the discussions between partners. – Are they able to ask questions relevant to the information in the graph? – Do they understand the data presented in the graph? – Can the creators answer the questions and offer proof from the graph? Conversations: If partners are not engaged in discussion, pose some of the following prompts: – What is this graph telling you? – What information do you understand? What do you wonder about? – What question could you ask that involves comparing? – What are two things that you could compare in this graph? – Did you try looking at our anchor chart for ideas? Consolidation (20 minutes) • Selectively choose some of the concrete graphs to discuss as a class. The visitors can share the questions they posed and the creators can explain what data they used in the concrete graph to answer the questions. • Pose questions to get at deeper analysis of the graphs so students are commenting on the information that is ‘right there,’ making comparisons, both qualitatively (people like cats more than they like dogs) and quantitatively (four more people like cats than like dogs), and are making inferences (e.g., a pet store should have more items for cats than for dogs). • Discuss that we collect information to answer questions. Connect this to students’ everyday lives and how they can use data to make decisions. Data 171

10Lesson Analyzing Data Teacher Possible Learning Goals Look-Fors • Reads data presented in concrete graphs, and describes the data using comparative language • Makes some inferences about the data and offers proof for their conclusions • Identifies and describes features of concrete graphs • U ses information in graphs to answer questions and offer proof for their responses • C ompares data in the graph • M akes some inferences about the data and gives reasons for their analysis Materials: Minds On (15 minutes) paper and markers, • Ask students what the seasons are. Write the names of the four seasons on four colours of sticky notes, Digital Slide 49: sheets of paper and post them on a wall. Have students come up one by one Our Favourite Seasons, and stand or sit in a line in front of the name of their favourite season. “Looking at Data” (pages 12–13 in the Patterns, • Ask students what kind of graph they have made. (e.g., a people graph, a Relations, Data, and Probability big book), concrete graph) Ask how many voted for each season. Ask how many voted BLM 32: Looking at Data altogether. Ask how they can check. Time: 45 minutes • Give each student a sticky note, using a different colour for each line (i.e., a different colour for spring, summer, etc.). Ask how they can make a concrete graph using the sticky notes and the labels on the wall. • Have students place their sticky note above the appropriate heading for their favourite season. Alternatively, project Digital Slide 49: Our Favourite Seasons and create the concrete graph on the template. Ask students the same questions you asked for the first graph. • Tell students to turn and talk to a partner, study the graph they just made, and discuss what conclusions they can make. • Have students share some of their ideas (e.g., Most people like… the most; more people like… than…). Co-create an anchor chart of students’ conclusions for easy reference during Working On It. Working On It Whole Group (15 minutes) • Project “Looking at Data” (pages 12–13 in the Patterns, Relations, Data, and Probability big book). Ask what the title of the selection is. Ask students what they notice and what they wonder. Draw students’ attention to page 13. Ask what different displays they see. (e.g., tally table, concrete graph, pictograph) Draw attention to the tally table and the concrete graph. Ask what the titles of the tally table and the concrete graph are. Ask what question they think was asked to collect the data represented on the two displays. 172 Patterns & Relations/Data & Probability

• For both displays, ask how the data are the same. (e.g., They show the same results.) Ask how the data look different in each display. • Ask students what data they can compare in these displays. Ask in which display the data is clearer/easier to read, and why they think so. Ask which display makes it easiest to order the seasons from the most to the least favourite, and why they think so. • Have students work in pairs. Provide BLM 32: Looking at Data, which shows the displays on page 13 of the big book. Have them compare the results on the class graph about favourite seasons that they made earlier in the lesson to the results of the displays in the big book. Differentiation • H ave students work with one display only from page 13 (allow them to choose either the tally table or concrete graph). • Provide a visual anchor chart for students who need language support to assist in their understanding of comparative terms (e.g., more than, less than, most, least). Assessment Opportunities Observations: Pay attention to how students make comparisons between the two sets of data. – Do they use comparative language? – Do they make qualitative comparisons (e.g., most, least)? Do they also make quantitative comparisons (e.g., 3 more people liked winter than liked summer in the big book displays and in our graph; 7 more people liked winter than liked summer)? – Which representation in the big book are students using the most and the least? Conversations: Pose some of the following prompts if students are having difficulty making comparisons: – What observations did you make about our graph? Are they the same as you made about the displays in the big book? Why? – How can you compare the results in the displays for summer? – Is there an idea on our anchor chart that you can use with this data? – Which display are you using for your conclusions? Is it easier to make a conclusion using a different display? Consolidation (15 minutes) • Have each pair share one comparison and conclusion, and offer evidence from the displays that their conclusions are true. • Ask whether the same number of people participated in each survey. • Co-create an anchor chart of students’ conclusions. Data 173

• Discuss how their class results compare to the results collected from the class surveyed in the big book. Ask students what would make it easier to be able to compare the data. (e.g., There should be the same number of students in each class.) Ask why the data results may not be the same and what conditions would affect it. Ask whether they think their class results would be the same as another grade one class with the same number of students. 174 Patterns & Relations/Data & Probability

11Lesson Guided Math Lesson: Reinforcing Data Concepts and Skills Math Curricular Competencies Learning Standards • R easoning and analyzing: Use reasoning to explore and make connections; model mathematics in contextualized experiences • Understanding and solving: Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving; visualize to explore mathematical concepts • C ommunicating and representing: Communicate mathematical thinking in many ways; use mathematical vocabulary and language to contribute to mathematical discussions; explain and justify mathematical ideas and decisions; represent mathematical ideas in concrete, pictorial, and symbolic forms • Connecting and reflecting: Connect mathematical concepts to each other and to other areas and personal interests Content • Concrete graphs, using one-to-one correspondence Teacher Possible Learning Goals Look-Fors • Applies data concepts and skills to solve problems Previous Experience • Reinforces understanding of data concepts by engaging in related activities with Concepts: Students have had • Applies a problem-solving model to describe and analyze data opportunities to sort and • C lassifies groups of sorted objects classify objects; collect, • E xplains choices for classification of objects organize, and display • A sks questions about a variety of data data; and read and pose questions about different data. Data 175

Math Vocabulary: About the sroguorrlrgaeta,p, ncahlit,azttersai,sblrilufyeyta,eds, ,ocqrotulilneegsctti,on, Marian Small notes that as students begin to problem solve, “the understand-the-problem stage is often the stumbling block for students as it involves discerning whether all the necessary information is provided and if extraneous information is included” (Small, 2009, p. 39). Teachers can offer support by asking questions that require students to reflect on what they know and what they still need to know. About the Lesson This lesson, which takes place over three to four days, includes a whole- class introduction to a problem-solving model, as well as two to three days when students rotate through a guided math lesson and a series of activity centres. After the whole-group introduction, you can carry out the guided math lesson with a small group [Centre 1], while the rest of the students engage in activities that reinforce sorting skills. In a follow-up session, the first group can work independently on problems discussed in the guided math lesson [Centre 2], while you meet with a different group [Centre 1], and the rest of the students rotate through activities [Centres 3, 4, and 5]. Eventually, you will meet with all groups, tailoring the guided math lesson to meet the specific needs of each group. The guided math lesson also allows you to: – assess small groups of students while they are problem solving; – provide ‘in the moment,’ responsive, and differentiated instruction; – offer descriptive feedback; and – plan next steps. You can set up activities through which students rotate over the course of a few days, or they can freely visit the centres. Select the way that best suits your class. The following schedule offers an example of how students may rotate from activity to activity. 176 Patterns & Relations/Data & Probability

Suggested Rotation Schedule: Activity/Day Group A Group B Group C Group D Session 1 Centre 1 Centre 5 Centre 4 Centre 3 Session 2 Guided Math Session 3 lesson with Centre 1 Centre 5 Centre 4 teacher Guided Math Session 4 Centre 2 lesson with Centre 1 Centre 5 Follow-up teacher Guided Math Session 5 problem solving Centre 2 lesson with Follow-up teacher Centre 3 problem solving Centre 4 Centre 3 Centre 2 Centre 1 Follow-up Guided Math problem solving lesson with teacher Centre 5 Centre 4 Centre 3 Centre 2 Follow-up problem solving Set-Up of Centres • If you decide to follow the rotation schedule (above) having students rotate through a series of five activities, you will need to create three other centres. It is beneficial if some are open exploration, so students can work independently. Some examples are given below. Reinforcement Ideas for Centres (Choose 3): • Games or Digital Games/Activities: Students can engage in digital math games and activities that are designed to reinforce sorting with attributes. • S orting Collections: Create various tubs of concrete materials for students to sort (e.g., loose parts, connecting cubes, toys, buttons, shells). Attach a simple prompt such as, “How many ways can you sort these objects? Sort these items using one attribute.” • Math Art: Students can create an image based on a sorting rule. Provide students with different-coloured stickers, paints, markers, and paper, and have them create a picture in which different parts of the image follow different sorting rules. On the back of the picture, have students describe the sorting rules they used. • Collect Some Data: Students create their own survey question, and collect and organize the data they collect. • G raph It: Leave graph templates and sets of data in tally tables at this centre for students to create concrete graphs. Once their graph is created, they can create a set of questions someone could answer about the graph. Data 177

Teacher Day 1 Look-Fors Possible Learning Goals • Experiences the problem-solving model by working through an example • Sorts and classifies a variety of data • Analyzes data presented in a variety of forms • Asks and answers questions about data • Uses a problem-solving model to answer questions • I dentifies and uses attributes and how they can vary to sort and classify sets • E xplains features of graphs and what information they convey • A sk questions about graphs • A nswers questions about data using information from the graph as proof Materials: About the Lesson Digital Slide 50: Data This whole-group lesson introduces students to a simple problem-solving and Digital Slide 51: model that helps them reflect on the questions being posed, and analyze the Picture of a Concrete situation within a context so they better understand the problem. This model Graph is embedded in Dasha’s Data, which students will use in the guided math Time: 30 minutes for lesson and in their own follow-up investigations. introductory lesson, 30 minutes for centres Model Setting the Context: Text and pictures give meaning to the math. What do you see? Looking at the data. (Can students identify the information on the page?) What do you know? Reading/analyzing the data. (Can students explain what the information means?) Minds On (10 minutes) • Project Digital Slide 50: Data so only the text is showing and the images are covered. Read the text together and ask what the two questions mean. • Show students the images on Digital Slide 50. Ask, “What do you see?” (e.g., think about what they see, what attributes they notice, what is visibly there). Have students share their thinking in partners and then as a whole group. (e.g., two groups of food, two groups of snacks) • Ask, “What do you know?” (e.g., The food is sorted into two groups; there are more foods on the right than on the left.) • Ask students how the foods are sorted and why they think so. Ask what other foods could go into the two categories. 178 Patterns & Relations/Data & Probability

Working On It (10 minutes) • Show Digital Slide 51: Picture of a Concrete Graph and explain that it is a picture of a concrete graph that was created by another grade one class. Ask students what they see on the page. • Ask students what they know. Have them offer proof from the graph. • Discuss what the survey question might have been. (e.g., What type of shoes did you wear to school?) • Have students turn and talk to a partner about the possible inferences or conclusions that they can make from looking at the graph. Discuss students’ responses. • Ask how they could order the types of shoes from the most common shoe worn to the least common shoe worn. • Ask how the type of question being asked would affect the conclusion that you can make. (e.g., More people wear running shoes than sandals; running shoes are the most popular; the store sells more running shoes than boots so they should order more running shoes.) • Ask whether the results would be the same if they carried out the survey in their classroom today, polling the same number of students. You may decide to carry out the survey so students can confirm their predictions. Consolidation (10 minutes) • Selectively choose two or three students to explain their thinking (e.g., students who asked questions or who talked about how many there are in each category). Ask them to explain how they knew what the information was telling them. • Review how the ‘What do you see? What do you know?’ questions can be a good problem-solving strategy. Tell students that they will be applying this strategy in an upcoming small-group lesson. Preparing for the Next Day (20–30 minutes) • Introduce each activity centre so students clearly understand all instructions, where to access the necessary materials, and what to do when they are done. Have two or three students model each activity. Answer any questions that students may have. This time investment will help to ensure that students can work independently and stay on task while you are working with another group on the guided math lesson. Following Days • Assign groups to their activity centres (including the guided math lesson) for the first rotation, which can last about 20–30 minutes. You can then carry out a second rotation on the same day, with the remaining rotations on other days. Data 179

Possible Guided Math Lesson: Dasha’s Data Teacher Look-Fors Possible Learning Goals Materials: • Identifies similarities and differences between groups of objects, and Dasha’s Data little books organizes them by sorting and classifying by one attribute • Analyzes tables and concrete graphs using features of the graph and their background knowledge NOTE: Adjust your learning goals to meet the individual needs of each group. Create a list of Teacher Look-Fors (see the Possible Teacher Look-Fors below) that will formulate the prompts to begin or shape the conversations with students. • Sorts and classifies objects using one attribute • Reads information presented in tables using titles and labels • Accurately counts tallies • Creates concrete graphs from given information • Describes and compares information presented in concrete graphs NOTE: If there is one group working with you in the guided math lesson, and another group simultaneously solving more of the problems independently, the books will need to be shared between the two groups. Differentiation • The sample guided math lesson offers many more prompts and problems than can feasibly be used in one lesson. They are intended to offer ideas about what you may ask and how you can differentiate from group to group. Choose the prompts that best suit your students’ needs. As you progress through your guided math lesson, your focus may change, depending on students’ responses or misconceptions that may arise. Cover • Read the title and ask students what they know about the word ‘data.’ Ask who they think Dasha is, and what they think they might be doing in this book. Ask students what they see on this cover, and how they could sort the displayed items. Pages 2–3 • Read the text to students or have them read along. Review the questions, “What do you see? What do you know?” and model again, if necessary. • Ask students what they see on these pages. • Ask students what the next step is. (e.g., to think about what we know) Ask students what they think we should do with the groups of objects. (e.g., describe them, classify them) • Have students work together to describe and classify the objects on the pages. Share as a group. 180 Patterns & Relations/Data & Probability