13Lesson Guided Lesson: Reinforcing Data Concepts and Skills Math Curricular Competencies Learning Standards • Reasoning 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; develop and use multiple strategies to engage in problem solving • Communicating and representing: Communicate mathematical thinking in many ways; use mathematical vocabulary and language to contribute to mathematical discussions; explain and justify mathematical ideas and decisions; represent mathematical ideas in concrete, pictorial, and symbolic forms • Connecting and reflecting: Reflect on mathematical thinking; connect mathematical concepts to each other and to other areas and personal interests Teacher Content Look-Fors • One-to-one correspondence with bar graphs, pictographs, charts, and tables Possible Learning Goal • Experiences a problem-solving model by working through an example • Understands the steps of a problem-solving model • Follows the prompts within the model Previous Experience About the with Concepts: Students have had Students require many different experiences in order to understand and opportunities throughout internalize data concepts, develop proficient graphing skills, and apply their the Data unit to practise knowledge in problem-solving situations. It is important to present data sorting, organizing, within real-life contexts since the ultimate goal is for students to use data graphing, and reading concepts to answer questions and not to solely create graphs in isolation. graphs to find information. About the Lesson Math Vocabulary: sriunoltreet,,rpocrlreagtsa,snriiefzyae,d,sgorratpinhg, 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 series of activity centres, including a guided math lesson. continued on next page Data 155
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 data concepts, such as sorting skills. In the next 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. ••••T hopapesfrlasfgoeenuvrsiisndddeseeemxsd‘tcianmrslit-lpeatghtptihresvo.-elumefpseosseomdonbfeanasltctsu,k’od;reeasnllptosownwsshiyvioleeu, tathnoe:dydairfefeprreonbtilaetmedsionlvstirnugc;tion; 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 rotation schedule that follows offers an example of how students may rotate from activity to activity. Example Rotation Schedule Activity/Day Group A Group B Group C Group D Session 1 Centre 5 Centre 4 Centre 3 Centre 1 Guided Math Lesson with teacher Session 2 Centre 2 Centre 1 Centre 5 Centre 4 Follow-up Guided Math Lesson problem solving with teacher Session 3 Centre 3 Centre 2 Centre 1 Centre 5 Follow-up Guided Math Lesson problem solving with teacher Session 4 Centre 4 Centre 3 Centre 2 Centre 1 Follow-up Guided Math Lesson problem solving with teacher Session 5 Centre 5 Centre 4 Centre 3 Centre 2 Follow-up problem solving •S eItf-yUopu of Centres the example rotation schedule (having students rotate decide to follow through a series of five activities), you will need to create three other centres. 156 Patterns & Relations/Data & Probability
It is beneficial if some centres are open exploration so students can work independently. Some example centres follow. Examples for Centres 3, 4, and 5: •C eGnatmree3s or Digital Games/Activities: Students can engage in digital math games and activities that are designed to reinforce data skills. C• eSnotrrtein4g Collections: Create various tubs of concrete materials for students to sort (e.g., loose parts, connecting cubes, toys, buttons, shells). Include a simple prompt such as, “How many ways can you sort these objects? Sort these items using two attributes.” C• eSnotrrtea5nd Graph: Give students a tub with objects of different colours (e.g., toys, blocks, markers). Include a prompt such as, “How can you sort these objects? Create a graph to show how you sorted.” Day 1 Whole-Group Lesson: Introducing the problem-solving model used in the guided math lesson Materials: About the Lesson Data Detectives little This whole-group lesson introduces students to the simple problem-solving books, Digital Slide 47: model embedded in Data Detectives, which they will use in the guided math Read! Think! Share! (1), lesson and in their own follow-up investigations. Digital Slide 48: Read! Think! Share! (2) Model: Setting the Context: Text and pictures give meaning to the math. Time: 50–60 minutes Read: Look at the image and read the words. What do they tell you? (Can students (30 minutes for see attributes they can sort by? Can they read information from the graph?) introductory lesson, Think: Use the image to help answer the question. (Can they sort by the chosen 30 minutes for attributes? Can they interpret the graph?) introducing centres) Share: Share what you know about the image. (Can they explain how they sorted and give a sorting rule? Can they explain what the graph is telling them?) Digital Slide 48: Read! Think! Share! (2) Minds On (10 minutes) Count the tallies. What do they mean? Digital Slide 47: Read! Think! Share! (1) • Show Digital Slide 47: Read! Think! Share! (1). Ask students what they see Read! How could you sort and graph these items? (e.g., foods, three words, a question). Number of Pets in Class • Read the words at the side of the slide: “Read! Think! Share!” Ask students ReaDdo!g Cat Hamster Other what the words mean and how they could help to answer a math problem. Think! • Have students READ the question on the slide or read it together. Ask how Think! they can ‘read’ the images (e.g., studying and making note of what objects are in the picture). Share! Data 157 Share! Scholastic Canada GR3 BC Patterns & Relations 3rd Pass Digital Slides November 9, 2021 Photos ©: first row, left to right: adventtr/iStockphoto; Pixelrobot/Dreamstime; Chernetskaya/Dreamstime; second row, left to right: Xavier Gallego Morell/Dreamstime, Unpict/ Dreamstime, Oleh Muslimov/Dreamstime; third row, left to right: Sopone Nawoot/Dreamstime, Tatiana Muslimova/Dreamstime, Pandaphotostudio290718/Dreamstime Scholastic Canada GR3 BC Patterns & Relations 3rd Pass Digital Slides November 9, 2021
• Have them THINK about the question by turning and talking to a partner and discussing different ways to sort and the tools that would be helpful for graphing the results. • Have students SHARE their ideas about ways to sort and the tools they could use, justifying their choices with proof. Be sure to discuss different ways of sorting the items and then graphing the results in different ways. Working On It (10 minutes) • Show students Digital Slide 48: Read! Think! Share! (2). • Have students READ the page (e.g., What do they see? What do they need to do?). • Students work in partners to THINK about how to count the tallies, what the information means within a context, what they learned from the data (e.g., which pet did most people have?). • Remind them to be ready to SHARE and explain their work. Consolidation (10 minutes) • Selectively choose two or three different pairs of students to explain their thinking. Ask how they counted the tallies and what they learned from this table. • Review how reading, thinking, and sharing can be a good problem-solving strategy. Explain that they will be applying this strategy in the upcoming guided math lesson when they meet with you. 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 they 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. Guided Math Lesson: Possible Learning Goals • Sorts and graphs objects in a variety of ways • Reads and interprets data presented in tables and graphs • Applies data concepts and selects strategies to solve problems NOTE: Adjust your learning goals to meet the individual needs of each group. Create a list of Teacher Look-Fors (see the possible Look-Fors, below) that will formulate the prompts to begin or shape the conversations with students. 158 Patterns & Relations/Data & Probability
Teacher • How do students sort and organize objects? How do they graph the results? Look-Fors • What kind of graph do they choose? Do they include titles and labels? • Can they read information in a table? Do they understand how the table is Materials: Data Detectives organized? Time: 20–30 minutes per session • Can they read information in a graph? Do they understand what the features mean and how they help to understand the data? • Do they need more of a challenge than what I am offering? 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 options about what you may ask and how you can differentiate from group to group. Pick and 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. • The book Data Detectives includes a range of data skills. Select the pages that best pertain to your group. Reading the Book: Cover • Read the title, Data Detectives, and ask what students think it means. Tell them that they are going to be data detectives as they analyze certain sets of data. Ask students if they know what detectives do (e.g., look for clues, solve puzzles) and why they do it (e.g., to answer questions). Page 2 • Setting the Context: Ask students what they see and what all the items have in common. Ask when the items may have been collected and why they think so. • Read: Read the text together. Ask students what they are supposed to do. • Think: Have students work individually or in pairs to think of different categories that could be used to sort the objects. • Share: Discuss their chosen categories. Ask how they could use the categories to create a tally table that shows the number of items in each category. • Follow-Up Activity: Have students create a tally table that reflects their sorts. They can create a graph to represent the data in the tally table. Page 3 • Setting the Context: Ask what is different on this page from page 2 (e.g., different natural objects have been added: flowers, pine cones, etc.). • Read: Ask students to ‘read’ the page. (e.g., What items are there? What attributes do they see?) continued on next page Data 159
• Think: Have students work in pairs to think of ways that they could sort the objects. Encourage them to find more than one way. • Share: Pairs within the group share their ideas. Together, sort some of the items. Cut out the shapes from a photocopy of the page so the objects can be moved from section to section. • Follow-Up Activity: Have students create a tally table of their results. They can also create a graph of their choice. Page 4 • Setting the Context: Ask what students see and how the pictures and title of the tally table help them understand the data. Take a quick survey of how students get to school by having them raise their hands. Ask what conclusions they can make. • Read: Together, read the text at the top of the page. Ask what each tally represents. Ask what the ‘other’ category might represent and why they think so. • Think: Have students work in partners interpreting the data. Use these differentiated goals for this page and the following pages: – If some students are making qualitative observations (e.g., less people walk than ride bikes) ask them “how many less?” – If some students are reading one piece of data (e.g., 5 students take the bus), extend their thinking by asking them to make a comparison. – For students who need more of a challenge, ask them who might have collected this data and what decisions may be made after knowing the results. • Share: Pairs share their findings and provide justification for their thinking. Ask what kind of graph could be used to display this data. • Follow-Up Activity: Students can create a graph of their choice to represent the data in the table. Page 5 • Setting the Context: Ask students what this table is about. Take a quick survey with the group on how many people live in their homes. • Read: Ask students how this table is different from the one on page 4 (e.g., there are numbers across the top of the table rather than words). Ask what the numbers represent (e.g., the number of people in a home). Ask what 2 tallies under 5 mean (e.g., there are 2 students who have 5 people in their families). • Think: Students work in pairs to analyze the data. Continue offering prompts that were suggested for page 4 to extend students’ thinking. • Share: Pairs share their conclusions about the data. Ask students what counting up all of the tallies tells us (e.g., the number of people surveyed). • Follow-Up Activity: Students can create a graph of their choice to represent the data in the table. 160 Patterns & Relations/Data & Probability
Page 6 • Setting the Context: Ask what they see on this page. Make connections by asking what their favourite type of weather in November is. Ask what type of graph this is and how they know (pictograph). • Read: Together, read the text above the pictograph. Discuss how the key helps to read the data. (e.g., It lets us know how many items the symbol represents.) • Think: Students work in pairs to interpret the data. Encourage them to make comparisons and read the whole data. • Share: Have pairs share their ideas. Ensure that they justify their reasoning by referring to the table and its features. • Ask students to figure out how many days are represented in the pictograph. Ask if the symbols represent all the days in November and how students know. Ask why all the days may not be represented (e.g., students only recorded the weather for the days they were in school). Page 7 • Setting the Context: Discuss what the pictograph is about and what the various activities are. Ask what categories they would use if they took a survey of favourite recess activities in this class. • Read: Have students ‘read’ the pictograph and make one or two observations. • Think: Have students work in pairs to interpret the graph. Continue extending students’ thinking so they are making observations, comparing, and reading the whole data. • Share: Have pairs share their findings. • Follow-Up Activity: Have students create some statements about the information in the graph. Page 8 • Setting the Context: Ask what type of graph they see and what it is about. Ask students what categories they would choose to represent favourite snacks. Discuss why their choices might be different from other people in the group. • Read: Have students ‘read’ the graph. Ask what the numbers on the vertical axis mean and how they are increasing. • Think: Students analyze the data in pairs. Continue to extend their thinking by using prompts suggested for previous pages. Observe whether their observations are becoming more advanced without needing to be prompted. • Share: Students share their findings. Discuss how many people took the survey and how they know. • Ask students how the graph might change if chocolate cake was added as one of the categories. • Follow-Up Activity: Have students represent the same data in a horizontal bar graph. continued on next page Data 161
Page 9 • Setting the Context: Discuss why Grade 3 classes might have a food drive. Ask why the items in the picture are appropriate for a food drive. • Read: Give students time to ‘read’ the graph. Ask what is different about this bar graph compared to the one on page 8. Ask why the intervals are increasing by 5 rather than by 1. Discuss what the categories are on the horizontal axis. • Think: Students work in pairs to analyze the data. Continue to note how students’ observations are evolving. Ask prompts to extend thinking. • Share: Have students share their findings. • Follow-Up Activity: Students can create a horizontal bar graph using the same data. Page 10 • Setting the Context: Have students read the title of the bar graph and explain what it is about. Ask students if they have a vegetable garden in their backyard or in their community. Discuss which vegetable they would plant in a vegetable garden and why. • Read: Have students read the graph. Ask how this graph is different from a vertical bar graph. • Think: Students work in pairs to analyze the data. Continue to observe and offer prompts. • Share: Pairs share their findings. Discuss how someone would use this information and why the information is important. • Follow-Up Activity: Students can convert the data into a vertical bar graph. Page 11 • Setting the Context: Discuss what the graph is about and how they know. • Read: Give students time to ‘read’ the graph and what the labels tell about the information. • Think: Students work in pairs to analyze the data. • Share: Students share their findings. Ensure that they offer proof for their statements from the bar graph. Ask why this information might be helpful to know. • Follow-Up Activity: Students can convert the data into a vertical bar graph. Page 12 • Setting the Context: Ask students what they see on this page. Have them identify and describe the attributes of the shapes and classify some of them. • Read: Read the text. Ask students what they are supposed to do. Discuss what they need to do to graph these items (e.g., sort, tally, choose a type of graph, choose an appropriate scale). • Think: Have students think of all the ways they could sort the shapes. • Share: Share their ideas. • Follow-Up Activity: Students can sort, classify, and graph their data. 162 Patterns & Relations/Data & Probability
First Peoples Consolidation of Guided Math Lesson Principles of Learning (15 minutes – after the last rotation) • Strategically select one graph to discuss with the entire class (e.g., the graph that students found the hardest to interpret). Discuss the graph’s features and how they contribute to understanding the data. • Compare some of the graphs and highlight their similarities and differences. Building Growth Mindsets: Discuss what students have learned about graphs and tables. Ask what they understand well and what they still find confusing. Ask which graph they find the most challenging to understand. Make a list of their comments. During the next week, revisit the list each day and take 5–10 minutes to review and reinforce one of the concepts. Students need to realize that once they have identified their strengths and areas needing improvement, it is important to take action and practise. This supports the First Peoples Principles of Learning that learning involves patience and time; and that learning involves recognizing the consequences of one’s action. Data 163
14 17Lessonsto Applying Data Concepts and Skills 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 investigated • Understanding and solving: Develop, demonstrate, and apply mathematical various organizational tables and graphs and have understanding through play, inquiry, and problem solving; visualize to explore described and analyzed mathematical concepts; develop and use multiple strategies to engage in various sets of data. problem solving • Communicating and representing: Communicate mathematical thinking in many ways; explain and justify mathematical ideas and decisions; represent mathematical ideas in concrete, pictorial, and symbolic forms • Connecting and reflecting: Reflect on mathematical thinking; connect mathematical concepts to each other and to other areas and personal interests Content • One-to-one correspondence with bar graphs, pictographs, charts, and tables About the Students need to understand that surveys are conducted to answer questions and make informed decisions. A good survey question needs to produce the answers that will help in the decision-making process. At first, students may ask yes/no questions, such as “Do you like ice cream?” If they want to know what kind of ice cream to buy for those who like it, they need to create a question that will elicit more information. For example, students could ask, “What is your favourite type of ice cream?” In this case, students need to consider possible answers, taking their population into consideration. While students may think of 25 different flavours, all types may not be viable choices for purchasing at the store. Students may decide to limit the choices to available flavours, asking respondents to choose from chocolate, vanilla, butterscotch, and strawberry. They may also consider including an ‘other’ category for students who prefer a flavour other than those listed. Once students have established their survey question and possible responses, they need to think of how they will collect and organize the data, ensuring that each person in the targeted population gets asked once and only once. Students can apply their understanding of tally tables to find a way to record their data. 164 Patterns & Relations/Data & Probability
MsdeuixasrptpvhlelaayiVyn,o,,ccrogearlalbaedpuc,lhtaq,,ruoyer:gsatinoinze, , Finally, students can choose from their repertoire of graphs the representation model that is best for their data. They need to select an appropriate scale and include all necessary titles and labels so the data can be easily read by other people. About the Lessons The following lessons allow students to apply their conceptual knowledge and skills learned throughout the Data unit as they carry out their own survey and display the data. Students create their own survey questions, collect and organize the data, and then display the data in an appropriate graph. Students share each other’s data, pose questions, and discuss and analyze the results. Data 165
14Lesson Analyzing Survey Questions Teacher Possible Learning Goals Look-Fors • Analyzes survey questions to understand what makes a good question • Creates survey questions and determines categories for the responses Materials: • Reads survey questions and explains or shows that the categories in the graph Digital Slide 49: Survey Question reflect people’s responses Do you like primary colours? • Determines categories that could be used as responses to survey questions Scholastic Canada GR3 BC Patterns & Relations Slide 3rd Pass • Creates questions to collect data Digital Slides • Explains what makes a good survey question November 9, 2021 49: Minds On (15 minutes) Digital • Review what students know about survey questions. Ask what survey questions Survey Question, were used in previous lessons and why they were asked. Explain that people BLM 35: Survey carry out surveys to answer questions and make decisions. Questions • Discuss what makes a good survey question and how to choose the categories Time: 50 minutes that reflect how people might respond. 56 © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 BLM 35: Survey Questions • Share Digital Slide 49. Ask them if it is a good survey question and whether Scholastic Canada GR3 BC Patterns & Relations Do you like Do you like Do you have Do you like the responses would answer questions. (e.g., It’s okay but doesn’t get us a Reproducibles summer? sports? a pet? school? lot of information.) Ask them what would make a better question and why. November 9, 2021 (e.g., What is your favourite colour?) Have them turn and talk and share what categories they might use for the new survey question. Do you have Do you like Do you like TV? Do you like a hobby? chips? music? • Discuss why this question might be important to ask. (e.g., knowing what 4th Pass Do you play Do you have Do you like Do you have a colour of paper to order, deciding what colour to paint a room, etc.) a musical a sister? skating? favourite book? instrument? Working On It (15 minutes) • Students work in small groups or in pairs. Tell students that they are going to get a survey question and make it better. (Give each pair or group a pre-cut survey question card from BLM 35: Survey Questions.) They can think about why it is important to ask the question, who the audience might be. They can change the wording of the question and choose suitable categories for possible responses. • Assign each group one of the survey question cards and have them create categories for the new survey question. Explain that they will share their original survey question, their ‘new and better’ question, and the categories they would use to collect their responses. • When they are finished, have individuals or pairs decide on a survey question that they would like to ask their peers, including possible responses. (Students will use this question in the next lesson.) 166 Patterns & Relations/Data & Probability
Materials: Differentiation BLM 35: Survey • For students who need language support, consider working in a small group Questions to assist with creating new survey questions and the categories they could use 56 © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 BLM 35: Survey Questions with the questions. Scholastic Canada GR3 BC Patterns & Relations Do you like Do you like Do you have Do you like • Have students select a question based on their interests. Reproducibles summer? sports? a pet? school? November 9, 2021 Assessment Opportunities Do you have Do you like Do you like TV? Do you like Observations: Conference with students about the survey questions they a hobby? chips? music? want to use in class to collect data: 4th Pass Do you play Do you have Do you like Do you have a – Is it a meaningful question that will generate data? a musical a sister? skating? favourite book? – Do they have a reason why the data might be helpful? instrument? – Are they considering their audience? – Can they select reasonable categories for the data? – Do they choose too many categories? Not enough? Conversations: Pose some of the following prompts: – Why might you ask this question? How could this information help you understand the situation better? – How could you word your question so you are getting more than ‘yes’ or ‘no’ as answers? – Think about the students in the class who will be answering this question. How do you think they will answer the question? Do your categories include all of the different ways? – Do you think you have too many categories? Can you cluster any of them together? What category could you make for people who don’t like any of the given choices? Consolidation (20 minutes) • Meet as a class. Have each group share their original and improved survey question. Ask each group how the question they changed could help to make decisions. • Review what makes a good survey question. Co-create an anchor chart. • Discuss how students decided which categories they should use to categorize the data. Ask how they could create a category for an answer they hadn’t anticipated. • Explain to students that, over the next few days (in the next lesson), they will be using the survey question that they developed to collect data and make their own graphs. • You may decide to give students an opportunity to refine their questions based on the class discussions. Further Practice • Independent Practice in Math Journals: Give students a different question from BLM 35 and have them create a better question, including possible responses. They can also explain why this information could be helpful for making decisions. Data 167
15Lesson Collecting and Organizing Data Teacher Possible Learning Goal Look-Fors • Conducts survey using their designed question and collects and organizes data Materials: • Conducts survey so every person is asked once and only once • Selects and uses an appropriate tool (e.g., tally table) to collect and organize Digital Slide 50: What’s the Data? their data Favourite Drinks of Students in Grade 3 Favourite Sports of Students in Our Class • Organizes data based on categories Drink Votes Sport Tally Number of Students Minds On (10 minutes) Apple Juice Hockey 6 • Explain to students that they are going to carry out their surveys. Ask what Pepsi Soccer 5 questions they have before they begin. Coke Basketball 4 • Discuss what they need to consider before carrying out their surveys. (e.g., an Milk Gymnastics 2 appropriate way to record and organize their data; how to keep track of the Favourite Lunch of Students in Grade 3 How Students in Our Neighbourhood students who have been surveyed, etc.) Get to School Food Items Tally Marks • Show students Digital Slide 50: What’s the Data? and ask them what they see. Method of Travelling Number of Children Discuss the various tables, what features they have in common, and which Burger Walking 8 are different. Pizza Car 9 • Ask how they can determine the total number of participants in the surveys. Fried Chicken Bus 4 Ask how they are going to make sure that they have asked the question only once to each person. Hot Dog Cycle 5 • Explain to students that they are going to use the survey question they created Train 1 in the previous lesson and collect data. They can survey all people in the class. Taxi 3 • Explain that their first job is to decide how they will collect and organize their Scholastic Canada GR3 BC Patterns & Relations Slide 3rd Pass Digital Slides data. They can choose from one of the types of tables in Digital Slide 50. Once November 9, 2021 50: What’s they have decided and show you, they can begin their survey. Explain that if their survey technique is not working, they may have to revisit the conditions Digital surrounding their question so they can make adjustments. the Data? Working On It (40 minutes) Time: 60 minutes • Students independently choose and create a way to organize the data they are going to collect. • Once their organizer is ready, students conduct their surveys in the class. You may decide to have half the class ask questions to the other half of the class and then switch. Students can then ask their survey questions of the people that are in their half of the class. • As students complete their survey, they can check over their data to ensure they asked everyone. 168 Patterns & Relations/Data & Probability
Differentiation • If students are struggling to create an organizer on their own, meet with a small group to help them choose an appropriate table. Students can ask their survey question to one person in the small group to ensure their process works. • You may have students limit the number of people they include in their survey to 10 people. Assessment Opportunities Observations: Pay attention to how students are collecting their data: – Are they using their table correctly? – Are they using tally marks and recording them properly? – Do they check to ensure they have asked everyone and don’t ask anyone twice? – Do they remember to include themselves in the survey? Consolidation (10 minutes) • Meet as a class. Discuss how the process of collecting and organizing the data turned out and any challenges they had. Have students share some of the things they learned today. • Review some of the ways in which they collected and organized their data for their survey question. Ask what they might do differently if they were collecting data again. Data 169
16Lesson Displaying Data: Creating Graphs Teacher Possible Learning Goal Look-Fors • Displays data in a graph with appropriate titles and labels Materials: • Selects an appropriate graph to display their data • Accurately labels graph with appropriate title and labels Digital Slide 51: Graphs of Favourite Things • Explains or shows the purpose for the features on their graph Favourite Vegetables of Students in Grade 3 Favourite Snacks of Students in Grade 3 Minds On (15 minutes) 5 Popcorn 4 • Explain to students that they are going to create a graph for the data they 3 Crackers 2 collected in Lesson 15. They can choose a type of graph that they think best 1 Snacks Trail Mix suits their data. 0 Cheese • Ask students what they need to consider when selecting a graph. Broccoli Green Beans Pepper Cucumbers None • Show students Digital Slide 51: Graphs of Favourite Things and ask them what they Vegetables see (e.g., different graphs). Fruit 123 4 5 0 Number of Votes • For each graph, have students explain/review the following: Favourite Shapes of Students in Grade 3 – type of graph Square – important features of each graph Triangle – the chosen scale Circle – why you might use each type of graph Trapezoid 1 shape = 2 students • Students can turn and talk to their partner about what type of graph on Scholastic Canada GR3 BC Patterns & Relations Slide 3rd Pass Digital Slide 51 they think best suits their data. Digital Slides November 9, 2021 51: Graphs Working On It (20 minutes) Digital • Students choose and create a type of graph to represent their data. • Once their graph is complete, have students record a way in which the data of Favourite Things, could be helpful for making a decision. They can print this on a separate strip BLM 36: Pictograph of paper and attach it to the back of their graph. Template, BLM 29: Differentiation Bar Graph Template • If students are struggling to create their own graph, give them a pictograph Time: 55 minutes template (BLM 36) or bar graph template (BLM 29) to use. BLM 36: Pictograph Template • Consider meeting with a small group to help them choose their graphs. Our Favourite Discuss the necessary features that need to be on the graph. BLM 29: Bar Graph Template • For students who need more of a challenge, encourage them to consider using Pictograph a scale that represents many-to-one correspondence if it is appropriate for © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 57 their data. Scholastic Canada GR3 BC Patterns & Relations 4th Pass Reproducibles © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 November 9, 2021 45 Scholastic Canada GR3 BC Patterns & Relations 4th Pass Reproducibles November 9, 2021 170 Patterns & Relations/Data & Probability
Assessment Opportunities Observations: Pay attention to how students are graphing their data: – Are they checking to see whether their graph will accommodate all of the data before filling it in? – Do they represent all of the categories that are in their table? – Are they including appropriate titles and labels? – Can they think of some meaningful questions to ask about the data? Conversations: Meet with a small group if they are having difficulty including all graph features. Pose some of the following prompts: – Compare your graph to your frequency table. Do they both have the same categories represented? – How can you prove that the number for this category on your graph matches the number on your table? – How can you tell the reader what your graph is about? – What does each of these circles represent? How can you let the reader know? Consolidation (20 minutes) • Hang up all students’ graphs and have a gallery walk. Students can move freely from graph to graph to see their peers’ work. • Meet as a class. Discuss how they created their graphs. Ask what part was most challenging about creating their graphs. Ask how they might represent their data differently if they were to do this activity again. Data 171
17Lesson Analyzing and Interpreting Data Teacher Possible Learning Goal Look-Fors • Asks and answers questions about data presented in a variety of graphs • Uses features of graphs (e.g., title, labels) to clarify the meaning of the data • Describes information on a graph in its context • Formulates questions from the data in the graph to ask peers • Answers questions about the presented data Materials: Minds On (15 minutes) Digital Slide 51: Graphs of Favourite Things • Explain to students that they are going to analyze the graphs they created in Favourite Vegetables of Students in Grade 3 Favourite Snacks of Students in Grade 3 Lesson 16. 5 Popcorn 4 • Ask what kind of observations they can make from ‘reading’ a graph (e.g., read 3 Crackers 2 individual parts of the data, compare parts of the data, analyze the whole data). 1 Snacks Trail Mix 0 • Show students Digital Slide 51: Graphs of Favourite Things. Explain that in the Cheese Broccoli Green Beans Pepper Cucumbers None last lesson, they studied the features of the graphs shown on that slide. This Vegetables time they are going to analyze the information in the graphs. Fruit 123 4 5 • Have students turn and talk to a partner. They can think of one statement 0 Number of Votes about one of the graphs and one question that they could ask about it. They Favourite Shapes of Students in Grade 3 can choose one of the graphs or you can assign the graphs to different groups, Square so all graphs are covered. Triangle Circle • Discuss some of the students’ responses. Have them prove that their statement Trapezoid 1 shape = 2 students is evident in the graph. Ask why they think their question is reasonable. Scholastic Canada GR3 BC Patterns & Relations Slide 3rd Pass Digital Slides November 9, 2021 51: Graphs Digital of Favourite Things, different coloured sticky notes Time: 60 minutes Working On It (20 minutes) • Hang up students’ work around the room. Explain that they are going to ask and answer questions about each other’s data. They can select any questions they feel are meaningful. • Give each pair two sticky notes of one colour and two sticky notes of a second colour. Have pairs visit two graphs other than their own and write questions that could be asked about the graph on one colour of sticky notes. They place those sticky notes on the graph. • Once the sticky note questions are placed, have students answer two questions that have been posted on different graphs. They can record their answer(s) on the other colour of sticky notes they have and post their answers beside the questions. 172 Differentiation • For students who need language support, have a list of fill-in-the-blank question stems they can use to help ask questions about graphs. Meet with a small group so they know how to use them. Patterns & Relations/Data & Probability
First Peoples Assessment Opportunities Principles of Learning Observations: • Pay attention to the questions asked: – Do students understand the information in the graph? – Are they posing simple questions (e.g., How many people like red?), or do their questions involve making comparisons? (e.g., How many more people like red than blue?) – Are the questions meaningful for understanding the data? • Pay attention to the answers given: – Are students using information from the graph to answer the question? Conversations: If students are struggling with creating questions, remind them of the questions the class suggested in the Minds On. Consolidation (25 minutes) • Have a gallery walk so students can read their peers’ questions and answers. • Revisit each graph one more time as a class. Have the creators of each graph reveal what question they think their graph answers and explain how the information helps to make decisions. • Building Growth Mindsets: Review and discuss some of the activities that students have done in Data unit. Ask students to share the most interesting thing they learned. Ask what they still find challenging and confusing. Make a list of some of their ideas. Ask what they think they could do to practise these concepts and add these to the list. Over the next few weeks, periodically revisit the list and engage in one of the suggested activities or another activity that will offer practice. In this way, students see that the learning does not just end when a unit is done. They can set goals and continue practising skills so they become more confident mathematicians who are on a lifelong journey. This supports the First Peoples Principles of Learning that learning involves patience and time. Further Practice • Reflecting in Math Journals: Have students reflect in their journals about their learning throughout the Data unit. Have them use pictures, numbers, and/or words to explain what they have learned through all the activities and investigations they have done. Data 173
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