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Number and Financial Literacy Front Matter Content Page Contents 1 2 Math Place Components for the Number and Financial Literacy Kit 4 11 Number and Financial Literacy Overview 12 15 Getting Started 21 Embedding Number Sense Throughout the School Day Introducing Social-Emotional Learning Skills: Your Fantastic Elastic Brain Introducing Number Sense



Contents 2 Math Place Components for the Number and Financial Literacy Kit 4 Number and Financial Literacy Overview 11 Getting Started 12 Embedding Number Sense Throughout the School Day 15 Introducing Social-Emotional Learning Skills: Your Fantastic Elastic Brain 21 Introducing Number Sense 27 1: Quantities and Counting to 500 98 2: Multiplication and Division 206 3: Quantities and Counting to 1000 256 4: Addition and Subtraction 380 5: Financial Literacy 422 6: Fractions 487 References

Math Place Components for the Number and Financial Literacy Kit Read Aloud Texts ODNIGLYITAL Five Read Aloud texts are included, setting a whole-class focus to build social-emotional learning skills, and to provide realistic contexts for the math concepts. Big Book The Number and Financial Literacy big book (with an accompanying digital version and 8 little book copies) is used to develop spatial reasoning and to create a context for math problem solving. Math Little Books Two math little books (8 copies of each) along with one digital-only little book are used in guided math lessons with small groups for focused and differentiated instruction tailored to the needs of the students. They also offer opportunities to observe and assess students as they verbalize what they visualize, and apply math concepts in problem-solving situations. 2 Number and Financial Literacy

Teacher’s Guide A Teacher’s Guide supports teachers in building students’ conceptual understanding of math by providing hands-on learning experiences, using a variety of concrete materials and tools. This allows students to apply all of the mathematical processes as they solve problems. • Lessons include an About the Math section, which incorporates recent research to explain math concepts and why they are so critical to students’ current and future learning. • Detailed three-part lesson plans include rich problems for the students to solve and many opportunities for collaborative learning, communication of ideas, independent problem solving, and practice. The consolidating prompts and discussions are designed to connect students’ mathematical thinking and bring clarity to the Big Ideas. • The three-part lessons offer suggestions on how to differentiate the learning to meet the specific needs of all students. • Activities develop mental math strategies based on conceptual understanding and many ‘visualization’ activities are included to support and develop students’ spatial reasoning skills. • Lessons support assessment for learning by offering suggestions on how to assess through observations, conversations, and products. There are also ‘Teacher Look-Fors’ to further support assessment and evaluation, and to serve as a guide for co-constructing success criteria with your students. • Further Practice and Reinforcement activities offer students the opportunity to practise newly acquired skills. • Math Talks provide support for posing comments and questions that promote interactive talk. • Blackline Masters (BLMs), such as number lines, are included in the book of Reproducibles and can easily be used to prepare for lessons. There are also some graphic organizers, which help students record and organize their observations and mathematical thinking. In addition, all BLMs are available digitally on the Teacher’s Website. Teacher’s Website A variety of online resources, including Digital Slides, are available to support instruction and students’ problem solving. Also included are a digital big book, modifiable Home Connections letters, and Observational Assessment Tracking Sheets. Overview Guide A digital Overview Guide provides support for teaching all strands of Math Place, Grade Three. The guide offers background information including the role of problem solving and spatial reasoning in mathematics, and how to build social-emotional learning skills throughout the lessons. It includes assessment strategies and ways to differentiate to meet the needs of all students in your classroom. In addition, the Overview Guide outlines and explains the various high-impact instructional approaches used in the resource. 3

Number and Financial Literacy Overview What Is Number Sense? Number sense can be defined as “a person’s general understanding of number and operations along with the ability and inclination to use this understanding in flexible ways to make mathematical judgments and to develop useful strategies for handling numbers and operations” (McIntosh, Reys, & Reys, 1992, p. 3). Kalchman, Moss, and Case explain that this includes “(a) fluency in estimating and judging magnitude, (b) ability to recognize unreasonable results, (c) flexibility when mentally computing, (d) ability to move among different representations and to use the most appropriate representation” (Kalchman, Moss, & Case, 2001, p. 2). Finally, Hilde Howden notes that number sense “develops gradually as a result of exploring numbers, visualizing them in a variety of contexts, and relating them in ways that are not limited by traditional algorithms” (Van de Walle & Lovin, 2006a, p. 42). Number sense is not only complex, encompassing many abilities, but takes time to develop, beginning in the early years and extending throughout students’ lives. As mathematicians, students need learning opportunities that help them perceive mathematics as more than a set of rules and procedures, but as conceptual ideas that make sense. They require opportunities to flexibly interact with numbers based on conceptual understanding. Students need to see that number sense permeates all strands, connects to other subject areas, and, most importantly, matters to their everyday lives. Including Algebra with Number Sense This resource also deals with the concepts of algebra that grade three students investigate, including an understanding of variables, expressions, and equalities and inequalities. Since number sense is about number relationships, understanding equality and inequality is critical, especially as students create equations to match their representations of the operations. Research indicates that many students in grades one to six have misconceptions of what the equal sign represents, assuming it means “the answer is” rather than indicating a balance on either side of the equation (Carpenter, Loef Franke, & Levi, 2003, p. 9). Integrating algebra throughout the resource is intended to help students start off with the correct interpretation of the equal sign and internalize its meaning as they continue in their future math education. While the mathematical modelling process falls within the Algebra strand of the curriculum, it is embedded throughout Math Place, including in the Number and Financial Literacy units, since problem solving forms the foundation of all mathematical learning. Students move through the process of mathematical modelling as they create and adapt models to solve real-life problems, make decisions, or deepen their understanding of math concepts. 4 Number and Financial Literacy

They use critical and creative thinking and apply social-emotional learning skills and the mathematical processes, as they develop, test, and refine the model. This is a fluid, iterative process, in which students move back and forth, and return to the components as they refine their model. The four components of the mathematical modelling process are: • understand the problem; • analyse the situation; • create a model; • analyse and assess the model. Students in the primary grades can be guided through the process, making them aware of their own thinking and ways of organizing, and channelling their approaches to solving problems. Coding concepts, which are also included in the Algebra strand, are also embedded throughout other strands in Math Place. Students learn coding concepts without the use of a computer, which develops the logical thinking necessary for reading and creating codes for a computer. For example, in Number, the counting principles and the properties of operations can be reinforced as students investigate how the order of a series of instructions can affect the desired outcome. What Is Financial Literacy? Financial Literacy is a critical, lifelong skill and a dedicated strand throughout the elementary math curriculum. Since the related concepts and skills strongly connect to other strands in math, especially Number, Financial Literacy is included with the Number strand in this resource. The goal is for students to acquire “the skills and knowledge to take responsibility for managing their personal financial well-being with confidence and competence” to make informed decisions (Ontario Ministry of Education, 2020). In the primary grades, students develop an understanding of the value of coins and bills and how to represent these values. The Importance of Multiple Representations The mathematical process of representing is evident as students make their thinking visible. Using multiple representations allows students to make connections among concepts and offers differentiation for students who may use different approaches to solving problems. Small notes that “the more flexible students are in recognizing alternative ways to represent mathematical ideas, the more likely they are to be successful in mathematics” (Small, 2009, p. 28). Providing opportunities for students to represent their thinking in many ways and to verbally explain their thoughts to peers allows all students to expand their repertoire and experiment with alternate models. “As children actively reflect on their new ideas, they test them out through as many different avenues as we might provide. […] As this testing process goes on, the developing ideas get modified, elaborated, and further integrated with existing ideas. When there is a good fit with external reality, the likelihood of a correct concept being formed is good” (Van de Walle & Lovin, 2006a, p. 8). 5

A Balanced Approach A conceptual understanding of mathematics allows students to develop a deep understanding of math concepts, which they can apply to a variety of real-world problems. Marian Small cites research by Carpenter and Lehrer that explains conceptual understanding as “the development of understanding not only as the linking of new ideas to existing ones, but as the development of richer and more integrative knowledge structures” (Small, 2009, p. 3). A balanced math program includes the implementation of various high-impact instructional practices. As noted in the curriculum, “the thoughtful use of these high-impact instructional practices—including knowing when to use them and how they might be combined to best support the achievement of specific math goals—is an essential component of effective math instruction” (Ontario Ministry of Education, 2020). High-impact practices in Math Place lessons include: learning goals, success criteria, and descriptive feedback; direct instruction; problem-solving tasks and experiences; the use of a variety of tools and representations; and small-group instruction using flexible groupings. Math conversations are critical, and throughout the lessons are several math talks that give students opportunities to reason and prove their own ideas and to hear and debate the ideas of others. Students see math from other perspectives at the same time as they build their own mathematical understanding and feelings of confidence. It is important for students to develop basic skills and proficiency within the different strands; for example, becoming proficient with skip counting as they determine the total number of tally marks in data. Practice plays a key role in students internalizing skills and being able to apply them independently in new situations. By using concrete materials and discussing their ideas during math talks, students develop mental math strategies that help them visualize concepts and gain automaticity of number facts and calculations. Marian Small also suggests using “rich tasks embedded in real-life experiences of children, and with rich discourse about mathematical ideas” (Small, 2009, p. 3), which aligns with Indigenous teaching that emphasizes “experiential learning, modelling, collaborative activity and teaching for meaning” (Beatty & Blair, 2015, p. 5). Gaining Automaticity with Operations and Number Facts Many experts, such as Cathy Fosnot, John Van de Walle, Marian Small, Alex Lawson, and Doug Clements, have written about learning calculations by applying strategies based on number relationships, rather than on memorization. In their works, they describe their rationale for this approach, the common strategies that students often acquire, as well as some supporting activities and games. Alex Lawson states that, “over time and with much experience and focused practice, children’s addition and subtraction calculations to 20 will become automatic” (Lawson, 2015, p. 21). She adds that this is not accomplished by memorizing isolated facts, but by working with various strategies and focusing on the relationships among the numbers. Clements and Sarama add that practice should be distributed over time and occur in a context of “making 6 Number and Financial Literacy

sense of the situation and the number relationships” (Clements & Sarama, 2009, p. 83). They further stress that using multiple strategies helps to build number sense. The focus is on learning and applying several strategies to internalize number facts and to mentally solve one-, two-, and three-digit equations as efficiently as possible. Over time, we want students to be able to select the strategy that is most appropriate for them and the types of problems they are solving. This takes a great amount of time and practice, beginning in grade one and continuing in the grades that follow. Developing Mental Math Strategies By representing operations with concrete objects and visuals, and discussing their findings in Math Talks, students create and may internalize a mental image that can later be retrieved for solving new problems. In grade three, it is valuable to nurture the development of mental strategies so students can gain more proficiency making calculations without using paper or pencil. Once students can automatically recall some number facts, they can use them to make new calculations that are related in some way. For example, if 4 + 4 is known, then 4 + 5 can be derived from knowing that 5 is 1 more than 4. As students begin to work with two- and three-digit numbers they can apply that same strategy. For example, when calculating 400 + 500, students may solve by adding 400 + 400 and then adding one more 100, thus using the doubles + 100 strategy, decomposing (500 = 400 + 100), as well as their understanding of place value (the 4 and 5 represent hundreds). Math Talks Numerous Math Talks linked to lessons throughout this resource support the understanding of math concepts through purposeful discussion, help to reinforce and extend the learning, and offer opportunities for further investigation. Many of the Math Talks support students in developing computational and mental math strategies. Sample scripts are included with many of the Math Talks and are intended to help you anticipate student strategies, as well as to provide sample questions and talk moves that you might use during your own Math Talks. (For more on Math Talks, see the Overview Guide.) Math Talk routine for ‘number talks’: Gather students together as a class or small group. Write the problem on the board for all to see. Tell students to show you that they’re thinking about the problem by holding a fist closed in front of their chests and to put up a thumb when they have a solution. If they have more than one solution they can raise another finger for each one. Explain that they are not to shout out the answer or raise their hand so that all mathematicians can think and solve the problem on their own. In order to maximize student participation and active listening, you can strategically integrate the following ‘math talk moves’ into all discussions. (Adapted from Chapin, O’Connor, & Canavan Anderson, 2009) 7

Math Talk Moves Chart Example Talk Move Description Wait Time Teacher waits after posing a question before – Wait at least 10 seconds after posing a calling on a student so all students can think. question. – If a student has trouble expressing, say “Take your time.” Repeating Teacher asks students to repeat or restate “Who can say what said in their what another student has said so more people own words?” hear the idea. It encourages active listening. Revoicing Teacher restates a student’s idea to clarify and “So you are saying…. Is that what you were emphasize and then asks if the restatement is saying?” correct. This can be especially helpful for ELLs. Adding On Teacher encourages students to expand upon a “Can someone add on to what proposed idea. It encourages students to listen just said?” to peers. Reasoning Teacher asks students to respond to other “Who agrees? Who disagrees?” students’ comments by contributing and justifying their own ideas. “You agree/disagree because .” (sentence starter) Student and Teacher Talk Moves Meaningful classroom discussions about math help students improve their understanding of mathematical concepts. They also help students develop flexible thinking and problem-solving skills as the conversations expose them to a variety of strategies and solutions. Talk moves help the teacher and students have meaningful conversations about math and are often used during the consolidation phase of a lesson as well as during Math Talks. Student talk moves enable a student to label, explain, reason, justify, compare, and question. Teacher talk moves help the teacher monitor understanding and misconceptions and consolidate the intended learning. Below is a list of possible talk moves. If you are already using a common math talk language in your school, continue to use the terms that work for you and your students. Math talk moves have to be introduced, modelled, prompted, and reinforced in order for students to use them consistently in a meaningful way. Start slowly and introduce one or two at a time. Post the prompts in the area where you have your math discussions. Include a visual with each prompt to support readers. Possible Student Talk Moves: I noticed . My strategy is . I did/think because . I agree/disagree with because . . I agree with and would like to add 8 Number and Financial Literacy

I think that is saying . I don’t understand I wonder . Can you explain it another way? I did it another way. I My strategy is like . This reminds me of . ’s because . . Possible Teacher Talk Moves: Please explain your thinking. Tell me more. How did you figure that out? Can you explain ’s strategy or solution? Are you saying ? Can you give us an example? I’ll wait for everyone to think about it for a minute before we share. Would someone like to add to this? Did anyone think of the problem in a different way? What other strategies could be used? Would this work with other numbers? Would this always work? Has anyone changed their thinking about this? Explain to your partner . Does anyone have a question about ’s solution? Did anyone make a great mistake that they learned from today? made a great mistake that we can all learn from today. Why is important? Let’s record what we learned about on our anchor chart. sabeStwttcLnBeenhrtaehuudaucronaeogdcoiwlkrnuhgeudbnaeogalnrieeinyavrhnbtskgseguoglw.ereusntSiShdetttmeohhkrdetctoeioholmdiuarlamesegttltia-seolhpaEietksnrnmasbaoetayks.enmooeryttinispsimo,sktns,sea, l Building Social-Emotional Learning Skills in Mathematics Math Place offers many opportunities to build and reinforce social-emotional learning skills beginning with three introductory lessons, which can be used at the beginning of the year to introduce the context and criteria. The pertinent messages can be regularly reinforced throughout the year using the prompts and suggestions that are embedded in many of the Number and Financial Literacy lessons. The three lessons include a Read Aloud, Your Fantastic Elastic Brain, to introduce the skills in context; a Thinking Like a Mathematician lesson, which is included in the Overview Guide; and Introducing Number Sense, which shows connections between math, number sense, and students’ lives. Following are just a few ways that Math Place helps students develop social- emotional learning skills and positive attitudes toward mathematics. • P roviding challenging problems to all students with the belief that all students are capable mathematicians. 9

Materials: • U sing Math Talks to build computational skills rather than worksheets or BLM 1: Represent timed drills that cause math anxiety. Your Number • U sing Math Talks to help students see the creativity and flexibility in math as they develop number sense. • H elping students see the value and application of math through real-life connections and authentic tasks. • P roviding opportunities for students to build confidence through collaboration. • P roviding questions and prompts that value processes rather than merely correct answers. • E xplicitly teaching students that their brain can stretch and grow as they make mistakes and tackle new challenges. • Including suggestions in several of the lessons on how to build social- emotional learning skills and reinforce positive attitudes toward math. Assessment Opportunities Assessment for learning is necessary so that you can determine goals for moving students forward mathematically. Observing students at work and analysing student work provides you with valuable information about students’ understanding and application of mathematical concepts. Student conferences/ math interviews are often necessary in the primary grades, particularly when you have unanswered questions about a student’s progress. Use BLM 1: Represent Your Number as an assessment check-in that can be done at various times throughout the year to monitor your students’ growth in number sense. It can be done whole class, in small groups, or in a one-to-one interview. You might assign students different numbers to ensure that they are completing the work independently. Assigning different numbers is also a way to differentiate for students. It is advisable to choose numbers that your students have previously worked with independently. You may instruct students to challenge themselves by choosing a higher number that they feel comfortable representing after they’ve finished representing the assigned number. 10 Number and Financial Literacy

Getting Started The sequence of units and lessons follows a general developmental trajectory of how students tend to acquire knowledge and skills. The sequence can be altered to suit your existing program; however, the lessons designed for earlier in the year should precede those designed for later in the year. Below is an overview of the included units and suggested timing during the school year. Unit Description 1 Quantities and Counting to 500 2 Multiplication and Division 3 Quantities and Counting to 1000 4 Addition and Subtraction 5 Financial Literacy 6 Fractions • There are two Quantity and Counting units (Units 1 and 3). One suggestion is to teach both units in the fall, so students have the understanding they need of numbers to 1000 in order to complete the other units. • There is one unit on Multiplication and Division (Unit 2). Students can focus on this unit after they have completed Quantities and Counting to 500. • Units 1, 2, and 3 can be taught in the fall/early winter months, interspersed with units from other strands (e.g., Spatial Sense, Algebra). • There is one unit on Addition and Subtraction (Unit 4), which focuses on developing various strategies for adding and subtracting numbers to 1000, including using a standard algorithm. Mental math strategies are interspersed throughout the unit so students can connect them to the strategies they represented using concrete materials and drawings. It would be beneficial to teach this unit after the Quantity and Counting units. • The units on Financial Literacy and Fractions (Units 5 and 6) can be used at any time throughout the year, although it is best if students have had some exposure to quantity and counting first. The Financial Literacy unit involves applying many of the number concepts and skills that students have learned earlier in the year. It is best to teach this unit in the spring. 11

Embedding Number Sense Throughout the School Day Developing number sense, including an ability to work flexibly with numbers, takes time and countless experiences. The routines below can be used daily as warm-up routines to practise counting and other number sense concepts. The routines you choose should respond to the current needs of your students. The goal of these warm-ups is to help students improve their counting, computational, and reasoning skills so that they can apply their number sense when solving problems. Reading Numbers Read a Number: In pairs, students use playing cards (values 2–9) to create a three-digit number for their partners. The partner who did not create the number attempts to read the number out loud correctly. Switch roles. The other partner creates the number for the other partner to read. Read a Number Variation (Fractions): In pairs, students use two-sided counters (maximum of 20) to create fractional amounts (e.g., student displays 20 counters, with 10 showing yellow and 10 showing red). The partner who did not create the fractional value determines the value and reads the number out loud correctly (e.g., one half of the counters are red). Switch roles. The other partner creates the fractional value for the other student to read. Counting Routines and Activities Sound Off: While students are lined up waiting to go somewhere, have them sound off, counting forward by 1s, beginning at any chosen number (e.g., 340 … 341, 342, 343, etc.). As they say their number, students can crouch down. On other occasions, have students count forward by 2s, 5s, 10s from any given starting point. You can also have them count forward by 25s from any multiple of 25. Sound Off (Counting Forward and Backwards): As students are lined up, have them skip count forward by various amounts to 100. Then have them count backwards by 2s, 5s, and 10s, using multiples of 2, 5, and 10 as the starting points. They can also count forward and backwards by 100s (up to 1000), using any number as a starting point. Calendar Counting: Ask, “How many more days until...? How many days are in the month...? How many days ago did…?”(count by 7s; count backwards; count the days of the year using 1s, 10s, and 100s) Attendance Routine: Assign a student to count heads or to total the names on the sign-in board. Ask, “How many students are here? How many students are absent?” 12 Number and Financial Literacy

Would You Rather? Write a question such as, “Would you rather have 3 toonies or 13 quarters?” Discuss and have students justify their choices. Number Sense Routines and Activities Number Patterns: Show a number pattern each day (e.g., 123, 133, 143) and ask students to extend it. Record their ideas in various ways (on a number line, using base ten blocks, etc.). Which One Doesn’t Belong? Project four images of pictures, numbers, etc. Students figure out which one doesn’t belong with the other three and justify their choices (there should be at least one reason why each image doesn’t belong). See the Which One Doesn’t Belong? website (wodb.ca) for many ideas and examples. Guess My Number: Give clues, such as, “I’m thinking of a number that is more than 300 but less than 400. What might it be?” As more clues are progressively given, students will be able to narrow down the number. Students can refer to the classroom place value chart or counting charts to 1000 as they solve the problem. What Might My Number Be? Choose a number for the day and print it on a piece of chart paper. Throughout the day, students can give meaning to the number by adding different representations of it on the chart. For example, if the number is 320, students may draw 320 cents represented by 3 loonies and two dimes, 320 units as represented by 3 metres and 20 centimetres, or 320 with base ten blocks represented by 3 flats and 2 rods. As the year progresses, you may wish to try using fractional amounts as the number of the day. Emphasize the concept that a number takes on meaning when a unit or description is added. Estimation Jars: Regularly display an estimation jar filled with items. Students can examine the jar and record their estimates throughout the day/ week. At the end of the time period, meet as a class, study the estimations, and then count the actual number of objects. Vary the size of the jars/containers and the number and type of objects. True or False? Pose equations or problems that students must solve to decide if they are true or false, and then justify their answer (e.g., 18 + 13 + 25 = 15 + 24 + 20; 5 quarters is enough to buy a toy that costs $2.75; 345 is greater than 435, etc.). Here’s the Answer. What’s the Question? Write a number on the board. Ask students to create a word problem or equation that has that particular answer. Find the Math: Project an image or show a picture from a book or calendar. Ask students to look for mathematical situations in the picture, including but not limited to things that they can estimate or count. Largest Number Wins: In pairs, each student uses playing cards (values 2–9) to create a three-digit number, by drawing three cards, one at a time. Students arrange the cards to make the largest number possible. Students compare numbers to determine who has the number with the largest value. The goal can be changed to making the smallest possible number. 13

Number Analysis: Write three numbers on the board and ask questions that prompt students to analyse the numbers. For example: Numbers: 327 372 786 Questions: • Which number is the greatest? Least? How do you know? • Which two numbers are closer together? How do you know? • What does the 7 represent in each number? • Name a number that is less/more than all of these numbers. • Add two of the numbers. What strategy did you use? • What’s the difference between the least and the greatest number? • How could you round these numbers? • What else can you tell us about these numbers? • What other questions can we ask? 14 Number and Financial Literacy

Introducing Social- Emotional Learning Skills: Your Fantastic Elastic Brain Language Introduction to the Read Aloud Curriculum Expectations The Read Aloud book Your Fantastic Elastic Brain introduces students to the social-emotional learning skills that will help them to become capable and Math confident learners, and to view math as an interesting, relevant, and creative Curriculum subject. During the reading of the book, students apply their literacy strategies Expectations such as making connections, inferring, and analysing, to understand how the brain works and the important functions that it carries out in our everyday lives. After the reading, you can revisit the text to co-create an anchor chart of the six social-emotional learning skills that students will develop throughout the year in math class and in school generally. The book can also initiate a discussion about students’ personal attitudes and levels of self-confidence in math. This helps nurture students’ belief that they can succeed in math with effort and patience. Oral Communication • 1 .3 identify a variety of listening comprehension strategies and use them appropriately before, during, and after listening in order to understand and clarify the meaning of oral texts • 1 .4 demonstrate an understanding of the information and ideas in a variety of oral texts by identifying the important information or ideas and some supporting details • 1.6 extend understanding of oral texts by connecting the ideas in them to their own knowledge and experience; to other familiar texts, including print and visual texts; and to the world around them Reading • 1.5 make inferences about texts using stated and implied ideas from the texts as evidence • 1.8 express personal opinions about ideas presented in texts Social-Emotional Learning (SEL) Skills and the Mathematical Processes • A 1. apply, to the best of their ability, a variety of social-emotional learning skills to support their use of the mathematical processes and their learning in connection with expectations in the other five strands of the mathematics curriculum 15

PMraotcheesmseast:ical Assessment Opportunities Problem solving, crreeoafmlsemocntuiinnnggic, aactnoindngnpercotviinngg,, Observations: Note each student’s ability to: – Make connections between the feelings of the girl in the story and their own feelings about math and other subjects – Synthesize the message of the story Materials: Read Aloud: Your Fantastic Elastic Brain Written by JoAnn Deak Illustrated by Sarah Summary: This book describes the different parts of the brain and how they Ackerley work to help people to develop, grow, and learn. It also highlights what people Text Type: Non-fiction: can do to help their brains grow. The text emphasizes the idea that the brain is Explanation–Report elastic and can change with input and practice, thereby encouraging students Time: 2 0–30 to acquire a growth mindset rather than a fixed mindset about being able to learn. minutes NOTE: Select the prompts that best suit the needs and interests of your students. All of the During Reading prompts are meant to be used after you have read the spread(s) in question to students. Before Reading Predicting/inferring Activating and Building On Prior Knowledge • Show the cover of the book, and read the names of the author and illustrator. Ask students what they think the book is about. Ask what the title means and why the phrase “Stretch It, Shape It” is included. • Ask students what they think the brain is, what it does, and why it is so important to us. Make a list of their ideas. Ask what they wonder about the brain. Include their ideas in the list. • Setting a Purpose: Say, “Now that we have made our predictions, let’s see what else we can learn about the brain.” During Reading Inferring/predicting “What does your brain…” and “Your brain helps you…” spreads • A fter reading the first two spreads, have the students look back at the co-created list. Ask what things they can add to it. Throughout the lesson, periodically check the list to confirm what students predicted and to add new understandings about the brain. • A sk what “feel—both touch and emotions” means. • A sk what the word “unique” means. Have students think/pair/share with a partner and discuss what makes them unique. 16 Number and Financial Literacy

Predicting/activating “So what is your brain?” spread prior knowledge • A sk what students think muscles and organs are. Explain that our bodies, including our muscles and organs, are made up of trillions of cells. Analysing/making “The brain has many parts…” and the following spread connections • A fter reading about each part of the brain, discuss what each part does and clarify the ideas by focusing on the examples that are given in each case. Have students make connections to their own lives. For example, ask what parts of the brain are working the most when they go swimming. Making connections/ “When you were born…” spread inferring • A sk why the author refers to the first ten years of life as “the magic decade,” and what this means about the opportunities students have to learn at a young age. • H ave students think about a task that they may have found hard to do when they were younger, but now find easy to do. Discuss what they needed to do to improve. Making connections/ “Like elastic bands…” spread inferring • H ave students relate the example of how the body learns to play a sport to other activities that they have done. • Discuss why practice is so important in order to get better. Ask what other things students need to practise in their lives in order to improve. • Ask why the author compares the brain to an elastic band. Making connections “Even when you make a mistake…” spread • A sk students how they feel when they make a mistake. Discuss the important role mistakes play in learning. For example, mistakes help you to identify what you don’t know or what you misunderstand so you know what to focus on in order to improve. Making connections “You can stretch the part…” spread • D iscuss times when students have been afraid to take a risk and how they overcame their fear. Ask whether doing the activity was really as scary as they thought it would be. Making connections/ “Learning something new…” spread inferring • D iscuss how making connections helps the brain become more elastic and how this helps students learn as they get older. Ask whether they think the brain gets more elastic if they don’t try to learn new things. Ask why it is so important, as far as the growth of the brain is concerned, to not give up when learning something. • Ask what new concept or skill students have recently learned that has helped their brain to grow. 17

Making connections/ “When you learn something new…” spread reflecting • H ave students reflect on how very young children have to put all of their effort into walking, and then when they get older, they don’t even need to think about it. Ask how being able to walk can help them learn to run and do other skills with their legs. • D iscuss how the parts of the brain work together in order to carry out one activity. Ask why the role of the amygdala is so important in order to learn new things. Making connections/ “The brain that makes…” and “The more different kinds...” spreads reflecting/analysing/ • H ave students reflect on the speed of growth in the brain during the first ten synthesizing years of life and what this means in terms of going to school, learning new sports, and other activities. • A sk how they feel about learning after reading the book and what they might do differently. • Ask what they think the message of the book is and why the author wrote it. Students can turn and talk to a partner before having a discussion with the class. After Reading Making connections/ • Co-create an anchor chart that identifies examples of the six social-emotional analysing/synthesizing learning skills. Below are points to highlight about each skill and sample prompts. Regularly make connections to students’ own emotions and experiences. Add some of these ideas to the anchor chart. Identify and Manage Emotions Highlight: It is important that students can identify their emotions by naming them and realizing their intensity. Students can also understand the feelings of others and why they may be reacting to a situation in a certain way. – R eread the page about the amygdala. Discuss ways in which students try to control their emotions. Have them reflect on how a baby cries each time it is hungry and how they control their emotions and express their feelings of hunger now that they are older. Stress Management and Coping Highlight: Students need to recognize what is causing them stress and then discover ways to cope with that stress. It is important to help students develop a repertoire of strategies throughout the year so they have constructive options when they are feeling overwhelmed. This helps them build personal resilience. – R evisit the page about the boy learning to dive and how he overcame his fear to dive in the pool. Have students discuss what they do to overcome their fear. 18 Number and Financial Literacy

Positive Motivation and Perseverance Highlight: It is important for students to try new ways of approaching a problem and then learn from mistakes if things don’t go as planned. This helps students view their own mistakes as learning opportunities. By persevering through a task, students feel better about the situation and then feel a sense of accomplishment when they finally succeed. – R evisit the pages about learning to play soccer and the girl learning to do a magic trick. Emphasize the importance of making mistakes in order to get better and how it is necessary to keep trying even though the task seems hard at first. Healthy Relationship Skills Highlight: Through experience, students discover that they can learn from working with others. It is important they know how to respectfully and cooperatively work and communicate with others, which includes listening attentively and understanding other people’s perspectives. – R evisit the page about the boy learning to dive and read what the little owl said. Discuss how learning something with another person can help. – D iscuss how they can learn more by working with others. Relate this to how they can respectfully help each other during math class. List some of the things they can do to support each other. Self-Awareness and Sense of Identity Highlight: Students need to see themselves as capable math learners and reflect upon what they did and can continue to do to improve. Students also need to take responsibility for their learning by self-assessing and setting goals. It is also important to discuss how they see themselves as math learners and ensure that they have a sense of belonging to the classroom community. – R evisit the page about the girl learning to play the piano. Discuss how understanding what they can do and what they still need to learn are important for setting goals for further learning. Ask what goals the girl in the story might be setting for herself and what she plans to do to meet those goals. – D iscuss how it is also important to recognize what they are good at since these abilities can help them overcome things that they are not as successful at doing. Critical and Creative Thinking Highlight: For math to be relevant to students, they need to make connections between the math they do in school and the math evident in their everyday lives. Students need to see math as a process rather than a result (find an answer), and they need to think critically about the problems they are solving. Thinking creatively often leads to new ideas that can help students view math as a wondrous and interesting subject to explore. 19

– Revisit the page that shows the boy sculpting a brain. Ask what he needs to think about in order to create a piece of art. – A sk how the mouse was able to make a sculpture that was so much bigger than it is. Discuss how being innovative, or thinking of creative ideas can help them solve problems. Throughout the Year • Post the anchor chart in the class and regularly refer to it. Throughout the lessons in the resource, there are suggestions for building and reinforcing the social-emotional learning skills within the context of a lesson and by applying the mathematical processes. This will help you monitor, assess, and evaluate students’ growth and development as they develop their social- emotional learning skills. Further Practice • H ave students make diagrams of their brain and its parts. They can add the names and what they do, relating it to their own activities. On the side, they can list activities they think they are good at, activities they want to improve at, and new activities that they would like to learn in the future. 20 Number and Financial Literacy

Introducing Number Sense Math Number Curriculum Expectations • B1. demonstrate an understanding of numbers and make connections to the Teacher way numbers are used in everyday life Look-Fors Possible Learning Goals • Describes, and gives examples of, ways people use numbers in their everyday lives • Understands and explains the meaning of numbers in context and solves problems presented in various contexts • Recognizes and correctly reads numbers in the pictures • Infers what the numbers mean and relates them to a real-life context • Explains how numbers are used and why they are important in their lives • Applies previous understanding of numbers to solve related problems PMraotcheesmseast:ical About the cPorombmleumniscoaltviningg, , arcreenofadnlesnscoettnrcianitnitgneg,ggsa,ieenrlsedepcprterinosgveinntotgion, lgs, Numbers and number sense underpin all strands of mathematics, permeate most subject areas, and play an integral role in our lives. The more students explore numbers in their environment, the more they recognize their relevance in real-life situations. Students also discover that numbers take on varying meanings, depending on the context in which they are presented and the units they are given, such as metres or minutes. Over time, students discover that they can describe and define numbers by other characteristics, such as being odd or even, or being a multiple of other numbers. They not only explore much larger numbers, but also smaller numbers in the form of decimals and fractions. This evolution of thinking requires flexibility and conceptual understanding so students can see numbers as interconnected and not as compartmentalized topics. It is important for us as educators to expose students to the world of numbers in order to build this understanding and evoke a sense of curiosity about math in their everyday lives. This sense of wonder is critical for nurturing positive attitudes and for developing social- emotional learning skills in all of our students. 21

Mcmampottadhelouuatdonnnhlciutsetteiiis,pVynoa,ovlonginafcnc,,rdaleaassustscubkei,,otbiu,iphnqotlaur,uncarnadsoycdn,iu:tvritnioeisttndiyion,,sng, ,, About the Lesson numbers This introductory lesson can be delivered as Math Talks based on pictures in “Numbers in Our Lives” from the Number and Financial Literacy big book. Each picture, or set of pictures, can support a stand-alone Math Talk and investigation. The pictures can be discussed on successive days, or used throughout the year to tie into a relevant unit. Some pictures can also be revisited throughout the year, using a different math focus and varied prompts. Using visual images stimulates rich discussion, which can further evoke inquiry about mathematics and how it relates to students’ lives. NOTE: Select the prompts that best meet the needs and interests of your students. Materials: Distance Signs “Numbers in Our Lives” • What numbers do you see on this sign? What units are the numbers (pages 2–3 in the expressed in? How far is 1 kilometre? [Show a metre stick.] Visualize Number and Financial 1000 metre sticks end to end. We can better visualize this if we measure Literacy big book and • oLuett’s10lomoketartesa. [Measure out 10 metres.] Imagine this length 100 times. little books), metre map of Canada and find these locations. What do you stick, map of Canada, • Wnohtiycea?re(et.gh.e, rTehseigynasrelikaell along the same highway.) chart paper this on the roads and highways? How do they Time: 20–30 minutes help the drivers? (e.g., Drivers can figure out how long their trip will per session • Wtakhea;tthdoeyykonuonwotwicheearebothuet ythceanorsdteorpofforthgeasnuomr fboeords?.)If you are comparing the numbers, what do you know? Which of the two locations • Aarbeoculot sheorwtomgeutchherf?arther is Inuvik than Tsiigehtchic? (e.g., It is about • 1W30ithkmyoufarrtphaerrtnoerr,aflminodsot utwt hicoewasfafrart.h)ese places are, using the chart paper to record your calculations. Find as many comparisons as you can. • What did you find? What strategies did you use to find your answers? Basketball Scoreboard • What is this board? In what sport is this scoreboard used? How do you know? How do you play basketball? Let’s act out a game right now. • What do “HOME” and “GUEST” mean? What do the numbers under these headings represent? Which team is winning? By how much? How do we correctly read these numbers? (e.g., one hundred six, one hundred seven) • W hat does the word “PERIOD” mean? There are 4 periods in a game of basketball and usually each period is 12 minutes long. How long would an entire game be? What numbers cannot be used to describe the periods? 22 Number and Financial Literacy

• H ow do they keep track of the time? This digital clock shows 8:29. What does that mean? (e.g., There are 8 minutes and 29 seconds left in the game.) What does the clock read at the beginning of a period? How does the clock work differently than the digital clocks we use to keep time? (e.g., The numbers of the scoreboard clock decrease down to 0, while the numbers on clocks that tell time increase in value.) About how much time has passed in this period? What numbers can be on this clock? What numbers can’t be on the clock? • What is the shot clock? Each time the ball goes to the other team, they put a certain time on the shot clock and then the team with the ball has that amount of time to shoot at the basket. It is usually 24 seconds. What numbers cannot be on the shot clock? Do you think the numbers on the shot clock increase or decrease in value? How much time has passed on the shot clock so far? • What do the fouls mean? Why is there a zero in front of the 3 and in front of the 5? • W hy are scoreboards so important during a game? What other sports do you know that use scoreboards? How are those scoreboards different? The same? Boarding Pass • Have you ever seen a piece of paper like this before? Where? Look at what is printed on the paper. What do you know and what do you wonder? • T his is called a boarding pass. Passengers get one of these before travelling on an airplane and they must show it before boarding the plane. • W hy are the names of two cities on the ticket? What do the two cities represent? Who is travelling? • There are several numbers on the boarding pass. What do they mean? Why do you think there is a number for the flight? • Where is this person sitting? Do you think it is near the front or the back of the plane? Why? Let’s visualize what a row of seats may look like on this plane. Every letter indicates a seat in the row. Judging from the letter on this boarding pass, how many seats might be in the row? Let’s draw a picture of this. Where might the aisles and windows be? • W hen is this person flying? How is the way the time is recorded different from how we often record time in the classroom? • What is the barcode for? Sandwiches • W hy do you think there are sandwiches on a page that is about math and numbers? What math do you see represented in the sandwiches? (e.g., fractions) 23

•• What are fractions? What fractions do you see in this picture? piece How is the sandwich on the left divided? How do we name one of the sandwich using fractional words? In order for the piece to be one fourth, what do you know about the size of all of the pieces? • If one piece of the sandwich on the left is eaten, what fraction of the sandwich remains? If someone eats two pieces of the sandwich, what fraction have they eaten? Is there another way to name two fourths? How do you know that two fourths and one half represent the same amount? What fraction of the sandwich is left over? • If you cut each of the four pieces in half, what fractional parts would all of the pieces be? If someone ate half of the sandwich, how many eighths would they have eaten? How do the eighths compare to the fourths? How do the fourths compare to the halves? • Look at the sandwich on the right. How could it be cut into fourths a different way? Draw some squares on a piece of paper to represent the sandwich and try some different ways (e.g., one vertical and one horizontal cut through the middle of the sandwich; three vertical cuts or three horizontal cuts). How do you know that the sandwich is still divided into fourths? • If we think of both sandwiches together as a whole (one whole lunch), what would one half of the whole be? What would one fourth of the whole look like? Why are these fractions different from when one sandwich represented the whole? Coupon • What is this piece of paper? Where have you seen something like this • bTehfiosreis? known as a coupon. Many stores give them out to people, hoping • tWhahtatthdeoy will shop in their stores. you know from looking at the coupon and what do you •• wWW ohhnaadttesirty?emmbioslsthdios you see that show you there is money involved? coupon for? What is the regular price? What is the • Wsalheepnridcoe?esHtohwe much money are you saving if you use the coupon? coupon expire? What does ‘expire’ mean? Why do you • Wthihnakt there is an expiry date on the coupon? are the conditions that you must follow if you want to get the deal advertised on the coupon? • Why do you think stores use coupons? Array of Eggs • What do you see in this picture? Why do you think the eggs are in this • tHyopwe of packaging? What do these eggs have to do with math? are the eggs arranged? How many rows are there? How many columns? What is the difference between rows and columns? 24 Number and Financial Literacy

• H ow many eggs are there altogether? How did you figure that out? How can you figure out the total number of eggs without counting the eggs • oHnoewbmy oannye?e(geg.gs.,asrkeiipncoonuentdionzge,nr?epWeahteerdeaddodiytoiouns, eme uolntiepldicoazteinoni)n this picture? How many dozens do you see altogether? How can we express •• tWHhoehwantumfmraabnceytriogonrfooudfpoaszleolnftsh5aeseegagggsfsrdadcootiyeosonuo?ns(eee.egh?.a,Wltfwhooaf taafnrddaoczateiohnnamlfoafdkoaezl?letn(oh)neeegfigfsthi)s • Hthoawt? Which is larger, one sixth or one fifth of the eggs? many groups of 6 are there? If there are 5 groups of 6, what operation could we use to find the total number of eggs? (e.g., repeated addition, multiplication, 5 × 6) Can we also find the total if we are looking at the number of groups of 5? How would we describe it? •• HH(e.oogww., 6 groups of 5 or 6 × 5) are multiplication and division related? the amount? How many many eggs would there be if we doubled dozens of eggs would we have now? Graph of Favourite Sports • W hat kind of graph is this? How do you know? What is the graph about? What do you know and what do you wonder? • Without looking at the numbers, about how many times more people like basketball than like tennis? (e.g., twice as many) About how many times more people like hockey than like tennis? (e.g., five times as many) • Look at the numbers on the left side of the graph. This is known as a scale. What do you know about the scale? How could you skip count up the scale? Why are the increments even? What do the numbers represent? • Study the graph with a partner. What comparisons can you make? Think of as many as you can. Write some of your ideas down on chart paper. •• What did you find? I will record some of your ideas. you think these How many people took part in this survey? Who do people might represent? • W hy do you think someone made this graph? What decisions could be made after studying the results on this graph? • Why do we often present data in graphs? Menu • What is printed on this piece of paper? Where have you seen something like this before? What is the purpose of having a menu? Why do you think many restaurants have Kids’ Menus? What do you think is different between an adult menu and a children’s menu? (e.g., selection of items, size of the portions, price) 25

• L ook at the menu with a partner. What do you know and what do you wonder? • How are the foods organized? Why do you think the restaurant organized the foods like this? • W hat do you know about the costs of the food? What symbols do you see to show the units of the costs? • W hat is the most expensive item on the menu? What is the cheapest item? Why do you think the costs for all of the items are not the same? About how much more is the most expensive item than the cheapest item? • If you have $10, what foods would you want to buy? Turn and talk to your partner. How do you know about how much the items will cost? • CH hoowosdeotyhorueekinteomwstthheatcowstilliscnosott over $10? under $10. About how much change will you get if you pay with a $10 bill? What other combinations of money could you use for your $10? How could you pay for your total with the exact change? • W hat can you buy for 3 toonies? How else could you pay for something that costs the same amount? • How do people pay for the food that they buy in restaurants? How do • tIhs egoreinstgautoraantrsesutaseurtahnetma onneeeyd they earn from the customers? or a want? Why do you think so? How often do you go to restaurants? Licence Plates • What are these and where have you seen them before? Why do you think cars have licence plates? Where are these licence plates from? How • dAoreyothuerkenaonwy? licence plates that are exactly the same? Why not? They use combinations of letters and numbers to make each plate different. How could you change the numbers on one of these plates to make it different? How many different combinations can you make by just changing the order of the numbers? Turn and talk to your partner and • rWechoartddsiodmyeouoffiynodu?rHfionwdicnogus.ld you make more combinations? • (We.gh.a, tchdaatnegsedtoheyoourdseereoofnththeeleltitceernscteopol;aatdesd? more numbers) stickers with dates on them? Why do the plates have Follow-Up Activity • S tudents can create a poster of numbers that they see in their daily lives. They can either draw the pictures or cut them out of newspapers and magazines. 26 Number and Financial Literacy