p9-88-Unit1-Gr2BC-Patterns-pass2

Unit 1: Patterns and Relations Lesson Content Page Getting Started with Patterns & Relations 9 Patterns and Relations Introduction 13 15 1 Introducing Patterns 22 2 Read Aloud: Pattern Fish: First Reading 26 3 Pattern Fish: Second Reading 30 4 Describing and Identifying the Core of a Pattern 34 5 to 8 Investigating Patterns and How They Repeat 36 5 Reviewing Patterns 39 6 Investigating Changing Attributes 43 7 Identifying, Describing, and Extending Patterns 46 8 Creating Patterns 48 9 to 11 Investigating Patterns That Increase 49 9 Investigating How Patterns Can Increase 56 58 10 Creating Patterns That Increase 61 11 Patterns with Money 64 12 Applying Patterning Concepts to Solve Problems 66 13 and 14 Investigating Positional and Circular Patterns 69 13 Creating Patterns by Positioning Shapes 71 14 Investigating Circular Patterns in Mandalas 73 15 to 18 Investigating Number Patterns 77 15 Patterns Using Number Lines 80 16 Patterns In a Hundred Chart 83 17 Investigating Patterns through First Peoples Storytelling 86 18 Adding to Create Patterns 19 Reinforcement Activities



Getting Started with Patterns & Relations There are two units in Patterns & Relations: Unit Description 1 Patterns and Relations 2 Equality and Inequality • Within each of these units, students will work through a progression of lessons to develop their understanding of the patterns and relations concepts. • Each unit includes a series of Blackline Masters and Digital Slides to support the visual nature of patterns and relations. • Each unit incorporates the use of a variety of concrete materials and tools that should be on hand and readily available for student use. • Each unit includes Math Talks, group discussions, and activities that target the Curricular Competencies—reasoning and analyzing, understanding and solving, communicating and representing, and connecting and reflecting—to support and develop student understanding. • Each unit includes activities to develop habits of mind, growth mindsets, and positive attitudes in the math classroom. • Making connections between patterns and relations and other strands or curricula will maximize student learning and support flexible thinking. When developing your long-range plans, consider the following: − Many of the patterns involving geometric designs make use of shapes investigated in Spatial Sense. − One lesson in the Patterns unit is devoted to simple patterns with money that could link to Financial Literacy. − The number patterns relate directly to Number with respect to skip counting, and addition and subtraction. − Partitioning numbers to demonstrate equality can be linked to composing and decomposing numbers in Number. • It is beneficial to use these units once students have a firm grasp of skip counting and simple operations (e.g., addition and subtraction). This will support them in making connections between what they know about number relationships and how they relate to patterning and equality. Patterns and Relations 9

Inviting Patterns and Relations into the Classroom Since math plays an integral part in our lives, it makes sense to take advantage of its role in everyday routines at school. Whether it is counting backwards to transition before starting an activity or counting all students as part of attendance, bringing math experiences into real-life contexts will deepen understanding of concepts in a meaningful way. There are many ways to embed patterns and relations concepts into daily routines. There are also quick 5–10 minute activities that can be carried out while the class waits in line to go somewhere, when there is 5 minutes at the end of a period, or when students need a quick break. Several ideas are described below. Classroom Number Line Number lines are powerful tools, yet they are often underused. Displaying a large number line up to one hundred in the classroom allows for incidental reference during discussions or while students are problem solving. • Progressively count the number of days in school up to the hundredth day and beyond. Each day, a mark can be put under the new number and students can count from zero to reach it. As the numbers get larger, students may decide to skip count in various ways to reach that number. Ask questions such as, “What would be the next day that we could skip count by 4?” • Use the number line for skip counting. Students can visually see the numbers that are being skipped over in uniform ‘hops’ and can quickly reason why counting by bigger numbers gets to larger quantities faster when counting forward, and smaller numbers faster when counting backwards. • Put a clothespin or marker of some sort on all of the multiples of 5 (or 2, 10, etc.) and draw attention to the spaces between the numbers so students have a visual of how much they are adding or subtracting each time they say a number in the counting sequence. Hundred Chart Display a large hundred chart in the classroom at all times so it can be used as a reference when discussions about numbers incidentally arise, or as a tool for planned activities throughout the day. • Practise counting, starting from a variety of different numbers. For example, ask students to start at 13 and count by 5s. This is the introduction to identifying a number pattern rule (e.g., I started at 13 and counted by 5s). Ask what patterns they notice in the numbers in this counting sequence. Ask them to predict what other numbers will appear in the same pattern. Students who have difficulty or low confidence with skip counting may benefit from using loose parts to check the count. • Discuss how the patterns in the hundred chart and the number line are linked so students can make connections between the two representations. • If you are using a hundred pocket chart with removable numbers, consider rearranging the numbers so zero is at the lower left, and the numbers 10 Patterns & Relations/Data & Probability

increase from the bottom. This can help students understand the increase in numbers as they move up the chart. • Consider building the hundred chart with students as the school days progress, one number at a time, so that students can infer and predict what numbers would appear in a certain number pattern based on the numbers already visible. Calendars Calendar activities can stimulate mathematical thinking around concepts such as the counting sequence and number patterns. Be sure to incorporate some patterning concepts when referring to the calendar. The key is to limit the amount of time on the activities so all students are engaged and actively participating. Vary some of the activities from month to month between ones that target number sense and others that target number patterns. Calendar activities do not need to be daily routines and can be used periodically throughout the year. Here are some of the ways that calendars can reinforce patterning concepts. • Like a hundred chart, the calendar reveals the counting sequence but in rows of seven rather than rows of 10. To reinforce number patterns, ask what number next Monday will be if this Monday is the first of the month. Have students find all of the Fridays and have them find out how many days are in between each one. Have students count by 2s, marking each number that is spoken. Discuss the pattern that emerges and how it is different from the ‘counting by 2s’ pattern that emerges on the hundred chart. First Peoples Perspectives Have students examine various pieces of local First Peoples artwork or regalia for examples of parallels, balance, and symmetry. Invite an Elder from the local community to speak to the class about the importance of balance and symmetry in Indigenous culture. Quick 5–10 Minute Activities Physical Movement Activities • Repeating Pattern Movements: Have students do a movement pattern that repeats, such as clap, snap, clap, snap (AB) or hop, hop, jump (AAB). Have students call out the pattern as they act it out, using the words for each movement. Or, they can name the pattern using letter combinations as above. • G roups in Motion: Have students walk around the room. As you say a pattern core (e.g., ABA), students need to get into a group of three and organize themselves in a physical representation of that pattern (e.g., facing forward, facing backwards, facing forward). • Sound Off: While students are lined up waiting to go somewhere, have them sound off, using a skip counting pattern. Provide the first number and the pattern rule (e.g., skip count backwards by 2s from 30). As students say Patterns and Relations 11

their number, they crouch down. Then have them sound off from the back of the line, standing up as they say their number. • Skip Counting Sound Off: Students decide what they want to count. For example, they may decide to count eyes (count down the line by 2s), fingers on right hands (count by 5s as they hold up one hand), or all fingers (count by 10s as they hold up both hands at the same time). Students can count backwards from the back of the line, putting their hands down with each count. • Line Up: Have students line up in different ways. For example, have them line up in pairs or in groups of three. Practise skip counting by the size of each small group. • ISpy: Spot and describe different visual patterns around the classroom or outside (e.g., wallpaper, bookshelves, floor tiles, bricks, trees) and have students try to identify what you are describing. “I spy with my little eye a pattern that has a black square then a white square” (e.g., the floor tiles). • M ake It Equal: Working in pairs as Partner A and Partner B, each partner chooses a number of fingers to hide behind their back. On the count of three, they show their fingers and have to decide how to make Partner B’s fingers equal to Partner A’s. Games • Guess My Number: Give clues, such as, “I’m thinking of a number. It’s part of a number pattern. My pattern starts at 5 and grows by 5 each time. My number is larger than 10 but smaller than 20. 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 number line or a hundred chart as they solve the problem. • Pattern of the Week!: Write a pattern rule (e.g., AAB) or a type of pattern (e.g., growing) on a predictable spot in the room. As the week progresses, have students identify and describe patterns that fit into the pattern of the week. • W hat’s the Pattern?: Organize students into a repeating pattern based on a secret rule (e.g., jeans, shorts, shorts OR glasses, no glasses, glasses). Have students guess what the rule is and then continue the pattern as far as they can, given what people are wearing that day. • A Handful of Concrete Materials: Bring out a certain type of concrete material (e.g., pattern blocks, relational rods, connecting cubes, counters, loose natural materials). In pairs, have students each take a handful of the materials. Together they need to create a repeating pattern using what they chose. • Daily Physical Activity: Create a pattern sequence of physical movements that you can model and call out and have students repeat after you (e.g., jump, jump, squat, jump, jump, squat). Do these to music to maintain the rhythm and have students identify the rule and core of the pattern (e.g., AAB). 12 Patterns & Relations/Data & Probability

Patterns and Relations Introduction About the Marilyn Burns notes how patterning is an important part of making sense of mathematical concepts. “The ability to create, recognize and extend patterns is essential for making generalizations, seeing relationships and understanding the order and logic of mathematics” (Burns, 2000, p. 112). Students in grade two investigate both repeating and increasing patterns, including more complex examples like positional and circular patterns. Students identify and extend the core of repeating patterns and work with a variety of increasing patterns involving concrete materials, actions, sounds, and numbers to 100. Patterns help students to investigate relationships between numbers as well as relationships in visual and geometric designs. As students study patterns in their primary years, their ability to describe, extend, translate, and create patterns helps develop their sense of algebraic reasoning, an important skill in the field of mathematics. Patterns and Relations 13

Lesson Topic Page 1 Introducing Patterns 15 22 2 Read Aloud: Pattern Fish: First Reading 26 30 3 Pattern Fish: Second Reading 34 36 4 Describing and Identifying the Core of a Pattern 39 43 5 to 8 Investigating Patterns and How They Repeat 46 48 5 Reviewing Patterns 49 56 6 Investigating Changing Attributes 58 61 7 Identifying, Describing, and Extending Patterns 64 66 8 Creating Patterns 69 71 9 to 11 Investigating Patterns That Increase 73 77 9 Investigating How Patterns Can Increase 80 83 10 Creating Patterns That Increase 86 11 Patterns with Money 12 Applying Patterning Concepts to Solve Problems 13 and 14 Investigating Positional and Circular Patterns 13 Creating Patterns by Positioning Shapes 14 Investigating Circular Patterns in Mandalas 15 to 18 Investigating Number Patterns 15 Patterns Using Number Lines 16 Patterns In a Hundred Chart 17 Investigating Patterns through First Peoples Storytelling 18 Adding to Create Patterns 19 Reinforcement Activities 14 Patterns & Relations/Data & Probability

1Lesson I ntroducing Patterns Math Curricular Competencies Learning Standards • Reasoning and analyzing: Use reasoning to explore and make connections • Understanding and solving: Develop, demonstrate, and apply Teacher Look-Fors mathematical understanding through play, inquiry, and problem solving; visualize to explore mathematical concepts • C ommunicating and representing: Communicate mathematical thinking in many ways • C onnecting and reflecting: Reflect on mathematical thinking; connect mathematical concepts to each other and to other areas and personal interests Content • R epeating and increasing patterns Possible Learning Goals • Reflects on the presence of patterns in real-life contexts • Begins to understand what patterns are and what they are not • Identifies patterns in real-life contexts • Describes patterns using mathematical language • Predicts how a pattern may continue and gives reasons for their responses • Explains what they think a pattern is and what it is not Math Vocabulary: About the Lesson PwdWifaMnneooyiyhntoosrrordeutcaortuesnrehtdpintbeuoseacieiemcftnopreuettmpptdedihhoroxceieoetnnporonptglrvmtaatrrorsoienneaacctauittatlnethtyhsbfi,,eto.eouetnrlartcasmoker.eys This lesson is made up of several Math Talks based on the pictures lessons. in “Pattern Hunt” (pages 2–3 in the Patterns, Relations, Data, and Probability big book). The visual images are meant to stimulate math talk, which can further evoke inquiry about mathematics and how it relates to students’ lives. If students can see this relevance in the activities they do at school, they are more likely to make connections and be curious about math. continued on next page Patterns and Relations 15

Each picture, or set of pictures, can support a stand-alone Math Talk and investigation. These can be used on progressive days, one Math Talk and partner investigation per day, to investigate and explore how patterns are all around us in our everyday lives. Through the discussion, a new investigation or problem may emerge. The Math Talks can also serve as a review of previously learned concepts to keep the concepts fresh in students’ minds. For each picture there are: • several possible prompts from which to pick and choose, depending on what concept you are working on or what your lesson is about, and • possible inquiries or problems for students to explore, since math talks also serve as natural springboards for carrying out investigations. Throughout the discussion, integrate the math talk moves on page 7. For example, continually encourage students to expand upon their responses and explain their reasoning. Have students respectfully react and respond to what other students are saying so they become active listeners. Have students repeat or paraphrase what their peers have said. Ask questions such as “Do you agree?” or “Can anyone add onto what she said?” Have students turn and talk to a partner before sharing with the group. Provide wait time so students can reflect on what is being asked. Below is one way in which the Math Talks may be structured. Math Talk (10 minutes) Based on your area of study and learning goal, select some of the prompts or design your own questions to create a framework for your Math Talk. Rather than following the prompts as they are written, allow the students’ responses to guide the flow of the discussion. Partner Investigation (10 minutes) Have students work in pairs to further explore one of the prompts or the sample inquiry problem provided. All students may work on the same inquiry, or some may work on different problems, depending on their interests and level of understanding. This is a good assessment opportunity to uncover what students know and what misconceptions they may have. 16 Patterns & Relations/Data & Probability

Consolidation (10 minutes) Building Growth Mindsets: Strategically choose some of the students’ findings or solutions to discuss as a class, and focus on how the math relates to their lives. Discuss how students feel about math and what they find interesting about it. By making connections and sparking curiosity throughout the discussion, students can develop a positive attitude towards math and be motivated to engage in and persevere at problem solving. Materials: NOTE: Select the prompts that best meet the needs of your students. “Pattern Hunt” (pages Calendar 2–3 in the Patterns, Relations, Data, and • What do we call this chart? Do you see something similar to this in our Probability big book) Time: 20 minutes classroom? Do you have something similar to this at home? per day (discussing 2–3 images • How is this calendar similar or different to the one in our classroom? How is each day) it different to the one at home? • What do you know about the calendar? • How many months do you see? • How many days are in the first month? The second month? The third month? Do you notice a pattern? • What is 2 days after July 5th? What is 2 days before July 5th? • What number is the first Monday of May? The second Monday of May? The third Monday of May? How does each number change? • How many days are there in one week? What is 7 days after June 2nd? And then 7 days after that? What do you notice? • Look at each Wednesday in July. What do you notice about the dates? Possible Partner Investigation • Explore patterns you can see in the calendar. • Find patterns in one of the months on the calendar. Do these patterns repeat in the next month? Bicycles • What do you see in this photograph? • Do you have a bicycle at home? Where do you ride your bicycle? • Where do you think these bicycles are? Have you been to a place like that before? • How many bicycles are there? How do you know? Can you count them a different way? Patterns and Relations 17

• How many tires are there? How do you know? Can you count them a different way? • What do you notice about all the bicycles? • Looking at the colour of the bicycles, what colour might come after the red one? How do you know? • Looking at the colour of the bicycles, what colour might come before the green bicycle? How do you know? Possible Partner Investigation • Go outside to the bicycle rack. Count the bicycles in different ways, making note of the growing total number of tires with each bicycle. Discuss the following pattern as you count: there are two tires on the first bicycle; the number of tires increases by two for each bicycle we count. Have students note any other patterns they see at the bicycle rack or on the playground. Honeycomb • What is this a picture of? Who or what lives here? • Have you ever seen a structure like this before? Where have you seen it? • What would you find in this structure? • What shape do you see in this structure? • Estimate how many hexagons are in this image. How did you figure out your estimate? • What patterns do you see in this image? Possible Partner Investigation • What other insects have shelters/homes like this one? Students can investigate different shelters/homes of insects and compare them to the honeycomb. • What types of shelters do animals build? Flowers • Do you know what type of flowers are in this image? • Have you seen this type of flower before? Where? • Do you have flowers like this in your garden at home? What time of year do we see these flowers in the garden? Why? • How many flowers are there in this image? How do you know? How did you count? Is there another way you could count the flowers? • What do you notice about the flowers? Do you see any patterns? Possible Partner Investigation • What is your favourite flower? With your partner, draw a pattern using your favourite flower. • Create a garden (e.g., using loose parts, drawing) with your partner. Create different patterns throughout your garden. 18 Patterns & Relations/Data & Probability

Wallpaper • Where might we find something similar to this image in a house? • Do you have wallpaper in your house? What does it look like? • What do you notice about this wallpaper? • What patterns do you see in this wallpaper? Do you see anything repeating in this pattern? • Does all wallpaper have repeating patterns? Why do you think that? Possible Partner Investigation • If you could create your own wallpaper, what would it look like? Draw what your wallpaper would look like. • As a home connection, have students look to see if they have any wallpaper at home and look for patterns. Music Notes • What is in this image? Have you seen anything like this before? • Why might we need sheet music? Who might use this sheet music? • What do we call the black circles on this sheet music? • How many notes are there on this sheet music? How did you count them? Is there a different way to count them? • What is the same on this sheet music? What is different? • Does anything repeat on this sheet music? Possible Partner Investigation • If you could create your own music pattern what would it sound like? Find something in the room that could be an instrument and create a music pattern with it. Houses • What do you notice about these houses? • Do you have houses similar to this in your neighbourhood? • What shapes do you see in this image? • What do you notice about the colours of the houses? If a house were to be built next to the yellow one, what colour might it be? Why do you think that? What colour house do you think is before (to the left of) the red house? Why do you think that? • Look at the triangles on the houses. What do you notice? Is there a pattern? What might it be? • If we could see the numbers on these houses, what might they be? How do you know? Possible Partner Investigation • Go for a community walk with the students. Have students look for patterns among the different houses. Have students find various patterns (e.g., colours or shapes of houses, the numbers on the houses). Patterns and Relations 19

Outdoor Patio Stones • What do you think we are looking at in this image? Where have you seen these before? • Why might people have these stones/tiles on their property? Do they have them in the front or the back of their house? • Do you have patio stones at your home? What do they look like? • Estimate how many tiles you think there are in this image. How would you count them? • Do you notice any patterns in these tiles? How are they the same? How are they different? • Why do you think people might like to have the tiles in patterns for their patios? Possible Partner Investigation • Using pattern blocks or square tiles, create a tile pattern with your partner. Show what is repeating. • If you could create your own patio with tiles, what would it look like? Draw what your patio would look like. Money • What coins do you see here? What value does each coin have? • Have you ever bought something for 25 cents? What might cost 25 cents? • Have you ever bought something for 10 cents? What might cost 10 cents? • How many quarters are in one pile? How many quarters altogether? How could we count them? • How many dimes are in one pile? How many dimes altogether? How could we count them? • How many coins altogether? How might we count them? • How can we figure out the value of the coins in each pile? How could we count the quarters to find out how much money is there? What about the dimes? Possible Partner Investigation • Have students use coins (actual, paper, or plastic) to count money in different ways (e.g., give students different numbers of nickels, dimes, and quarters and have them organize and count the money in different ways). Building Growth Mindsets: • A positive attitude towards math begins with curiosity and the desire to learn more. Students need to see math as a creative subject that lives all around them. It is important for them to wonder about their environment and learn to think differently about everyday things. As you look at different 20 Patterns & Relations/Data & Probability

items throughout the day (e.g., on walks, in different subject areas), pose the following prompt to students: – What do you notice about this? What do you wonder? What math do you see here? What do you want to know more about? • Create a Math Wonder Wall to which students can add their math wonders. Using sticky notes, students can add details or information to the board as they learn about the wonders and gather more information around them. Further Practice • Pattern Scavenger Hunt: − Take students on a tour of the school and have them find patterns in the building. Take pictures and have students create a patterns book. − Practise counting patterns throughout the school (e.g., count the outdoor shoes by 2s, count steps while walking), helping students notice numbers growing as you count up. For each pattern, ask students how the numbers are changing (e.g., adding one). • Independent Activity in Math Journals: Pose one of the following prompts: − Use pictures, words, and/or numbers to show what patterns are. − Use pictures, words, and/or numbers to show what patterns you see in your everyday life. − Use pictures, words, and/or numbers to show a number pattern that grows by two. Create a number pattern using your favourite number. Explain how it is a pattern. Extension • Begin collecting pictures that can initiate discussions about math. The images can reflect any ways that math concepts are embedded into students’ lives. Ideas include: interesting shapes in the environment; patterns or symmetry in nature; arrays of fruits and vegetables in a store; or plants growing in a garden. Include photos of your students around the school or on field trips that reflect that math is in their lives. The more students pay attention, the more math they will see. Patterns and Relations 21

2Lesson P attern Fish: First Reading Introduction to the Read Aloud The Read Aloud text introduces math concepts in a meaningful context that allows students to make connections to their everyday lives. During the first reading of Pattern Fish, students apply their literacy strategies, such as inferring, using prior knowledge, and synthesizing information, to understand the context of underwater animals. (See the Literacy and Mathematics Links chart in the Overview Guide for more on comprehension strategies.) Discussion of the context and images in the story supports selected grade two Science learning standards and helps students make connections across subject areas. During the second reading, students discover and explore the math concepts embedded in the story. Both readings are also valuable for assessing where students are, what some of their misconceptions might be, what concepts need greater emphasis, and what differentiation may be necessary. English Curricular Competencies Language Arts Learning Standards • Comprehend and connect: Use sources of information and prior Science knowledge to make meaning; use developmentally appropriate reading, Learning listening, and viewing strategies to make meaning; engage actively as Standards listeners, viewers, and readers, as appropriate, to develop understanding of self, identity, and community; use personal experience and knowledge to connect to stories and other texts to make meaning Content • Story/text: Text features • Strategies and processes: Oral language strategies Curricular Competencies • Q uestioning and predicting: Demonstrate curiosity and a sense of wonder about the world Content • Similarities and differences between offspring and parent Visual Literacy The key words that describe the pattern are in larger, bolder font and highly supported by the visual representation on the page. There is a visual link throughout the book between the pictures and the text, supporting students’ ability to predict the words and patterns. 22 Patterns & Relations/Data & Probability

Materials: Assessment Opportunities Observations: Note each student’s ability to: – Use visual cues to make and support predictions – Make inferences and demonstrate understanding by engaging in discussions and follow-up activities Written by Trudy Harris Read Aloud: Pattern Fish Illustrated by Anne Summary: In this book, underwater animals introduce students to different Canevari Green pattern types (e.g., AB, ABB, AABB) through meaning, text features, and visuals. Using rhyming language, students are led to predict the missing Text Type: Fiction: pattern element based on repetition of ideas and visual cues. Description – Poem NOTE: There are more prompts than it is feasible to use in this amount of time. Time: 1 5–20 Select the prompts that best meet the needs and interests of your students. minutes Before Reading Inferring/predicting Activating and Building On Prior Knowledge Connecting/ • Show students the front cover and ask them what they see. Read the title and using prior knowledge the names of the author and illustrator. Ask students to predict what they Inferring think the book might be about (e.g., fish, patterns we see in the water) and have them explain their reasoning (e.g., there are different fish on the cover). • Ask if any of the students have been to an aquarium or to the zoo, where they might have seen underwater animals. Ask how the needs of underwater animals are different from the needs of humans. Ask students, “What kind of fish or other animals do you think we might see in this book? What might they be doing?” List all students’ answers on chart paper. • Setting a Purpose: Tell the students, “Now that we have made our predictions, let’s read the story together to see what we will find in the water.” During Reading Predicting/ • After reading the first spread (“Yellow-black...”), ask the students what word using text features comes next. Have them explain how they know. Ask them how the picture Predicting/analyzing/ helps us figure out what comes next. inferring • Ask students what living things they see in the picture. Ask what features the fish has to help it live in the water. • After reading the word on the next spread, ask the students what word would come after black and have them explain how they know (e.g., why does it have to be yellow?). • Ask what an eel is and what features it has. Explain that it is also a fish, but it looks different. Ask how the colours and patterns on the eel can help it hide from its enemies. Patterns and Relations 23

Visualizing • After reading about the eel (“Stripe-dot-dot...”), have students close their Inferring eyes and visualize the pattern. Repeat “Stripe-dot-dot” to students and ask them, “Without opening your eyes, show me with your hands, what Analyzing/ comes next?” using text features • Ask students what features the sea horse has and what they think it eats. Analyzing Explain that the sea horse moves by fluttering the bumpy fin on its back. Ask how its patterns could help it hide from enemies. Explain to students that a sea horse can change colours to match the plants and surroundings. • After reading the spreads about the seahorse (“Chomp-chomp-munch- munch...”), have students examine the word ‘munch.’ What do they notice about the letters? Why do they think the author did that? • After reading about the octopus (“Stretch-spurt-glide...”), ask students if the pictures match the words in the description (e.g., which words match with which octopus). Why might the author do this? Inferring • Ask students which animals they see on this page. Ask what features an octopus has. Explain that an octopus moves by squirting jets of water from its bag-like body. Ask students how they think an octopus hides from enemies. Explain that an octopus can change the colour and the texture of its skin to match its surroundings. How is this similar to the sea horse? Using text features • Before reading the right-hand page on the first shark spread, ask students to identify the punctuation mark on the page as well as what it is used for and how it helps us read the word out loud. Using text features • Before reading the text on the second shark spread out loud to the students, ask them to explain how they think we should read the word out loud. What clues on the page tell them this? (e.g., all caps, two exclamation marks) Inferring/using prior • Ask students what they know about sharks or where they have seen sharks knowledge before. Ask what features a shark has. Ask what a shark’s enemy might be. Connecting/using prior • After reading the last spread in the story, ask students how they think the knowledge/using text shark feels. Ask, “Why would it feel this way? What do you think would help features the shark?” • Ask students what they notice about the word ‘dive.’ Why do they think it is written that way on the page? After Reading Synthesizing • Ask students to turn and talk with a partner about the different kinds of water Using text features animals you read about in the book. Share the answers as a class. • Ask students to turn and talk with a partner about the text features they learned about in this book (e.g., directionality of text, punctuation, size of font) and how these features helped them understand what they read. 24 Patterns & Relations/Data & Probability

Making connections • Together make a list of other animals students have seen before that have Synthesizing patterns (e.g., zebra with its stripes, snake skin). • Create an anchor chart of the features of the underwater animals that students encountered and discussed throughout the reading (e.g., what they look like, movement, predators, adaptations). Materials: Further Practice BLM 1: Word Cards • Actions and Words: Students could use BLM 1: Word Cards to create their BLM 1: Word Cards own patterned text using words from the book. Once they have created a short patterned text, have them add actions to the text and share with Yellow Black Yellow Black the class. Stripe Dot Stripe Dot • V isual Arts and Patterns: Have students create their own patterned fish or Chomp Munch Chomp Munch animal and write a description following the model of the book. If necessary, students could use the word cards from BLM 1 to support their writing. Bubble Pop Bubble Pop • Science: Initiate a mini-inquiry on animals, their features, how they move, Stretch Spurt Glide Stretch how they adapt to their environment, and how they protect themselves from Spurt Glide Wiggle Jiggle predators. Float Wiggle Jiggle Float © 2022 Scholastic Canada Ltd. GRADE 2: PATTERNS & RELATIONS/DATA & PROBABILITY ISBN 978-1-4430-7187-1 3 Scholastic Canada GR2 BC Patterns & Data Fourth Pass Reproducibles October 25, 2021 Patterns and Relations 25

3Lesson Pattern Fish: Second Reading Math Curricular Competencies Learning Standards • Reasoning and analyzing: Use reasoning to explore and make connections • U nderstanding and solving: Develop, demonstrate, and apply Teacher Look-Fors mathematical understanding through play, inquiry, and problem solving • C ommunicating and representing: Communicate mathematical thinking in many ways; use mathematical vocabulary and language to contribute to mathematical discussions • Connecting and reflecting: Connect mathematical concepts to each other and to other areas and personal interests Content • Repeating and increasing patterns Possible Learning Goals • Reflects on the importance of patterns in real-life contexts • Begins to recognize the core of a repeating pattern and uses it to extend the pattern • Recognizes, names, and represents the core of a variety of repeating patterns (e.g., AB, AAB) • Extends a repeating pattern • Identifies attributes that can change in a pattern About the Many math concepts are embedded in Pattern Fish, giving them meaning in a realistic context. The story focuses on patterns and how the core continuously repeats. The core of a pattern is the elements of the shortest part of the pattern that repeats. Marian Small notes that at times, students can have difficulty identifying the core when there are more elements in the core. Small recommends that for students to be able to recognize and identify a repeating pattern, educators must provide students with a minimum of three repetitions of the pattern core (Small, 2017, pp. 358–359). 26 Patterns & Relations/Data & Probability

Math Vocabulary: This text introduces students to a variety of patterns, including preaptteeartni,nga,ttcroibruete, patterns in geometric designs. The patterns become increasingly complex and take different forms. Just as students experience Materials: patterns in their environment through sound, colour, shape, text, and number, Pattern Fish shows them patterns in the images and Pattern Fish book, text, and links the patterns and objects found in the images to the connecting cubes, words in the text. This helps students make connections between coloured counters and the visual, written, and symbolic representations of patterns. tiles, pattern blocks Throughout the text, students can identify patterns in various Time: 15–20 minutes ways and the context allows them to extend patterns by describing per session and representing the different patterns throughout the book. Through questioning, students can learn about the difference between the cores of various patterns (e.g., AB, AAB). There is also an opportunity for students to make connections between the various representations of each pattern that can be found on the page. It is important that students have time to reflect on and explain the patterns they notice, and to communicate their thinking to others. About the Lesson Within the lesson plan, there are more prompts than are feasible to use in one session. Some options for delivering the lesson are: – Focus on some rather than all of the pages, using the pages in between to highlight simple versus complex patterns – Carry out the second reading over two or three days, reading a few pages each day, followed by one of the Further Investigation activities – Revisit some of the pages on other days to explore the Further Investigation activities that may pertain to specific concepts (e.g., extending patterns with two attributes) Assessment Opportunities Observations: Throughout the reading, the related problem solving, and discussions, note which concepts are too difficult or too easy for students so next steps can be planned and lessons can be differentiated to meet individual needs. Note each student’s ability to: – Identify patterns – Identify the core of a pattern – Extend a pattern – Identify attributes in a pattern Patterns and Relations 27

Before Reading Connecting and reflecting Activating and Building On Prior Math Knowledge • Ask students why the name of the book is Pattern Fish. Ask students, “What is a pattern?” Have students turn and talk to share patterns that they know. Can they notice and name any patterns in the classroom? • Setting a Purpose: Tell students, “We are going to revisit the story as math detectives, and discover all the patterns that we see on the different pages.” During Reading Reasoning and analyzing • After each page, have students identify all the patterns they notice on the Communicating and page. Help students notice the link between the written words and the representing images and coloured border on the page. Connecting and reflecting • After reading the pages on the yellow/black fish, ask the students what Connecting and reflecting/ comes next. Have them explain how they know that the next colour is communicating and yellow. Ask students what repeats in this pattern (e.g., yellow-black). Explain representing that the core is the smallest part of the pattern that continually repeats. Reasoning and analyzing Further Investigation: Provide students with concrete materials (coloured tiles, connecting cubes, coloured counters, etc.) and challenge them to create Connecting and reflecting/ their own AB pattern. communicating and representing • After reading the pages on the eel, ask the students what comes next. Have students describe the core of this pattern. Ask students how this core is the same/different from the one in the previous pattern. Have coloured counters on the whiteboard so that students can show the similarities and differences between the patterns. • After reading the pages on the sea horse, ask the students what comes next. Ask students how many different patterns they can find on this page. Have students use concrete materials to represent the patterns they find and have them describe the core. • After reading the pages on the puffer fish, ask students what comes next and have them describe the core of this pattern. Focusing on the illustration of the fish, have students identify the different ways that patterns on the fish change (i.e., shape and colour). Have the students look at the frog and fish on the bottom right-hand side and identify how that pattern changes. Explain to students the word ‘attribute’ and how these patterns change with two attributes (e.g., fish and purple, frog and green). Further Investigation: Give students pattern blocks and have them create and extend patterns that use the same core (AAB) as the patterns on this page. Have students do a gallery walk and identify the attributes their peers used. • After reading the pages on the octopus, ask students what comes next and have them describe the core. Have students identify and extend the core in all the patterns they can find on the page (e.g., page border, shapes on the purple fish, the grass, the turtle shell, the stripes on the fish). 28 Patterns & Relations/Data & Probability

Understanding and solving Further Investigation: Focus on the pattern in the page border. Have students investigate ways to change the pattern to a pattern with a different Connecting and reflecting/ core. communicating and representing • After reading the pages on the jellyfish, ask the students what comes next. Ask students how many different patterns they can find on this page. Have them use concrete materials to represent the patterns they find. Have students describe the core in the patterns they find. • After reading the pages with the shark, ask the students what comes next and have them describe the core of the pattern. Have students share where else they see this core on the page. Further Investigation: Provide students with concrete materials (coloured tiles, connecting cubes, coloured counters, etc.) and challenge them to create their own pattern. After Reading Connecting and reflecting Building Growth Mindsets: • Ask students for examples of where they saw math in this story (e.g., patterns on the fish, patterns in the borders). Discuss where they have seen patterns in real life (e.g., other animals, in their homes). • Ask students what questions they still have about patterns and create an anchor chart of these questions. Talk about how mathematicians ask questions about math so that they can keep learning. Explain that together, you will keep exploring ideas about patterns to help answer their questions, so if they are not sure YET, you will keep working on activities to help them get there. Further Practice • Reflecting in Math Journals: Verbally pose one of the following prompts: − Using pictures, letters, and/or words, show the patterns that are in the book. − Using pictures, letters, and/or words, show patterns in the classroom that are similar to the patterns in the book. − Create a pattern that is the same as one of the patterns in the book. Describe your pattern. [If necessary, provide students with stickers or stamps (etc.) they could use to create their patterns.] • Community Walk: Take students on a walk through the playground and/or community: − Notice and name patterns while on the walk. − Collect loose parts students could use to create and name patterns upon your return (e.g., rock, rock, leaf, twig — AABC). − Take photographs of patterns you see along the way. Encourage students to use a digital tool to mark up the patterns they spot in the photographs. Patterns and Relations 29

4Lesson Describing and Identifying the Core of a Pattern Math Curricular Competencies Learning Standards • Reasoning and analyzing: Use reasoning to explore and make Teacher connections; model mathematics in contextualized experiences Look-Fors • Understanding and solving: Visualize to explore mathematical concepts Previous Experience • C ommunicating and representing: Communicate mathematical thinking with Concepts: Students have identified in many ways; use mathematical vocabulary and language to contribute to the core of a pattern and mathematical discussions; explain and justify mathematical ideas and decisions; discussed how it helps us represent mathematical ideas in concrete, pictorial, and symbolic forms extend the pattern. Content • Repeating and increasing patterns Possible Learning Goals • Recognizes patterns and describes them using appropriate mathematical language • Identifies and explains the core of a pattern and describes it using a letter coding system • Uses the core of a pattern to extend it • Describes how a pattern is repeating and what attributes are changing • Identifies the core and uses it to accurately extend a variety of patterns • Matches pattern cores with letter coding descriptions • Describes and explains how a core matches its letter code description About the As students compare patterns by their structure, they should use a letter coding system to help them describe the core of the pattern. Using letter codes was first introduced in grade one so students should be somewhat familiar with it. Marian Small explains that primary students need opportunities to label patterns using a letter code system to help them “see how two seemingly dissimilar patterns can be the same mathematically” (Small, 2010, p. 3). 30 Patterns & Relations/Data & Probability

Math Vocabulary: For example, using the letters ABC to represent the changing pccAaooBtrdteBee,,rsanAt,(AetrrB.eigb,p.u,AetABaeBt,Cin,)legt,ter attributes in a pattern with three elements in its repeating unit, or core, helps students see how two patterns (e.g., one using shapes, the other using rhythmic moves such as clap, snap, and jump) can have the same core. It is also important that students be able to extend a pattern once they have identified it and its core. Small states that having students extend the pattern is a better representation of their understanding than having them solely describe the pattern (Small, 2017, p. 361). Materials: Minds On (20 minutes) concrete materials • Make a pattern using colour tiles (e.g., red square and blue square, that (colour tiles, pattern blocks, connecting repeats at least three times). Ask students which attributes are changing and cubes, loose materials), which are staying the same. Ask what the core of the pattern is. Review the chart paper concept of the core and how it helps to extend a pattern. Time: 50 minutes • Explain that mathematicians spend a great deal of time figuring out patterns and how they work. They also like to compare patterns to see how they are the same and how they are different. Tell students that the problem they will solve is to figure out and compare some patterns. • Ask students what they think mathematicians need to understand about a pattern to figure it out and compare it to others (e.g., what a pattern is, what the core is, what the pattern rule is). • Explain that mathematicians sometimes make a model or a system that will help them solve problems. For patterns, they created a naming system so they could better understand and compare patterns. • Draw attention to the pattern created with colour tiles. Tell students that the red square can be called ‘A’ and the blue square can be called ‘B.’ Record these letters under the first two squares. Ask students what they think the ‘A’ and ‘B’ represent. (‘A’ means red and ‘B’ means blue.) Ask what attribute is changing (colour) and what attribute remains the same (shape). Ask what letters would come next. Have students say the letters so they can also hear the pattern repeat. • Draw a shape pattern with the following core on chart paper (draw outlines of the shapes only, using the same colour): rectangle, rectangle, triangle. Ask students what the core of the pattern is. (two rectangles, one triangle) Ask them how many different elements are in the core. (two, rectangles and a triangle) Ask what attribute stays the same from shape to shape (colour) and what attribute is changing (shape). Ask students what letter they could call the rectangles and what letter they could call the triangles. Record the letters below the pattern as students name them. Explain that we call this an AAB pattern. Patterns and Relations 31

• Ask students whether they could create an AAB pattern using colour tiles so the changing attribute is colour. Ask what the letters represent. (e.g., ‘A’ is red and ‘B’ is blue.) Ask students whether they could represent an AAB pattern with different colours. Highlight how the patterns all have the same structure, AAB, but the A and B represent different attributes and changing characteristics. • Repeat this with a pattern that has three different elements in its core (ABC). Working On It (15 minutes) • Tell students they are going to explore how the letter coding system works and how it helps them figure out and compare patterns. • Small groups of students work at centres, with each centre having some concrete materials. Together, students represent the following cores in as many different ways as possible: AB, ABC, ABB. • Students take turns creating a pattern. The rest of the students decide what the letter code should be. Together, they define what each letter represents. Differentiation • For ELL students, ensure that students understand how the letter code system works. • For students who need a challenge, have them create their own pattern core and represent it in different ways. Assessment Opportunities Observations: Note students’ ability to create the core of the pattern from the letter code. Conversations: If students are having difficulty creating the core of the pattern, pose some of the following prompts: – If the core is AB, how can you say the pattern using the letters? (e.g., ABABABAB) – H ow would you say it if the A is a square and B is a triangle? – W hat else could A and B represent? What if you used colours? Make this pattern using colour tiles. – H ow could you represent an AB pattern using the concrete materials at your centre? 32 Patterns & Relations/Data & Probability

Consolidation (15 minutes) • Discuss how the letter coding system can help us to figure out the core and compare patterns. Highlight how two patterns can look very different but have the same core pattern, which means they repeat in the same way. Explain to students that they will have several more opportunities to use the letter coding system. Ask why the model may not work. (e.g., It is hard to know what the letters represent if too many attributes are changing.) Ask students what is important to include when using letter codes. (e.g., what attributes or characteristics the letters represent) • Create an anchor chart that explains how the letter coding system works. • B uilding Growth Mindsets: Ask students which letter codes were easiest to represent and which were the hardest. Remind them that sometimes tasks can get tricky, but mathematicians work hard and keep practising in order to learn. Ask students how they can learn from making a mistake, such as thinking a different code applied to a pattern. Explain that mistakes make us reflect on what we are doing and try tasks from another perspective. First Peoples Perspectives Core patterns can be found in nature. One example can be seen in a Bracken Fern leaf. The core of the pattern is a triangle, and the triangle core repeats throughout each section of leaf in a smaller dimension. Encourage students to find the core patterns in nature photos or in various loose materials found in nature. Patterns and Relations 33

to5 8LessonsInvestigating Patterns and How They Repeat Math Curricular Competencies Learning Standards • R easoning and analyzing: Use reasoning to explore and make connections; model mathematics in contextualized experiences • Understanding and solving: Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving; visualize to explore mathematical concepts • C ommunicating and representing: Communicate mathematical thinking in many ways; use mathematical vocabulary and language to contribute to mathematical discussions; explain and justify mathematical ideas and decisions; represent mathematical ideas in concrete, pictorial, and symbolic forms • C onnecting and reflecting: Reflect on mathematical thinking Content • Repeating and increasing patterns • M ultiple attributes of 2D shapes and 3D objects (sorting 2D shapes and 3D objects, using two attributes, and explaining the sorting rule) About the Students gain experience with a variety of patterns throughout elementary school. In grade two, students identify and describe patterns that repeat and grow. Discussions should focus on how the attributes are changing (e.g., Are these shapes repeating in some way? Does the design appear to be increasing/growing?). Working with patterns is essential for students in the primary years as it enhances their ability to see relationships in patterns and determine pattern rules. This becomes important as students work with more complex patterns and generalizations later in their school careers. Describing patterns involves identifying the changing attributes, the number of elements in the pattern core, and the kinds of elements in the core. When students are initially identifying patterns, they might have difficulty identifying the core of a pattern when multiple attributes are involved (e.g., shape and orientation). Marian Small notes that having students begin by listing the attributes they see can help them focus on identifying the core 34 Patterns & Relations/Data & Probability

Math Vocabulary: core, (Small, 2017, p. 367). Students also experience more difficulties repeating, describing a pattern than they do extending it. Providing students pattern, attribute, with opportunities to read the pattern aloud (e.g., orange square, extend, describe, blue square, orange square, blue square) will assist them in create, developing their ability to describe the patterns using identify mathematical language. When creating patterns in the early years, it is important for students to begin with concrete materials before they move to drawing or using numerical representations. It is also important for students to focus on translating patterns: representing equivalent patterns (patterns with the same core) using different materials and attributes. Small notes that being able to translate a pattern from one medium to another demonstrates students’ understanding of the core, or the “mathematical structure of the pattern” (Small, 2017, p. 363). As students begin working on more complex patterns, they need opportunities to work with a variety of patterns, attributes, and concrete materials in order to practise visualizing and representing the core of a pattern. This will help students generalize the pattern so they can extend it and translate it into different pattern representations. About the Lessons The following four lessons review and build on students’ knowledge of patterns and the various ways in which they can repeat. The investigations allow students to build their understanding of the core of a pattern as well as investigate the attributes of the shapes used and how they change. The patterns throughout these lessons involve a variety of attributes, including orientation as a way to incorporate working on spatial reasoning in patterning. Recreating the patterns they see using concrete materials gives students further opportunities to translate from one form to another, reinforcing the concept that patterns can be represented in many different ways. Patterns and Relations 35

5Lesson Reviewing Patterns Teacher Possible Learning Goals Look-Fors • Recognizes patterns that use one attribute Previous Experience • Identifies the core in a one-attribute pattern with Concepts: • Represents patterns using concrete materials Students have had • Extends patterns using one attribute experience identifying, extending, creating, and • Uses counters to recreate patterns representing patterns. • A ccurately describes a visual pattern • E xtends a pattern by explaining what comes next Materials: • R ecreates patterns using concrete materials (e.g., pattern blocks, square BLM 2: Patterns tiles, connecting cubes) (One Attribute) or Minds On (15 minutes) Digital Slides 1–15, • Give each student about 10 counters or other concrete materials that vary in counters BLM 2: Patterns (One Attribute) 3 ways (e.g., 3 colours, 3 shapes, or 3 sizes). and/or other • Start by clapping the following simple pattern: Clap, Snap, Clap, Snap, Clap, concrete Snap, Clap. materials • Stop and ask students what comes next. Have students explain how they Time: knew what came next. Have students both share the pattern in this clapping 45 minutes sequence and visualize in their minds what the pattern looks like. Model the pattern on a whiteboard using circles (e.g., small circle, large circle, small 4 © 2022 Scholastic Canada Ltd. GRADE 2: PATTERNS & RELATIONS/DATA & PROBABILITY ISBN 978-1-4430-7187-1 circle, large circle; or red circle, blue circle, red circle, blue circle) and discuss with students what the core of this pattern would be and how we could label Scholastic Canada GR2 BC Patterns & Data Fourth Pass the pattern type (ABAB). Have students explain which attribute changes and Reproducibles which characteristic of the attribute each letter represents (e.g., size changes; October 25, 2021 A is small, B is big). Have students then use their counters to represent the pattern type. Digital Slide 15: Patterns (One Attribute) • Repeat this exercise with a few of the following movement patterns: Digital Slide 14: Patterns (One Attribute) − Tap your head, clap your hands, tap, clap, tap, clap (ABAB) Digital Slide 13: Patterns (One Attribute) Digital Slide 12: Patterns (One Attribute) Digital Slide 11: Patterns (One Attribute) − Tap right foot, tap left foot, tap right, tap left, tap right, tap left (ABAB) Digital Slide 10: Patterns (One Attribute) − Tap right, tap left, clap, tap right, tap left, clap (ABC) Digital Slide 9: Patterns (One Attribute) • Show students one of the patterns from BLM 2: Patterns (One Attribute) (or Digital Slide 8: Patterns (One Attribute) Digital Slides 1–15). Have students turn and talk with their elbow partner to share what comes next in the pattern sequence. Have them describe what the Digital Slide 7: Patterns (One Attribute) pattern is and how they knew what comes next. Have students close their eyes and visualize the core of the pattern. Ask them to represent the core of Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slide 6: Patterns (One Attribute) the pattern using their counters. Ask students how they could use letters to Digital Slides represent the core (the pattern structure). October 25, 2021 Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slides October 25, 2021 Digital Slide 5: Patterns (One Attribute) Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slide 4: Patterns (One Attribute) Digital Slides Fourth Pass October 25, 2021 Scholastic Canada GR2 BC Patterns & Data Digital Slides Digital Slide 2: Patterns (One Attribute) October 25, 2021 Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slides October 25, 2021 Digital Slide 2: Patterns (One Attribute) Fourth Pass Digital Slide 1: Patterns (One Attribute) Scholastic Canada GR2 BC Patterns & Data Digital Slides Scholastic Canada GR2 BC Patterns & Data October 25, 2021 Digital Slides October 25, 2021 Fourth Pass Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slides October 25, 2021 Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slides October 25, 2021 Scholastic Canada GR2 BC Patterns & Data Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slides Digital Slides Fourth Pass October 25, 2021 October 25, 2021 Fourth Pass Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slides October 25, 2021 Scholastic Canada GR2 BC Patterns & Data Digital Slides Scholastic Canada GR2 BC Patterns & Data October 25, 2021 Digital Slides October 25, 2021 Fourth Pass Scholastic Canada GR2 BC Patterns & Data Digital Slides October 25, 2021 Fourth Pass 36 Patterns & Relations/Data & Probability

• Repeat with three to four more examples, and for each, have students 1) share what comes next, 2) visualize the pattern core, 3) recreate the pattern with counters, and 4) identify the core using letters. Ensure that students clarify which changing characteristic of the attribute each letter represents. Working On It (15 minutes) • Have students work in pairs. Give each pair a pattern from BLM 2 and some counters. Have pairs take turns showing their pattern to another pair of students who then describe the pattern, tell what comes next and how they know, and then represent the core using the counters. • Additionally, have student pairs create their own patterns (using bingo dabbers or drawings), and have them switch with another pair to find the core of the newly created patterns. Differentiation • For students who may need a challenge, engage them with ABC patterns from BLM 2 or have them create their own patterns and switch with a partner. Assessment Opportunities Observations: • P ay attention to the students’ ability to identify the core of the pattern as well as their ability to represent and extend patterns. • W hen students recreate the pattern using counters, are they able to demonstrate the core? Conversations: If students are having difficulty describing the core of the pattern, ask them what comes next in the pattern and have them describe how they know. Have them show you what is repeating in the pattern. Place your hands around the repeating core to demonstrate for students what the core of that pattern is and ask them to represent that core with counters. Teaching Tip Consolidation (15 minutes) Co-create an anchor • Have a group discussion about things students know about the patterns they chart of the vocabulary discussed investigated. You may wish to use a few student-created patterns from the in this lesson (e.g., Working On It section to anchor the discussion. repeating pattern, core). Include examples with • Talk about how students know a pattern is repeating and discuss the the co-created definitions. These terms meaning of the word ‘core.’ can be added to the Math Word Wall. • Ask students how visualizing the pattern first helped them recreate the pattern with counters. • Inside/Outside Circle: Divide the class into two groups and make two circles, one inside the other, and have the two circles turn towards each other facing a partner. Each student has a pattern (pre-made or one they Patterns and Relations 37

created) behind their back. Students take turns showing their partner the image and then the partner describes the core of the pattern and what would come next. After everyone is done, have the outer circle move one partner over to the left. Students repeat the game again with their new partner. • Building Growth Mindsets: Ask students which patterns it was easiest to identify the core of, and which it was difficult. Remind students that they may not be able to recognize the core of some patterns YET but they will have plenty of opportunities and activities to help them learn to do this. Over the next few days, incidentally present a pattern for students to analyze. Spend 5−10 minutes discussing strategies for identifying the core. With practice, students will become more confident in their abilities. First Peoples Perspectives You can explore aural patterns through the heartbeat pattern in First Peoples drumming which replicates the human heartbeat. Invite a First Peoples drummer from your community to model the pattern and share the teachings. Drum teachings can be incorporated into your Social Studies program, and the tanning of hides in the Science program. If your school district’s Indigenous Education department has classroom drum sets, you can integrate drumming into your Fine Arts program. Nuu-chah-nulth storyteller Ren Louie has written a children’s book titled “Drum from the Heart” sharing the drum teachings of his people. Materials: Math Talk: “Animal Patterns” Math Focus: Identifying patterns in real-life contexts (page 4 in the Patterns, Relations, Data, and Let’s Talk Probability big book and little books) Select the prompts that best meet the needs of your students. Teaching Tip • Show page 4 to the students and ask them what they see. Have them turn and Integrate the math talk talk with a partner. moves (see page 7) throughout Math Talks • W hat animals do you notice? Where have you seen these animals before? Why to maximize student participation and might the animals have different colourings? What do you notice about the active listening. colourings of all these animals? • Read the title of the page to the students. Ask them why they think the page is titled “Animal Patterns.” Ask them what types of patterns they see. • Draw students’ attention to the zebra on the page. Does the zebra have a pattern on its skin? What pattern do you see? Does the pattern repeat? What is the core of the pattern? • Continue asking similar questions about the other animals on the page. 38 Patterns & Relations/Data & Probability

6Lesson Investigating Changing Attributes Teacher Possible Learning Goals Look-Fors • R ecognizes attributes in patterns Previous Experience • Determines which attributes change to create the core of the pattern with Concepts: Students have had • Explains or shows what changes in the pattern experience with • Names the attributes that change in the pattern investigating attributes. • Explains or shows where the attributes are in the core of the pattern About the Patterns rely on the changing attributes in the elements within the pattern. An attribute is defined as a characteristic of an object, shape, or event that can be qualitative (e.g., colour) or quantitative (e.g., number of sides). In early primary grades, students begin by investigating patterns in geometric designs where one attribute of the shapes changes. As patterns become more complex, the attributes students work with become more difficult; the number of attributes that change increases; and the type of attribute that changes can be different (e.g., shape, size, orientation). Marian Small suggests that educators use a variety of concrete materials (e.g., attribute blocks, loose parts) to help students develop an understanding of multi- attribute patterns (Small, 2017, p. 360). About the Lesson In this lesson, students explore a variety of geometric patterns and designs to help define and develop an understanding of attributes. Students will identify and describe the attributes and how they change within the patterns. Patterns and Relations 39

Materials: Minds On (15 minutes) Pattern Fish book, • Ask students to close their eyes and listen carefully. Clap the following BLM 3: Patterns pattern a few times: Soft Clap, Soft Clap, Loud Clap, Loud Clap. (Two or More BLM 3: Patterns (Two or More Attributes) • Have students describe to a partner what they heard, what they think the Attributes) or pattern was, and what would come next. Digital Slides • Ask students to describe what changed to create the pattern. • Show students the spread about the eel in Pattern Fish. Draw the core of the 16–30, sticky pattern on the eel on the board (i.e., red stripe, green dot, green dot). Ask notes, attribute students to describe the pattern and the pattern core. Then have them describe what changes to create the core (e.g., the shape and the colour). blocks, BLM 2: • Talk to students about the word ‘attribute’ and its meaning and definition. Patterns (One © 2022 Scholastic Canada Ltd. GRADE 2: PATTERNS & RELATIONS/DATA & PROBABILITY ISBN 978-1-4430-7187-1 9 Attribute) Discuss different attributes that can be changed when creating a pattern Scholastic Canada GR2 BC Patterns & Data Fourth Pass (e.g., colour, size). Reproducibles October 25, 2021 • Show one of the patterns from BLM 3: Patterns (Two or More Attributes) (or Time: 35 minutes Digital Slides 16–30) and ask students to describe the attributes they see that are changing. Digital Slide 30: Patterns (Two or More Attributes) • Do two to three examples with students, having them name the changing Digital Slide 29: Patterns (Two or More Attributes) attributes. Digital Slide 28: Patterns (Two or More Attributes) Digital Slide 27: Patterns (Two or More Attributes) Digital Slide 26: Patterns (Two or More Attributes) Digital Slide 25: Patterns (Two or More Attributes) • Tell students that they are going to investigate patterns and discover the Digital Slide 23: Patterns (Two or More Attributes) Digital Slide 24: Patterns (Two or More Attributes) changing attributes. Ask students what this means and whether they have any questions. (e.g., Could there be more than one pattern?) Digital Slide 22: Patterns (Two or More Attributes) Working On It (10 minutes) Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slide 21: Patterns (Two or More Attributes) Digital Slides • Assign each group different patterns from BLM 3 and have students October 25, 2021 investigate their pattern and name the attributes that are changing. Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slides • Have students write down the attributes that changed in the pattern on October 25, 2021 a sticky note and place it on the pattern page. Digital Slide 20: Patterns (Two or More Attributes) Differentiation Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slides • For students who might struggle identifying attributes, use BLM 2: Patterns October 25, 2021 (One Attribute) in a small-group format to engage students in a discussion Scholastic Canada GR2 BC Patterns & Data Digital Slide 19: Patterns (Two or More Attributes) about attributes. Additionally, use attribute blocks to discuss different ways Digital Slides Fourth Pass that attributes can change as you look at the blocks. October 25, 2021 • For students who need a challenge, have them create their own pattern that Digital Slide 18: Patterns (Two or More Attributes) uses multiple attributes and have them switch with a partner who will name Scholastic Canada GR2 BC Patterns & Data Fourth Pass the attributes that change. Digital Slides October 25, 2021 Digital Slide 17: Patterns (Two or More Attributes)Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slides October 25, 2021 Digital Slide 16: Patterns (Two or More Attributes) Fourth Pass Scholastic Canada GR2 BC Patterns & Data Digital Slides October 25, 2021 Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slides October 25, 2021 Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slides October 25, 2021 Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slides October 25, 2021 Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slides October 25, 2021 Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slides October 25, 2021 Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slides October 25, 2021 Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slides October 25, 2021 Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slides October 25, 2021 40 Patterns & Relations/Data & Probability

Assessment Opportunities Observations: • Pay attention to students’ ability to identify and name the different attributes found in their pattern. • Pay attention to students’ ability to recognize more than one attribute that changes in a pattern. Conversations: If students are having difficulty distinguishing between different attributes in the images, prompt by asking, “What is the core of the pattern? What is changing in the core?” Materials: Consolidation (10 minutes) “What Comes Next?” • Have students do a gallery walk of the different patterns in the classroom. (page 5 in the Patterns, Relations, Data, and Ask them to look for common attributes that change. Probability big book and little books), attribute • Bring students together and share what they noticed during their gallery blocks, pattern blocks walk. • Discuss the strategies that students used to find the patterns. Ask whether they changed or added to these strategies as they investigated more patterns. • Select two or three students to share their patterns and describe the attributes they saw changing. • Take pictures to add to a class patterns collage. • Co-create a “Changing Attributes” list of all the attributes students have found that can be changed. Math Talk: Math Focus: Investigating what attributes are changing in the patterns on the page Let’s Talk Select the prompts that best meet the needs of your students. • Show the students the first pattern (e.g., leaf pattern) and ask them to describe what they see to their elbow partner. • W hat attributes did you see changing in this pattern? (e.g., I saw size changing.) Put your thumb up if you agree. How did you see the size changing? (e.g., from big to small) Did anyone see a different attribute changing? (e.g., Yes, I saw colour changing.) How did you see the colour changing? (e.g., It changed from green to red.) • Repeat this line of questioning with the next pattern on the page. continued on next page Patterns and Relations 41

Teaching Tip • W ere the attributes in the first pattern the same or different from those in the Integrate the math talk second pattern? How were they similar? How were they different? moves (see page 7) throughout Math Talks • Repeat all of the above with the rest of the repeating patterns on the page, or to maximize student participation and active have the students do the following partner investigation. listening. Partner Investigation • Do you think we could use concrete materials to create a pattern similar to the lollipop pattern? • H ave students work in pairs to create patterns similar to those in the big book. Walk around and have students show how their pattern is similar and how it is different. 42 Patterns & Relations/Data & Probability

7Lesson Identifying, Describing, and Extending Patterns Teacher Possible Learning Goals Look-Fors • Identifies patterns that involve more than one attribute • Identifies the core of a pattern made using more than one attribute • Independently extends patterns made using more than one attribute • Describes the attributes that change in the pattern • Identifies the core of the pattern • Explains or shows how they use the core to extend the pattern Minds On (10 minutes) Materials: • Review the “Changing Attributes” list that was co-created in Lesson 6. • Show a pattern from Digital Slides 16–30. Ask students to identify and Digital Slides 16– describe the pattern as well as how the attributes have changed. Have 30: Patterns (Two students turn and talk with a partner about the core of the pattern. Ask students, “What comes next? How would you extend the pattern?” Ask what or More BLM 3: Patterns (Two or More Attributes) they need to know to extend the pattern (e.g., identify the core) and how they know the pattern is still repeating. Be sure to have students explain how Attributes), they know they have correctly extended the pattern. attribute Working On It (15 minutes) blocks, BLM 3: Patterns (Two or More © 2022 Scholastic Canada Ltd. GRADE 2: PATTERNS & RELATIONS/DATA & PROBABILITY ISBN 978-1-4430-7187-1 9 Attributes) Scholastic Canada GR2 BC Patterns & Data Fourth Pass Reproducibles October 25, 2021 Time: 40 minutes • Redistribute two patterns from BLM 3: Patterns (Two or More Attributes) to Digital Slide 30: Patterns (Two or More Attributes) each pair of students. For each of the images, have students: Digital Slide 29: Patterns (Two or More Attributes) − describe the pattern Digital Slide 28: Patterns (Two or More Attributes) Digital Slide 27: Patterns (Two or More Attributes) − identify and name the core of the pattern Digital Slide 26: Patterns (Two or More Attributes) Digital Slide 25: Patterns (Two or More Attributes) Digital Slide 23: Patterns (Two or More Attributes) − tell what comes next (extend the pattern) Digital Slide 24: Patterns (Two or More Attributes) Differentiation Digital Slide 22: Patterns (Two or More Attributes) • Some students may need more experience with identifying different pattern Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slide 21: Patterns (Two or More Attributes) Digital Slides cores. You may want to engage these students in small-group learning, starting October 25, 2021 with simple AB patterns and gradually increasing the complexity of the patterns (e.g., different types of patterns, patterns involving more than one attribute). Scholastic Canada GR2 BC Patterns & Data Fourth Pass Using attribute blocks to help students represent different patterns may also Digital Slides assist students in describing different patterns. October 25, 2021 Digital Slide 20: Patterns (Two or More Attributes) Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slides October 25, 2021 Digital Slide 19: Patterns (Two or More Attributes) Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slides October 25, 2021 Digital Slide 18: Patterns (Two or More Attributes) Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slides October 25, 2021 Digital Slide 17: Patterns (Two or More Attributes) Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slides October 25, 2021 Digital Slide 16: Patterns (Two or More Attributes) Fourth Pass Scholastic Canada GR2 BC Patterns & Data Digital Slides October 25, 2021 Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slides October 25, 2021 Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slides October 25, 2021 Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slides October 25, 2021 Scholastic Canada GR2 BC Patterns & Data Fourth Pass Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slides Fourth Pass Digital Slides October 25, 2021 October 25, 2021 Scholastic Canada GR2 BC Patterns & Data Digital Slides October 25, 2021 Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slides October 25, 2021 Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slides October 25, 2021 Patterns and Relations 43

• For students who might need a challenge, have them create their own pattern but keep it hidden from their partner. Have them describe the pattern to their partner who then builds or draws it, and extends it. The partner can then check to see if they got it correct. Have partners switch roles so each partner has a turn. Assessment Opportunities Observations: • W hile students are working, observe and listen to find out if they are recognizing, describing, and extending a variety of patterns. • P ay attention to students’ ability to recognize the use of more than one attribute in a pattern and how they use that knowledge to extend the pattern. • Pay attention to how students extend the pattern. Are they using the core of the pattern or just extending it piece by piece? Conversations: As students are working, check in with pairs of students to discuss their thinking around the patterns: – Describe the pattern. How did you know that was the pattern? – What attributes are changing in the pattern? How do you know? How does this help you extend the pattern? – Show me how you would extend the pattern. How did you know how to extend the pattern? – What is the core of the pattern? Explain or show how you know. Teaching Tip Consolidation (15 minutes) Choose student work • Bring the students together and discuss their strategies for identifying and that connects back to the learning goals. naming the pattern and how they have changed their previous strategies. • Choose one of the patterns students used and place it on the whiteboard. Ask students how they would extend the pattern. Ask students what they used to help them extend the pattern. (e.g., used the core to extend it) Ask students how figuring out the core of a pattern helps them extend it. Ask them why the core is so important. (e.g., helps us figure out what changes, helps us describe the pattern, helps us extend the pattern) • Inside/Outside Circle: Engage students in an Inside/Outside Circle (as described in Lesson 5). Each student has one pattern from BLM 3 behind their back. They take turns showing their partner the image and then the partner describes the core of the pattern and what would come next. After everyone is done, have the outer circle move one partner over to the left. Students repeat the game again with their new partner. 44 Patterns & Relations/Data & Probability

Materials: Further Practice “What Comes Next?” • Create clapping sequences for different pattern types (e.g., AB, ABC, ABB, (page 5 in the Patterns, Relations, Data, and AABB). Have students listen carefully as you model the pattern and have Probability big book and them describe the pattern and identify the type of pattern. little books), BLM 2: Patterns (One Attribute) • H ave students create their own clapping and/or dance sequence to share BLM 2: Patterns (One Attribute) with the class, and have the class identify and describe the pattern. 4 © 2022 Scholastic Canada Ltd. GRADE 2: PATTERNS & RELATIONS/DATA & PROBABILITY ISBN 978-1-4430-7187-1 Math Talk: Scholastic Canada GR2 BC Patterns & Data Fourth Pass Math Focus: Identifying and describing the core of the pattern, and extending Reproducibles the pattern to show what comes next October 25, 2021 Let’s Talk Teaching Tip Select the prompts that best meet the needs of your students. Integrate the math talk moves (see page 7) • Show students the first pattern (e.g., leaf pattern) and ask them to describe what throughout Math Talks to maximize student they see to their elbow partner. participation and active listening. • W hat is the core of this pattern? (e.g., The core of this pattern is a big green leaf, a small red leaf.) Put your thumb up if you agree. What would the next item in this pattern be? Can you extend it further? How did you know what comes next? • Repeat this line of questioning with the next five patterns on the page. • Conclude with a discussion about how identifying the core of the pattern helps us figure out how to extend the pattern. Differentiation • Depending on the experience of students with identifying and extending patterns, you may wish to first conduct this Math Talk with simple one- attribute patterns (see BLM 2) before using the “What Comes Next?” page. Patterns and Relations 45

8Lesson Creating Patterns Teacher Possible Learning Goals Look-Fors • Independently creates patterns using more than one attribute • Accurately describes the attributes they use when creating patterns • Accurately describes and identifies the pattern created • Creates a pattern using more than one attribute • Explains or shows how attributes change within their pattern • Explains or shows where the core is in their pattern • Explains how to use the core of the pattern to extend it Materials: Minds On (15 minutes) “What Comes Next?” • Give students mini-whiteboards. Project “What Comes Next?” (page 5 in (page 5 from the Patterns, Relations, Data, and the big book). Ask students to describe the first pattern on the page. Have Probability big book), them also explain and describe the attributes used in the pattern (size, mini-whiteboards, colour, shape). whiteboard markers, concrete materials (e.g., • Pose the question, “If you were going to create a pattern similar to this one, tiles, counters, pattern blocks, connecting what would it look like?” Have students draw this on their whiteboards. cubes, attribute blocks) Time: 40 minutes • Share what students have drawn and share how they created their pattern. Discuss with students how to create patterns. Model the following on the whiteboard: create the core and then repeat the core to create a pattern. • Repeat this exercise with a few more of the patterns on the “What Comes Next?” page. Working On It (15 minutes) • Have students work in pairs. Challenge them to create three different patterns. Write the following requirements for the pattern challenge on the whiteboard and discuss them as a class so students know what they need to create: − AB pattern using two attributes − AABB pattern using two attributes − Your choice—create whatever pattern you would like Differentiation • If students are struggling to create patterns, have them start by creating simple AB patterns with one attribute and work towards creating more complex patterns with two attributes. 46 Patterns & Relations/Data & Probability

Materials: Assessment Opportunities camera, BLM 4: Observations: While students are working, pay attention to how they are Extend It! Create It! building their patterns: BLM 4: Extend It! Create It! – Are they able to build the core first and use the core to extend the Name: pattern? Part 1: Extend it! Can you find the core of these patterns? Conversations: While students are working, use some of the following Can you find what comes next? prompts to determine their ability to describe the patterns they are Underline the core and then extend the pattern two more times! creating: © 2022 Scholastic Canada Ltd. GRADE 2: PATTERNS & RELATIONS/DATA & PROBABILITY ISBN 978-1-4430-7187-1 13 – What is the core of your pattern? Can you show me the core? How did the core help you create your pattern? Scholastic Canada GR2 BC Patterns & Data Fourth Pass Reproducibles – W hat attributes did you use in your pattern? October 25, 2021 – C an you describe your pattern and how it changes? Consolidation (10 minutes) • Have students share their patterns with another pair. One pair will choose one of their patterns to share and the other pair will describe the pattern, identify the core, and identify the attributes used. Then they will switch so that the other pair can share one of their patterns. • Discuss the patterns with students. Which pattern was easy to create? Which one was more difficult to create? • Revisit with students how to create patterns using two attributes and co-create an anchor chart, “How to Create a Pattern.” Further Practice • Take photographs of student-created patterns. Print these photographs and have students use them to practise identifying, describing, and extending patterns. • Students can independently work on BLM 4: Extend It! Create It! to practise creating and extending patterns. • Independent Problem Solving in Math Journals: Verbally pose one of the following prompts: − My pattern is an AABB pattern and has shape and colour as its attributes. What might my pattern look like? − My pattern uses size and shape as attributes to create an ABBC pattern. What might it look like? Patterns and Relations 47

9 11LessonstoInvestigating Patterns That Increase Math Curricular Competencies Learning Standards • R easoning and analyzing: Use reasoning to explore and make connections; model mathematics in contextualized experiences • U nderstanding and 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 Content • R epeating and increasing patterns Mitenexacrtrtmeehn,aVdsido,ineccgnar,etbipafuyatl,eatdtreyer:sncrruiblee,, About the Primary students are naturally interested in patterns. They enjoy identifying patterns in books, rhymes, songs, and chants, and they will experiment with creating patterns as they play. Growing patterns follow a predictable rule as they increase. These patterns can include shapes or numbers. Certain growing patterns, such as the counting sequence 1, 2, 3, 4…, will be very familiar to students (Small, 2013, p. 608). Other growing patterns will be new to them. It is important to provide students with many opportunities to describe what they observe. Students will also need practice in representing and translating growing patterns from one form to another (e.g., from square tiles to counters, from connecting cubes to actions). When students represent the same growing pattern using different concrete materials or forms, they are working with the pattern’s structure and how it changes rather than looking at which attributes change. About the Lessons Lessons 9–11 build on students’ knowledge of being able to describe what they see in patterns and what attributes or operations are repeating or increasing. Students will investigate a variety of growing patterns that they will describe and represent in various ways. Students will also create their own growing patterns using a variety of elements to represent each term (e.g., concrete materials, actions). 48 Patterns & Relations/Data & Probability

9Lesson Investigating How Patterns Can Increase Possible Learning Goals • Describes a variety of patterns and how they grow • Represents growing patterns using concrete materials and actions (e.g., connecting cubes, clapping, callouts) Teacher • Extends patterns that increase Look-Fors • Identifies what comes next in a variety of simple growing patterns Previous Experience • Describes or shows the pattern rule for a simple growing pattern with Concepts: • Represents a simple growing pattern using a method of their choice Students have had experience identifying, (e.g., clapping, jumping, counters) extending, creating, and representing patterns. Minds On (15 minutes) • Call students to your gathering spot and begin the transition into the lesson by clapping and by stating in a soft voice, “If you can hear me, clap once. If you can hear me, clap twice. If you can hear me clap three times,” etc. Materials: • Once students are all listening, ask them what would come next in the pattern. Ask them to explain how they know. Have them turn and repeat the a variety of concrete pattern with a partner. Repeat the pattern with the entire class from the materials (e.g., beginning to check for understanding. Ask the following questions: connecting cubes, – How could you describe this pattern? (e.g., You start with one clap, counters, square tiles, then you do two, then three, etc.) pattern blocks, etc.), BLM 5: Geometric – How do you know how many claps to do each time? (e.g., You do one more clap than the last time, you add one clap each time, etc.) Designs That BLM 5: Geometric Designs That Increase Increase or – H ow many claps are there in each part of the pattern? (e.g., one, two, three, etc.) Share that each part of the pattern is called a ‘term.’ Digital Slides 31–33, Digital Slide 34: © 2022 Scholastic Canada Ltd. GRADE 2: PATTERNS & RELATIONS/DATA & PROBABILITY ISBN 978-1-4430-7187-1 15 • Ask, “How else might we represent this pattern? What does it mean to Describe This Pattern Scholastic Canada GR2 BC Patterns & Data Fourth Pass ‘represent a pattern’? What could we use to represent the pattern?” (e.g., We Reproducibles could use our math tools, connecting cubes, counters, pattern blocks, square Time: October 25, 2021 tiles, etc.) “How many would we use to start?” (e.g., start with one, then put 45 minutes two, then three, etc.) Have students represent this pattern visually with Digital Slide 32: Geometric Designs That Increase whichever tool they choose. Their representation might look like one of the Digital Slide 33: Geometric Designs That Increase examples on the first page of BLM 5: Geometric Designs That Increase or Digital Slide 31: Geometric Designs That Increase Digital Slide 34: Describe This Pattern Digital Slides 31–33. Scholastic Canada GR2 BC Patterns & Data Fourth Pass • Leave this representation visible (e.g., on a whiteboard or using a document Digital Slides October 25, 2021 Scholastic Canada GR2 BC Patterns & Data camera), and label each term of the pattern (Term 1, Term 2, etc.) for Digital Slides FourthPass students to access during the Working On It activity. Scholastic Canada GR2 BC Patterns & Data October 25, 2021 Digital Slides Fourth Pass October 25, 2021 Fourth Pass Scholastic Canada GR2 BC Patterns & Data Digital Slides October 25, 2021 Patterns and Relations 49

Working On It (15 minutes) • Organize students in pairs. Have each pair choose a way to represent the pattern that was modelled in the Minds On (e.g., clapping hands, shapes, counters, connecting cubes, letters [A/AA/AAA/...], musical instrument). They can refer to any previous anchor charts that were created to describe patterns for ideas. • When complete, have one member of each pair stay, and the other stray to visit the other pairs’ representations. At each representation, have the ‘stayers’ describe their representation and the ‘strayers’ check that it matches the same pattern rule. Switch. Differentiation • For pairs that may be struggling representing the modelled pattern, engage them in small-group instruction and/or ask prompting questions during Working On It. • For pairs that may need an additional challenge, ask them to create a more sophisticated representation of the pattern, such as the ones on pages 2 and 3 of BLM 5. Assessment Opportunities Observations: Pay attention to the students’ ability to translate from the modelled pattern to their own representation. Conversations: Use the following prompts to check for understanding: – What would be the next term in the pattern? How do you know? – What is the pattern rule to get from one term to the next term? – How else could you represent the same pattern? – H ow might you use these counters (clap, jump, etc.) to show me the same pattern? Teaching Tip Consolidation (15 minutes) Co-create an • Discuss as a group the things students know about the ways in which patterns anchor chart of the vocabulary discussed might grow. (e.g., gets bigger from term to term; gets bigger by the same in this lesson. Include amount each time; each part of a pattern is called a term; the amount it gets examples with the bigger by is called the pattern rule) co-created definitions. Add this chart to the • Project Digital Slide 34 and ask students to consider the two patterns. Have Math Word Wall. them describe what makes them patterns and how they are the same and how they are different. • Then have students share their thinking with an elbow partner. Ask students to give reasons for their choice. • Determine as a group which type of pattern each pattern is (repeating; growing). 50 Patterns & Relations/Data & Probability

First Peoples • Building Growth Mindsets: Ask students how they are feeling after learning Principles of Learning about growing patterns. Have them identify their emotions and why they might be feeling overwhelmed or frustrated. Reassure students that they will Materials: have many experiences ahead to practise and to clear up what might seem confusing. Make a list of things that students can do if they feel frustrated BLM 5: Geometric (take a break; ask a friend for help; check out an anchor chart; etc.). This Designs That Increase, supports the First Peoples Principles of Learning that learning involves BLM 6: Describe patience and time. the Pattern Further Practice Name: BLM 6: Describe the Pattern BLM 5: Geometric Designs That Increase • Independent Activity in Math Journals: Provide one of the pages from Repeating Growing BLM 5 to each student to paste into their Math Journals. Students name and describe what type of pattern these are and how they know. How do you know: • Students can complete BLM 6: Describe the Pattern to practise identifying Repeating Growing and distinguishing between repeating and growing patterns. How do you know: Math Talk: © 2022 Scholastic Canada Ltd. GRADE 2: PATTERNS & RELATIONS/DATA & PROBABILITY ISBN 978-1-4430-7187-1 19 Math Focus: Exploring more complex repeating and increasing patterns Scholastic Canada GR2 BC Patterns & Data Fourth Pass Reproducibles © 2022 Scholastic Canada Ltd. GRADE 2: PATTERNS & RELATIONS/DATA & PROBABILITY ISBN 978-1-4430-7187-1 Curricular Competencies October 25, 2021 • R easoning and analyzing: Use reasoning to explore and make connections 15 • Understanding and solving: Engage in problem-solving experiences that Scholastic Canada GR2 BC Patterns & Data Fourth Pass are connected to place, story, cultural practices, and perspectives relevant to Reproducibles local First Peoples communities, the local community, and other cultures October 25, 2021 • C ommunicating and representing: Communicate mathematical thinking Math Learning in many ways; use mathematical vocabulary and language to contribute to Standards mathematical discussions • Connecting and reflecting: Connect mathematical concepts to each other and to other areas and personal interests; Incorporate First Peoples worldviews and perspectives to make connections to mathematical concepts Content Repeating and increasing patterns • Explore more complex repeating patterns (e.g., positional patterns, circular patterns); Métis finger weaving; First Peoples head/armband patterning Math Vocabulary: About the Math Talk pipcnaalcottrtcteeekarrwnsn,ii,snrregeo,,ptlaceinitareect,iunolgaf,r symmetry This lesson is made up of several possible Math Talks based on the pictures in “Creative Patterns” (pages 6–7 in the Patterns, Relations, Data, and Probability big book). The purpose of using visual images is to stimulate math talk, which can further evoke inquiry about mathematics and how continued on next page Patterns and Relations 51

Materials: it relates to other cultures and to students’ lives. If students can see this relevance in the activities they do at school, they are more likely to make “Creative Patterns” connections and be curious about math. (pages 6–7 in the Patterns, Relations, Data, Finger Weaving and Probability big book and little books) While discussing the patterns on the sashes and the tumpline, you can Time: 20 minutes per day integrate the following information about finger weaving: (discussing 2−3 images each day) • The images display the art of finger weaving, which was practised early among the Indigenous Peoples of the Eastern Woodlands. Other Indigenous groups across Canada learned and practised finger weaving and adapted it to their cultures. For example, weavers in Quebec used dyed wool of many colours and developed more design patterns. They wove sashes for the voyageurs of the early fur trade era. • In the past and present, Métis made sashes, which are cultural symbols of their identity, and are worn at special events such as festivals. Families often used the same colours in order to identify who they were. The sashes were used as belts, ropes, towels, and as tumplines in order to carry heavy packages on their backs. The “Assomption Sash” became very popular with the Métis people, and is to this day a very important part of Métis culture. • One artist, Mechtild Morin, shares some facts about the process of her finger weaving. It takes her 100 to over 200 hours to finger weave a sash. It takes approximately one hour to complete 10 rows of weaving. It requires a lot of planning ahead of time, and counting of threads in order to successfully weave a pattern. As she measures out her materials, she must ensure that the strings are at least double the length of the end product (e.g., if the sash is to be 2 metres long, the individual strings have to be at least 4 metres long). If long fringes are desired, the length of strings must be increased accordingly. If you decide to teach your students the art of finger weaving, there are several online sites that can be of assistance. It is recommended that you check with members of your local First Peoples community to see which techniques and online information are most relevant to them. Source: http://www.metismuseum.ca/fingerweaving/weaving.php Let’s Talk Select the prompts that best suit the needs and interests of your students Headband by Gail Jackson (Tlingit) • L ook at this headband. What do you see? What materials were used to make the headband? It is made of red felt that has a blue edging and is decorated with beads. • What patterns do you see? Turn and talk to your partner. 52 Patterns & Relations/Data & Probability

Teaching Tip • W hat colour patterns do you see? What are the colour patterns in the flower Integrate the math talk and leaves? moves (see page 7) throughout Math Talks • L ook at the top petal of the flower. Imagine rotating the flower around the centre to maximize student participation and in a clockwise direction. How many times would the top petal match onto one of active listening. the other petals until it returns to its original position? (6) This is a circular pattern. • W hat would the artist need to do to make sure that each petal looks exactly the same so there is a repeating pattern? (e.g., count the number of beads of each colour) • What increasing patterns are there? (e.g., in the leaves, each row includes more and more beads as you move from the inside to the outside) • What do you notice about the left and right sides of the headband? (e.g., the two sides are mirror images of each other) How is a mirror image different from two identical images that are side by side? (e.g., the one side is the reverse or a reflection of the other side) Imagine flipping the design over to the other side. This is how the mirror image is made. The two designs are the same, but they are just in different positions. • If you folded the headband in half so the two sides match up, where would the fold line be? This is also known as the line of symmetry. Artists can create the pattern, starting at the line of symmetry and then work outwards on both sides, making sure that the two patterns are mirror images of each other. • W hat other natural materials do you see on the headband? (e.g., shells) Dancer from Kamloopa Powwow, Kamloops, 2015 (page 6) • T his young woman is a Northern Traditional Dancer. She made all of her own regalia. The women’s Northern traditional dancers dance with their feet rarely leaving the ground. This shows significance and staying grounded with mother earth. • What patterns do you see in her headband? What are the colour patterns? What are the shape patterns? • H ow would counting be important when creating this pattern? • W hat patterns do you see in the earrings? How would the artist ensure that the two earrings are identical and follow the same pattern? Dancer from Kamloopa Powwow, Kamloops, 2015 (page 7) • T his young man is a Men’s Fancy Dancer. All regalia worn by the dancer is handmade by himself. • W hat patterns do you see in his headband? What are the colour patterns? What are the shape patterns? • A re there any circular patterns? How can you describe how the circular patterns repeat? Look at the red and blue segment in the circle. If you rotated the circle around the middle in a clockwise direction, how many times would it repeat on part of the pattern before returning to its original position? (2) • Look at the band that goes around the head. What patterns do you see? Are these colour patterns or shape patterns or both? How do you know? How could you fold the headband in half so the design on one side matches the design on the other side? What is another name for the fold line? continued on next page Patterns and Relations 53

Leggings (Nisga’a) • W hat do you see? These are ceremonial leggings made from two separate chilkat-style blankets and/or aprons. How do you think they are worn? • A re the designs on the two leggings identical? How do you know? What colour patterns do you see on the legging on the left side? What do you notice about the left and right side of this first legging? If you were to fold the legging in half so the designs on both sides match onto each other, where would the fold line be? Repeat this line of questioning for the legging on the right side. • W hat patterns do you see on the two leggings? • W hat shapes did the artist use in this design? (e.g., ovoid, U-shapes) The design is said to show a diving killer whale. How do you see a diving killer whale? • Many natural materials were used to make the leggings, including mountain goat hair fibre, dye, sheep skin, cedar bark, cotton fibre, copper, and hemlock bark. Goulet Sash by Carol James (Métis) • What overall pattern do you see in this sash? (e.g., arrow-and-lightning pattern) • H ow does the pattern repeat? • How could you fold this sash so the design on one side matches onto the design on the other side? • W hich colour of strands do you think was used the most? How do you know? • L ook at the ends of the strands. How does this help you visualize how the pattern was made using finger weaving? Sash from office of Niwîk, ôwin Métis Family Services Society • T his sash was found at an estate sale. There is little known about it except that it is over 100 years old. • L et’s be detectives. What questions would you ask if you wanted to learn more about this sash? What would be important to know? Turn and talk to your partner. • What patterns do you see? Are they colour patterns and/or shape patterns? • Compare the patterns on this sash to the patterns on the Goulet sash. What is the same and what is different? Grant Family Sash (Métis) Mechtild Morin - weaver • Compare the patterns on this sash to the patterns on the other two sashes. What features are the same or similar and what features are different? • Compare the end strands on this sash to the end strands on the Goulet sash. What is different about them? What was done differently to the strands on this sash? • Look at the patterns on all of the sashes. What makes them all patterns? Tumpline (Coast Salish) • What do you see? This is known as a tumpline. Tumplines are often tied to baskets when both hands are needed for climbing or collecting. The woven band is normally worn against the forehead. The band of the tumpline narrows at each end and warp fibres are braided to create the carrying straps. Knots have been tied at both ends. 54 Patterns & Relations/Data & Probability

• What overall pattern do you see on the tumpline? (e.g., zigzag) What shapes do you see within the zigzag? (e.g., squares) • How can this be considered an increasing pattern as you look at the squares? (e.g., in the triangles at the bottom, there are more squares added onto each row as you move down the triangle) • H ow many different colours of strands did the artist use? What colour patterns do you notice? What is the pattern rule for each pattern? First Peoples Perspectives Many Indigenous cultures bead in some form and most beadwork is patterned. Invite First Peoples in your community to visit and share teachings about beading and patterning, and how these are important to their culture. Another option is to contact your school district’s Indigenous Education department for support or referral. Patterns and Relations 55

10Lesson Creating Patterns That Increase Teacher Possible Learning Goals Look-Fors • Independently creates patterns that increase • Represents a given pattern using different materials (e.g., square tiles, connecting cubes, pattern blocks) • Creates four terms of a pattern • Describes patterns and explains what the pattern rule is Materials: Minds On (20 minutes) Digital Slide 35: • Project Digital Slide 35: A Pattern That Increases showing the first term in a A Pattern That Increases, growing pattern. Digital Slide 36: Patterns • Explain that this is the first term in a geometric pattern. Have students turn That Increase, BLM 7: and talk to a partner about what the next term in the geometric pattern could be. My Pattern That Increases, • Ask students to share their ideas with the group. various concrete • Ask students some of the following prompts to help clarify/direct their materials BLM 7: My Pattern That Increases thinking: (e.g., five- and ten- Name: − How many red squares do you predict are in Term 2? Could there be My Pattern That Increases another answer? Draw your growing pattern: − What is the pattern rule? Can we tell what the pattern rule is from Term 1? frames, Term Term Term Term • Together, co-create a growing pattern. Discuss what the pattern rule is. Ask square tiles, Describe your pattern. students if there is another way to make a pattern that increases. pattern What is your pattern rule? blocks, connecting © 2022 Scholastic Canada Ltd. GRADE 2: PATTERNS & RELATIONS/DATA & PROBABILITY ISBN 978-1-4430-7187-1 21 Scholastic Canada GR2 BC Patterns & Data Fourth Pass Reproducibles October 25, 2021 cubes, colour counters) Time: 60 minutes • Show the growing patterns on Digital Slide 36: Patterns That Increase and Pattern Digital Slide 35: A Pattern That Increases compare them to the pattern you co-created. Digital Slide 36: Patterns That Increase Working On It (20 minutes) Term 1 Term 2 Term 3 Term 4 Term 3 Fourth Pass • Provide each student with two copies of BLM 7: My Pattern That Increases. Term 1 Term 2 Term 4 Our pattern rule: Explain to students that they will be creating two different growing patterns on their own. In each case they need to describe the pattern, identify the Scholastic Canada GR2 BC Patterns & Data Fourth Pass pattern rule, and extend the pattern for 4 terms. Ask students if they have Digital Slides any questions. Ask what would help to make the problem clearer. Together, October 25, 2021 Scholastic Canada GR2 BC Patterns & Data create an anchor chart of success criteria using student-friendly language, Digital Slides for example: October 25, 2021 − I can describe my pattern. − I can identify the pattern rule. − I can extend my pattern for 4 terms. 56 Patterns & Relations/Data & Probability