p10-86_Unit1_PatternsRelations

Unit 1: Patterns and Relations Lesson Content Page Getting Started with Patterns and Relations 10 Inviting Patterns and Relations into the Classroom 11 Introducing Patterns and Relations 15 1 Introducing Patterns 17 2 Read Aloud: Pattern Bugs: First Reading 23 3 Pattern Bugs: Second Reading 27 4 Is This a Pattern? 31 5 and 6 Action Patterns 34 5 Investigating Action Patterns 36 6 Creating Action Patterns 40 7 and 8 Investigating Attributes and How Patterns Repeat 42 7 Looking at Attributes 44 8 Investigating How Patterns Repeat 46 9 and 10 Describing and Extending Patterns 49 9 Describing Patterns 51 10 Extending Patterns: What Comes Next? 55 11 Investigating Number Patterns 58 12 Exploring Number Patterns in a Fifty/Hundred Chart 65 13 Pattern Detectives 69 14 Creating Patterns 72 15 Creating Patterns Using Barrier Games 76 16 Translating Patterns 80 17 Patterns and Relations Reinforcement Activities 84

Getting Started with Patterns and Relations There are two units in Patterns and Relations, as outlined below. 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 patterns and algebra concepts. • Each unit includes a series of Blackline Masters (BLMs) and Digital Slides to support the visual nature of patterns and algebra. • Each unit incorporates the use of a variety of concrete materials and tools that can be on hand and readily available for student use. • Each unit includes Math Talks, group discussions, and activities that target the curricular competencies (e.g., reasoning and analyzing, understanding and solving, communicating and representing, and connecting and reflecting) to support and develop students’ understanding. • Each unit includes activities to develop habits of mind, growth mindsets, and positive attitudes toward math in the classroom. • Making connections between patterns and algebra and other areas of math will maximize students’ learning and support flexibility in their thinking. When developing your long-range plans, consider the following: – Many of the geometric patterns make use of shapes that are investigated in Spatial Sense; – Lessons that involve number patterns and directly relate to Number with respect to skip-counting forward and backward and carrying out the operations of addition and subtraction; – Lessons that involve change in quantity and creating equality use concrete materials to build different numbers and can be linked to composing and decomposing numbers in Number and Operations; – Lessons on change in quantity and creating equality with numbers to 20 link to the operations of addition and subtraction. • It is beneficial to use the Patterns and Relations and Equality and Inequality units once students have a considerable grasp of skip-counting and simple operations (e.g., addition and subtraction). This will support students in making connections between what they know about number relationships, and how they relate to patterning and equality. 10 Patterns & Relations/Data & Probability

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 backward in order 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 patterning and equality/inequality concepts in daily routines. There are also quick five- to ten-minute activities that can be carried out while the class waits in line to go somewhere, when there are five 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 20 and beyond in the classroom allows for incidental reference during discussions or while students are problem solving. • Progressively count up the number of days in school. 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 (i.e., by 1s, 2s, 5s, 10s) in various ways to reach that number. Ask questions such as, “What would be the next day that we could count by 2s?” • 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 backward. • Consider using some off-benchmark number routines as well. Ask, “If we counted by 2s starting at 1, would we land on 8? Let’s use the number line to try.” • Put a clothespin or marker of some sort on all of the multiples of 5 (or 2 or 10) so students have a visual of how much they are adding or subtracting each time they say a number in the counting sequence. Fifty/Hundred Chart • Display a large fifty/hundred chart in the classroom at all times to use as a reference when discussions about numbers arise incidentally, or as a tool for planned activities throughout the day. • Practise counting forward and backward by 1s, 2s, 5s, or 10s, using the hundred chart. This is the introduction to identifying a number pattern rule (e.g., I started at 5 and counted by 5s). Ask students what patterns they Inviting Patterns and Relations into the Classroom 11

notice in the numbers that make up this counting sequence. Ask them to predict what other numbers will appear in the same pattern. • Discuss how the patterns in the fifty/hundred chart and the patterns on the number lines are linked, so students can make connections between the two representations. • If you are using a fifty/hundred pocket chart with removable numbers, consider rearranging the numbers so zero is at the lower left and the numbers increase from the bottom. This can help students understand the increase in numbers as they move up the chart (gfletchy.com). 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 math concepts. • Like a fifty/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 fifty/hundred chart. Quick 5–10-Minute Activities Physical Movement Activities • Opening Patterns: Begin each day throughout this unit by acting out, clapping, singing, chanting, etc., a pattern that you can use to bring the class together to begin the lesson. For instance, you could start with a repeated action [clap, clap, snap, clap, clap, snap,…] and continue the pattern until the entire class joins in. To reinforce their understanding, ask a few clarifying questions: – What were the elements of our pattern? – What order are they in? – What other actions could we substitute to make the same type of pattern? – How is this pattern the same as yesterday’s pattern? How is it different? You may also wish to keep an anchor chart of each day’s opening pattern for students to use as a reference to compare and contrast. Through classroom experiences in identifying, extending, and creating patterns, students 12 Patterns & Relations/Data & Probability

develop the ability to describe the patterns and recognize relationships between patterns. • 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 of each movement. They can also name the pattern using letter combinations such as A, B, C, etc., as above. • G roups in Motion: Have students walk around the room and then, when you say a pattern letter code such as 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 backward, facing forward). • S ound 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 backward by 2s from 20). As they say their number, they crouch down. Then have them sound off from the back of the line, standing up as they say their number. • S kip-Counting Sound Off: Students decide what they want to count. For example, they may decide to count eyes so they count down the line by 2s, or they might count fingers on right hands and count by 5s as they hold up one hand and then the other, or count by 10s holding up both hands at the same time. They can count backward 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, etc.) 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) • Make It Equal: Students find a partner, and label off Partner A and Partner B. They each secretly choose a number of fingers to hide behind their back. On the count of three, they both show their fingers and have to decide how to make Partner B’s fingers equal to Partner A’s. Games • G uess My Number: Give clues such as, “I’m thinking of a number between 0 and 20. Guess my number.” As students guess, use the terms ‘more’ or ‘less’ to help guide them toward your numbers. • Pattern Rule of the Week: Write a pattern rule (e.g., AAB) on a predictable spot in the room. As the week progresses, have students identify and describe patterns they see that fit the pattern rule of the week. • W hat’s the Pattern?: Organize students into a pattern based on a secret rule (e.g., jeans, shorts, shorts OR glasses, no glasses, glasses, etc.). Have students guess what the rule is and then continue the pattern as far as they can, based on what people are wearing that day. Inviting Patterns and Relations into the Classroom 13

• A Handful of Objects: Bring out collections of a specific type of concrete materials (e.g., pattern blocks, relational rods, connecting cubes, counters). In pairs, have students each take a handful of objects. Together, they need to create a 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 letter code of the pattern (e.g., AAB). • Snap It!: Give students connecting cubes and have them make a train. In partners, they count to three and snap their train, hiding one of the two pieces behind their backs. Partners show the piece left in their hands to each other and figure out how many connecting cubes their partner is hiding behind their back. 14 Patterns & Relations/Data & Probability

Introducing Patterns and Relations About the Doug Clements and Julie Sarama describe patterning as “the search for mathematical regularities and structures” to bring “order, cohesion, and predictability to seemingly unorganized situations and allows you to make generalizations beyond the information in front of you” (Clements & Sarama, 2009, p. 190). They explain that patterning goes beyond a content area to study in school to be a “process, a domain of study, and a habit of mind” (p. 190). Young children are very good at finding a variety of patterns in their world, including in behaviours, sounds, movements, visual representations, and designs. They also enjoy extending and representing the same pattern with different materials (translating). With experience, they also learn to create their own patterns and describe the pattern rule. Lesson Topic Page 1 Introducing Patterns 17 23 2 Read Aloud: Pattern Bugs: First Reading 27 31 3 Pattern Bugs: Second Reading 34 36 4 Is This a Pattern? 40 42 5 and 6 Action Patterns 44 46 5 Investigating Action Patterns 49 51 6 Creating Action Patterns 55 58 7 and 8 Investigating Attributes and How Patterns Repeat 65 69 7 Looking at Attributes 8 Investigating How Patterns Repeat 9 and 10 Describing and Extending Patterns 9 Describing Patterns 10 Extending Patterns: What Comes Next? 11 Investigating Number Patterns 12 Exploring Number Patterns in a Fifty/Hundred Chart 13 Pattern Detectives Patterns and Relations 15

Lesson Topic Page 14 Creating Patterns 72 76 15 Creating Patterns Using Barrier Games 80 84 16 Translating Patterns 17 Patterns and Relations Reinforcement Activities 16 Patterns & Relations/Data & Probability

1Lesson Introducing Patterns Math Curricular Competencies Learning Standards • Reasoning and analyzing: Use reasoning to explore and make connections • 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 • C onnecting and reflecting: Reflect on mathematical thinking; connect mathematical concepts to each other and to other areas and personal interests Content • R epeating patterns with multiple elements and attributes About the Lesson This lesson is made up of several Math Talks based on the pictures in “Spot the Patterns” (pages 2–3 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 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. Each picture or set of pictures can support a stand-alone Math Talk and investigation. The Math Talks can be used on progressive days, one Math Talk and partner investigation per day, to investigate and explore how patterns are all around us and can be seen 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 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. continued on next page Patterns and Relations 17

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 the framework for your Math Talk. Rather than following as they are written, allow students’ responses to guide the flow of the discussion, keeping in mind the goal of the lesson. Partner Investigation (10 minutes) Have students work in partners 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 levels of understanding. This is a good assessment opportunity to uncover what students know and what misconceptions they may have. Consolidation (10 minutes) B uilding 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. Build and nurture habits of mind and growth mindsets by discussing 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 toward 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. “Spot the Patterns” Dogs (pages 2–3 in the Patterns, Relations, Data, • What do you see in this photograph? Does anyone have a pet at home? and Probability big book) • What do you notice about the dogs? Time: 20 minutes per day • What patterns do you see on the dogs? Do the patterns repeat? How do they (discussing 2–3 images each day) repeat? Are the patterns the same on each dog? Why do you think they are not exactly the same? • Are there any other pets you can think of that have patterns on them? Possible Partner Investigation • Have students investigate different pets that have patterns on their bodies. Discuss the patterns they see and how they see them. 18 Patterns & Relations/Data & Probability

• Let students create their own patterned pet. Challenge them to draw their creation. They can verbally explain their creations to the rest of the class. Socks • What do you notice about these socks? Who has socks like these? • D o you notice a pattern on these socks? What pattern is it? How does it repeat? • If we continued the pattern on these socks, what would come next? How do you know? • What other patterns have you seen on socks? Possible Partner Investigation • Students can create their own patterned socks with a partner. Have them share with another partner, who then has to describe the pattern they see. Honeycomb • What is this picture about? What lives here? • Have you ever seen a structure like this before? Where have you seen it? • What would you find inside this structure besides the animals? • What shapes do you see in this structure? Why do you think hexagons are a good shape for the animals’ home? • Estimate how many hexagons there 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? Checkerboard • What game is this? Have you played this game before? How do you play it? • What do you notice about the board? What patterns do you see? • How many light squares are there on the board? How does the pattern of the squares help you know how many there are? Are there as many dark squares as light squares? Why do you think so? • What do you notice about the checkers on the board? How many black pieces are on the board? How do you know? How many light pieces are on the board? How do you know? Possible Partner Investigation • H ave students explore other board games and see what patterns they can find. Patterns and Relations 19

Snake • What do you see in this image? Have you ever had a close-up look at a snake? What did you notice? • Estimate how many white stripes are on the snake. Based on your estimate, how many red sections does the snake have? • Do you notice any patterns on the snake? • Why might snakes have patterned skin? How might their stripes help them? How might their stripes help others (e.g., people, animals)? Possible Partner Investigation • Have students investigate why animals have stripes. • Have students investigate what other reptiles have patterns on their bodies. • Students can draw their own patterned snake or reptile. Zebra • What animal do you see? Where might we see zebras? Do zebras live in Canada? What other animals do you know that look similar to a zebra? • What patterns do you see on the zebra? • Why do you think zebras have stripes? • Estimate the number of stripes on the zebra. How could we count them? Possible Partner Investigation • Have students investigate other mammals that have stripes and share their findings with the class. Bricks • What do you see in this image? Where have you seen these objects before? • Why might people have bricks on their property? • Do you have bricks at your house? What do they look like? Where are they? • Estimate how many bricks are in this image. How could we count them? • What patterns do you see in these bricks? How are they the same? How are they different? • Why do you think people might put bricks into patterns? Possible Partner Investigation • Go for a community walk. Have students look for patterns on the different houses. They can look for patterns (e.g., colours or shapes of houses) as well as growing and/or shrinking patterns (e.g., the numbers on the houses). 20 Patterns & Relations/Data & Probability

Materials: Math Talk: Patterns in Beadwork “Spot the Patterns” Math Focus: Investigating patterns in beadwork (pages 2−3 in the Patterns, Relations, Let’s Talk Data, and Probability big book and little books), Select the prompts that best meet the needs of your students. collection of different- coloured beads Earrings Teaching Tip • Show students the earrings in “Spot the Patterns” on page 2 of the big book. Integrate the math What do you see in this picture? Where have you seen earrings before? talk moves (see page 7) throughout • W hat patterns do you notice on the earrings? What is the pattern that you see Math Talks to maximize student in the colours used in the earrings? (e.g., white, dark blue, light blue, dark participation and blue, and then it repeats) If another row of beads is added to the bottom of the active listening. earrings, what colour would be used? What colour would be used after that? How do you know? • Look at the top ‘arrow’ that is made with dark-blue and light-blue beads. How many of each colour is used to create one column in the arrow? (one dark-blue bead, one light-blue bead, one dark-blue bead) Why is it important to use the same number of beads in each column to make the pattern? • Look at the pattern above the arrows that is made up of light-blue and dark- blue beads. How many beads does the artist use in each column? (one dark- blue bead, one light-blue bead, one dark blue-bead) Both patterns use the same colour and same number of beads in each column. Why do the patterns look different? (e.g., Each column in the top pattern starts at the same place so you have rows that are all the same colour. Each of the first five columns in the arrow starts one row lower than the previous column.) Partner Investigation • S tudents can explore different pieces of Indigenous artwork and look for patterns. Encourage them to explain why they think they are patterns and how they repeat. • S tudents can create their own patterns with beads of different colours. Flower Pattern with Beads • Show students the flower brooch on page 3 of the big book. What do you see in this picture? What materials did the artist use to create this design? • W hat colours do you see in the heads of the flowers? How are the colours used so they make a pattern? (e.g., There are different colours on the outside of all three flowers than on the inside of the flowers.) • W hat is the same about all of the flower patterns? (e.g., They all have light- coloured beads in the centres and rows of different-coloured beads on the outside.) • Look at the leaves. What colour patterns do you see? Is the pattern similar to the pattern in the flower heads? In what way? (e.g., The outside has a continued on next page Patterns and Relations 21

d ifferent shade of green beads; there are rows of different-coloured beads, just like the flower heads.) • Look at one petal in the large flower. How does its design repeat? (e.g., As you go around the flower, each petal has the same pattern.) • H ow is counting going to help the artist as this pattern is made? Partner Investigation • G ive pairs of students beads of various colours and have them create a flower that has a repeating pattern. After they have completed it, have them create another flower that has the same pattern but looks different, such as using different colours. • Students can meet with another pair and explain their patterns and how they repeat. Moccasin Beadwork • Show students the moccasins on page 3 of the big book. What do you see in this picture? These are called moccasins, and they are shoes that are usually made from moose hide or other animal hides. • W hat has the designer used to decorate the moccasins? What shapes or pictures do the beads make? • Look at the big flower. How is it similar to the flower pattern that we just looked at? (e.g., Both are flowers with blue petals; the petals on both designs have three colours of beads.) • How are the flowers different? (e.g., The one flower has light-blue and dark- blue beads making a round shape, and the other flower has light-blue and dark-blue beads making a teardrop shape.) • How are the patterns different on the two flowers? (e.g., The flowers on the moccasins have more beads in the middle and they have one loop of light blue with two extra strands of light blue at the top of the petal.) • Look at the other flowers and leaves on the moccasins. What patterns do you see? How do they repeat? • P oint to the stamens on the yellow flower. These parts of the flower are called ‘stamens.’ How do you think they help the flower? (e.g., They make the pollen.) The bees collect the pollen from the flower and then take it back to their hives to make it into food for the queen. What pattern do you see on the stamens? If you continued this pattern, what might it look like? (e.g., some white beads and then one orange bead) How is the pattern repeating? • Is there another way to make a pattern? (e.g., You could add orange beads so there are the same number of white beads, then keep adding the same number of white beads and then the same number of orange beads.) Are all of our ideas patterns? Why? What makes them patterns? Partner Investigation • G ive pairs of students three different colours of beads. Have them create a single line of beads that has a repeating pattern. 22 Patterns & Relations/Data & Probability

2Lesson Pattern Bugs: 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 Bugs, students apply their literacy strategies, such as inferring, using prior knowledge, and synthesizing information, to understand the context of bugs. (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 support selected grade one science learning standards and help students make connections across subject areas. During the second reading, students become mathematicians and apply the curricular competencies to discover and explore the math concepts embedded in the story. Both readings are also valuable for assessing where students are, what some of their misconceptions might be, what concepts need greater emphasis, and what differentiation may be necessary. English Curricular Competencies Language Arts Learning Standards • C omprehend and connect: Engage actively as listeners, viewers, and Science readers, as appropriate, to develop understanding of self, identity, and Learning community; use personal experience and knowledge to connect to stories Standards and other texts to make meaning Curricular Competencies • Q uestioning and predicting: Demonstrate curiosity and a sense of wonder about the world; make simple predictions about familiar objects and events • A pplying and innovating: Generate and introduce new or refined ideas when problem solving • C ommunicating: Express and reflect on personal experiences of place Content • C lassification of living and non-living things • Behavioural adaptations of animals in the local environment 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. Patterns and Relations 23

Materials: Assessment Opportunities Observations: Note each student’s ability to use visual cues to make and support predictions, and to make inferences and demonstrate understanding by engaging in discussions and follow-up activities. Written by Trudy Harris Read Aloud: Pattern Bugs Illustrated by Anne Canevari Green Summary: This book uses the context of bugs, text features, and visuals to Text Type: Fiction: expose students to different pattern types. The rhyming language, repetition of Description—Poem ideas, and visual clues help students predict the missing pattern elements Time: 15–20 throughout the story. minutes NOTE: There are more prompts than it is feasible to use in this amount time. Select the prompts that best meet the needs and interests of your students. Before Reading Inferring/predicting Activating and Building On Prior Knowledge Building on • Show students the front cover and ask what they see. Read the title and the prior knowledge Inferring names of the author and illustrator. Ask students to predict what they think the book might be about (e.g., bugs, patterns we see in nature) and have them explain their reasoning (e.g., there are different bugs on the cover). • Ask students if they have a garden or have visited a park with plants that might attract bugs. Discuss how the needs of bugs are the same as and different from the needs of humans. Ask, “What kind of bugs or other animals might we see in this book? What might they be doing?” List students’ answers on chart paper. • Setting a Purpose: Tell students, “Now that we have made our predictions, let’s read the story together to see what we will learn out about bugs and patterns.” During Reading Predicting • A fter reading the first spread (“Fluter-float...”), ask students what word comes next. Have them explain how they know. Ask them how the picture helps to predict what comes next. Using text features • Ask students what they think the three dots (ellipsis) at the end of the line are and what they might mean. (e.g., They make us read on to find out what happens next; the sentence finishes on the next page and then we see a period.) Refer to this punctuation when it appears on upcoming pages. Making connections • Ask students what living things they see in the picture. Ask what features the Predicting/analyzing butterfly has and what they know about this insect. Begin a co-created anchor chart of all of the bugs and other animals that are featured as you progress through the book. • After reading the next spread (“float”), ask what word would come after ‘float’ and have students explain how they know. 24 Patterns & Relations/Data & Probability

Using text features • Have students notice the organization of the letters in the word ‘float.’ Ask Visualizing/analyzing why they think the letters are written in this way. (e.g., They make you feel Inferring the movement in the word ‘float’ by moving up and down.) Have students act out the word ‘float.’ Using and analyzing text features • After reading the next spread (“Skitter-scoot-crawl...”), have students close Using and analyzing their eyes and visualize the pattern. Repeat “skitter-scoot-crawl” and ask text features/ students what they think each word means. making connections • Ask what features the beetle has and what they think it eats. Using text features • After reading the next page, have students examine the word ‘crawl.’ Ask Analyzing/ what they notice about the letters. (e.g., They’re on a slant.) Ask why they are making connections printed in this way. (e.g., to show us the direction the beetle is crawling in) Using text features/ • Before reading the next spread (“Buzz-buzz-buzz...”), ask students what they making connections see on the pages (e.g., bee and flowers) and have them predict what the bee is Using text features doing (e.g., collecting nectar to take to the hive to make honey). Read the Analyzing/ pages to confirm students’ predictions. making connections • After reading the next spread (“sip”), ask students what they notice. Using text features Inferring (e.g., The bee is using a straw; there’s a drop of liquid coming from the bee’s mouth; there are three drops of liquid used to dot the ‘i’ in the word ‘sip.’) Using text features/analyzing Ask how these clues help us understand the word ‘sip.’ (e.g., We know it is drinking from the flower.) • A fter reading the next two spreads (“Nibble-nibble-bite...” and “chew”), ask what the caterpillar is eating. (e.g., leaves, stems, and petals) Ask students if they have seen bugs eating plants. Have them share their experiences and help them to make connections about what living things provide for other living things. • B efore reading the next two spreads, ask students what they notice (e.g., flowers, an insect/cricket, some music notes) and what they think the music notes mean (e.g., this insect makes music). Make the connection to the diverse physical characteristics of animals. • R ead the next two spreads (“Chicka-chirp-chirp...” and “chirp”). Ask students what they notice about the word ‘chirp’ on the second spread (e.g., there is a big music note above it) and what they think it means (e.g., the insect is singing). • Before reading the next two spreads, ask what has changed in the background. (e.g., The sky is dark; there are stars in the sky; the houses have their lights on.) Ask what this means. (e.g., It is nighttime.) • Read the next two spreads (“Twinkle-twinkle-dim...” and “dim”). Ask students what they think the words ‘twinkle’ and ‘dim’ mean. Have them give examples of things that twinkle and dim from their own lives. • Before reading the next two spreads, ask students what they notice in the picture. (e.g., It’s still dark out; there’s a lamp; the bugs have light.) • Ask students to infer what kind of insect this is, using the clues they have identified. (e.g., This is a moth because it’s attracted to the light.) • Read the next two spreads (“Up-down-around...” and “around”). Check students’ predictions. Ask students what they notice about the “around” Patterns and Relations 25

Analyzing/ pages. (e.g., All of the bugs from the first part of the story are shown; the making connections word ‘around’ is curvy.) Ask them what the presence of all of the bugs might mean. (e.g., maybe we’re getting close to the end of the story; ‘around’ looks round; etc.) • Read the next three spreads. Ask students what they see on the “good night” spread. (e.g., the eyes of all of the bugs) You may wish to have students match the pairs of eyes to the bugs, based on physical characteristics. After Reading Synthesizing • Have students turn and talk with a partner about what kinds of bugs were in Using text features Making connections Pattern Bugs. Share the answers as a class and revisit the anchor chart created at the beginning of the book and add to the list. • Discuss the text features that students learned about in this book (e.g., directionality of text, punctuation, size of font) and how it helps us understand what we read. • Together, make a list of other bugs or animals students have seen that have patterns (e.g., dragonfly, wasp, zebra, snake skin, tiger, ladybug). Materials: Further Practice BLM 1: Word Cards • A ctions and Words: Have students create their own patterned text using BLM 1: Word Cards. Once they have created a short, patterned text, have them add actions to the text and share with the class. • Words and Patterns: Have student pairs sort the words on cards from BLM 1 based on what patterns they see (e.g., number of letters, starting letters, the bug that did these actions in the story). • V isual Arts and Patterns: Have students create their own pattern bug and write a description following the model of the book. To support their writing, you can have them use the cards from BLM 1 and/or scribe for them. • Science: Using the co-created anchor chart of bugs from Pattern Bugs, initiate a mini-inquiry on bugs: their features, how they move, what they eat, their environment, and what they provide for other living things. 26 Patterns & Relations/Data & Probability

3Lesson P attern Bugs: 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; visualize to explore mathematical concepts • Communicating and representing: Communicate mathematical thinking in many ways • Connecting and reflecting: Reflect on mathematical thinking; connect mathematical concepts to each other and to other areas and personal interests Content • R epeating patterns with multiple elements and attributes Possible Learning Goals • Demonstrates an understanding of attributes and characteristics that can repeat in various patterns • Reflects on the importance of math in real-life contexts • Connects some math ideas about patterns learned in school (e.g., patterns) to patterns in the environment • Identifies what is repeating in the pattern • Identifies and explains the rule for a pattern • D escribes, explains, or shows how a pattern is changing • E xtends a pattern • Identifies and describes attributes that can change in a pattern • R epresents patterns using a variety of materials About the Several patterning concepts are embedded in the story of Pattern Bugs. Students are introduced to a variety of patterns, which become increasingly complex as the story progresses. The words in the text are also linked to the patterns and illustrations on the page, thereby helping students make connections between the visual and written representations. Students are not only challenged with finding and describing patterns, they also continued on next page Patterns and Relations 27

Math Vocabulary: have opportunities to explain the rule and extend the patterns preaptteearnti,nagt,tcriobruete, accordingly. These experiences are important, since research indicates that while three-fourths of students entering school can copy a repeated pattern, only one-third can explain the rule and extend the pattern (Clements & Sarama, 2009, p. 190). 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 of the pages, rather than all, using the pages in between to highlight simple patterns 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; and/or • revisit some of the pages on other days to explore the Further Investigations that pertain to specific concepts (e.g., extending patterns with two attributes). Materials: Assessment Opportunities Pattern Bugs, concrete Observations: Throughout the reading, the related problem solving, and materials (e.g., colour discussions, note which concepts are too difficult or too easy for students tiles, connecting cubes, so next steps can be planned and lessons can be differentiated to meet colour counters, pattern individual needs. Note each student’s ability to: blocks) Time: 15–20 minutes – Identify attributes and characteristics that repeat in patterns per session – Identify the part of the pattern that repeats (core) – Extend the pattern – Identify attributes in the pattern Before Reading Connecting and reflecting Activating and Building On Prior Math Knowledge Reasoning and analyzing • Ask students why the book is called Pattern Bugs. Ask, “What is a pattern?” Have students turn and talk with a partner to share patterns that they know and identify some patterns in the classroom or on students’ clothing. • 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 • After each page, have students describe all the patterns they notice on the page. Help students notice the written words and their link to the images and coloured border. 28 Patterns & Relations/Data & Probability

Reasoning and analyzing • After reading the pages about the butterfly, have students look carefully at Communicating and the colours and identify the pattern on the butterfly’s wings. representing • Ask students what part of the pattern is repeating. You may decide to explain Connecting and reflecting that this is known as the ‘core’ of the pattern. Alternatively, you can refer to Connecting and reflecting/ it as the part of the pattern that continually repeats. Communicating and representing • Draw attention to the border around the page. Have students explain how Connecting and reflecting Reasoning and analyzing the pattern is repeating and what attributes are involved. Ask what would come next if the pattern kept repeating. Communicating and representing/ reasoning and analyzing • Further Investigation: Provide students with concrete materials (e.g., colour Connecting and reflecting/ tiles, connecting cubes, colour counters, etc.) and challenge them to create a communicating and representing pattern that follows the same rule as one of the patterns on the page. Understanding and solving • After reading the pages about the beetle (skitter, scoot, crawl), ask students Connecting and reflecting/ communicating and representing what the beetle and the border have in common. Have students identify what part of the pattern is continuously repeating (e.g., purple-green-yellow). Ask how the pattern is different from the pattern on the butterfly page. Students can make comparisons between the two patterns using concrete materials. • After reading the pages about the bee, ask students what patterns they see on the bee. (e.g., yellow-yellow-yellow-black) Have them represent the pattern with their counters. Draw attention to the border on the page. Students can identify and represent the pattern (e.g., red-red-red-yellow). • Ask students what is similar between the two patterns. (e.g., They follow the same pattern of AAAB.) • After reading the pages about the caterpillar, have students describe the pattern on its body and what is changing (e.g., shape and/or colour). Explain that features such as shape and colour are known as ‘attributes.’ Ask what attributes on the page change and what attributes remain the same. • Students can also predict what would come next. Have them look at the bugs on the leaves and describe the patterns and what features change. • Further Investigation: Give students pattern blocks and have them create an AAB pattern. Students can do a gallery walk and identify the attributes their peers used. • After reading the pages about the cricket, have students describe the pattern and what attributes are changing, and identify what is repeating (i.e., AAB). Ask students what would come next. Have students identify and extend the repeating part in all the patterns they can find on the page (e.g., page border, size and colour of leaves, musical notes). • Further Investigation: Focus on the pattern in the page border. Have students investigate ways to change the pattern to a pattern that repeats in a different way. • After reading the pages about the firefly, challenge students to find as many different patterns as they can. Ask students what patterns they see, what attributes are changing, what is repeating, and what comes next. Students can use concrete materials to represent one or two of the patterns. They can identify what is continuously repeating. Patterns and Relations 29

Reasoning and analyzing • After reading the pages about the moth, have students identify the changing attributes, the part that repeats, and what comes next. Have students compare the pattern rules of the various patterns on the page. • Further Investigation: Provide students with concrete materials (e.g., colour tiles, connecting, colour counters, etc.) and challenge them to create their own ABCC pattern. After Reading Connecting and reflecting • Ask students for examples of patterns they saw in this story. (e.g., patterns on the bugs, patterns in the borders, patterns with the words) Discuss where they have seen patterns in real-life (e.g., other animals). • B uilding Growth Mindsets: Ask students what questions they still have about patterns and create an anchor chart of their queries. Discuss how mathematicians ask questions about math so they can keep learning. Explain that as the class continues to explore patterns, they should be able to answer many of the questions. Periodically refer to the chart throughout the unit and ask whether any of their questions have been answered. In this way, students can see that they are learning. Take time to record any new questions that may arise. 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 story. – Using pictures, letters, and/or words, show patterns in the classroom that are similar to the patterns in the book. − C reate 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., to use to create their patterns.] • C ommunity Walk: Take students on a walk through the playground and/or community: − Notice and name patterns while on the walk. – If it does not damage the environment, collect loose items students could use to create and name patterns upon your return (e.g., rock, rock, leaf, rock, rock, leaf—AAB). – Take photographs of patterns you see along the way. Encourage students to use digital tools to mark the pattern they spot in the photographs. 30 Patterns & Relations/Data & Probability

4Lesson Is This a Pattern? Math Curricular Competencies Learning Standards • Reasoning 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 • 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 • Connecting and reflecting: Connect mathematical concepts to each other and to other areas and personal interests Content • Repeating patterns with multiple elements and attributes Teacher Possible Learning Goals Look-Fors • Recognizes patterns in the environment and what attributes are changing in them Previous Experience • Describes patterns using mathematical language with Concepts: • R ecognizes patterns found around the classroom and community Students have had • Accurately describes a pattern using words such as ‘repeating,’ ‘changing attributes’ experience identifying, • E xplains what attributes are changing in the patterns extending, creating, • D emonstrates how a pattern repeats, and identifies the part that repeats (core) and representing patterns. About the Math Vocabulary: Young students come to school with an intuitive knowledge of patterns. It pcahtatnegrnin, grepeating, is important to activate this prior knowledge so they can build on it and deepen their understanding. First, students need to be able to differentiate between what constitutes a pattern and what does not. Marian Small describes pattern as “identified regularities. There is always an element of repetition, whether the same items repeat over and over, or whether a ‘transformation,’ for example, adding 1, is what repeats” (Small, 2009, p. 567). Students also need to understand that a pattern goes on forever, beyond what they may see. About the Lesson This lesson is intended to activate students’ previous knowledge about patterns, and review vocabulary that will help them throughout the unit. It will also give you an opportunity to assess what students already know about patterns. Patterns and Relations 31

Materials: Minds On (15 minutes) Digital Slides 1–2: Is • Display Digital Slide 1: Is This a Pattern? and ask students, “What do you This a Pattern?, Digital Slide 3: Let’s Compare, notice? What do you wonder?” As students share what they notice and chart paper, camera wonder, record their answers. (e.g., I see rectangles; I see orange; I see yellow; (optional) I see a pattern.) Time: 45 minutes • Repeat using Digital Slide 2: Is This a Pattern? • Display Digital Slide 3: Let’s Compare, which shows both of the previous images. Ask, “What is the same and different about these two images?” If necessary, show the slides again. Discuss how one image shows a pattern and one does not. Ask why they think this is true. • Co-create an initial definition of what makes a pattern, based on what students know at this point. Working On It (15 minutes) • Students work in pairs. Explain that they are going to go on a pattern hunt around the classroom. • Students can draw their patterns on chart paper or take photographs of them. Alternatively, they can find patterns and then remember their two favourites. Differentiation • For students who need language support, ensure they understand the definition of a pattern before they go on their pattern hunt. If necessary, provide small-group instruction and show them more examples. • For students who need a challenge, once they have found their patterns, have them figure out how to extend them. Assessment Opportunities Observations: Pay attention to students’ abilities to identify a pattern. Can they identify the pattern but not explain the rule? Can they explain why one example is a pattern and another example is not? Can they identify the part of the pattern that repeats? Can they name and identify the changing attributes and describe how they are changing? Check to see whether students can explain whether it is a pattern or not. Conversations: Ask any of the following prompts to clarify and advance students’ thinking: – Is this a pattern? How do you know? – What makes this a pattern? – What would come next in the pattern? – What part is repeating? 32 Patterns & Relations/Data & Probability

Consolidation (15 minutes) • Have pairs of students stand beside one of the patterns they found in the room. • Each pair can share the pattern they found and explain how they know it is a pattern. • As a class, add to the definition started in the Minds On about what a pattern is and what a pattern is not. Add visual examples for each. • Begin an anchor chart of math vocabulary related to patterning. Add co-created definitions and examples of terms discussed in the lesson. Further Practice • Conduct a walk around the school, playground, or in the community to search for patterns. Take pictures and, as a class, create a bulletin board of the various pattern. • Have students search for and bring in pictures of patterns they find at home. • Independent Practice in Math Journals: Have students show what a pattern is and what it is not by drawing one example of each. 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 33

and5 6Lessons Action Patterns Math Curricular Competencies Learning Standards • Reasoning and analyzing: Use reasoning to explore and make Arts connections; model mathematics in contextualized experiences Education • Understanding and solving: Develop, demonstrate, and apply Learning Standards mathematical understanding through play, inquiry, and problem solving Physical • C ommunicating and representing: Communicate mathematical thinking and Health Education in many ways; use mathematical vocabulary and language to contribute to mathematical discussions; explain and justify mathematical ideas and Learning decisions; represent mathematical ideas in concrete, pictorial, and symbolic Standards forms • Connecting and reflecting: Connect mathematical concepts to each other and to other areas and personal interests Content • Repeating patterns with multiple elements and attributes Curricular Competencies • Exploring and creating: Explore elements, processes, materials, movements, technologies, tools, and techniques of the arts Content • Elements in the arts: Dance: body, space, dynamics, time, relationships, form; music: beat/pulse, rhythm, tempo, pitch, dynamics, form Curricular Competencies • Physical literacy: Develop and demonstrate a variety of fundamental movement skills in a variety of physical activities and environments About the Understanding of patterns can be developed by making connections to other areas of the curriculum, such as English language arts, the arts, and physical education. This gives students the opportunity to apply what they know, be creative, and have fun experimenting with inventing new patterns. Peter Liljedahl explains that through rhythm and rhyme, students experience the cyclic structure of repeated patterns (Liljedahl, 2004). Educators gain access to understanding how young mathematicians recognize the structure of a given rhythm, and how they represent and extend the patterns. 34 Patterns & Relations/Data & Probability

Math Vocabulary: Students can investigate how the structure of rhythmic patterns can be prcearpettraeetrsene,,nsrute,bpdseetaisttcu, rtiebe, translated, or expressed, in various ways. For example, clap, snap, snap, clap, snap, snap, and red, blue, blue, red, blue, blue both have an ABB pattern rule with identical regularity (du Plessis, 2018). About the Lessons The following two lessons build on students’ knowledge of patterns. The activities are intended to explore the sequence of elements in patterns, particularly those involving movement and sound, and how they create rhythm when students act them out. The pattern elements are initially introduced using a visual representation, in order to support all learners. There are also several suggestions for incorporating physical actions and sound with voices and musical instruments, supporting a multi-modal experience. Patterns and Relations 35

5Lesson Investigating Action Patterns Possible Learning Goals • R ecognizes patterns that use one attribute (e.g., action, sound) • Describes the attributes in a pattern and how they change and repeat • R epresents a given pattern in a variety of ways Teacher • A ccurately performs the elements of a pattern (e.g., movement, voice) Look-Fors • Accurately recreates a familiar pattern by substituting elements (e.g., a different Previous Experience action, a sound, a tone of voice) with Concepts: Students have had • Accurately identifies a pattern from a series of actions experience recognizing, • D escribes a pattern and identifies the repeating elements exploring, describing, and comparing patterns. Minds On (15 minutes) Students have shared how to extend, translate, and • Have students stand up, making sure there is a bit of room between them. create patterns by using the part that repeats to Explain that they are about to start marching. Face the same direction as the predict what comes next. students and model each action as you say, “Everyone step on your left foot. Good! Now everyone step on your right foot. Good! Now all together and Materials: let’s keep going. Ready... 1, 2, 3... left, right, left, right,...” • Try to create a rhythmic pattern with your speaking voice using the key words (i.e., left, right,...) to support the pattern that the students are acting out. Continue until the pattern is clear and everyone is stepping together. Digital Slide 4: Action • Ask students what they noticed about the actions. (e.g., We did one action Patterns, Digital Slide 5: Action Cards, BLM 2: [left foot] and then the other one [right foot]; we kept switching from up to Action Pattern Strips, down.) Ask what we call it when something continually repeats. (e.g., a “Ready, Set, Action!” pattern) (page 4 in the Patterns, Relations, Data, and • Show Digital Slide 4: Action Patterns. Ask students which pattern is the most Probability big book) Time: 50 minutes like the one they just did, and why they think so. Have students turn and talk to a partner before sharing ideas as a class. (e.g., the second pattern, because it goes one action and then a different action each time like we did, and the first pattern goes two of the same action right after each other) • Divide the class into two groups and separate them. Assign “jump” to one group and “clap” to the other group. Demonstrate the actions. Explain that they are going to try to act out the second pattern on Digital Slide 4. Say the actions shown aloud together, “jump, clap, jump, clap, jump, clap, jump, clap,” to ensure everyone understands. • Have the students act out the pattern as you call out the actions. It may be helpful to point to each picture on the slide or to each group as their action arises in the pattern. 36 Patterns & Relations/Data & Probability

Teaching Tip Working On It (15 minutes) Modify the actions • Show Digital Slide 5: Action Cards and review the four actions represented. in each pattern if needed. Whenever an Perform each action together as a class. action pattern involves left and right, face • Students work in small groups. Provide each group with a strip from BLM 2: the same direction as students so they can Action Pattern Strips. Match the size of the student group to the number of follow your left and actions, so that each student has their own action to perform. For example, a right. triad may work best for a strip in which three different actions are shown. • Groups practise performing a pattern by repeating the sequence of actions on their action strip four times. Tell them they will be presenting the pattern to their classmates. Differentiation • For students who may struggle with maintaining the pattern, offer them an alternating AB option. • For students who may need a challenge, give them a strip with more than two actions and/or have them switch roles once they have mastered their pattern. Assessment Opportunities Observations: • P ay attention to the students’ abilities to describe and perform an action when it is their turn. • Check to ensure that students understand the sequence of the action strip. Can they follow along and connect the action strip to the actual movements? Conversations: Ask any of the following prompts to clarify and advance students’ thinking: – What action comes first in your strip? – What action comes next? How do you know? – Would it help to say the action aloud as you do it? – What part is repeating? Consolidation (20 minutes) • Display “Ready, Set, Action!” (page 4 in the Patterns, Relations, Data, and Probability big book). One at a time, have groups perform the pattern by repeating the sequence on their strip four times. After each performance, have the rest of the class identify which strip the group had by pointing to it on page 4. Prompt them to give reasons for their choices. Patterns and Relations 37

• Building Growth Mindsets: As a class, discuss which part of this activity they found most challenging. Ask whether the group was able to act out the pattern on their first attempt and what they did to improve. Ask how they knew they were acting out the pattern correctly. Explain that practice is an important part of learning, and that sometimes we need to analyze what we did the first time and then try again in order to improve. Further Practice • Have groups switch action strips with another group. They can practise and present them to each other. • Create action pattern strips using images of instruments that are available in your classroom. Provide instruments to students and have them practise and present patterns by sounding the instruments in the sequence shown and repeating it several times. • R eflecting in Math Journals: Ask students to draw a pattern they learned about today and share it with, or teach it to, their families. Materials: Math Talk: “Ready, Set, Action!” Math Focus: Investigating patterns involving actions and words (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. connecting cubes, pattern blocks • Show students the first pattern on page 4 of the Patterns, Relations, Data, Teaching Tip and Probability big book (clap, snap, clap, snap) and ask them to describe to their elbow partner what they see. Integrate the math talk moves (see page 7) • W hat actions do you see in this pattern? (e.g., hands clapping) Put your throughout Math Talks to maximize student thumb up if you and your partner saw the same thing. Did anyone see participation and something different? (e.g., fingers snapping) Put your thumb up if you and active listening. your partner saw the same thing. • What did you notice about the order of the actions? (e.g., We saw one action and then the other, and then it repeats, clapping, snapping, clapping, snapping.) Put your thumb up if you and your partner saw the same thing. • Let’s try doing this pattern together. Once we can do the actions, let’s try saying the actions as we do them. Model this along with your students until you create a class rhythm. • Repeat this line of questioning with the next pattern on the page. • Are the actions in the first pattern the same as or different from those in the second pattern? How are they the same? How are they different? • R epeat this line of questioning for the rest of the patterns on the page or have students do the following partner investigation. 38 Patterns & Relations/Data & Probability

Partner Investigation • H ow do you think we could use other objects or materials to create a pattern that repeats like the first pattern on the big book page? • H ave students work in pairs using connecting cubes or pattern blocks to create a pattern similar to the first one in the big book. Walk around and ask students to show how their pattern is similar and how it is different. Patterns and Relations 39

6Lesson Creating Action Patterns Teacher Possible Learning Goals Look-Fors • C reates a pattern that has attributes that repeat • D escribes a pattern and identifies the changing attributes • R epresents a pattern in a variety of ways (e.g., picture, action, sound) • A ccurately represents their created pattern with the appropriate actions • Extends the pattern by accurately repeating the sequence at least three times • Describes the order of the actions in their pattern • Represents a pattern in more than one way Materials: Minds On (15 minutes) Digital Slide 5: Action • Tell students you are going to call out their names one at a time using your Cards, BLM 3: Action Cards (1 set in an voice in a special way. They are to answer “Here” in the same tone of voice envelope per pair), that you used, and then come to the meeting area. BLM 4: Pattern Templates (1 copy per pair), glue • Do a roll call of the class, using three different notes or voice changes that Time: 50 minutes you alternate in an ABC pattern. For example, you could sing their names using a high, mid-range, and low note, or say them using a whisper, a normal speaking volume, and a louder volume. Repeat the pattern until all students are gathered at the meeting area. • Ask students how they would describe the pattern in your tone of voice. (e.g., high, medium, low; loud, medium, soft) • Tell students they are to stand up and then sit down when they hear you use the tone you said their name in. Call out the description of the pattern, using the same tones (e.g., sing, “high, medium, low”). • Have students describe the order of the pattern you just used. (e.g., high, medium, low) Ask, “How could we change the order of our pattern?” (e.g., low, medium, high) Repeat the pattern together several times, until the rhythm is clear. • If needed, ask for another pattern (e.g., medium, low, high) and/or suggest a pattern in which one tone is repeated (e.g., low, high, low, medium). Working On It (20 minutes) • Project Digital Slide 5: Action Cards. Review the actions that correspond with the pictures. • Students work in pairs. Give each pair an envelope containing a set of all the cards from BLM 3: Action Cards and a copy of BLM 4: Pattern Templates. 40 Patterns & Relations/Data & Probability

• Students choose four action cards from their envelopes and use them to create an action pattern. They record their pattern on BLM 4 by gluing the cards in the template and writing a description in the blanks. • Students practise and present their action pattern to the rest of the class. Differentiation • Students who might struggle with a four-action pattern can create a pattern using the three-action template on BLM 4, or they can create an alternating two-action pattern using the four-action template (e.g., clap, snap, clap, snap). • For students who need a challenge, have them create a pattern that repeats one action within the four-action template (e.g., an ABBC pattern) or by using an action not given on BLM 3. Assessment Opportunities Observations: • Pay attention to the students’ abilities to describe and perform an action. • D o they understand that the sequence of actions in their template must be repeated to perform the pattern? Conversations: While students are working, use some of the following prompts to help determine their abilities to create, identify, and describe patterns: – What are the actions in your pattern? – What is the order of the actions? Why did you put them in that order? – Have you tried switching the actions in your pattern? Consolidation (15 minutes) • Have pairs present their patterns to the class. Have the rest of the class use the extra action cards in their envelopes to represent each pattern as it is presented. • Ask the class to identify the pattern presented. Have the pair presenting confirm whether the pattern is correct. Further Practice • Post the patterns created by each pair and have the class perform one to begin each math lesson for the remainder of the unit. • Independent Problem Solving in Math Journals: Have each student select three or four action cards from their envelope and glue them in a pattern in their Math Journals. Students can describe and practise their pattern. First Peoples Perspectives • If you are integrating Métis peoples ways of knowing into your practice, Métis rhythm sticks, Métis spoons, and Métis jigging all have action patterns that can be explored mathematically. Patterns and Relations 41

and7 8LessonsInvestigating Attributes and How Patterns Repeat Math Curricular Competencies Learning Standards • Reasoning and analyzing: Use reasoning to explore and make connections; model mathematics in contextualized experiences • Understanding and solving: Visualize to explore mathematical concepts; develop and use multiple strategies to engage in problem solving • 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 • R epeating patterns with multiple elements and attributes About the When investigating patterns, students need to be able to identify the changing attributes in order to recognize the repeating part of the pattern. Attributes are the quantitative or qualitative characteristics of shapes or objects. Marian Small notes that it is important for students to understand that an object can have many attributes (Small, 2017, p. 572). For example, an attribute block has the attributes of shape, size, thickness, and colour. Students also need to identify how attributes can change. When beginning to learn about attributes, students should be given ample opportunities to describe objects in order to become comfortable with what an attribute is and how it might change. It is beneficial to make a list of attributes that can change, so students can more readily identify them and use them to create a greater variety of patterns. Small explains the core of a pattern as “the part of the pattern that repeats” (Small, 2017, p. 358). Finding the core of a pattern or the part that continually repeats can be difficult for some students, depending on the complexity of the pattern and students’ understanding of what is repeating. Small advises providing at least three repetitions of the core so students can adequately identify what attribute is repeating and how it repeats (Small, 2017, p. 359). 42 Patterns & Relations/Data & Probability

Van de Walle and Lovin state that young students need to work with patterns using concrete objects and materials that can be moved around, since “children are able to test the extension of a pattern and make changes without fear of being wrong” (Van de Walle & Lovin, 2006, p. 276). Creating patterns on paper can be limiting as it can be hard to make corrections and students think they can extend the pattern only within the space of the sheet. About the Lessons The following lessons focus on deepening students’ understanding of attributes and how patterns repeat. Students first focus on what attributes are and how they can change. They continue their exploration by looking at what repeats and identifying it in a variety of patterns. Patterns and Relations 43

7Lesson Looking at Attributes Possible Learning Goals • Recognizes attributes in various shapes • Describes various characteristics of different attributes, using mathematical language, and explains how the attribute’s characteristics change Teacher • D escribes a shape by number of sides, colour, vertices Look-Fors • Describes other attributes of objects • Identifies how the attribute blocks change by size and colour Previous Experience • E xplains or shows how different shapes can be changed with Concepts: Students have had some Minds On (15 minutes) experience identifying, extending, creating, and • Tell students to listen carefully to the sound you are about to make. Clap representing simple patterns. once. Have them describe what they heard. Math Vocabulary: • Tell students to listen as you clap in a different way. Clap once, but more pattern, repeating, attribute loudly. Have them describe what they heard. Discuss their responses, reinforcing the comparative language. Explain that it was the loudness of the Materials: clap that changed. Ask what would be another way you could change the pattern blocks, loudness. (e.g., clap very quietly) attribute blocks, chart paper • Clap two times at the same loudness. Ask students what changed this time. Time: 45 minutes (e.g., the number of claps) Ask how you could vary the clapping using the number of claps. (e.g., clap three or four times) • Clap four times, clapping slowly for the first two claps and quickly for the last two. Ask what was different between the first two claps and the second two claps. Explain that it was the speed of the claps that changed. • Summarize all of the ways you changed the claps (e.g., loudness, number of claps, speed). Explain that these differences in the claps are called ‘attributes’ and that they will be exploring more about attributes in the lesson. Working On It (15 minutes) • Provide pairs of students with a variety of different attribute blocks and/or pattern blocks. • With their partner, students describe their shapes and determine all the ways the shapes differ (e.g., size, colour). They can record their ideas on chart paper. 44 Patterns & Relations/Data & Probability

Differentiation • Ensure students who need language support understand the term ‘attribute,’ as well as terms to name them (e.g., size, colour) and describe them (e.g., colour names, thin, thick, etc.). You can start a visual dictionary as a picture reference of such terms, with these students, and with any other students who may benefit. • For students who need a challenge, have them create a pattern using an attribute of their choice and then describe what changes in their pattern. • For students who have difficulty describing attributes, show them two of the same shape in different colours, such as a red square and a blue square. Have them describe how the shapes are the same and how they are different. Assessment Opportunities Observations: Pay attention to students’ vocabulary when they are describing the shapes. Can they identify the attributes? Can they describe how the different attributes of shapes can change? Conversations: Ask some of the following prompts to clarify and advance students’ thinking: – What do you notice about the shape? Can you describe it to me? What colour is it? How big is it? – What could you change about your shape? How could your shape be different? Consolidation (15 minutes) • S trategically choose two to three pairs of students who were able to describe shapes using multiple attributes. Have them describe their shapes to the class. • Define or review the word ‘attribute’ for the class and add it to the patterning math vocabulary anchor chart if you have not previously done so. Instead or as well, you could co-create an anchor chart entitled ‘Attributes’ to list attributes that could be changed. Further Practice • To assess understanding of attributes, give students the following question as an exit pass: – What attributes does the following shape have? • Have each student find an object in the classroom and then describe the attributes of that object during a community circle. Patterns and Relations 45

8Lesson Investigating How Patterns Repeat Teacher Possible Learning Goals Look-Fors • Identifies attributes of shapes and objects, and explains how they can vary Previous Experience • D escribes a pattern that changes by one attribute with Concepts: • Identifies the part of the pattern that repeats (the core) Students have explored and described which • D escribes the pattern they see by naming the attribute that is changing or attributes change and repeating (e.g., colour, shape, or size) which stay the same in patterns. • Explains or shows what repeats in the pattern (e.g., red, blue, red, blue) • Explains or shows what part of the pattern repeats (the core) Math Vocabulary: paatttrtiebrunt,er,ecpoeraeti(nogp,tional) Minds On (15 minutes) Materials: • Display Digital Slide 6: What Changes? Ask students to describe what they Digital Slides 6–7: What see. Ask what attribute is changing and how it is changing. Changes?, BLM 5: Pattern Strips (Set 1) • Have students turn and talk to a partner about whether the slide shows a Time: 45 minutes pattern. • As a class, discuss what makes this a pattern and what part of the image is repeating (e.g., one square and one triangle). Ask what stays the same. (e.g., colour, because all the shapes are blue) • Draw a box around the part of the pattern that is repeating. If you introduced the term ‘core,’ review that this is called the core of the pattern, and it is the part of the pattern that keeps repeating over and over. • Show Digital Slide 7: What Changes? and repeat the same line of questioning. Working On It (15 minutes) • Tell students that they are going to be pattern hunters who hunt for the way in which patterns repeat. • Provide student pairs with pattern strips from BLM 5: Pattern Strips (Set 1). Students find the part of the pattern that repeats and draw a box around it. Differentiation • Select the pattern strips that best meet the needs of specific pairs of students. • For students who need language support, help them to understand ‘the repeating part’ and to add an accompanying image to their visual dictionary. • Students who need more of a challenge can create their own patterns and identify the part that repeats. 46 Patterns & Relations/Data & Probability

Assessment Opportunities Observations: • P ay attention to how students are describing the visual aspects of the pattern. Are they able to identify the various attributes in the pattern, which ones change, and which ones stay the same? • P ay attention to students’ understanding of what the repeating part of a pattern is. Are they able to identify the smallest part of the pattern that keeps repeating? Conversations: Ask any of the following prompts to clarify and advance students’ thinking: – Describe the pattern that you see. Why is it a pattern? – What words can you say that show the way the pattern repeats? (e.g., up, down, up, down, up, down) What words do you keep saying over and over? How does hearing the words help you know what part of the pattern is repeating? Consolidation (15 minutes) • H ave pairs meet and share their patterns. Have them explain why they think the part they marked is the repeating part. • Meet as a class. Show two or three pattern strips. Have the pairs of students who worked with the strips discuss how they found the repeating part of the pattern. Ask how they know that it is the smallest part of the pattern to repeat. Further Practice • Have students create their own patterns. Students exchange their patterns with a partner, and each identifies the repeating part of the received pattern. • Have students identify the repeating parts of the patterns below as an exit pass: • B uilding Growth Mindsets: Ask students how they felt when they couldn’t identify the part that repeats right away. It is important that they can identify, name, and describe the intensity of their emotions and what is causing them to feel that way. Reassure students that they have lots of time and more experiences to work with patterns, and they do not need to immediately understand everything. Invite any students who overcame frustration to share what they did. Discuss what students can do when they are feeling overwhelmed with a task or situation (e.g., take a break, stretch, ask a friend). Have them identify the patterns that they found most challenging. Inform students that they will spend 5–10 minutes a day for the Patterns and Relations 47

First Peoples next few days practising those types of patterns. Students will feel better Principles of when they know there is a plan in place to help them improve. This supports Learning the First Peoples Principles of Learning that learning involves patience and time. Materials: Math Talk: Math Focus: Identifying and describing the repeating part of a pattern Let’s Talk You may wish to use this Math Talk after students have had more practice describing and extending patterns in Lessons 9–10, depending on your class. Select the prompts that best meet the needs of your students. “How Does It Repeat?” • SahnodwPr“oHboawbilDitoyebsigItbRoeopke)a. tC?”ov(perageeac5hfrpoamttetrhnewPiatthtearnpsie, cReeloaftipoanpse,rDaantda, (page 5 in the Patterns, Relations, Data, and reveal each pattern one at a time. Look at the first pattern. Turn and talk to Probability big book) a partner about whether there is a pattern and what the pattern might be. Teaching Tip • Describe what you see. (e.g., shapes) What attributes do these shapes have? Integrate the math talk moves (see page 7) How do the attributes change? throughout Math Talks to maximize student • What pattern do you see? What attributes do you see changing in this participation and active listening. pattern? (e.g., colour and shape) What attributes are not changing? • What is the repeating part of this pattern? (e.g., The repeating part is triangle, square, because it keeps going triangle, square, triangle, square.) Put your thumb up if you agree. • rWepheaattienlsgepcaorut?ld(gthreeepna,trteedrn) be? (e.g., green, red, green, red) What is the of How is this repeating part like the repeating part the first pattern? (e.g., Both have one thing and then a different thing, and then they have the same first and second things again.) • Repeat this line of questioning with the other patterns on the page. As is the case for the first pattern, some of these can be described in different ways. It is important to discuss this with students and to accept multiple answers when they can describe and explain the patterns they see. • How does describing the attributes of a pattern helps us identify its repeating part? 48 Patterns & Relations/Data & Probability

and9 10LessonsDescribing and Extending Patterns Math Curricular Competencies Learning Standards • R easoning and analyzing: Use reasoning to explore and make connections; model mathematics in contextualized experiences • Understanding and 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 Content • R epeating patterns with multiple elements and attributes About the As students become more comfortable with identifying and recognizing patterns, it is helpful to introduce the letter coding system to help them describe the pattern’s structure or repeating part (core). 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). For example, the letter coding system, such as using ABC to represent the changing attributes in the pattern, 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 repeating unit. It is also important that students be able to extend the pattern once they have identified the repeating part. 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). continued on next page Patterns and Relations 49

Mp(cAoaoapAtdtttBheieo,rsnVnA(ao,eBlcr.)Ceg,a)p.ab,,etnuAtaelrBatixbi,rntuyAg:tB,ecB, ol,eretter About the Lessons The following two lessons help students to deepen their understanding of patterns by having them describe the pattern and its repeating part using letter codes and then extending the pattern. The first lesson introduces students to letter codes by having them work at various centres. This gives you an opportunity to focus on a small group to assist or assess students. The second lesson allows students to apply what they have learned to this point to extend the pattern. 50 Patterns & Relations/Data & Probability

9Lesson Describing Patterns Possible Learning Goals • Recognizes patterns and describes them using appropriate mathematical language • Identifies and explains the repeating part of a pattern and describes it using a letter coding system • Uses the repeating part of the pattern to extend it Teacher • R ecognizes when an image represents a pattern and when it does not Look-Fors • Describes how a pattern is repeating and what attributes are changing • Identifies the repeating part of a pattern Previous Experience • Matches repeating parts of patterns with letter coding descriptions with Concepts: • Describes and explains how a repeating part of a pattern matches its letter code Students have identified the part of the pattern description that repeats (core) and discussed how it helps us Minds On (20 minutes) extend the pattern. • Show students Digital Slide 8: What Is the Pattern? and ask what part of the Materials: pattern repeats (core). (e.g., orange rectangle, blue rectangle) Ask which Digital Slides 8–11: attributes are changing and which are staying the same. What Is the Pattern?, BLM 6: Pattern Strips • Explain to students that you will show them several patterns that they will (Set 2), pattern blocks Time: 50 minutes figure out and compare. • 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 part repeats [core], 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. • Using Digital Slide 8, explain how the model or letter code system works. Tell students that the orange rectangle can be called ‘A’ and the blue rectangle can be called ‘B.’ Record these letters under the first two rectangles. Ask what they think the ‘A’ and ‘B’ represent. (‘A’ means orange and ‘B’ means blue.) Ask what attribute is changing (colour) and what attribute remains the same (shape). Ask what letters would come next in the pattern. Have the students say the letters so they can also hear the pattern repeat. • Show Digital Slide 9: What Is the Pattern? Ask what attribute stays the same from shape to shape (colour) and what attribute is changing (shape). Ask what part of the pattern repeats. (two squares, one triangle) Ask how many different elements are in the part that repeats. (two: squares and a triangle) Patterns and Relations 51

Teaching Tip Ask what letter they could call the squares and what letter they could call the triangles. Record the letters below the pattern as students name them. In this activity, Explain that we call this an AAB pattern. students rotate through a series of • Repeat this discussion for Digital Slide 10: What Is the Pattern? and Digital six centres. Ahead of time, set up each Slide 11: What Is the Pattern? In each case, ask what attributes change and centre with a pattern what attributes stay the same. Ensure that students understand what each strip cut from BLM 6 letter represents. and pattern blocks. Working On It (15 minutes) • Tell students they are going to work with the letter coding system to see how it works and how it helps them figure out and compare patterns. • Students work in small groups of two or three, rotating through a series of centres, each of which contains pre-cut pattern strips from BLM 6: Pattern Strips (Set 2) and pattern blocks. • At each centre, students recreate the pattern shown on the strip, identify the repeating part of the pattern, and label the pattern using the letter code system. Differentiation • For students who need language support, ensure that they understand how the letter code system works and help them record their new learning in their visual dictionary. • For students who need a challenge, have them determine what repeats (e.g., AB, AAB, ABC) and then create a different pattern that uses the same letter code. Assessment Opportunities Observations: Note students’ abilities to recognize and identify the part of the pattern that repeats, and to recreate the pattern with the blocks. Conversations: If students are having difficulty recognizing what repeats in the pattern, pose some of the following prompts: – What do you think comes next in the pattern? Why do you think so? What is the part that repeats over and over? – You have identified “red, green, red, green, red, green” as the part that is repeating. What is repeating within what you are showing? (red, green) How many times does it repeat? What is the smallest part that repeats over and over? 52 Patterns & Relations/Data & Probability

Consolidation (15 minutes) • Display all the pattern strips. Using a fishbowl strategy, have students analyze each pattern strip, using some of the following prompts: – How can you describe this pattern? What words are you repeating as you describe it? What attribute is changing and how is it changing? – What is the part of the pattern that repeats (core)? How do you know? What part are we describing when we use the letter codes? (the smallest part that repeats over and over) – How can we label this pattern with a letter code? Explain how you figured that out. What does each letter represent? How many letters did you use? Why? • D iscuss how the letter coding system can help us to figure out what repeats in a pattern and compare patterns. Highlight how two patterns can look very different but have the same letter code, which means they repeat in the same way. Explain that students will have several more opportunities to practise 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 what is important to include when using the letter code system. (e.g., what attributes or characteristics the letters represent) • A dd new student learning, with examples, to the class patterning anchor chart (e.g., letter code system). • B uilding Growth Mindsets: Ask students which letter codes were easiest to recognize 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 how they can learn from making a mistake, such as thinking a different code applied to the pattern. Explain that mistakes make us reflect on what we are doing and try tasks from another perspective. Further Practice • Independent Problem Solving in Math Journals: Display the pattern shown below and verbally pose the following questions for students to answer in their Math Journals. – What is repeating in this pattern? – What letter code describes this pattern? Patterns and Relations 53

Materials: Math Talk: “Ready, Set, Action!” Math Focus: Representing a given pattern in a variety of ways, and identifying (page 4 in the Patterns, a rule Relations, Data, and Probability big book) Let’s Talk Teaching Tip Select the prompts that best meet the needs of your students. Integrate the math talk • Ssnhaopw) students the first pattern on “Ready, Set, Action!” (clap, snap, clap, moves (see page 7) and ask them to describe what they see to their partner. throughout Math Talks to maximize student • fWinhgaetrsascntiaopnpsidnog)yPouutthyionukr these pictures are showing? (e.g., hands clapping, participation and thumb up if you agree. active listening. • If we call the first picture “clap” and the second picture “snap,” let’s see if we can say this pattern together. As I point to each picture, let’s say the pattern out loud. Repeat the pattern until the class says it at the same pace, to reinforce the rhythm created by the repetition. • tLheet’spaatlltetrrny doing the actions in the pictures together. Model while you say aloud. Let’s get our hands ready to clap. One, two, three, go. Repeat until the class performs the pattern at the same pace. • Itws tohesnreapasn.y)thing that repeats in this pattern? (e.g., There are two claps and • SPeots,eAtchteioanb!o”voerphraovmeptthsewstiuthdethnetsrdesot of the patterns on the page “Ready, the following partner investigation. Partner Investigation • Create a pattern that repeats like the one we just did, using different actions. • sHtuavdeensttsudshenowts work in pairs to create a similar pattern. Circulate and have different. how their pattern follows the same pattern and how it is Follow-Up Talk • How can we use letters to describe the patterns we see in our big book? • L et’s look at the first pattern again: clap, snap, clap, snap. If we used a letter A to represent the clap, how many A’s would we need? (two) Could we use the A letter for the snap, too? Why? (e.g., No, it’s a different action.) What letter do you think we could use? (e.g., B) How many B’s would we need? (two) What would our letter pattern be? (e.g., ABAB) • Choowntsintuudeewntisthmoitghhetrrpepatrteesrennst in “Ready, Set, Action!” If necessary, discuss the pattern with a third action. Some of you have noticed there is a third action in this pattern. How can we represent it with a letter? (e.g., use C) What would our letter pattern be? (e.g., ABCC) • How can you represent the patterns using something different from letters? What are some things you think you could use? (e.g., concrete materials, sounds) • wYoauysc.oHualdvehsatvuedpenatisrsshoof wstuhdoewnttshreeirprpeastetnertnsoismseimofiltahreapnadttheorwnsitinisddiiffffeerreenntt. 54 Patterns & Relations/Data & Probability

10Lesson Extending Patterns: What Comes Next? Possible Learning Goals • Describes patterns using mathematical language and identifies the pattern rule by identifying what repeats • Identifies the part of the pattern that repeats and describes it using words and/or the letter code system Teacher • E xtends patterns and explains why their extension follows the pattern rule Look-Fors • D escribes or shows how they see a pattern repeating Previous Experience • Identifies the attributes that are changing and how they are changing with Concepts: • Identifies the part of the pattern that repeats and describes it using words and/or Students have had experience identifying, a letter code extending, creating, and representing patterns. • E xtends patterns and explains their reasoning Materials: Minds On (15 minutes) Digital Slides 12–13: • Show students Digital Slide 12: What Comes Next? Ask what attributes are What Comes Next?, BLM 7: Pattern Strips (Set 3), changing, and what attributes are staying the same. (e.g., The shapes change, chart paper, markers, glue but the colour and orientation of the shapes stay the same.) Time: 45 minutes • Ask students what is repeating in the pattern. (e.g., pentagon, trapezoid, trapezoid) Ask what letter code they can use to describe the pattern (ABB) and have them explain what the different letters represent. • Ask students what comes next in this pattern and why they think so. • Show Digital Slide 13: What Comes Next? Ask students to turn and talk to their partner about what attributes are changing and which ones are staying the same. (e.g., The shapes change, but the colour stays the same.) Ask whether the consecutive arrows are the same shape or different, and why they think so. Discuss how the shape doesn’t change, but the position of the shape does (e.g., the first arrow points up and the second arrow points down). • Ask students what part of the pattern repeats and what letter code they would use. (e.g., ABC) Ask what each letter represents. (e.g., A is circle, B is arrow pointing up, and C is arrow pointing down.) Some students may describe this as an ABB pattern if they are paying attention only to shape, not orientation. This is fine, as long as they make it clear that A represents a circle and B represents an arrow. This is a good opportunity to probe further and help them recognize that the pattern can also be defined in terms of a shape’s orientation. • Have students turn and talk to a partner about what comes next in the pattern. As you discuss their predictions as a class, make it clear to all students that the last repetition has already been started. They must look carefully and not just add the part that repeats to the end of the pattern. Patterns and Relations 55

Working On It (15 minutes) • Students work in pairs. Give each pair a set of pattern strips from BLM 7: Pattern Strips (Set 3). For each pattern, students describe the pattern, identify the part that repeats, create a letter code for the repeating part, and then extend the pattern. Students can glue their strips to chart paper and write on and around the patterns. – Make an anchor chart that clearly outlines what students need to do. – Ask what other information they may need to know before working with the patterns. Refer to any anchor charts that may help them. – Review the letter coding system, if necessary. – Test to see if the letter code for the part that repeats helps them to extend the pattern. Differentiation • For students who need language support, ensure they understand how the letter code system works and what each letter represents. Assist them in adding any new vocabulary to their visual dictionaries. • For students who need a challenge, have them determine the pattern type (e.g., AB, AAB, ABC) for one or more of the strips, create a different pattern that follows the letter code they identified, and then extend the pattern(s). Assessment Opportunities Observations: Pay attention to students’ abilities to recognize and identify the part of the pattern that repeats and then assign a matching letter code. Can they explain what each letter means? Conversations: Pose prompts similar to the following to clarify and advance students’ thinking: – What pattern do you see? What attributes change and what attributes stay the same? – What do you think is repeating in the pattern? Draw a circle around it. How does the pattern change? – What letter could you give each different part of the pattern that repeats? You have two rectangles beside each other. What letter could you give to the first rectangle? Now look at the second rectangle. Is it exactly the same as the first rectangle? Would you give it the same letter or a different letter? (the same letter) – In this pattern, there is a third shape. Would you give the third shape the same letter or a different letter? Why? (No, because it is a square so it is different.) What letter can you give to it? – Are there any other different parts to identify? Explain how your letters will repeat. 56 Patterns & Relations/Data & Probability

Materials: Consolidation (15 minutes) BLM 5: Pattern Strips (Set 1) • H ave students meet with another pair and compare their patterns and letter codes. Make note of any patterns that caused confusion or resulted in different letter codes. • M eet as a class and have students compare their codes. Strategically choose any groups that have given the same pattern different letter codes. Have the groups explain their reasoning and identify what each letter represents. In some cases, both letter codes may make sense, depending on the patterns that students saw and how they defined each letter. It is important for students to realize there can be more than one correct answer, depending on the reasoning for the pattern. • D iscuss whether the letter coding system helped them extend the pattern. Emphasize that it is important to know what each letter represents so they can better understand the patterns. Ask whether they think there are times when the letter code system may not help them extend a pattern. Further Practice • Inside/Outside Circle: Give each student a pattern strip from BLM 5: Pattern Strips (Set 1), and have them independently study it so they know what part repeats. Arrange students into two circles, one inside the other, so that students face each other and everyone has a partner. To begin, all students hold their patterns behind their backs. Then, Partner A shows their pattern to Partner B, who describes the part of the pattern that repeats and what comes next. Partners switch roles. After all pairs are finished, have the outer circle move one partner over to the left. Repeat with the new partners. • Extending Patterns: Students can practise extending patterns using strips from BLM 5. • Independent Problem Solving in Math Journals: Project (or draw on the board) the following two patterns. Have students choose one, draw it in their Math Journals, circle the part that repeats, record the letter code, and then extend the pattern. Pattern 1 Pattern 2 Patterns and Relations 57

11Lesson Investigating Number Patterns Math Curricular Competencies Learning Standards • Reasoning and analyzing: Use reasoning to explore and make Teacher connections; develop mental math strategies and abilities to make sense of Look-Fors quantities Previous Experience • U nderstanding and solving: Develop and use multiple strategies to engage with Concepts: Students have had in problem solving experience identifying and describing patterns • C ommunicating and representing: Communicate mathematical thinking in real-life contexts, and with investigating and in many ways; explain and justify mathematical ideas and decisions; creating patterns using represent mathematical ideas in concrete, pictorial, and symbolic forms concrete materials (e.g., coloured cubes). • C onnecting and reflecting: Connect mathematical concepts to each other and to other areas and personal interests Content • Repeating patterns with multiple elements and attributes • Number concepts to 20 • Change in quantity to 20, concretely and verbally Possible Learning Goals • Describes number patterns and their rules and extends the patterns • Identifies what repeats in number patterns and extends the patterns • S kip-counts by 2s, 5s, and 10s • D escribes a variety of number patterns (e.g., growing, shrinking, repeating) • Describes what repeats in number patterns • Extends a repeating number pattern and explains what comes next • C ompares the structure of a number pattern to that of a geometric or action pattern • R epresents a number pattern in some other form About the As students become more proficient at describing visual patterns represented by concrete materials and drawings, they can apply this understanding to the patterns in sets of numbers. The transition from a visual representation (e.g., geometric shapes—circle, square, circle, square,…) to a numeric representation (e.g., 1, 2, 1, 2,…) can be challenging for younger students. It can be difficult for them to 58 Patterns & Relations/Data & Probability