p10-86_Unit1_PatternsRelations

Math Vocabulary: see such patterns as mathematically alike, because they often focus on pn(caoauobptmltotueivbomrenenn,,rabsrlp)e,e,aprfdtooetiwregaerist,tni,snn,b,gece,xoltorew, the actual attributes of the shapes rather than the progression of the pattern (Small, 2009, p. 569). Students require many opportunities to explore patterns in numbers and compare their elements to those in visual patterns (e.g., lining up red, blue, red, blue… 1, 2, 1, 2…). By making these connections explicit, students can not only recognize the common structure in patterns, but can translate a pattern using their own representation. When investigating number patterns, students will also encounter patterns that grow or shrink because of a skip-counting pattern or a repeating operation, especially when they are skip-counting or repeating an operation such as addition or subtraction to create the pattern. They also identify important patterns in our number system as the numbers increase or decrease in magnitude. It must be remembered that grade one students do not need to classify patterns as repeating, shrinking, or growing. The focus is on attributes or operations that are changing. About the Lesson This lesson builds on students’ knowledge of patterns by providing them with multiple opportunities to make connections between that knowledge and how those same patterns might be represented using numbers. Activities incorporate and build upon students’ experiences with counting and skip-counting. There are a series of five Math Talks at the end of the lesson. These should be done before Lesson 12, since they introduce concepts and skills that students will need to work with fifty or hundred charts in that lesson. In the Math Talks, students discuss the patterns they see as they move across rows and down columns in fifty or hundred charts. Students also explore how numbers are related to one another, and they use the patterns they see to determine whether certain numbers will be included in a given skip-counting sequence. While students in grade one work extensively with numbers to 20, they can extend their understanding to recognize and predict patterns that extend beyond 20. This reinforces the big idea that repeating elements in a pattern can be identified, and supports the inquiry of what number patterns live in a hundred chart. Number sequences and patterns are reinforced in the Math Talks using choral counting. Choral counting is a great way to help young students develop their understanding of number and to identify patterns. Students learn the sequence as they count aloud by 1s, 2s, 5s, 10s, and other increments. By exploring number patterns that are grounded in the base ten number system, students will be able to predict what number comes next (Franke, Kazemi, & Chan Turrou, 2018). Patterns and Relations 59

Materials: Minds On (15 minutes) Digital Slide 14: Number • P ost the numerals 1 to 5 around the room. Have each student number off Patterns and/or BLM 8: Number Patterns from 1 to 5 (in a circle or table groups as you point to them) until all Time: 45 minutes students are assigned a number. • Have students form groups according to their numbers. Have them talk with a partner about the number pattern they just made as a class as they called out their numbers (i.e., 1, 2, 3, 4, 5, 1, 2, 3, 4, 5,...). Ask how many groups there are. (5) • H ave students in each group number off from 1 to 3. Students then move to form groups according to their new numbers. Have them talk with a partner about the number pattern made by the new numbers (i.e., 1, 2, 3, 1, 2, 3, 1, 2, 3,...). Ask how many groups there are now. (3) • Ask students what the first number pattern was. (1, 2, 3, 4, 5, 1, 2, 3, 4, 5,...) Ask what numbers were repeated. (1, 2, 3, 4, 5) Ask what the second number pattern was and what numbers were repeated. (1, 2, 3, 1, 2, 3, 1, 2, 3,...; 1, 2, 3) • Ask students to reflect on a time when they might have used a number pattern like this one (e.g., during a daily physical activity; when dancing; to decide teams in gym class). Working On It (20 minutes) • Have students sit in a circle in their original groups of five created in the Minds On activity. • Project Digital Slide 14: Number Patterns and/or provide each group with a copy of BLM 8: Number Patterns. Have students say the first number pattern as a class. Ask what they notice about the number pattern. (e.g., It’s 1, 2, 3, 4,...; it repeats the same numbers 4 times.) • Have students say the first number pattern again, but in their groups. Students choose a person to start, and then go around the circle until all of the numbers in the first pattern have been said aloud. • Ask students what they noticed this time. (e.g., The first time I said 2, and the second time I said 3; I had to listen to the person before me to know which number to say.) Ask why they think they don’t say the same number each time. • Have students continue with the other three patterns on Digital Slide 14, choosing a different person to start each time. Differentiation • For students who are struggling, have them use their finger on BLM 8 to track the numbers already said. • For students who need language support, ensure that they know the words for the numbers in each sequence so they can participate successfully. • For groups who finish early and want a challenge, have them retry the patterns but switch places in the circle, start with a different person, or go in the other direction. 60 Patterns & Relations/Data & Probability

Materials: Assessment Opportunities Digital Slide 15: There’s Something in My Observations: Are students able to follow the pattern presented? Pay attention Numbers!; BLM 9: to the group dynamic and how students co-ordinate to support each other. There’s Something in My Numbers! Conversations: Ask students to identify the part of the pattern that repeats. Ask how they know what to say when it is their turn. Consolidation (10 minutes) • Read each of the patterns aloud as a whole group. Ask students what they should do when they reach the end of each pattern strip. (e.g., start back at the beginning) • Building Growth Mindsets: Ask students how practising the number patterns in small groups compared to sharing them as a whole class. (e.g., It was easier with less people because we could stop at the end of the strip, but in the whole class we needed to start back at the beginning.) Discuss how they need to respectfully interact in small groups so everyone feels safe and comfortable contributing their ideas. Ask how they can help a group member who makes a mistake or may not understand something. Have students role-play some ways in which they could interact to support each other. Emphasize that everyone in the class is part of the math community, and all students can learn more if they feel sure they can participate without being embarrassed or feeling badly about themselves. Further Practice • S tudents work in small groups. Display Digital Slide 15: There’s Something in My Numbers! or give each group BLM 9: There’s Something in My Numbers! Students say the patterns aloud, which substitute words for one of the numbers in a repeating number pattern. • Independent Problem Solving in Math Journals: Have students identify the number that is being substituted with a picture on BLM 9 and explain how they know. Students could also create a similar number pattern of their own and share it with the class the next day. NOTE: The following Math Talks should be done before beginning Lesson 12. Materials: Math Talk 1: Digital Slide 16: Number Patterns to 50 Math Focus: Describing number patterns in a fifty chart; identifying number patterns that emerge by counting in a variety of ways Let’s Talk Select the prompts that best meet the needs of your students. • nPuromjebcetrDs sighiotawlnSl(i1d–e3106):aNlouumdbbeyr Patterns to 50. As a class, count the 1s. continued on next page Patterns and Relations 61

Teaching Tip • On your own, think about what patterns you see in these numbers. Then, Integrate the math talk share what you found with a partner. moves (see page 7) throughout Math Talks • A fter partners have shared, discuss their ideas as a class. Highlight the to maximize student participation and patterns as students share. Possible patterns include the following: active listening. – You count by 10s as you move down each column. – You count by 1s as you move across each row. – The second digit is the same in each column. – The first digit of each number is the same in each row, from the second row on. • W hat would the next number after 30 be? What number would come after that? • What is the pattern rule? • What might the next row look like if we extended the pattern? How are the numbers changing? (e.g., They are growing as we move down the chart.) • How many rows will it take to get to 50? How do you know? • What would the pattern be if we went up the chart? What is happening to the numbers now? (shrinking) Materials: Math Talk 2: Math Focus: Describing number patterns in a fifty chart; identifying number patterns that emerge by counting in a variety of ways Let’s Talk Select the prompts that best meet the needs of your students. Digital Slide 17: Number • Project Digital Slide 17: Number Patterns to 50. What do you notice about Patterns to 50 these numbers? How are they changing? By how much are the numbers increasing each time? Let’s count together by 2s. • Look at the numbers in the counting sequence. What patterns do you see? Turn and talk to a partner. • Let’s share our ideas. Possible observations include: – The second digit is the same in each column. – In each row, the first digit is the same from the second row on. – The second digits are the same in each column but the first digits go up by 1. – The number directly below a number is always 10 more. – Every row has 2, 4, 6, 8, 0. • What is the pattern rule? • How much are the numbers increasing each time? • What happens to the pattern if we start at the bottom and move up the chart? • What numbers are missing on the chart? How do you know? 62 Patterns & Relations/Data & Probability

Materials: Math Talk 3: Digital Slide 18: Number Patterns to 50 Math Focus: Describing number patterns in a fifty chart; identifying number patterns that emerge by counting in a variety of ways Let’s Talk Select the prompts that best meet the needs of your students. • Project Digital Slide 18: Number Patterns to 50. Let’s count together by 5s, starting at 5. I am going to track the numbers that we say as we count. • What patterns do you see in these numbers? Turn and talk to a partner. • Let’s discuss the patterns you found. Possible observations include: – The numbers all end in either 5 or 0. – The first digit increases by 1 as you go across a row, from the second row on. – Each number increases by 10 as you go down a column. • What is the next number in the counting sequence? How do you know? What is happening to the numbers as we say this counting pattern? • What happens to the pattern if we start counting from the bottom of the slide and move backward? • What numbers are missing on the slide that would normally be in our counting order? • Give a number between the numbers shown (e.g., 46). Where would this number be? How can you prove that? Why isn’t it in our counting pattern? Repeat for another number (e.g., 29). Materials: Math Talk 4: Digital Slide 19: Number Patterns to 50 Math Focus: Describing number patterns in a fifty chart; identifying number patterns that emerge by counting in a variety of ways Let’s Talk Select the prompts that best meet the needs of your students. • P0.roAjsecsttuDdiegnittaslcSoluidnet,1t9r:aNckumthbeenruPmatbteerrns.s to 50. Let’s count by 10s, starting at • What patterns do you see? Turn and talk to a partner. • As a class, discuss the pattern students find. Possible observations include: – The first digit increases by 1, but the number increases by 10. – The last digit is always a 0. – Each number in the column increases by 10. continued on next page Patterns and Relations 63

– Five jumps equal 50. • What is the next number? How do you know? • What is happening to the numbers each time we count? • What happens to the numbers if we start counting from the bottom of the chart? • Look at our fifty/hundred chart. Where can you find this pattern? • What numbers are missing in our pattern that are on the fifty/hundred chart? • Where would number 49 be? Why isn’t it in our counting pattern? Materials: Math Talk 5: Digital Slide 20: Number Patterns to 50 Math Focus: Describing number patterns in a fifty chart; identifying number patterns that emerge by counting in a variety of ways Let’s Talk Select the prompts that best meet the needs of your students. • Project Digital Slide 20: Number Patterns to 50. Let’s count to 20 by 1s. • What patterns do you see in this counting pattern? Turn and talk to a partner. • Let’s talk about the patterns you found. Possible observations include: – The second digits increase by 1 as you go across. – The first digits increase by 1 as you go down. • What is happening to the numbers as we count? • How does the number pattern change if we start at 20, farther down the chart, and move backward? • nLuoomkbaetrsthcehalansgtet?w(To hneuymgboerfsroinme9actho row. How does the second digit of these 0.) What happens to the first digits in the columns? (They increase by 1.) Why do you think that happens? • Point out the column going from 16 to 46. What do you notice about the (It’s always 6; it doesn’t change.) Does the second second digit in this column? digit change as you go down the other columns? Why do you think this is so? How does this connect to the patterns we discovered in the first Math Talk? 64 Patterns & Relations/Data & Probability

12Lesson Exploring Number Patterns in a Fifty/Hundred Chart Math Big Idea Learning Standards • Repeating elements in patterns can be identified (What number patterns live in a hundred chart?) Previous Experience Curricular Competencies with Concepts: Students have had some • Reasoning and analyzing: Use reasoning to explore and make experience using a fifty chart to count forward connections; develop mental math strategies and abilities to make sense of and backward, and to quantities skip-count using numbers that may appear • U nderstanding and solving: Develop and use multiple strategies to engage in a pattern on a fifty chart. in problem solving • C ommunicating and representing: Communicate mathematical thinking in many ways; explain and justify mathematical ideas and decisions; represent mathematical ideas in concrete, pictorial, and symbolic forms • Connecting and reflecting: Connect mathematical concepts to each other and to other areas and personal interests Content • Repeating patterns with multiple elements and attributes • Number concepts to 20 • Change in quantity to 20, concretely and verbally Possible Learning Goals • Identifies and describes patterns and number relationships using a fifty chart • Explains and/or shows the pattern rule • Creates a variety of number patterns using a fifty chart, using a variety of strategies including skip-counting Teacher • R ecognizes some number patterns in the fifty chart and describes the Look-Fors pattern rule • Recognizes different patterns when skip-counting by 2s, 5s, and 10s • Recognizes that numbers increase by 10s down a column and by 1s across a row • Identifies repeating elements in number patterns (e.g., when skip-counting by 5s from 0, all numbers end in 5 or 0) Patterns and Relations 65

Math Vocabulary: About the pncaauobtmlotuevmbreenn,r,bsrp,eearfpootetwreaesrt,n,inn,begdex,ilgtoiwts,, Using a fifty/hundred chart to understand number relationships is critical. Teaching Tip Van de Walle and Lovin explain that “as children explore number patterns on the hundred chart and become more and more adept at filling in Do the Math Talks in missing numbers on the chart, they are learning about the structure of the Lesson 11 before written numbers in our place-value system” (Van de Walle & Lovin, 2006, beginning this lesson. p. 137). By using the charts, students can explore growing patterns Materials: (counting forward), shrinking patterns (counting backward), and repeating elements within the numbers (e.g., the repetition of the numbers 1 to 9 through all the two-digit numbers), even though the focus in grade one is on numbers to 20. Using their knowledge of numbers to 20, they can predict patterns of larger numbers. This supports the big idea that repeating elements of a pattern can be identified and the inquiry of what number patterns live in a hundred chart. As students explore rows, columns, and diagonals on the fifty/hundred chart, they develop a sense of number, operations, and patterns. About the Lesson In this lesson, students explore various patterns evident in a fifty chart when skip-counting. Like patterns with shapes, students learn that number patterns also have a part that repeats. You may decide to use a hundred chart if your students are competent with numbers to 100. Alternatively, use a fifty chart to limit the counting of numbers to 20 as described in the curriculum. Students should only be assessed on their ability to count and work with numbers to 20. Digital Minds On (15 minutes) Slide 21: Fifty Chart • Project Digital Slide 21: Fifty Chart (or Digital Slide 22: Hundred Chart). and BLM 10: Fifty Chart (or Digital Slide 22: Shade in the numbers 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. Hundred Chart and BLM 11: Hundred Chart ), 1 2 3 4 5 6 7 8 9 10 highlighters in various 11 12 13 14 15 16 17 18 19 20 colours 21 22 23 24 25 26 27 28 29 30 Time: 45 minutes 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 • Ask students what patterns they see in the shaded numbers. They can turn and talk to a partner. • Ask a few students to share their observations. (e.g., We are skip-counting by 2s; the last digits are 2, 4, 6, 8, and 0.) • Ask what patterns the numbers in between the shaded numbers make. • Challenge students to hunt for additional number patterns. 66 Patterns & Relations/Data & Probability

Working On It (15 minutes) • Have students work in pairs. Provide each pair with various colours of highlighters and BLM 10: Fifty Chart (or BLM 11: Hundred Chart). • Tell students to find as many patterns in the chart as they can. They can use a different colour to mark each pattern. Encourage them to look across rows, up and down columns, and from corner to corner. Differentiation • Encourage students who need a challenge to consider the pattern counting forward and backward, and to find and describe patterns in both directions. • For students who need language support, ensure they understand positional vocabulary needed to describe their pattern clearly to their peers (e.g., above, below, every other space, diagonally, column, row). • For students who are not yet clear on what makes a pattern, provide them with their own copy of BLM 10 and transparent counters. They can place counters on the BLM to try out patterns, adjusting as needed before using their highlighters. Assessment Opportunities Observations: • Do students know where to start looking for number patterns in the fifty/ hundred chart? • D o students use a system (e.g., row, column, similar digits) to identify a pattern, or do they need a prompt to help them move forward? • As you circulate and provide prompts and feedback, take anecdotal notes of the patterns students are noticing in order to have a variety of shared patterns during the Consolidation. Conversations: Use some of the following prompts to further probe students’ thinking: – What numbers are in the pattern you noticed? – Why do you think they make a pattern? – What is happening to the numbers in your pattern? (e.g., They are getting larger by 5 each time.) How does this help you know what the pattern rule is? – Where do your pattern numbers appear in the fifty/hundred chart? Patterns and Relations 67

Teaching Tip Consolidation (15 minutes) Incorporate math talk • P roject Digital Slide 21: Fifty Chart (or Digital Slide 22: Hundred Chart). moves (see page 7) • Based on your anecdotal notes, strategically select pairs of students to share to help students make connections to others’ with the class and represent the patterns they found. patterns and to facilitate a student-led • Show students a number pattern such as 4, 8, 12, 16, and 20. Ask students sharing of work. where these numbers are on the fifty/hundred chart. Shade in the numbers. Have students turn and talk to a partner about the patterns they see. Materials: Further Practice • Independent Practice in Math Journals: Provide a copy of BLM 12: Fifty Chart Patterns (or BLM 13: Hundred Chart Patterns). Alternatively, students can make their own pattern using one of the blank fifty/hundred charts on the BLMs. Students can glue the charts in their Math Journals. Scribe for any students who need assistance to describe their patterns. BLM 12: Fifty Chart Patterns or BLM 13: Hundred Chart Patterns, glue 68 Patterns & Relations/Data & Probability

13Lesson Pattern Detectives Math Big Idea Learning Standards • R epeating elements in patterns can be identified (What numbers live in a hundred chart?) Curricular Competencies • R easoning and analyzing: Use reasoning to explore and make connections; develop mental math strategies and abilities to make sense of quantities • U nderstanding and solving: Develop and use multiple strategies to engage in problem solving • C ommunicating and representing: Communicate mathematical thinking in many ways; explain and justify mathematical ideas and decisions; represent mathematical ideas in concrete, pictorial, and symbolic forms • Connecting and reflecting: Connect mathematical concepts to each other and to other areas and personal interests Content • Repeating patterns with multiple elements and attributes • N umber concepts to 20 Possible Learning Goals • Identifies errors in patterns, describes how to correct them, and justifies their reasoning by explaining the pattern rule • Identifies what is needed to complete patterns that have missing elements and justifies their reasoning Teacher Look-Fors • Identifies the part of the pattern that repeats and uses it to accurately extend a variety of patterns Previous Experience with Concepts: • Recognizes errors that occur in a pattern Students have experience • Describes what needs to be added to a pattern to make it correct identifying patterns in • Recognizes what is needed to complete patterns with missing elements the classroom, creating • Explains, shows, or justifies why their adjustments make the pattern and describing patterns with familiar objects, and rule continue predicting what comes next in a pattern. About the As students become proficient at recognizing patterns and their rules, it is important to challenge their thinking by providing them with patterns with missing elements or non-examples of patterns. The non-examples could be missing an element of the pattern or have an error in the continued on next page Patterns and Relations 69

Math Vocabulary: sequence. Students must apply their knowledge and understanding of pc(eao.trgtee.,,reAnr,BrroBer),p, lemeatittsiensrignc,gode patterns to find and correct the irregularities. Challenging students to fill in the missing element or correct an error requires students to look closely at what part of the pattern repeats and determine what part and how much of it is omitted. As they fill in the missing part, they also need to check the pattern in its entirety to see if it still repeats. About the Lesson In this lesson, students apply their knowledge of patterns to find and correct missing elements or errors in a variety of patterns. They also create a pattern that has a missing element, so others in the class can correct it. This is a good opportunity to assess students’ understanding of patterns and to identify any misconceptions that they may still have. Materials: Minds On (10 minutes) Digital Side 23: Is the • Display Digital Slide 23: Is the Pattern Correct? Have students turn and talk Pattern Correct?, BLM 14: Fix the Pattern, concrete to a partner about which attributes are changing and which are staying the materials (e.g., two-sided same. They can also talk about the pattern rule. counters, pattern blocks, connecting cubes, colour • Discuss students’ ideas as a class. Ask whether the entire pattern is correct. tiles) Time: 50 minutes (e.g., No, something is wrong at the end.) Ask what they think is repeating in the pattern. (e.g., triangle, hexagon, rhombus; green shape, yellow shape, blue shape) • Ask what is wrong with the pattern. Ask where it stops repeating. • Ask students for ideas on how to fix the pattern, and to explain how their changes do so. Ask how they can check whether the pattern is correct now. • Tell students they are going to be math detectives and investigate some different patterns to make sure they are complete and follow the pattern rules. Working On It (20 minutes) Part 1 • Students work in pairs. Give each pair a copy of BLM 14: Fix the Pattern. • Students play the role of mathematics detectives who identify the error or missing element in each strip and then fix it. They can show their corrections on the pattern strips. Part 2 • Using concrete materials, students create a pattern with three repetitions of the part that repeats. They then remove one or two of the elements of their pattern. • Students’ patterns will be used in the Consolidation. 70 Patterns & Relations/Data & Probability

Differentiation • Meet with students who may need more practice. Show Pattern 1 on BLM 14 (AAB) and work together to identify what is repeating and the missing element. Give partners another pattern strip to work on. Observe, listen to their conversations, and prompt when necessary (see the Assessment Opportunities). When they appear ready, have them continue working in pairs without you. • Ensure that students who need support understand the need to identify the pattern rule in order to solve and communicate which part of the pattern is missing. Assessment Opportunities Observations: Observe how, or if, students are using the pattern (e.g., the part that repeats, the letter code) to determine the missing part or the error. Conversations: Use the following prompts if students are struggling: – What do you notice about the pattern? Can you find the part that repeats in the pattern? – Do you notice anything wrong with the pattern? Is something missing? Is there an error? – What can you do to fix the error? Can you replace one of the elements so the pattern continues correctly? – How can you check to see if you fixed the error? Materials: Consolidation (20 minutes) concrete materials (e.g., two-sided • Students meet with another pair to compare how they solved for the missing counters, pattern blocks, connecting cubes, colour part or fixed the patterns in Working On It: Part 1. tiles) • Student pairs then take turns showing the patterns they made in Working On It: Part 2, and having the other pair determine what is missing. Students check each other’s corrections to make sure the pattern is complete. Encourage them to explain the pattern rule and identify the part that repeats. • Meet as a class and discuss the steps students took to solve for the missing element or error. Ask why it is important to check the pattern after they think they have corrected it. Further Practice • Students create their own patterns with a mistake or missing element. They can meet with another student and correct each other’s patterns. Patterns and Relations 71

14Lesson Creating Patterns Math Curricular Competencies Learning Standards • R easoning 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 • Understanding and solving: Develop and use multiple strategies to engage with Concepts: Students have had experience in problem solving describing concrete elements of patterns and • Communicating and representing: Communicate mathematical thinking may have used letter codes to describe those in many ways; explain and justify mathematical ideas and decisions; elements. represent mathematical ideas in concrete, pictorial, and symbolic forms • C onnecting and reflecting: Connect mathematical concepts to each other and to other areas and personal interests Content • R epeating patterns with multiple elements and attributes • C omparison of 2D shapes and 3D objects: Sorting 3D objects and 2D shapes using one attribute, and explaining the sorting rule Possible Learning Goals • C reates a variety of patterns using one attribute, and identifies the core and pattern rule • C reates patterns that follow a letter code (e.g., AB, AAB, ABB, ABC) in more than one way • D escribes the attributes used in a pattern, and describes how they change throughout the pattern • C hooses an attribute to change (e.g., shape, size, colour) and creates a pattern with at least three repetitions • E xplains or shows how the attribute they chose changes in their pattern • E xplains or shows the part of the pattern that repeats • U ses a letter code (e.g., AB, ABB) to describe the part of the pattern that repeats • C reates a pattern following a given letter code About the Young children love to create patterns in a variety of ways, such as by clapping, making necklaces on bead strings, or using pattern blocks. It is also important that students have experiences creating as many different pattern types as possible (e.g., using different attributes, rules, 72 Patterns & Relations/Data & Probability

Math Vocabulary: complexity). This may not happen if students can always establish their pccaootrdteee(ro(nep,.tgrie.o,pnAeaBal)Bt,in)legt,ter own rule, since instead of trying different types of patterns, they may continually use a familiar pattern such as ABAB and represent it with different materials or in different ways. Marian Small suggests using structured criteria for students when creating patterns (Small, 2009, p. 573). Some examples of criteria could be using specific letter codes, making sure the pattern has a triangle in it, or requiring that the fifth shape is a rhombus. Such parameters challenge students to think critically, reason through the restrictions, and creatively build a pattern that meets the given requirements. About the Lesson In this lesson, students create a variety of patterns that meet specific criteria. They also identify and describe their patterns and what repeats. Materials: Minds On (10 minutes) Digital Slide 24: Describe • Show students Digital Slide 24: Describe the Pattern (1) and have them the Pattern (1), BLM 15: Criteria Cards, various describe the pattern and the pattern rule. Ask what letter code they can give concrete materials to this pattern. (e.g., AB) (e.g., pattern blocks, attribute blocks, • Have students draw an AB pattern. When they are finished, have them turn connecting cubes, loose parts), paper, pencils, and talk to their partner to share each other’s patterns. Have them check camera that both follow the AB pattern. Time: 45 minutes • As a class, discuss how students knew that their partner had created an AB pattern. (e.g., One thing represented A and another thing represented B and then it repeated.) • Have the same pairs repeat the process, but using a different letter code. Working On It (20 minutes) • Ahead of time, set up six or seven different centres for students to visit. Have a different concrete material and one of the criteria cards from BLM 15: Criteria Cards at each centre. • Students work in groups of three or four. Groups will rotate through the different centres to create patterns. Explain that each centre has a criteria card that says what needs to be in their pattern. For example, it could say to use a triangle in a pattern or to create an AB pattern. • Take photographs of students’ patterns to use during the Consolidation. Choose patterns that vary in complexity and creativity. Patterns and Relations 73

Differentiation • For students who need language support, ensure they understand the task at each centre and what the criteria cards mean. You can offer small-group instruction and go through the criteria cards before they work independently. • For students who a need a challenge, give them criteria cards that require higher-level thinking and reasoning skills (e.g., a triangle is the 5th and the 8th item in this pattern). Assessment Opportunities Observations: While students are working, pay attention to how they are building their patterns. Do they build the part that repeats first and use it to repeat the pattern? Do they follow the criteria right away or do they build a pattern and then adjust it so it meets the criteria? Conversations: While students are working, use some of the following prompts: – What does the card say that your pattern must include? What does this mean? How can you use this information to start your pattern? – What is the part of the pattern that repeats? How do you know? How did that help you create your pattern? – What attribute did you use in your pattern? How is it changing? – Can you describe your pattern? How is it changing? What letter code best describes your pattern? Consolidation (15 minutes) • M eet as a class. Show some of the photographs that you took during the Working On It activities. Discuss how the patterns differ. You may wish to scaffold the discussion by showing simple patterns first and then progressing to complex patterns. • For each pattern, use some the following prompts: – How does this pattern include the criteria on the card? – What attribute changes in this pattern? – What is the pattern rule or the part of the pattern that repeats? How do you know? – What letter code would you assign to this pattern? – How could you recreate this pattern with different materials? • B uilding Growth Mindsets: Ask students which criteria cards were easiest to use to create patterns and which cards were more challenging. Talk about what made them challenging, and discuss how important it was that they worked through these challenges, even if they may have made mistakes. Remind them that when we work hard and work through our mistakes, we 74 Patterns & Relations/Data & Probability

grow new brain connections. Even if we didn’t create patterns YET, with all of our practice, we will. Further Practice • Print the photographs you took at the centres and use them as flashcards for students to practise identifying, describing, and extending patterns. • Independent Practice in Math Journals: Have students create and describe a pattern in their Math Journals. You can also verbally pose one of the following problems for students to answer: – Make an ABB pattern and use colour as the changing attribute. What might my pattern look like? – Create an ABC pattern and include triangles somewhere in it. Patterns and Relations 75

15Lesson Creating Patterns Using Barrier Games Math Curricular Competencies Learning Standards • Reasoning and analyzing: Use reasoning to explore and make connections • U nderstanding and solving: Develop, demonstrate, and apply mathematical Teacher Look-Fors understanding through play, inquiry, and problem solving; visualize to explore mathematical concepts Previous Experience with Concepts: • C ommunicating and representing: Communicate mathematical thinking Students have had experience in identifying in many ways the part of the pattern that repeats and in • C onnecting and reflecting: Reflect on mathematical thinking; connect describing the elements of a pattern aloud. mathematical concepts to each other and to other areas and personal interests Content • Repeating patterns with multiple elements and attributes Possible Learning Goals • Creates a variety of different patterns using one attribute • C reates patterns using different letter codes (e.g., AB, AAB, ABB, ABC) • G ives or follows instructions to create a pattern • Independently creates a pattern using one attribute • E xplains or shows the attribute that changes in their pattern • E xplains or shows what part of the pattern repeats • Describes the repeating part of the pattern using a letter code • Listens to and follows partner’s instructions to create the part of the pattern that repeats About the Spatial reasoning plays an important role in students’ success in mathematics across all strands. Research indicates that spatial reasoning is malleable and can be improved with practice (Newcombe, 2010, p. 31). One way to develop students’ spatial skills is by having them play barrier games, which require them to use spatial language as they give and receive instructions. Throughout the process, students need to think carefully about position, direction, and orientation (Moss et al., 2016, p. 180). They can visualize and mentally rotate shapes, and then think of the vocabulary that best describes how the pattern looks. 76 Patterns & Relations/Data & Probability

Mpbdauaetitstlhdeig,rnVnbeo,arccr,orabirebuerui,l(ldoaepryrti:onal), Barrier games are effective language-learning activities as they provide opportunities to develop both listening and speaking skills. Speakers learn the importance of providing explicit and comprehensive information to listeners and, reciprocally, listeners learn the importance of monitoring information and clarifying understanding through questioning. As students become more familiar with the barrier game, they will begin to use more detail when giving instructions, (e.g., “Put the green triangle to the right of the blue rhombus.”) and ask more clarifying questions if they feel unsure about next steps (e.g., “What comes after the yellow hexagon? Is the orange square last? Can you say it again?”). About the Lesson In this activity, students sit side-by-side with a barrier in between them. One student creates a pattern and then verbally describes to their partner how to create it on their side of the barrier and identify the part that repeats. Students then remove the barrier to confirm the pattern and the repeating part. Materials: Minds On (10 minutes) Digital Slide 25: Describe • Show students Digital Slide 25: Describe the Pattern (2). Have them identify the Pattern (2), barrier (e.g., a book, cardboard, the part of the pattern that repeats (e.g., triangle up, triangle down, triangle or file folder), concrete down). Have them identify the letter code associated with it (ABB). Ask what materials (e.g., pattern is changing and what is staying the same. (e.g., The direction of the triangles blocks, colour tiles), chart is changing, but the shape and colour are staying the same.) Ask how they paper, camera could describe this pattern to someone who could not see it. Highlight any Time: 45 minutes words they use that make their instructions clear. • Show students three different shapes (e.g., square, triangle, hexagon). Ask how they could create an ABC pattern using these shapes. • As a class, create a few different patterns using some or all of the three shapes. Label the repeating part of each pattern together. Have students use words to describe what repeats and how the shapes are positioned. Ask how they would describe the pattern to someone who cannot see it. Working On It (20 minutes) • Students will be playing a barrier game. If this is the first time your students have played a barrier game, you may wish to model it. Choose a student to be your partner. Sit side-by-side with your partner and place a barrier (e.g., a book) between you. Design the repeating part of a pattern and then describe to your partner how to build it. Your partner can ask questions if they are unsure about some of your instructions. Tell your partner to repeat the pattern two more times. Remove the barrier and compare the two patterns to see if they are the same. Patterns and Relations 77

• Make an anchor chart of some of the spatial language that you used to describe the pattern. • Give students the following instructions for game play: – Player 1 (the designer) creates the part of a pattern that repeats using concrete materials, and describes it to Player 2 (the builder). – The builder recreates the part that repeats, and repeats it two more times to create a pattern. – When the builder finishes, both partners lift the barrier to check that their patterns are the same. – Partners switch roles and play again. • Ensure instructions are understood and answer any questions before students play their own games. • Take photographs of several patterns students create to discuss during the Consolidation. Differentiation • Some students may need more guidance to understand how the barrier game works. Work with a small group to clarify the rules and highlight the language they can use to describe the patterns. Assessment Opportunities Observations: • P ay attention to the positional language students use (e.g., beginning, first, second, right, left, middle, beside, corner, at the end, upside down, and turn). What words are they using easily? Which words need reinforcement, clarification, and practice? • N ote how the designers pick up tiles and organize the pattern (e.g., Are they gathering tiles in groupings to make a repeating unit, or are they choosing one tile at a time, unsure of what comes next?). Conversations: • If there are slight differences between the work of the designer and the builder, ask the designer, “What words can you use to help the builder recreate and repeat your pattern?” • Check with the builder by asking, “What is repeating in the pattern your partner described? What questions might you ask so you understand your partner’s instructions better?” 78 Patterns & Relations/Data & Probability

Consolidation (15 minutes) • Meet as a class. Show some of the photographs that were taken as students worked. Ask what words they could use to describe the pattern that is being created. Add the words to the anchor chart started in Working On It. • Discuss what students found most challenging to describe. As a class, think of words that could help clarify the description and add them to the anchor chart. • Building Growth Mindsets: Discuss how partners had to co-operate in order to create the same pattern. Ask what was important when describing the patterns. Ask what kinds of questions they can respectfully ask their partner if they were not sure what the instructions meant. Make a list of their ideas. Highlight the idea that, in order to be successful at barrier games, students must work together as a team and help each other. Patterns and Relations 79

16Lesson Translating Patterns Math Curricular Competencies Learning Standards • R easoning and analyzing: Use reasoning to explore and make connections • Understanding and solving: Develop, demonstrate, and apply Teacher Look-Fors mathematical understanding through play, inquiry, and problem solving; visualize to explore mathematical concepts Previous Experience with Concepts: • Communicating and representing: Communicate mathematical thinking Students have had experience with in many ways describing patterns and the pattern rules • C onnecting and reflecting: Reflect on mathematical thinking; connect (the part that repeats). mathematical concepts to each other and to other areas and personal interests Content • Repeating patterns with multiple elements and attributes Possible Learning Goals • T ranslates a given pattern into a different representation (e.g., concrete materials, colour, actions, sounds, numbers) • Justifies how the translated pattern is the same as and different from the original pattern • Identifies and describes the part of the pattern that repeats, using words or letter codes • Identifies the attributes that are changing and the attributes that stay the same • Links the letter code to the different representations of the same pattern • S elects various materials, sounds, and actions, and translates the pattern • Accurately explains how the patterns follow the same pattern rule but are represented differently About the As students gain more proficiency at identifying the part of the pattern that repeats (pattern rule), they can use it to extend the pattern and to translate it into a different representation. By translating the pattern, students are focusing on the pattern’s structure rather than on its physical appearance, which is “the beginnings of algebraic representation” (Clements and Sarama, 2009, p. 191). Students also need to be able to explain how two patterns are the same in structure, yet different in how they are represented. This reasoning and communication help students to make generalizations, which is foundational to algebraic reasoning. 80 Patterns & Relations/Data & Probability

Math Vocabulary: About the Lesson ptscr(aeaoairltpmnectetmlsieerloan,sent,d,naepritf,lesa)fr,peteeterpeexarrtnteneitnsn,cegdcon,oirntne,gc,ept This lesson provides students with the opportunity to build on their learning from previous lessons that involved representing patterns in different ways (e.g., actions, shapes). Students are introduced to a learning tool called a concept circle that allows them to make connections among a variety of representations (e.g., concrete materials, pictures, letters, numbers). The concept circle allows students to make their thinking visible and is particularly beneficial for students who need language support, since it allows them to represent their choice of strategy with a limited amount of language (Marks Krpan, 2018, pp. 205–213). Materials: Minds On (10 minutes) Digital Slide 26: Concept • Have students brainstorm different examples of patterns that they have Circle, BLM 16: Concept Circles, variety of worked on previously (e.g., patterns with numbers, shapes, actions, concrete materials sounds, letters). Time: 50 minutes • Project Digital Slide 26: Concept Circle. Write ‘AB’ in the centre. Have students turn and talk to a partner about what these letters have to do with patterning. • Discuss students’ ideas as a class. Ask what ‘AB’ means. (the order of the pattern) Ask how many different elements would be in this type of pattern. (two: one for each letter) Ask how they would continue the pattern. (add more AB combinations) • Ask students to visualize different ways to represent an AB pattern. • Students can choose various concrete materials to represent an AB pattern (e.g., pattern blocks, attribute blocks, counters, colour tiles, connecting cubes, dice, money, coloured markers), or they can use representations such as actions or sounds. • Select some students to share their representations and prove that they are AB patterns. Draw one of the examples in each section of the concept circle, choosing patterns that differ in how they are represented (e.g., by colour, sound, action, shape, orientation of shape, number). Working On It (20 minutes) • Have students work in groups of four. Assign each group one of the five concept circles from BLM 16: Concept Circles (i.e., ABC, ABA, ABB, ABBC, or AABC). Each member of the group can use one of the sections on the concept circle and create a representation of the pattern rule as identified by the letter code. They can then draw a picture of their representation or you can take a photograph of the completed concept circle. • Encourage students to use various ways to create their patterns. Have a variety of concrete materials available for them to work with (e.g., pattern blocks, tiles, dice, 3D solids, connecting cubes, money). Patterns and Relations 81

• Once students have finished creating their patterns, they can work on a new concept circle with a different pattern letter code. They need to find a way that is different from the pattern they created on the first concept circle. NOTE: You may want all students to complete all five concept circles. This can be done in another session, after they have gained more ideas from sharing in the Consolidation. Differentiation • F or students who need more experience with selecting appropriate tools and using a given pattern to make another pattern, you may wish to have them work on a two-element pattern (e.g., AB, ABB, ABA) before moving to a three- element pattern (e.g., ABCC). You can use the blank concept circle at the end of BLM 16, if needed. • Provide students with specific materials to create patterns. Encourage them to use the specific materials in different ways (e.g., with pattern blocks, create patterns by colour, shape, orientation). • In each of the four quadrants of the concept circle, write down a different element students are to use when making their patterns (e.g., sounds, shapes, dice). • Adjust the concept circle to include more or fewer spaces for students, as determined by the size of the group. Assessment Opportunities Observations and Conversations: At this point in the unit, it is best to let students investigate and demonstrate what they have learned about identifying, creating, extending, and translating patterns. Rather than imposing a strategy, prompt students to visualize what the repeating part (e.g., ABC) of a pattern may look like. Encourage them to use different tools, numbers, or actions to represent it. Consolidation (20 minutes) • If students drew their representations on BLM 16, post them and have a gallery walk to share students’ work. Alternatively, two groups can meet and share their work. • S trategically select five examples to discuss (five drawn concept circles or five photographs). Meet as a class. Show one example, but cover the centre that shows the letter code. Have students turn and talk to a partner to identify the pattern rule by looking at the examples. • Discuss students’ responses. Ensure that they are justifying their reasoning with proof. • Repeat this with the other four concept circles. • Ask students which representation they find most interesting and why they think so. 82 Patterns & Relations/Data & Probability

Materials: Further Practice BLM 16: Concept Circles, concrete • Send home one of the five concept circles on BLM 16 so students can materials practise creating different ways of making patterns using materials found at home. • Take students outdoors and use chalk to draw concept circles. Students can use natural materials (e.g., sticks, stones, leaves) to fill in the circles. Patterns and Relations 83

17Lesson Patterns and Relations Reinforcement Activities Math • All of the learning standards identified in this unit Learning Standards Teacher • Identifies, describes, extends, and creates a variety of patterns Look-Fors • E xplains or shows their thinking about patterns and justifies that they are Previous Experience patterns with Concepts: Students have had several • Identifies the part of the pattern that repeats (pattern rule) and uses it to opportunities to identify translate the pattern using different elements patterns in a variety of forms (e.g., actions, About the Lesson sounds, visuals, numbers). The following activities can be carried out by the whole class in small Math Vocabulary: groups, or as centres through which students can rotate. The activities can pirdaeepttnreetrisfnye,,nrdete,pssectarrutibicnetgu,,reextend, also be used throughout the unit any time you decide to offer guided math lessons as extra practice for students, or for early finishers. Materials: Centre 1: Pattern Detectives • Have students find patterns in the book Pattern Bugs. For each pattern they find, have them record the page number where it appears, describe it in words or drawings, and write its letter code (e.g., ABB). Pattern Bugs, paper, pencils 84 Patterns & Relations/Data & Probability

Materials: Centre 2: Creating Action Patterns BLM 3: Action Cards, blank • Students work in small groups. Have students create pattern strips of four paper, glue actions by affixing four cards from BLM 3: Action Cards to blank paper. Groups practise performing each pattern four times, to some popular music if possible. Groups model and lead the class in a 16-beat action-pattern activity at the end of each day. Materials: Centre 3: Pattern Tic-Tac-Toe BLM 17: Tic-Tac-Toe Boards, variety of • Using concrete materials of their choosing (e.g., pattern blocks, attribute concrete materials, pencils blocks, connecting cubes, colour tiles, coins), students create patterns to fit criteria in any three cells in a line on a tic-tac-toe board from BLM 17: Tic- Tac-Toe Boards. Students can use an X to mark which cells their patterns fit. • Ensure that students understand the criteria in all cells on the board before they begin. • If students are ready, have them see whether they can mark an X on more than one cell on the board for any of their patterns. Materials: Centre 4: Spot and Extend the Patterns • Using “Spot the Patterns” (pages 2–3 in the little books), have students identify a pattern and then describe it using words or pictures. Then, have them extend the pattern. For example, a student might find and describe the colour pattern on the snake as ‘red, black, white, black,’ and then extend it using this pattern rule. Students can record their work in their Math Journal. “Spot the Patterns” (pages 2–3 in the Patterns, Relations, Data, and Probability little books) Materials: Centre 5: Exploring Number Patterns BLM 10: Fifty Chart, highlighters in • Have students identify patterns on BLM 10: Fifty Chart. They can use a various colours different colour to highlight each pattern they find. Students can describe their patterns in their Math Journals or, if they have limited written language, they can describe their patterns orally in a mini-interview. Patterns and Relations 85

Materials: Centre 6: Translating Patterns “Spot the Patterns,” “Ready, Set, Action!” and • Provide students with the blank concept circle from BLM 16: Concept “How Does It Repeat?” (pages 2–5 in the Circles. Patterns, Relations, Data, and Probability little • Students find a pattern in the images on pages 2–5 of the little books or in books); blank concept circle from BLM 16: the classroom. They describe or draw the pattern in one of the spaces in the Concept Circles; variety of outer ring of the concept circle. They identify the pattern structure (e.g., concrete materials; ABB) and record it in the centre of concept circle. camera (optional) • Students then translate their pattern in four ways using concrete materials. You may wish to take a picture for assessment purposes. Building Growth Mindsets: Have students think about the patterning lessons they did throughout this unit. Pose some of the following prompts to evoke reflection on personal growth and reinforce positive attitudes toward math: – What were your favourite activities? (Math is interesting and fun to investigate.) – What did you find challenging? (Hard tasks are good and if we keep trying, we can be successful.) – What did you learn? (Celebrate our accomplishments.) – What do you still have to learn? (We may not know it YET, but we will with time.) – How can mistakes help us to learn? (Mistakes help us to try new strategies and learn new ways of trying so we can do things better.) 86 Patterns & Relations/Data & Probability