p9-88-Unit1-Gr2BC-Patterns-pass2

Differentiation • Some students will be more successful creating their patterns with concrete materials rather than drawing them on the BLM. Be prepared to photograph their work and allow them to describe their patterns and pattern rules either on paper or orally. Assessment Opportunities Observations: Use a checklist to assess students’ ability to create a pattern, describe it, and identify the pattern rule. Conversations: Ask students any of the following clarifying questions as they work on creating their patterns: – Describe your pattern to me. – What is the pattern rule to get to the next term? Consolidation (20 minutes) • Have a gallery walk so students can observe each other’s patterns. • As a class, discuss what students found interesting in their peers’ patterns and what they may want to try when creating patterns in the future. Ask where they might see growing patterns in real life. • Building Growth Mindsets: Have students evaluate their own work using the success criteria for the task established in Working On It. • Collect student work to review. Patterns and Relations 57

11Lesson Patterns with Money Math Curricular Competencies Learning Standards • Reasoning and analyzing: Use reasoning to explore and make connections • Understanding and solving: Visualize to explore mathematical concepts MpqicdeuaoenatunnhrnttiieetVfisrynos,,gc,c,naprilebcoaakuotettlneealis,rern,ys:dkruiimplee,st,erm, • C ommunicating and representing: Explain and justify mathematical Teacher ideas and decisions; represent mathematical ideas in concrete, pictorial, and Look-Fors symbolic forms Materials: Content • R epeating and increasing patterns • F inancial literacy—coin combinations to 100¢, and spending and saving Possible Learning Goals • Identifies patterns found in real-life contexts (money) • Creates patterns and represents them using pictures of coins and/or play money coins • Describes patterns involving coins using either the value or the number of coins • Creates and describes patterns using coins • Explains their pattern rule • Compares their pattern to other patterns created by peers Minds On (15 minutes) “Pattern Hunt” (pages • Project Digital Slide 37: Coins and ask: 2–3 in the Patterns, − What do you know about these coins? What is the name of each one? What Canadian symbol is on each of them? How much is each of these Relations, Data, BLM 8: Coins coins worth? and Probability • Project page 3 of the Patterns, Relations, Data, and Probability big book and big book), coins draw students’ attention to the stacks of quarters and dimes at the bottom of (actual or toy), the page. Digital Slides − Look at the piles of dimes. What do you notice? (e.g., There are 5 in each pile.) 37–42: Coins, − What do we know about the value of a dime? (e.g., It’s worth 10 cents.) BLM 8: Coins, scissors, glue 22 © 2022 Scholastic Canada Ltd. GRADE 2: PATTERNS & RELATIONS/DATA & PROBABILITY ISBN 978-1-4430-7187-1 Scholastic Canada GR2 BC Patterns & Data Fourth Pass Reproducibles October 25, 2021 sticks, paper, sticky notes Time: 40 minutes Digital Slide 41: Coins Digital Slide 42: Coins − What pattern might we use when counting the value of the dimes in Digital Slide 39: Coins Digital Slide 40: Coins each pile? (e.g., a growing pattern: 10¢, 20¢, 30¢, 40¢, 50¢) Digital Slide 38: Coins Digital Slide 37: Coins − What other pattern do you see with the dimes? (e.g., We could count the number of piles: 1, 2, 3, 4, 5.) Illustration: © Natsmith1/Shutterstock Illustration: © Natsmith1/Shutterstock Fourth Pass − Look at the piles of quarters. What do you notice? (e.g., There are 4 in Fourth Pass each pile.) Scholastic Canada GR2 BC Patterns & Data Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slides Digital Slides October 25, 2021 October 25, 2021 Illustration: © Natsmith1/Shutterstock Fourth Pass Scholastic Canada GR2 BC Patterns & Data Illustration: © Natsmith1/Shutterstock Digital Slides October 25, 2021 Scholastic Canada GR2 BC Patterns & Data Digital Slides Illustration: © Natsmith1/Shutterstock October 25, 2021 Scholastic Canada GR2 BC Patterns & Data Illustration: © Natsmith1/Shutterstock Fourth Pass Digital Slides October 25, 2021 Scholastic Canada GR2 BC Patterns & Data Digital Slides 58 October 25, 2021 Fourth Pass Patterns & Relations/Data & Probability

− What do we know about the value of a quarter? (e.g., It’s worth 25 cents.) − What pattern might we use when counting the value of the quarters in each pile? (e.g., 25¢, 50¢, 75¢, 100¢) − What other pattern might we use when counting the number of dimes? (e.g., 1, 2, 3, 4, 5) Teaching Tip Working On It (15 minutes) Some students may • Provide each student with a copy of BLM 8: Coins, scissors, a glue stick, struggle with the concept of unitizing, legal-size paper, and access to physical coins (e.g., actual, toy). Students can meaning that a group work in pairs. Explain that they will be making various patterns using coins. of individual units can They can use any of the attributes that the coins have. They need to show at be combined to create least 4 terms and be able to explain their pattern rule. a new unit. Students may need additional • Have students fold their paper in half twice and then unfold practice or explore time to investigate multiple it. The creases will divide the paper into 4 equal sections in representations. a row. • Have students work with physical coins to start. (There will be a gallery walk where other students can provide feedback. Pairs may wish to consider some of this feedback before cutting out and gluing down their final pattern.) • As students work on creating their patterns, circulate and clarify and advance their work with some of the following prompts: – Tell me about your pattern. – Which coin(s) did you choose to use? Why? – What is your pattern rule? How do you know? – How many coins will be in your next term? How do you know? • Once students have created a pattern on their paper with concrete objects, give each pair three sticky notes and ask them to visit and view the patterns of three other groups. • Students provide feedback on three patterns by leaving a sticky note with one of the following symbols: P (“We get it. Your pattern is like ours.”), ! (“Cool idea. We did something else!”), or ? (“We have a question.”). • Have students consider their peer feedback when cutting out and gluing down the final version of their pattern using paper coins from BLM 8. Differentiation • Provide a suggestion of pennies, nickels, or dimes to groups that are more comfortable skip counting by 1s, 5s, or 10s. • Use Digital Slides 38–42: Coins to work with students who may need practice skip counting with each of the coins before beginning to create their patterns. • For groups that need a challenge, suggest that they create a pattern using a combination of coins. Patterns and Relations 59

Assessment Opportunities Observations: Use a checklist to observe students at work. Include look- fors such as students’ ability to: – Create a pattern – Identify and explain the pattern rule for their pattern Conversations: Record anecdotal notes using the clarifying and advancing prompts on the previous page. Consolidation (10 minutes) • Put two student pairs together to share their patterns with each other using the following prompts: – In our pattern, we used… (pennies/nickels/dimes/quarters/loonies) – Our pattern rule is… • You may choose to share and discuss one pattern with the class to ensure understanding. • Have students submit their final money pattern. Further Practice • Reflecting in Math Journals: Have students write in their Math Journals about a challenge they had today and how they worked through it. 60 Patterns & Relations/Data & Probability

12Lesson Applying Patterning Concepts to Solve Problems Math Curricular Competencies Learning Standards • Reasoning and analyzing: Use reasoning to explore and make Teacher connections; model mathematics in contextualized experiences Look-Fors • Understanding and solving: Develop, demonstrate, and apply Previous Experience with Concepts: mathematical understanding through play, inquiry, and problem solving; Students have had several visualize to explore mathematical concepts; develop and use multiple opportunities to identify strategies to engage in problem solving and describe patterns. • Communicating and representing: Communicate mathematical thinking in many ways; explain and justify mathematical ideas and decisions; represent mathematical ideas in concrete, pictorial, and symbolic forms • Connecting and reflecting: Connect mathematical concepts to each other and to other areas and personal interests Content • R epeating and increasing patterns Possible Learning Goals • Applies knowledge of patterns to find and sort patterns in a picture • Applies knowledge of patterns to solve problems • Accurately identifies growing and repeating patterns • C lassifies objects according to given categories • E xplains orally, physically, or in writing the reasoning for their sort About the In addition to developing their patterning knowledge and skills, students need to experience patterns in a wide variety of situations in order to apply these skills in new contexts. Problem-solving situations set in real-life contexts can help students build this ability and make sense of the math. Small suggests that using real-life problems helps students build connections between math concepts they are learning and how to apply them (Small, 2017, p. 95). Van de Walle also says that another important aspect to using problem-solving situations is asking students to justify and explain their thinking (Van de Walle, 2001, p. 43). continued on next page Patterns and Relations 61

Math Vocabulary: About the Lesson sort, identify, pattern, describe This lesson provides students with the opportunity to look for patterns extend, in a real-life context—a toy store. This problem-solving situation asks students to find and describe patterns in a given image. Students are introduced to the context in the Minds On section and continue identifying and describing patterns in the Working On It section. Materials: Minds On (10 minutes) “Spot the Pattern” • Show students “Spot the Pattern” on page 8 in the big book, and ask a few (page 8 in Patterns, Relations, Data, and questions to establish context. Questions might include: Probability big book and little books), chart paper, − Where is this scene taking place? Have you ever been to a toy store? counters, square tiles Time: 50–60 minutes − What kinds of things do you like to look for at a toy store? − What are some of the objects in the picture? How do you know? • Draw students’ attention to the patterned floor. Ask them what they notice about the floor. Have students turn and talk with a partner about what they notice (e.g., repeating pattern on the floor tiles). Have students describe the pattern and identify the pattern structure. (e.g., Tiles are patterned by colour—blue, green, blue, green; this is an AB pattern.) Have students extend the pattern in a particular location on the page (i.e., what would come next here). Working On It (30 minutes) • Tell students that they are going to be pattern detectives. They are going to find and sort all of the different patterns on the “Spot the Pattern” page. On chart paper, they will describe each pattern and identify the pattern rule. They will also sort the patterns by type—growing or repeating. Have students explain in their own words the problem they are solving and what they are expected to do. Ask what else they may need to know before they begin. • S tudents can work in groups of two or three. Provide a copy of the little book to each group. Two pairs of students can also use the big book. • Tell students that they need a strategy for finding and sorting the patterns. They also need a way to check that they have found all the patterns on the page (e.g., each partner looks for patterns and then shares what they have found; mark each pattern with a counter, check with another group when finished). Differentiation • For students who need more experience using concrete materials, have them represent the patterns they find using counters or square tiles. 62 Patterns & Relations/Data & Probability

Assessment Opportunities Observations: Observe which students are able to identify the different types of patterns in the image. Watch to see how students sort the different patterns they find to ensure they are placing them under the correct pattern type. Some students may not have internalized the different pattern types yet. They may need more small-group practice identifying and describing the patterns they see in real-life images. Consolidation (10–20 minutes) • Bring students back together. Strategically pick one of the pattern types to discuss as a whole group (e.g., Which patterns did students find that fit into this category?). Have students share what they found. • Ask students to share the most interesting (or the most challenging) pattern they found. Ask what made it challenging (or interesting). • B uilding Growth Mindsets: Discuss how students found, sorted, and checked their patterns. Ask what they might do differently if they were going to solve a similar problem. Further Practice • Independent Problem Solving in Math Journals: Have students choose one of the patterns they found and represent (e.g., draw) it a different way. Have them describe the pattern, name the pattern, and extend it. • Reflecting in Math Journals: Ask students what other types of patterns they have seen outside of school. Have them draw and describe these patterns. • Community Walk: Go on a walk with the students to search for more patterns outside and inside the school. • At Home: Challenge students to find patterns they notice at home to share with the class the next day. Patterns and Relations 63

13 14Lessonsand Investigating Positional and Circular Patterns Math Curricular Competencies Learning Standards • Reasoning and analyzing: Use reasoning to explore and make Teacher connections; model mathematics in contextualized experiences Look-Fors • Understanding and solving: Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving; visualize to explore mathematical concepts • C ommunicating and representing: Communicate mathematical thinking in many ways; use mathematical vocabulary and language to contribute to mathematical discussions; explain and justify mathematical ideas and decisions; represent mathematical ideas in concrete, pictorial, and symbolic forms • Connecting and reflecting: Connect mathematical concepts to each other and to other areas and personal interests Content • R epeating and increasing patterns • Multiple attributes of 2D shapes and 3D objects (sorting 2D shapes and 3D objects, using two attributes, and explaining the sorting rule) Possible Learning Goals • Identifies patterns in geometric designs that are evident in our everyday lives, and identifies how the position of the shapes affects the pattern • Creates a geometric design that repeats on the other side of a line of symmetry (vertical or horizontal) • Co-operatively works with a group to create a geometric design that repeats in a circular manner • Explains how the position of the shapes contributes to the pattern • E xplains or shows how patterns can be mirror images of each other, or can repeat in a circular manner • V isualizes how the repeating pattern will look before physically placing the shapes • Positions concrete objects on one side of a line of symmetry so they align with each other to make a pattern • P ositions concrete objects, one at a time, on the other side of a line of symmetry so they mirror the design being created piece by piece on the first side 64 Patterns & Relations/Data & Probability

Math Vocabulary: About the gmphtemlraeiioinrtaaxrmetoannerggedronoltaifemr,nli,sac,tay;turgrmdrshaeneyomp,smmepicegzomibtronricuneyi,dustt,,lr,ayr, Patterns in geometric designs are prevalent in our everyday lives, such as (optional) in floor tiles, architectural construction, and artwork. When studying geometric designs, students need to pay attention to many of the geometric attributes of two-dimensional shapes, such as angles and side lengths, to describe the patterns. Symmetry can also play an important role in patterning since the lines of symmetry often determine how and where a pattern will repeat. Although students do not formally study symmetry until grade four, young children have an intuitive understanding of symmetry, including mirror and rotational symmetry, and often produce symmetry in their play (Clements & Sarama, 2009, p. 131). An informal understanding of symmetry helps students recognize more complex patterns, such as positional and circular patterns. Students can describe such patterns in terms of matching halves or parts. About the Lessons In Lesson 13, pairs of students work together to create a geometrical design with a symmetrical pattern. The leader places pattern blocks on one side of a line of symmetry, while the partner places blocks on the other side to create the symmetrical image. This activity has been done in several ways over the years with students of all ages (see for example Taking Shape, Moss et al., 2016, pp. 74−79). It is worthwhile to read other versions of this activity and note adaptations that can be made and to learn more about the research that has been carried out with young students and their understanding of symmetry and patterning. In Lesson 14, students work in groups of four to create circular patterns (inspired by mandalas), using the centre and the quadrants of a circle. Patterns and Relations 65

13Lesson Creating Patterns by Positioning Shapes Materials: Minds On (15 minutes) Digital Slide 44: Geometric Designs • Show students Digital Slides 43 and 44, one at a time. Discuss the patterns Digital Slide 43: Geometric Designs they see. Encourage students to refer to the geometric attributes of the Photo: © SeamlessPatterns/Shutterstock shapes in their descriptions. Ask how the patterns repeat. You can point out and describe lines of symmetry as the lines over which patterns repeat. Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slides • Show students a repeating design made of pattern blocks October 25, 2021 and have them describe the repeating pattern. For example: Photo: © Francisco Javier Zea Lara/Dreamstime Have them visualize folding the pattern to determine if the Scholastic Canada GR2 BC Patterns & Data Slides Fourth Pass two sides match. Discuss how the two sides are mirror Digital Slides images of each other. You can place a mirror (or mira) October 25, 2021 43−44: along the fold line where they visualized it to show what a mirror image is. Explain that the design repeats on the other side of the Digital line. You may decide to introduce the term ‘line of symmetry,’ or ‘mirror line.’ Discuss how it is the positioning of the shapes that makes the pattern Geometric Designs, repeat on the other side. BLM 9: Pattern Blocks • On a blank piece of chart paper, draw a vertical line of symmetry down the Grid Paper, pattern centre. Put a pattern block on the left side so it is touching some part of the line. Ask students what they could do to create a mirror image on the other blocks, mirror or mira, side of the line. Ask a student to put a matching block on the other side, and have another student check the block’s position and whether a mirror image, half or quarter pieces or symmetry, has been created. Place a mirror (or mira) along the line and ask whether the reflection is the same as what they created on the other side. of chart paper • Ask a student to put another pattern block on the left side of the line. Ask Time: 55 BLM 9: Pattern Blocks Grid Paper minutes a second student to put a block on the other side to make a mirror image. Have a third student use the mirror or demonstrate how the two sides create © 2022 Scholastic Canada Ltd. GRADE 2: PATTERNS & RELATIONS/DATA & PROBABILITY ISBN 978-1-4430-7187-1 23 symmetry (are mirror images of each other). Scholastic Canada GR2 BC Patterns & Data Fourth Pass • Have a student add a third block on the left side of the line. In response, Reproducibles October 25, 2021 purposely place a block on the right side of the line so it does not create a mirror image. For example, place a rhombus so it faces in the same direction as the one on the other side rather than being its mirror image. Ask the class whether it is in the right position and if it is not, ask for feedback on how you can place it correctly. Have another student explain how it is now a mirror image. • Show students another piece of paper that has a horizontal line of symmetry. Place a block on the top half of the page. Ask where they will build the mirror image. (e.g., below the line) 66 Patterns & Relations/Data & Probability

Working On It (20 minutes) • Ask students to work in pairs to make mirror-image patterns. Put a line of symmetry on a half or quarter piece of chart paper or have students fold the paper in half. You can assign to each group a line of symmetry to work with (vertical or horizontal), or you can let students choose. One partner can be the leader for the entire design, or partners can take turns with the first student leading on the placement of the first block, and the second student leading on the placement of the second block. • W hen students have completed a design, have partners meet with another pair and discuss whether the creations show patterns that are mirror images of each other. Students can use a mirror to check whether their designs on the right- hand side look the same as the reflection of the left-hand side. Differentiation • For students who are finding it challenging to accurately place the blocks, have them work on pattern block grid paper. They may also find it easier to work with a vertical line of symmetry. • For students who need more of a challenge, have them place two or three blocks at a time before the partner creates the mirror image. • For students who need more of a challenge, have them work with a horizontal line of symmetry. • For a further challenge, students can begin to create their design with a block that is not touching the line of symmetry. Students can also be challenged to build a robot or animal that includes details such as legs, arms, and eyes. Assessment Opportunities Observations: Pay attention to whether students are building from the line and creating a reflection, or whether they are just creating a duplicate design. If that is the case, they may not understand the process of ‘flipping’ over the line of symmetry to create a mirror image. Conversations: Challenge students to prove that the design is a mirror image. If students are not certain, try the following: • Show students a piece of paper that is folded in half. Put a hexagon on the left side along the line of symmetry. Pose some of the following prompts: – Imagine that we folded this over so the design flips onto the other side. Where would the hexagon be? (e.g., It would be on the other side touching this hexagon.) Repeat this with the trapezoid. What happens to the trapezoid when we fold and flip it to the other side? (e.g., It faces in the other direction.) Why? (e.g., We folded it over.) Show me what you mean using the trapezoid. Repeat this with the rhombus. This time visualize folding the rhombus over onto the other side. Put another rhombus on the other side to Patterns and Relations 67

show what you visualized. How is that different from making the exact same design that your partner made? (e.g., This side is folded so it doesn’t look exactly the same.) • On the students’ pattern block design, slide the right-hand side of the design down so it is below the original design on the left, but still along the line of symmetry. Put a mirror beside the design on the left along the line of symmetry. Imagine folding along this line and flipping this design over. What you see in the mirror is what you would see on the other side. Compare this design with the one I slid below. Is this what your design looks like? (e.g., No, this design looks exactly the same as the first one.) • L et’s try again. You place a block and your partner will visualize folding it over onto the other side. Where do you think the block would go? Let’s add another block. Consolidation (20 minutes) • Have a gallery walk so students can see each other’s geometric designs. Move as a class to look at each design. Ask students about the patterns that they see within the geometric designs. Discuss how the positioning of the shapes on either side of the mirror line determines how the pattern repeats. As students share, reinforce the use of geometric language to describe the attributes of the shape. Further Practice • Joan Moss and her colleagues suggest doing this activity on grid chart paper using colour tiles (Moss et al., 2016, p. 93). The leader places four or five pieces while the partner is not looking. The partner then creates the mirror image on the other side. Partners can continue taking turns and making the patterns in the designs more and more complex. (See BLM 9: Pattern Blocks Grid Paper.) 68 Patterns & Relations/Data & Probability

14Lesson Investigating Circular Patterns in Mandalas Materials: Minds On (20 minutes) Digital Slide 49: Mandalas Digital Slide 48: Mandalas • Show students Digital Slides 45 and 46. Ask what patterns they see in the Digital Slide 47: Mandalas Digital Slide 46: Mandalas Digital Slide 45: Mandalas geometric designs. Discuss how the designs repeat in a circular manner. Have students visualize turning the design so it matches onto itself. Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slides • Show Digital Slide 47. Explain that mandalas like the one shown here are October 25, 2021 spiritual symbols in Hindu and Buddhist cultures. They are circles or Scholastic Canada GR2 BC Patterns & Data Fourth Pass squares that are divided into equal sections and organized around the centre Digital Slides Fourth Pass point. A pattern is created and repeated in each section. Tibetan monks October 25, 2021 engage in sand art to make mandalas. They sit around the outside of the circle or square and co-operatively create a symmetrical design with Photo: © Marie Velde/Dreamstime coloured sand from the central point outwards. It is interesting that shortly after it is created and completed, the mandala is destroyed to symbolize that Scholastic Canada GR2 BC Patterns & Data Fourth Pass nothing lasts forever in the world. Digital Slides October 25, 2021 • Show the design made of pattern blocks on Digital Slide 48. Ask students to Photo: © Alexander Melnikov/Dreamstime describe or show where they see patterns. Choose one block and have students visualize moving it in a circle around the design, to see how it Scholastic Canada GR2 BC Patterns & Data repeats in each part of the circle (quadrant). (You could also recreate the Digital Slides design with pattern blocks on a piece of chart paper and have students October 25, 2021 physically walk around the design to see the repetition.) Repeat with the design on Digital Slide 49. Photo: © Deboracilli/Dreamstime • Show students a large square cut out of chart paper that has been folded two Scholastic Canada GR2 BC Patterns & Data Slides Fourth Pass Digital Slides times, creating 4 equal sections (quadrants). Have a student sit in front of October 25, 2021 45−49: each quadrant. Ask one student to place a pattern block down in their section so it is touching the central point. The other three students can each Digital place a block down in their section so it matches what the leader placed. Have a different leader place the second piece while the other students Mandalas, pattern follow. Have students repeat this three or four times to begin creating a circular pattern. blocks, chart paper Working On It (20 minutes) Time: 55 minutes • Students work in groups of four to create their own mandala-like patterns, as demonstrated in the Minds On. Encourage students to visualize how the pieces will fit before they place them on the chart paper. Also encourage them to regularly check that everyone is correctly placing pieces so they follow the leader’s directions. • W hen they are finished, students leave their creation intact so they can enjoy each other’s work in the Consolidation. Patterns and Relations 69

Differentiation • For students who have difficulty perceiving the design from the opposite side, encourage them to walk around to the other side to view what the pattern looks like from another perspective. Alternatively, all four students can sit side by side and complete two sides and then move to the next side to complete a new side by matching it to the completed side that is adjacent to it. They can then move to the next side to complete the final quadrant. • For students who need more of a challenge, have the leader place two blocks while their partners’ eyes are closed. The other group members then open their eyes and complete the design without witnessing how the leader did it. Assessment Opportunities Observations: Observe how students place their blocks. Do they visualize how to place the pieces to create the pattern? Do they manipulate the pieces before placing them, indicating that they did visualize how the pieces fit together? Do they place the piece and then have to move it to match the leader’s configuration? Can they detect if a block is not placed in a way that creates a pattern? Do the group members communicate with each other to ensure the pattern is evident in all quadrants? Conversations: If students are having difficulty creating a pattern that repeats in a circle, pose some of the following prompts: – How do you know that your design has a circular pattern? Prove each section, one at a time. Let’s all stand on the same side so we can see these two sections that are side by side. Show how the shapes in these two sections repeat. Now let’s move to the next side. How do the shapes here repeat? Let’s do this for the remaining sides. Consolidation (15 minutes) • Have a gallery walk so students can look at each other’s mandalas. Discuss what they found interesting about making the patterns. • Meet as a class. Use one mandala as an example. Have students prove that the pattern repeats in a circular manner. • Discuss the strategies that students used to ensure they were following the pattern being created. • When the lesson is finished, have students take photos of their creations. They can then dismantle them, indicating that nothing lasts forever. Building Growth Mindsets: Ask students how they felt creating their own geometric designs. Discuss how they could express their creativity but still needed to follow pattern rules to complete their designs. Explain to students that geometric designs play an integral role in our lives, including in the construction of buildings, the patterns on clothing and materials, and many art creations. Encourage them to look for geometric patterns over the next few days. If possible, have students take photos of some of their findings and bring them to class. These photos can be used in Math Talks so students can appreciate the beauty in the designs and discuss the patterns within them. 70 Patterns & Relations/Data & Probability

to15 18Lessons Investigating Number Patterns Math Curricular Competencies Learning Expectations • R easoning and analyzing: Use reasoning to explore and make connections; Previous Experience develop mental math strategies and abilities to make sense of quantities with Concepts: Students have had • Understanding and solving: Develop, demonstrate, and apply experience identifying, extending, creating, and mathematical understanding through play, inquiry, and problem solving; representing patterns. develop and use multiple strategies to engage in problem solving Students will transfer what they have learned • C ommunicating and representing: Communicate mathematical thinking about the characteristics of these patterns to a in many ways; explain and justify mathematical ideas and decisions; more abstract represent mathematical ideas in concrete, pictorial, and symbolic forms representation using numbers. • C onnecting and reflecting: Reflect on mathematical thinking Content • Repeating and increasing patterns • Number concepts to 100 • Addition and subtraction facts to 20 About the As students become more comfortable working with numbers, they begin to notice the patterns that are a part of our number system. When they count forward, for example, they will recognize that the 1 to 9 pattern extends throughout the number system. When students are proficient in using this sequence, they will be able to count forward and backwards with confidence because the pattern is predictable. As they progress with their investigation of numbers, students will notice the patterns that occur when they skip count. They may also notice the number patterns they see in the calendar, on a hundred chart, or when representing skip counting on a number line. Students will also begin to recognize the patterns that occur when investigating basic addition and subtraction facts and mental math strategies, which will in turn support them when adding and subtracting with larger numbers. It is important when students are describing number patterns that they identify both the starting point in the pattern (i.e., “Start at ___ , then…”) and the pattern rule (i.e., the operation needed to get to the next term) for the pattern to be complete (Small, 2013, p. 611). continued on next page Patterns and Relations 71

Math Vocabulary: About the Lessons ncpieudhaxmeattntrebettn,erifdniryn,,lrcicudnrrleeeeea,sa,schttiereuni,brngmed, ,,red Lessons 15–18 build on the knowledge and experience students adding have gained working with visual patterns in the previous lessons, as well as the practice they have had using skip counting and addition in Number and Operations. Students learn some important features of number patterns (e.g., a pattern starts at a certain point; there is a predictable rule that allows us to develop a conjecture about what comes next). Students will use a variety of tools (e.g., calendar, hundred chart, a variety of number lines, calculators) to help them identify, describe, and extend number patterns. Students will also create their own number patterns which they will describe by identifying the starting point of the pattern and the pattern rule (e.g., add 1) that is used to move from one term to the next. 72 Patterns & Relations/Data & Probability

15Lesson Patterns Using Number Lines Teacher Possible Learning Goals Look-Fors • Represents a given pattern using jumps on a number line at regular intervals • Determines the pattern rule in a skip counting rule on a number line by identifying the length of the jump • Translates patterns to a number line • Skip counts to demonstrate number patterns • Explains the pattern rule using a number line • Shows the pattern rule on a number line Materials: Minds On (20 minutes) Digital Slide 56: Hundred Chart • Have students stand up and spread out enough so that they can jump up and 1 2 3 4 5 6 7 8 9 Dig1it0al Slide 52: Number Lines (1s) down safely. 11 12 13 14 15 16 17 18 19 20 • Project Digital Slide 50 for students to reference while they do this activity. 21 2D2igita2l3Slid2e453: 2N5umb2e6r Lin2e7 s (22s8) 29 30 Use the following prompts: 31 32 33 34 35 36 37 38 39 40 Digital Slide 54: Number Lines (5s) 41 42 43 44 45 0 46 1 47 428 49 3 50 4 5 6 7 8 9 10 51 52 53 D5ig4ital 5S5lide 5565: Nu57mbe5r8Line5s9 (10s6)0 0 2 4 6 8 10 12 14 16 18 20 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 0 5 10 15 20 25 30 35 40 45 50 81 82 83 84 85 0 816 2 87 3 848 5 89 6 970 8 9 10 11 12 13 14 15 16 17 18 19 20 0 9110 92 20 93 3904 9540 96 50 97 6908 9970 100 80 90 100 0 2 4 6 8 10 12 14 16 18 20 Scholastic Canada GR2 BC Patterns & Data Fourth Pass – W e are going to jump on the spot and say one number for each jump Digital Slides 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 while we do it. We’re going to 20. Ready! [Count off the jumps together.] October 25, 2021 Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slides 0 10 20 30 40 50 60 70 80 90 1O0ct0ober 251,120021 120 130 140 150 160 170 180 190 200 Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slides October 25, 2021 Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slides October 25, 2021 Scholastic Canada GR2 BC Patterns & Data 50: Fourth Pass – Now find a partner and we will do that again. One partner will do the Digital Slides jumps and the other will count how many jumps there are. (1, 2, 3, 4, 5, October 25, 2021 Number 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20) Digital Slide – How many jumps did you count? (20) Lines to 20, Digital Slide – Let’s have a look at our number lines. Can someone remind us how we counted? (by 1s) Yes. And how did that sound? (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 51: Tic-Tac-Toe Board 11, 12, 13, 14, 15, 16, 17, 18, 19, 20) How might we show that on our number line? [Show jumps of 1, starting at 0, all the way to 20.] How (and/or BLM 10), Digital many jumps were there altogether? (20) [Trace/draw the jumps on the whiteboard and have students count along to show how many jumps.] Slides 52–55: Number – This time, we are going to do the same thing, but we are also going to Lines, Digital Slide 56: skip count by 2s. How might we start counting? (2, 4, 6,….) Hundred Chart, BLM 11: – We’re going to 20 again. Everyone jumps. Ready! Go! (2, 4, 6, 8, 10, 12, 14, 16, 18, 20) Number Lines BLM 11: Number Lines (1s, 2s, 5s, 10s) 5s Time: 45–50 BLM 10: Tic-Tac-Toe Board minutes Choose three 0of the fo5 llowing10 patter1n5s to s2h0ow ho2w5 they 3w0 ould lo35ok on 4a0 45 50 number line. Make a Tic-Tac-Toe with your choices. A number pattern A number pattern A number pattern that starts at 1 that starts at 2 that starts at 17 and grows0 by5 10 15 an20d 2g5 ro3w0 s35by40 45 50 an55d 6g0 ro6w5 s70by75 80 85 90 95 100 jumps of 2 each jumps of 30 each jumps of 5 each time. time. time. A number 1p0asttern A number pattern A number pattern that starts at 2 that starts at 50 that starts at 13 and grows by and grows by and grows by jumps of 40 each10 jtuim2m0 ep.s o30f 10 e40ach 50 jtuimmep6.0s of 3700 eac8h0 time. 90 100 Digital Slide 51: Tic-Tac-Toe Board A number pattern A number pattern A number pattern that starts at 23 that starts at 16 that starts at 11 A number pattern aAndnugmrobwers0pba1yt0te2r0n 30 Aa4n0ndu5mg0 rbo6e0wrsp70abty8t0ern90 100 a1n10d1 2g0 ro13w0 s140b1y50 160 170 180 190 200 Digital Slide 50: Number tLhiantesstatrots2a0t 1 juthmatpsstaorfts5aeta2ch tjhuamt psstaortfs1a0t 1e7ach jumps of 20 each taimnde.grows by atinmdeg. rows by time. and grows by jumps of 30 each jumps of 5 each jumps of 2 each time. 26 time. time. © 2022 Scholastic Canada Ltd. GRADE 2: PATTERNS & RELATIONS/DATA & PROBABILITY ISBN 978-1-4430-7187-1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 A number pattern A number pattern A number patternScholastic Canada GR2 BC Patterns & Data Fourth Pass that starts at 2 Reproducibles October 25, 2021 that starts at 50 that starts at 13 and grows beyach24 and grows by and grows by jumps of 4 jumps of 10 each jumps of 30 each© 2022 Scholastic Canada Ltd. GRADE 2: PATTERNS & RELATIONS/DATA & PROBABILITY ISBN 978-1-4430-7187-1 0 1 2 3 4 5 6 7 8 9 10 11 12tim1e3. 14 15 16 17tim1e8 . 19 20 time. Scholastic Canada GR2 BC Patterns & Data Fourth Pass Reproducibles October 25, 2021 A number pattern A number pattern A number pattern that starts at 23 that starts at 16 that starts at 11 and grows by and grows by and grows by 0 1 2 3 4 5 6 7 8 9 10 11 12jum13ps 1o4f 515eac1h6 17jum18ps 1o9f 1200 each jumps of 20 each time. time. time. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Fourth Pass – Switch jobs. The person who did the jumps the first time is now the counter. Ready! Go! (2, 4, 6, 8, 10, 12, 14, 16, 18, 20) Scholastic Canada GR2 BC Patterns & Data Digital Slides October 25, 2021 Scholastic Canada GR2 BC Patterns & Data Fourth Pass Digital Slides October 25, 2021 – How many jumps did you count? (10) Patterns and Relations 73

Teaching Tip – Let’s look at our number lines again. Can someone remind us how we counted? (by 2s) Yes. And how did that sound? (2, 4, 6, 8, 10, 12, 14, 16, You might take this 18, 20) How is this pattern different from the first one? (The first one opportunity to draw grows by 1s and this one grows by 2s.) How might we show that on our students’ attention number line? [Show jumps of 2, starting at 0, all the way to 20.] How to the equivalence many jumps were there altogether? (10) [Trace/draw the jumps on the between the two whiteboard and have students count along to show how many jumps.] number lines (counting by 1s and counting by – Why are there fewer jumps on the second number line? (Because we 2s) and the size of the counted by 2s instead of 1s.) jumps (twice as big) as they talk about there • Ask students to predict if they think there will be more or fewer jumps when being fewer jumps on the second number counting by 5s and 10s and have them repeat the above process to check line. their predictions. Working On It (20 minutes) • Project Digital Slide 51 or hand each student a copy of BLM 10: Tic-Tac-Toe Board to discuss the activity for this section. Use the following prompts: – You are going to work with a partner to show some number patterns on a number line. Remember that when we have a pattern, we need to know two things: where the pattern starts AND how we move to the next number. – In this activity, you need to choose three patterns to show on a number line, and the three that you choose should be in a line on your Tic-Tac-Toe board. – W e have copies of different number lines that you can use to show the number patterns, depending on the patterns you choose and where they start. • Project Digital Slides 52–55 to show students the different options. • O rganize students in partners and project Digital Slide 51 for them to consider which patterns they are going to choose. • Provide copies of the various number lines from BLM 11: Number Lines for students to choose to represent their work. Differentiation • Use this independent work time to pull students who may need one-to-one support to complete the task. • Encourage students who are ready to do so to represent their pattern using an open number line (i.e., one without numbers, which may or may not have incremental marks) where students can add the necessary information to explain their pattern. 74 Patterns & Relations/Data & Probability

Assessment Opportunities Observations: • Pay attention to where students are beginning their patterns (e.g., start point indicated on the Tic-Tac-Toe board). • Pay attention to the jumps that students are showing on their number lines and that they are the right size and that they are consistent. Conversations: Prompt students as necessary using any of the following questions: – Where does this pattern start? How do you know? – Is the number line you chose the right one for this pattern? How do you know? – Would another number line work better? – How big is each jump in your pattern? Are the jumps all the same size? How can you check? Consolidation (5–10 minutes) • B uilding Growth Mindsets: Discuss with the group what they found challenging in this activity. Pose the following prompts: – What did you find challenging? Did anyone else find that challenging as well? How did you work through that? – Did you collaborate with your partner to figure out what to do? Did you ask other groups if they had a suggestion? – What advice might you give to another group doing the same activity? – What might you do differently the next time you do an activity like this one? – Discuss how respectfully working together can help to move students’ learning forward. Further Practice • Reflecting in Math Journals: Have students do a short reflection in their Math Journals about a challenge they had today and how they worked through it. Patterns and Relations 75

Materials: Math Talk: “Count with Me” Math Focus: Investigate patterns generated by the repeated addition of 1s, 2s, (page 9 in the 5s, and 10s and how this relates to a hundred chart Patterns, Relations, Data, and Probability big Let’s Talk book), Digital Slide 56: Hundred Chart Do a shared reading of the rhyme on page 9 of the big book. Digital Slide 56: Hundred Chart Select the prompts that best meet the needs of your students. 1 2 3 4 5 6 7 8 9 10 • W hat do you see in the first picture? What do you see in the second picture? What 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 do you see in the third picture? 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 • H ow did you count (the eggs? the goody bags? the moves on the snakes and ladders 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 board?) (e.g., We counted the eggs by 1s; the goody bags by 2s; the moves by 5s 71 72 73 74 75 76 77 78 79 80 and by 10s.) How did that sound? (e.g., 1, 2, 3, 4; 2, 4, 6, 8; 5, 10; 10, 20) 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 • W hy did you choose that way? Put your thumb up if you counted that way, too. Scholastic Canada GR2 BC Patterns & Data Fourth Pass Who counted another way? (e.g., We counted by 1s.) Digital Slides October 25, 2021 • W hat would be the next three numbers you say if there were more eggs? Teaching Tip (e.g., counting by 1s: 5, 6, 7) If there were more goody bags? (e.g., counting by 2s: 10, 12) If the boy were to roll another 5 on his next turn? (e.g., counting by 5s: 15) Integrate the math talk moves (see page 7) • W hat do we call it when we count by a certain number, for example 1, 2, 5, 10, etc.? throughout Math Talks to maximize student (skip counting) participation and active listening. • H ow is skip counting like a pattern? Project Digital Slide 56: Hundred Chart. • Think about the boy who rolls a 5 and lands on the 5 spot on the game board. Circle the 5 on the hundred chart in blue. What would happen if he rolled a 5 each time he took a turn? What would be the next spot he lands on? Circle the 10 in blue. And the next time? Circle the 15 in blue. • W hat do you notice about this pattern? What number are we skip counting by in this example? What do you predict will be the next spot he lands on if he rolls 5 again? • Let’s skip count together by 5s to 100 (5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100). How can the hundred chart help you predict the next spot he would land on? (e.g., The 5s are in one column; the 10s are in another column; all of the numbers in the 5s column end in 5; all of the numbers in the 10s column end in 0; etc.) • Look at the hundred chart. Do you see any other number patterns? Share what you see with a partner. Follow-Up Talk • H ave a few students share and describe what patterns they noticed. • P rompt students to use their Math Talk gestures to indicate understanding (e.g., Thumbs up if you see the pattern that ____ is describing.). 76 Patterns & Relations/Data & Probability

16Lesson Patterns In a Hundred Chart Teacher Possible Learning Goals Look-Fors • Identifies and describes, through investigation, patterns on a hundred chart (e.g., The numbers in each column end in the same digit; the numbers in each row after the first row begin with the same digit, etc.) • Connects a pattern rule (e.g., jumps of 5) to the visual pattern it creates on a hundred chart (e.g., When skip counting by 5s, the numbers [terms] all appear in the same two columns.) • E xplains or shows where a pattern starts (e.g., not always skip counting from 0) • C ircles/highlights the terms in a number pattern accurately (e.g., using regular jumps according to the pattern rule) • M akes a visual connection or observation between the number pattern and its placement on the hundred chart (e.g., When I skip count by 10s, I can just highlight the numbers in the last column.) Materials: Minds On (15 minutes) Digital Slide 56: Hundred Chart • Project Digital Slide 56 on the whiteboard. • Say, “Today, we are going to see if we can find some patterns in a hundred 1 2 3 4 5 6 7 8 9 10 chart. Remind me what we know about a pattern.” (e.g., It starts at a certain 11 12 13 14 15 16 17 18 19 20 spot; it grows by the same amount each time.) 21 22 23 24 25 26 27 28 29 30 • Say, “Look at the hundred chart and think about the patterns that you see 31 32 33 34 35 36 37 38 39 40 there.” Give students a minute or so of wait time to consider. 41 42 43 44 Di4g5ital S46lide 5477: W4h8at’s 4O9ur N5u0mber Pattern? 51 52 53 54Sample55Pattern:56 57 58 This5i9s our nu6m0ber pattern: 61 62 63 64Our pa6tt5ern star6ts6at ___6__7_8______6.8 8, 186,928, 38,7408, 58, 68, 78, 88, 98 It grows by ______1_0_____. 71 72 73 74 75 76 77 78 79 80 Pattern 1: This is our number pattern: 81 82 83 84 85 86 87 88 89 90 Our pattern starts at ____________. 91 92 93 94It grow9s5by ____9_6_______9. 7 98 99 100 Pattern 2: This is our number pattern: Scholastic Canada GR2 BC Patterns & Data Our pattern starts at ____________. Fourth Pass Digital Slides It grows by ____________. October 25, 2021 Pattern 3: This is our number pattern: Our pattern starts at ____________. It grows by ____________. Scholastic Canada GR2 BC Patterns & Data Fourth Pass • Say, “Turn to a partner and share one pattern that you see.” Digital Slides October 25, 2021 56: • Come back to the large group and have students share the patterns that they Digital Slide noticed. Use highlighters of different colours to represent the patterns the students noticed. Hundred Chart, Digital Slide 57: What’s Our • If there is any confusion around extending the pattern, use any of the Number Pattern?, BLM 12: Hundred Chart, BLM 13: What’s Our Number Pattern?, following prompts as necessary to support student thinking: counters that fit into – Where does your pattern start? the spots on the hundred BLM 13: What’s Our Number Pattern? – What is the pattern rule? How do I get from one number (term) to the chart, next one? whiteboard, Name: highlighters – What visual pattern do you see? Did this help you extend the pattern? Sample Pattern: This is our number pattern: BLM 12: Hundred Chart Our pattern starts at _____8______. 8, 18, 28, 38, 48, 58, 68, 78, 88, 98 It grows by ______1_0_____. Pattern 1: 1 2 3 4 This is5 our nu6mber pa7ttern: 8 9 10 20 Our pattern 1s1tarts a1t 2_______1_3___. 14 15 16 17 18 19 30 It grows by _2_1______2_2___. 23 24 25 26 27 28 29 Time: 45 Pattern 2: 31 32 33 34This i3s5our nu3m6ber p3a7ttern: 38 39 40 – Can you say the pattern aloud? minutes Our pattern 4s1tarts a4t 2_______4_3___. 44 45 46 47 48 49 50 – How would you describe the pattern? (Use the following sentence It grows by _5_1______5_2___. 53 54 55 56 57 58 59 60 Pattern 3: 61 62 63 64This i6s5our nu6m6ber p6a7ttern: 68 69 70 Our pattern 7s1tarts a7t 2_______7_3___. 74 75 76 77 78 79 80 It grows by _8_1______8_2___. 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 starter: The pattern starts at _______. It grows by _______ 28 © 2022 Scholastic Canada Ltd. GRADE 2: PATTERNS & RELATIONS/DATA & PROBABILITY ISBN 978-1-4430-7187-1 each time.) Scholastic Canada GR2 BC Patterns & Data Fourth Pass Reproducibles October 25, 2021 © 2022 Scholastic Canada Ltd. GRADE 2: PATTERNS & RELATIONS/DATA & PROBABILITY ISBN 978-1-4430-7187-1 27 Scholastic Canada GR2 BC Patterns & Data Fourth Pass Reproducibles October 25, 2021 Patterns and Relations 77

Working On It (20 minutes) • While projecting Digital Slide 56, say, “My pattern starts at 8.” Circle this on the whiteboard. “My pattern grows by 10. That is my pattern rule. What would be the next number in my pattern? (18) Yes.” Circle that number also. “What would be the next number in my pattern?” (28) • Continue until the number you have circled is less than 50 (e.g., 48). • Ask students to predict the next numbers in the pattern and share with a partner. Ask, “What numbers do you predict will also be in this pattern?” (e.g., 58, 68, 78, 88, 98) • Project Digital Slide 57 to show how you can record this pattern. (Our pattern starts at 8. It grows by 10. Our number pattern is 8, 18, 28, 38, 48, 58, 68, 78, 88, 98.) • Organize students into pairs. Give each pair a copy of BLM 12: Hundred Chart and BLM 13: What’s Our Number Pattern? and a handful of counters. With their partner, they will create three number patterns using the hundred chart, and record their pattern information on BLM 13. • Review the process that you just modelled: – One student chooses a number between 1 and 10 and then puts a counter on that number (e.g., 8). – The other student chooses a pattern rule (e.g., grows by 10). – Together the partners identify aloud the numbers in the number pattern up to 50. They predict and then check the next numbers in the pattern. – Partners record the pattern on their sheet. – Repeat two more times. Differentiation • Consider providing starting points and pattern rules for students who may need support or additional challenge. Assessment Opportunities Observations: • Do students identify a starting point for their patterns? • Can students extend the pattern using the pattern rule? • Can students describe the pattern? (e.g., starts at 15 and grows by 3 each time) Conversations: Ask any of the following prompts to clarify and advance students’ thinking: – Where does your pattern start? – What is the pattern rule? – How did you know the next number in the pattern? – Did you predict the bigger numbers in your pattern correctly? 78 Patterns & Relations/Data & Probability

Materials: Consolidation (10 minutes) BLM 12: Hundred • Discuss students’ strategies for extending the pattern. Chart, pencil crayons, • Have students share how the hundred chart helped them predict the other markers numbers in the pattern. BLM 12: Hundred Chart Further Practice 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 • Provide a fresh paper copy of BLM 12: Hundred Chart to each student. Provide 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 them with some pencil crayons/markers and have them identify a variety of 41 42 43 44 45 46 47 48 49 50 number patterns within the same hundred chart, using a different colour to 51 52 53 54 55 56 57 58 59 60 mark each pattern. 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 • Have students participate in Daily Physical Activities (DPA) (e.g., jumping 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 jacks) while skip counting, using a hundred chart to support their counting. © 2022 Scholastic Canada Ltd. GRADE 2: PATTERNS & RELATIONS/DATA & PROBABILITY ISBN 978-1-4430-7187-1 27 • Independent Problem Solving in Math Journals: Verbally pose one of Scholastic Canada GR2 BC Patterns & Data Fourth Pass the following prompts: Reproducibles October 25, 2021 − Choose a number between 20 and 50. Create a pattern starting with your chosen number that grows by 2 or by 5. Teaching Tip − Draw a number line and a hundred chart. Choose a skip counting Hundred charts can be pattern and show how it looks on both. How are they the same? How laminated or placed are they different? into page protectors for reuse when identifying − Write down these two number patterns in your journal: 2, 4, 6, 8, 10,… patterns. AND 3, 5, 7, 9, 11. Describe each pattern. How are they the same? How are they different? Patterns and Relations 79

17Lesson Investigating Patterns through First Peoples Storytelling Math Curricular Competencies Learning Standards • Reasoning and analyzing: Model mathematics in contextualized experiences • Understanding and solving: Develop, demonstrate, and apply mathematical Previous Experience with Concepts: understanding through play, inquiry, and problem solving; visualize to explore Students have worked mathematical concepts; engage in problem-solving experiences that are with increasing number connected to place, story, cultural practices, and perspectives relevant to local patterns. First Peoples communities, the local community, and other cultures Teacher • C ommunicating and representing: Explain and justify mathematical ideas Look-Fors and decisions; represent mathematical ideas in concrete, pictorial, and symbolic forms • C onnecting and reflecting: Incorporate First Peoples worldviews and perspectives to make connections to mathematical concepts Content • R epeating and increasing patterns Possible Learning Goals • Identifies a variety of number patterns in our number system • Solves problems that are presented through storytelling • Understands the context of the story and what the problem is to solve • Recognizes patterns in our number system, including counting by 2s, 5s, and 10s • Identifies the pattern rule and uses it to extend the pattern • Explains problem-solving strategy using mathematical language Math Vocabulary: About the Lesson ninucmrebaesrinpga,ttceorunnst,ing Students are familiar with learning through read alouds that embed math and related problems in a story. Similarly, First Nations Elders often use stories from the past and present to make problems relevant to the lives of their youth. In both cases, the context makes the math meaningful and relevant. In this lesson, students help Small Number —a boy who lives in a tipi settlement on the plains in the past—solve a math problem, thereby highlighting the universality of counting and mathematics. 80 Patterns & Relations/Data & Probability

Materials: Minds On (20 minutes) “Small Number • Show students the video “Small Number Counts to 100.” (A transcript of the Counts to 100” (story available at story is also available.) https://www.sfu.ca/ mathcatcher/ • Before discussing the question presented at the end of the video, discuss the StoriesMovies/ CountsTo100.html), storyline. Ask students when and where this story may have taken place. Ask chart paper, markers, students whether they have ever encountered a skunk and how they would BLM 14: 5 Tipis, feel if they were Small Number. Ask how they would describe Small Number’s BLM 12: Hundred Chart grandmother. Ask how their own grandparents or family members have helped them through a predicament. Time: 55 BLM 12: Hundred Chart minutes • After discussing the context, ask what problem Small Number has to solve. BLM 14: 5 Tipis • Ask students how they can prove that Small Number is correct. 1 2 3 4 5 6 7 8 9 10 • Draw a diagram of 7 tipis in a circle on a piece of chart paper and mark Small 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Number’s tipi. As a class, count around the tipis until the 100th tipi is identified. 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 Working On It (20 minutes) 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 • Students work in partners to solve a similar problem: Find the 100th tipi 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 when going around a circle of 5 tipis. 91 92 93 94 95 96 97 98 99 100 • Have students record their strategies and solutions on chart paper. © 2022 Scholastic Canada Ltd. GRADE 2: PATTERNS & RELATIONS/DATA & PROBABILITY ISBN 978-1-4430-7187-1 27 Differentiation Scholastic Canada GR2 BC Patterns & Data Fourth Pass Reproducibles 29 • Adjust the problem by changing which tipi students should find (e.g., find October 25, 2021 the 50th tipi, find the 76th tipi). © 2022 Scholastic Canada Ltd. GRADE 2: PATTERNS & RELATIONS/DATA & PROBABILITY ISBN 978-1-4430-7187-1 • For students who may find the task challenging, distribute the illustration of Scholastic Canada GR2 BC Patterns & Data Fourth Pass Reproducibles 5 tipis in a circle on BLM 14. October 25, 2021 Assessment Opportunities Observations: Pay attention to how students begin to solve the problem. – Do they understand what is being asked? – Can they use the given information and extend it to solve for the 100th tipi? – Do they change their strategy if it is not working? Conversations: You may want to meet with students who don’t know how to get started in a small group. Discuss the context and then offer a simplified version of the task. For example, ask which would be the 6th tipi. This can help them develop a strategy that can be applied to larger numbers. Consolidation (15 minutes) • As a class, share students’ strategies for finding the 100th tipi. Ask if they found any patterns. • Ask them what they notice about the other numbers that landed on the 100th tipi. If nobody recorded all of the numbers, do so as the class counts around the tipis to 100. Then have students count these numbers by 5s to 100. • Ask students how they would figure out the 100th tipi if there were 10 tipis. From the patterns, they should realize that it is the same tipi. Patterns and Relations 81

• Ask how Small Number’s strategy of counting on his fingers might be the same as their strategies. Discuss why his problem was more difficult (e.g., 7 is not a friendly number like 5 and 10). • Have students colour in the patterns of counting by 5s and 10s on a hundred chart. Ask how they are the same. Have them add counting by 2s. Ask what they notice. 82 Patterns & Relations/Data & Probability

18Lesson Adding to Create 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; use technology to explore mathematics • U nderstanding and solving: 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 mathematics discussions; explain and justify mathematical ideas and decisions; represent mathematical ideas in concrete, pictorial, and symbolic forms • Connecting and reflecting: Reflect on mathematical thinking Content • Repeating and increasing patterns • Addition and subtraction facts to 20 Possible Learning Goals • Creates patterns using addition • Demonstrates an understanding that adding can create increasing patterns • Describes a visual pattern using numbers • Uses addition to create a pattern • Identifies the pattern rule for number patterns Patterns and Relations 83

Materials: Minds On (15 minutes) Digital Slide 58: Adding to Create a Pattern • Project Digital Slide 58 (smiley faces). • Ask, “How many smiley faces do you see in Term 1? (1) Term 2? (3) Term 3? Scholastic Canada GR2 BC Patterns & Data Slide Fourth Pass Digital Slides (5).” Write these numbers below each term in the pattern. October 25, 2021 58: Adding • Ask, “What is the pattern rule?” (e.g., add two more smiley faces each term) Digital • Ask, “What is another way that we could write the rule using numbers?” to Create a Pattern; (+2) Write “+2” between the 1 and 3 slightly lower than the 1 and 3 to show the transition between them. You can also write 1 + 2 = 3 below that. page 4 from BLM 5: • Ask, “What about going from 3 to 5? What is the pattern rule?” (e.g., It’s the Geometric BLM 15: More Geometric Designs That Increase same, +2.) Write “+2” between the 3 and 5 slightly lower than the 3 and 5 to Designs That show the transition between them. You can also write 3 + 2 = 5 below that. Increase, BLM 5: Geometric Designs That Increase • Ask students if they see a pattern. Rewrite: BLM 15: More 1+2=3 Geometric 3+2=5 Designs That • Ask students what they think would come next in the number pattern. Increase; mini- 30 © 2022 Scholastic Canada Ltd. GRADE 2: PATTERNS & RELATIONS/DATA & PROBABILITY ISBN 978-1-4430-7187-1 whiteboards; − What pattern rule would we use with the 5 to get to the next number in Scholastic Canada GR2 BC Patterns & Data Fourth Pass the pattern? (+2) Reproducibles October 25, 2021 − What would that look like if we were starting at 5? (5 + 2 = 7) Add this below the other two equations. whiteboard markers; paper, 18 © 2022 Scholastic Canada Ltd. GRADE 2: PATTERNS & RELATIONS/DATA & PROBABILITY ISBN 978-1-4430-7187-1 Scholastic Canada GR2 BC Patterns & Data Fourth Pass Reproducibles October 25, 2021 pencils, calculators Time: 45 minutes − What do you think the next term would look like? (7 + 2 = 9, etc.) • Ask, “What other tool could we use to check our work?” Suggest a calculator if they do not. • Model how to use a calculator to check their work. Working On It (20 minutes) • Organize students into triads. Provide each group with a copy of page 4 from BLM 5: Geometric Designs That Increase (smiley faces, rectangles) and BLM 15: More Geometric Designs That Increase, mini-whiteboards and whiteboard markers OR paper and pencils, and a calculator. • Have rotating roles within each triad: one student records the number count on the BLMs, one student writes down the addition rules on the whiteboards or paper, and one student checks the addition sentences on the calculator. • Together they are going to determine the number pattern associated with each of the visual patterns. • Suggest that students use the smiley face one to start as this has already been modelled and can serve as an anchor. Differentiation • Provide guided support for students who may need it. • For students who are struggling, provide them with the simpler visual patterns (e.g., that grow by one) from BLM 5 (pages 1 and 2). 84 Patterns & Relations/Data & Probability

Assessment Opportunities Observations: • P ay attention to students who are recording the pattern on the BLM to see if they have the correct number count recorded. • P ay attention to students who are writing down the addition sentences to see if they can identify the pattern rule clearly in the way they have written it down. • P ay attention to students who are using the calculator to see if they are plugging in the correct sequence of numbers and symbols. • S upport the collaboration of each triad with descriptive feedback. Conversations: Ask any of the following prompts to clarify and advance students’ thinking: – What is the starting point for this pattern? – What is the pattern rule? How do you know? – How would you write the pattern rule? – What keys did you touch on the calculator to check the math? Consolidation (10 minutes) Building Growth Mindsets: • Have a group discussion to share what parts of today’s activity were challenging. • Ask, “What makes a pattern more difficult to extend?” (e.g., bigger numbers, a bigger pattern rule such as +3 instead of +1) • Ask, “What strategies helped you to complete the activity?” (e.g., asking my triad, double checking our work on the calculator, drawing the pattern) • Ask students what they think they still need to practise with patterns. Make a list of their suggestions. Over the next week or two, spend 5–10 minutes per day reviewing one or two of the concepts. Regularly refer to the list and ask students whether they have a better understanding. Add any concepts that they have questions about to the list so they can be reinforced, too. This helps students realize that practice plays an important role in improving. Further Practice • Independent Problem Solving in Math Journals: Verbally pose the following prompt: − My pattern starts at 2. The pattern rule is +4. The pattern has four terms. What might it look like? Patterns and Relations 85

19Lesson Reinforcement Activities Math • All of the learning standards identified in this unit Learning Standards Teacher • Identifies, extends, and creates a variety of patterns in different situations Look-Fors • Explains or shows their thinking around a variety of patterns • Is able to translate a variety of different patterns using different pattern sets Previous Experience with Concepts: or concrete materials Students have had several opportunities to work About the Lesson with a variety of visual and numeric patterns. The following activities can be carried out by the whole class in small groups, or as centres that students can rotate through spending MpeaxatttethenrdVn,o, cdsaeobsrtcu,rlaiibdreey:ntify, 20–25 minutes per selected centre. They can 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 Fish Detectives Pattern Fish book, • Have students use Pattern Fish to find all the other patterns in the BLM 1: Word Cards book. Have students also use the word cards from BLM 1: Word Cards and BLM 1: Word Cards create patterns with them. Students need to create actions to go along with their word patterns. Yellow Black Yellow Black Stripe Dot Stripe Dot Chomp Munch Chomp Munch Bubble Pop Bubble Pop Stretch Spurt Glide Stretch Spurt Glide Wiggle Jiggle Float Wiggle Jiggle Float © 2022 Scholastic Canada Ltd. GRADE 2: PATTERNS & RELATIONS/DATA & PROBABILITY ISBN 978-1-4430-7187-1 3 Scholastic Canada GR2 BC Patterns & Data Fourth Pass Reproducibles October 25, 2021 86 Patterns & Relations/Data & Probability

Materials: Centre 2: Creating Patterns counters, connecting • Have students use the cards from BLM 16: Creating Patterns to create cubes, square tiles, BLM 16: Creating patterns. Have them create the patterns using concrete materials and transfer Patterns what they create to a drawing in their Math Journals. BLM 16: Creating Patterns Centre 3: Extend the Spotted Patterns A growing A growing A repeating A number • Using the “Spot the Pattern” image, have students extend the patterns they shape number pattern: pattern that pattern pattern ABAB skips by 2 have identified. Students will need to re-identify the pattern and then extend it. For example, a student will find the tile floor pattern (e.g., light green, A repeating A growing A growing A repeating blue, etc.) and extend it using the core. Have students use their Math pattern: number pattern that pattern: Journals to keep track of their work at this centre. ABB and pattern that skips by 2 AABB and changes two starts at 3 changes one attributes attribute A number A number A repeating A number pattern that pattern that pattern: pattern starts at 7 skips by 5 ABCC and and skips changes two by 2 attributes A repeating A growing A number A number pattern: number pattern pattern that ABC and pattern that from the skips by 10 changes starts at 13 hundred three chart attributes © 2022 Scholastic Canada Ltd. GRADE 2: PATTERNS & RELATIONS/DATA & PROBABILITY ISBN 978-1-4430-7187-1 31 Scholastic Canada GR2 BC Patterns & Data Fourth Pass Reproducibles October 25, 2021 Materials: “Spot the Pattern” (page 8 in the Patterns, Relations, Data, and Probability little books) Materials: Centre 4: Creating Geometric Designs pattern blocks • Have students use pattern blocks to create geometric designs that include various patterns. They can build a design with certain pattern parameters (e.g., it must have a triangle, it must have two attributes that are changing). Materials: Centre 5: Number Patterns BLM 17: Number • Students will use BLM 17: Number Pattern Strips to identify the pattern rule. Pattern Strips, number lines (optional) Have students identify what is being added to each term (i.e., what is the pattern rule) and extend the pattern by adding 3 terms. Students could also BLM 17: Number Pattern Strips use the number line to practise translating their number patterns. 2, 4, 6, 8... Patterns and Relations 87 1, 6, 11, 16... 23, 33, 43, 53... 7, 9, 11, 13... 47, 49, 51, 52... 32 © 2022 Scholastic Canada Ltd. GRADE 2: PATTERNS & RELATIONS/DATA & PROBABILITY ISBN 978-1-4430-7187-1 Scholastic Canada GR2 BC Patterns & Data Fourth Pass Reproducibles October 25, 2021

Materials: Centre 6: Creating Number Patterns BLM 18: Creating • Students will use the concept circle on BLM 18: Creating Number Patterns Number Patterns That Increase That Increase to create number patterns starting with a number of their choice. BLM 18: Creating Number Patterns That Increase Name: Pick any number between 1 and 100. Put that number in the middle circle! Create a growing number pattern using the pattern rule found in each section. +2 each +1 each +5 each +10 each 34 © 2022 Scholastic Canada Ltd. GRADE 2: PATTERNS & RELATIONS/DATA & PROBABILITY ISBN 978-1-4430-7187-1 Scholastic Canada GR2 BC Patterns & Data Fourth Pass Reproducibles October 25, 2021 Materials: Centre 7: Translating Patterns counters, square tiles, • H ave students select a pattern strip from BLM 19: Translating Patterns, and connecting cubes, number lines, BLM 19: translate it using concrete materials. Students will need to identify the Translating Patterns pattern on the strip before they can translate it using the tools they select. BLM 19: Translating Patterns Building Growth Mindsets: Reflect back on the lessons and pose some of the following prompts to reinforce growth mindset messages: © 2022 Scholastic Canada Ltd. GRADE 2: PATTERNS & RELATIONS/DATA & PROBABILITY ISBN 978-1-4430-7187-1 35 – W hat were your favourite activities? (Math is interesting to investigate.) Scholastic Canada GR2 BC Patterns & Data Fourth Pass – W hat did you find challenging? (Hard tasks are good and if we keep Reproducibles October 25, 2021 trying, we can overcome them.) – W hat have you learned? (Celebrate the accomplishments.) – W hat do you still have to learn or practise? (We may not know it YET, but we will with time.) – H ow can mistakes help us learn? (Mistakes help us learn new ways of trying so we can do things better.) 88 Patterns & Relations/Data & Probability