p9-72Gr3-BC_Patterns_unit1-patterns

Unit 1: Patterns and Relations Lesson Content Page 1 and 2 Getting Started with Patterns and Relations 9 1 Inviting Patterns and Relations into the Classroom 10 2 Patterns and Relations Introduction 13 Investigating Patterns in Real-Life Situations 15 3 to 5 Read Aloud: Pattern: What Are Patterns? 16 3 Investigating Patterns in Our Lives 23 4 Investigating How Patterns Increase and Decrease 34 5 Investigating How Patterns Can Increase 36 Investigating How Patterns Can Decrease 38 6 and 7 Creating Patterns That Increase or Decrease 41 6 Investigating Patterns in Numbers 43 7 Patterns in a Hundred Chart 45 Patterns in a Number Line 49 8 and 9 Creating and Extending Number Patterns 52 8 Creating Number Patterns from a Rule 53 9 Translating Number Patterns 56 10 Representing Geometric Patterns with Numbers 58 11 Representing Geometric Patterns in Various Forms 62 12 Guided Math Lesson: Camp Blast-Off! 66 13 Reinforcement Activities 71



Getting Started with Patterns and Relations The order of the Patterns and Relations units follows a general developmental trajectory of how students tend to acquire knowledge and skills. The order can be altered to suit your existing program; however, the lessons designed for earlier in the year should precede those designed for later in the year. Below is an overview of the included units and instructional suggestions. Unit Description 1 Patterns and Relations 2 Equality and Inequality • Within each of these units, students will work through a progression of lessons to develop their understanding of the concepts relating to patterns and equality/inequality. • Each unit includes a series of BLMs and Digital Slides to support the visual nature of concepts relating to patterns and equality/inequality. • Each unit incorporates the use of a variety of concrete materials and tools that should be on hand and readily available for student use. • Each unit includes Math Talks, group discussions, and activities that target the curricular competencies (reasoning and analyzing, understanding and solving, communicating and representing, connecting and reflecting) to support and develop student understanding. • Each unit includes activities to develop a culture of building habits of mind, growth mindsets, and positive attitudes toward math. • Making connections between Patterns and Relations, Equality and Inequality, and other math units or curricula will maximize student learning and support flexibility in their thinking. When developing your long-range plans, consider the following: – Many of the patterns make use of shapes that would be investigated in Spatial Sense (geometry). – The number patterns relate directly to Number with respect to counting and the operations and properties of addition, subtraction, multiplication, and division. 9

Inviting Patterns and Relations into the Classroom Since math plays an integral part in our lives, it makes sense to take advantage of its role in everyday routines at school. Whether it is counting backwards to transition before starting an activity or counting all students as part of attendance, bringing math experiences into real-life contexts will deepen understanding of concepts in a meaningful way. There are many ways to embed patterning and equality/inequality concepts in daily routines. There are quick 5- to 10-minute activities that can be carried out while the class waits in line to go somewhere, when there is five minutes at the end of a period, or when students need a quick break. Several ideas are described below. Classroom Number Line Number lines are powerful tools, yet they are often underused. Displaying a large number line up to 100 and another to 1000 in the classroom allows for incidental reference during discussions or while students are problem solving. • Progressively count the number of days in school up to the one hundredth day and beyond. Each day, a mark can be put under the new number and students can count from zero to reach it. As the numbers get larger, students may decide to skip count in various ways to reach that number. Ask questions such as, “What would be the next day that we could count by 10?” • Use the number line for skip counting. Students can visually see the numbers that are being skipped over in uniform ‘hops’ and can quickly reason why counting by bigger numbers gets to larger quantities faster when counting forward, and smaller numbers faster when counting backwards. • Put a clothespin or marker on all of the multiples of the numbers you are studying so students have a visual of how much they are adding or subtracting each time they say a number in the counting sequence. • Use an open number line with various starting and ending points (e.g., 0 to 1000) and ask students to stand where they think a certain number would be (e.g., 300, 500) and ask them to justify their choice of spot using the given benchmarks and spatial reasoning. Hundred Charts Display a large hundred chart in the classroom at all times so it can be used as a reference when discussions about numbers incidentally arise, or as a tool for planned activities throughout the day. You can also display other hundred charts (e.g., 101–200, 201–300) for numbers up to 1000. • Practise counting starting from a variety of different numbers. For example, ask students to start at 14 and count by 10s. This is the introduction to identifying a number pattern rule (e.g., I started at 14 and counted by 10s). 10 Patterns & Relations/Data & Probability

Ask what patterns they notice in the numbers that make up this counting sequence. Ask them to predict what other numbers will appear in the same pattern, even beyond 100. • Discuss how the patterns in the hundred chart and the number line are linked so students can make connections between the two representations. • If you are using a hundred pocket chart with removable numbers, consider rearranging the numbers so zero is at the lower left and the numbers increase from the bottom. This can help students understand the increase in numbers as they move up the chart (gfletchy.com). Calendars Calendar activities can stimulate mathematical thinking around concepts such as the counting sequence and number patterns. Be sure to incorporate some patterning concepts when referring to the calendar. The key is to limit the amount of time spent on activities so all students are engaged and actively participating. Vary some of the activities from month to month between ones that target number sense and others that target number patterns. Calendar activities do not need to be daily routines and can be used periodically throughout the year. Here are some of the ways that calendars can reinforce patterning math concepts. • Like a hundred chart, the calendar reveals the counting sequence but in rows of seven rather than rows of ten. To reinforce number patterns, ask what number next Monday will be if this Monday is the first of the month. Have students find all of the Fridays and have them find out how many days are in between each one. Have students count by 5s or 7s, marking each number that is spoken. Quick 5–10 Minute Activities Physical Movement Activities • Repeating Pattern Movements: Have students do a movement pattern that repeats, such as clap, snap, clap, snap (AB) or hop, hop, jump (AAB). Have students call out the pattern as they act it out, using the words of each movement. They can also name the pattern using letter combinations as above. • Groups in Motion: Have students walk around the room and then, when you say a pattern core such as ABA, students need to get into a group of three and organize themselves in a physical representation of that pattern (e.g., facing forward, facing backward, facing forward). • Sound Off: While students are lined up waiting to go somewhere, have them sound off, using a skip counting pattern. Provide the first number and the pattern rule (e.g., skip count backwards by 2s from 30). As they say their number, they crouch down. Then have them sound off from the back of the line, standing up as they say their number. • Skip Counting Sound Off: Students decide what they want to count. For example, they may decide to count fingers so they count down the line by 10s, from various starting points. Or, they might raise one hand and count backwards by 5s from 100, putting their hands down with each count to see what number they get to. 11

• Line Up: Have students line up in different ways. For example, have them line up in pairs or in groups of three. Practise skip counting by the size of each small group. • I Spy: Spot and describe different visual patterns around the classroom or outside (e.g., wallpaper, bookshelves, floor tiles, bricks, trees, etc.) and have students try to identify what you are describing. “I spy with my little eye a repeating pattern that has a black square then a white square.” (e.g., the floor tiles) Games • Guess My Number: Give clues such as, “I’m thinking of a number. It’s part of a number pattern. My pattern starts at 3 and grows by 5 each term. My number is larger than 10 but smaller than 50. What might it be?” As more clues are progressively given, students will be able to narrow down the number. Students can refer to the classroom number line or a hundred chart as they solve the problem. • Pattern of the Week: Write a pattern rule (e.g., AAB) or a type of pattern (e.g., growing) on a predictable spot in the room. As the week progresses, have students identify and describe patterns that they see that fit into the pattern of the week. • What’s the Pattern? Organize students into a repeating pattern based on a secret rule (e.g., jeans, shorts, shorts OR eyeglasses, no eyeglasses, eyeglasses, etc.). Have students guess what the rule is and then continue the pattern as far as they can, knowing what people are wearing that day. • A Handful of Objects: Bring out a certain type of manipulative (e.g., pattern blocks, relational rods, snap cubes, counters, beans). Put students in pairs and have them each take a handful of objects. Together, they need to create a repeating, growing, or shrinking pattern using what they chose. • Daily Physical Activity: Create a pattern sequence of physical movements that you can model and call out and have students repeat after you (e.g., jump, jump, squat, jump, jump, squat). Do these pattern sequence physical movements to music to maintain the rhythm and have students identify the core of the pattern (e.g., AAB). 12 Patterns & Relations/Data & Probability

Patterns and Relations Introduction Introduction to Patterning According to Clements and Sarama, “patterning is the search for mathematical regularities and structures. Identifying and applying patterns helps bring order, cohesion, and predictability to seemingly unorganized situations and allows you to make generalizations beyond the information in front of you… it is a process, a domain of student, and a habit of mind” (Clements & Sarama, 2009, p. 190). Ruth Beatty notes that patterns “afford young students the opportunity to develop their algebraic thinking in developmentally appropriate ways. They offer teachers a powerful visual tool for introducing sophisticated algebraic concepts” (Beatty, 2014, p. 1). Young students have an intuitive sense of patterns in their environment, including visual representations, actions, and sounds. Through experiences, they learn to recognize pattern rules and use them to create and extend patterns. As they see similarities in structure between various patterns, they can also translate patterns, or represent the same structure in a different form. At this point, students are making generalizations. Developmentally, students tend first to recognize repeating patterns and identify the core or the smallest part of the pattern that continually repeats. Students can apply their understanding of repetition to identify and extend growing and shrinking patterns. This is especially useful for understanding the patterns inherent in our number system. Grade three students investigate the repeating elements in increasing and decreasing patterns and use them to create, extend, and translate patterns and fill in missing elements. They represent patterns in various ways, including with shapes, numbers, and in tables of values. As students transition to number patterns, they are also learning more about the relationships of numbers up to 1000. Patterns and Relations 13

Lesson Topic Page 1 and 2 Investigating Patterns in Real-Life Situations 15 16 1 Read Aloud: Pattern: What Are Patterns? 23 34 2 Investigating Patterns in Our Lives 36 38 3 to 5 Investigating How Patterns Increase and Decrease 41 43 3 Investigating How Patterns Can Increase 45 49 4 Investigating How Patterns Can Decrease 52 53 5 Creating Patterns That Increase or Decrease 56 58 6 and 7 Investigating Patterns in Numbers 62 66 6 Patterns in a Hundred Chart 71 7 Patterns in a Number Line 8 and 9 Creating and Extending Number Patterns 8 Creating Number Patterns from a Rule 9 Translating Number Patterns 10 Representing Geometric Patterns with Numbers 11 Representing Geometric Patterns in Various Forms 12 Guided Math Lesson: Camp Blast-Off! 13 Reinforcement Activities 14 Patterns & Relations/Data & Probability

1 2LessonsandInvestigating Patterns in Real- Life Situations Math Curricular Competencies Learning Standards • Reasoning and analyzing: Use reasoning to explore and make connections; model mathematics in contextualized experiences • Understanding and solving: Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving; visualize to explore mathematical concepts • Communicating and representing: Communicate mathematical thinking in many ways; use mathematical vocabulary and language to contribute to mathematical discussions; explain and justify mathematical ideas and decisions • Connecting and reflecting: Connect mathematical concepts to each other and to other areas and personal interests Content • Increasing and decreasing patterns • Pattern rules using words and numbers, based on concrete experiences About the Lessons In these first two lessons, students investigate patterns in their environment. They review repeating patterns that were studied in grades one and two and then transition to the study of increasing and decreasing patterns. Both lessons are in the form of Math Talks so students can engage in whole-group discussions and reflection. This allows you to assess what students know, what misconceptions they may have, and what areas to focus on in the lessons ahead. Throughout the discussions, integrate the math talk moves on page 8. For example, continually encourage students to expand upon their responses and explain their reasoning. Have students respectfully react and respond to what other students are saying so they become active listeners. Have students repeat or paraphrase what their peers have said. Ask questions such as, “Do you agree?” or “Can anyone add on to what she said?” Have students turn and talk to a partner before sharing with the group. Provide wait time so students can reflect what is being asked. Below is one way in which the Math Talks may be structured. Patterns and Relations 15

1Lesson Pattern: What Are Patterns? Teacher Possible Learning Goals Look-Fors • Recognizes and describes a variety of visual patterns found in real-life situations and explains why they are patterns • Reflects on why there are patterns in the world and the functions they can serve • Identifies and describes visual patterns in real-life situations • Explains what a pattern is by giving examples • Explains and/or shows the repeating elements of a pattern • Understands the difference between repeating, increasing, and decreasing patterns • Extends a pattern by following the pattern rules Materials: About the Math Talks There are more pictures than are feasible for individual Math Talks. Divide up the pictures into groups of three or four and do several Math Talks over the next few days. Some of the pages have investigations that allow students to further explore the various patterns. Math Talk: Written by Math Focus: Investigating patterns in the environment Henry Pluckrose NOTE: Select the prompts and pages that best meet the needs and interests of Time: 20–30 minutes your students. per Math Talk Let’s Talk Teaching Tip Cover Integrate the math talk moves (see page 8) • Show the cover of the read aloud book, Pattern. What is the name of this book? throughout Math Talks to maximize student What do you think patterns have to do with math? Turn and talk to a partner. participation and active What do you think? listening. • We are going to read this book and find out if we can create a definition for patterns by looking at the examples in the photographs. Show pages 4–5 without reading the text • What do you notice on these two pages? What is the same and what is different? • Do both pictures represent a pattern? Turn and talk to a partner. What do you think? 16 Patterns & Relations/Data & Probability

• Read the text. According to the text, why does the game board on the left show a pattern and the game board on the right does not? • Look at the chessmen on the gameboard. Do they make a pattern? Why? Show and read page 6 • What patterns do you see in the flowers? • What colour patterns do you see? • What patterns do you see in the petals? Do you think there are the same number of petals on each flower? Why? • Visualize turning the flower. How many times does the top petal match up onto other petals as you turn it? It is repeating in a circle. This is known as turn symmetry. Show and read page 7 • What patterns do you see in the leaf? Notice how there are big veins that branch out and then there are smaller veins that branch out from them and so on. This is known as a fractal. It is a pattern that repeats the design as it grows, but each repetition is smaller than the previous one. • What do you think the function of the veins are on a leaf? Why would a branching fractal pattern be helpful to the leaf? Further Investigation • Bring in leaves from outdoors so students can get a closer look at the fractal pattern the veins make. Have students trace the outline of one of the leaves and then create their own fractal pattern on the leaf. Show pages 8–9 • What animals do you see in these pictures? How are the patterns on the two animals the same? (e.g., They both have mirror symmetry with a vertical line of symmetry dividing the pattern in half.) • How are the two patterns different? • Look at the pattern on the peacock. What elements are repeating? (e.g., colour, shape) • Where do you see a branching fractal pattern on the feathers of the peacock? • What patterns do you see on the wings of the butterfly? • Read the text on the two pages. • Do you think that the patterns on these two animals are perfectly the same on either side? Why? Usually in nature, there are some imperfections in the pattern, but overall, they are very close. Further Investigation • Have students make butterflies by folding paper in half and unfolding it, putting blobs of paint on one side, and refolding the paper. They press down on the outside of the folded paper, pushing the paint into the shape of a butterfly. continued on next page Patterns and Relations 17

Show pages 10–11 • What patterns do you see on these two animals? How are they the same and how are they different? • Look at the pattern on the snail. How can you describe the pattern? This is known as a spiral pattern. It starts from the middle and then curves around the middle in circles that keep getting larger and larger. This is a growing pattern because it increases in size. • What do you think the shell looked like when the snail was younger? If the snail continues to grow, visualize how the spiral pattern will grow. • What pattern do you see on the zebra? Are the stripes exactly the same in their shape and size? • What do you find most interesting about the zebra’s pattern? • Read the text on the two pages. Further Investigation • Show students how to cut spirals out of a square piece of paper by cutting a larger circle and then continuously cutting further inside, making smaller and smaller circles until reaching the centre of the circle. Ask whether this is an increasing (growing) or decreasing (shrinking) pattern and why they think so. Show and read pages 12–13 • What is different about these patterns compared to the ones we have studied so far? (e.g., The first patterns were created by nature and these are made by humans.) • Why do you think humans like patterns? • Look carefully at the picture on page 12. What patterns do you see? • Where do you see the repetition in the pattern on the wall? This is a difficult pattern to see because it doesn’t repeat very often. This makes it harder to see how the pattern works. • What patterns do you see on the carpet? • Do you have any wallpaper or carpets with repeating patterns in your home? What do they look like? Show and read pages 14–15 • What patterns do you see on the bowl and on the plate? How are they the same and how are they different? • Do you see any pattern in the thickness of the stripes or the way the colours are arranged? What makes the pattern? (e.g., all the stripes are parallel to each other and go around the bowl one time) • What pattern do you see on the plate? Does the colour of the dots help to make the pattern? Why? • What other patterns do you see on this page? (e.g., the placemat) How can you describe this pattern? (e.g., by colour and shape) 18 Patterns & Relations/Data & Probability

Show and read pages 16–17 • How are the patterns in the two pictures the same and how are they different? • What other patterns do you see on what the man is wearing? • Look around at our clothes. What patterns do you see? • Why do you think people like patterns on their clothes? Further Investigation • Have a Pattern Day and challenge students to wear a piece of clothing with a pattern on it. As a class, study and sort the different patterns. Show and read pages 18–19 • Both of these pages have patterns. How are the patterns different? • Which pattern is easier to find? How is the pattern on the left repeating? • Look at the pattern on page 19. Turn and talk to a partner about the pattern that you see. How is the pattern repeating? • What parts do you see that look like they are repeating? • What would help to understand this pattern better? (e.g., to see a larger picture of it to see how it is repeating beyond this page) It is important when we study patterns that we can see enough of the pattern to make sure we know what the rule is. Show and read pages 20–21 • What patterns do you see on the crane? Why is the crane built with this type of pattern? In this case, there is a pattern of triangles to make the structure stronger. Why are triangles good shapes to make stable structures? • Look at the cobblestones. What pattern do you see and what kind of pattern is it? • Why is it a growing pattern? What is increasing each time a new circle is added around the centre? (the number of stones) Are the same number of stones added with each circle? Why not? (e.g., The circle keeps getting bigger so you need to add more stones each time to complete the circle.) • How is this circular pattern different from the circular pattern on the snail on page 10? Further Investigation • Have students use some concrete objects like colour tiles to create the growing pattern evident in the cobblestones. They can figure out how many tiles they need for each consecutive circle. Show pages 22–23 • How are these patterns the same and how are they different? • Read the text on the two pages. • What shapes do you see in the honeycomb? Why do you think the bees need the shapes to fit tightly together? Why are hexagons good shapes for this purpose? continued on next page Patterns and Relations 19

• Why don’t the pencils fit tightly together? What patterns do you notice between the pencils? How can you describe the shapes the spaces make? • Do the pencils make a colour pattern? How do you know? Further Investigation • Have students make patterns with the hexagonal pattern blocks. Challenge them to make different patterns with the other blocks. They can also make patterns with two different types of blocks. Show and read page 24 • Turn and talk to a partner about all of the patterns that you see. • What colour patterns do you see? • What shape patterns do you see? • How many swimmers are creating this pattern? Do you think that nine swimmers could also make this pattern? Why? Show and read page 25 • What kind of pattern do you see? How do you know that it is a growing pattern? How far do you think this pattern will continue? Why? What might stop the pattern from growing? (e.g., other waves on the water) • Have you ever made a pattern like this in the water? How did you make it? (e.g., dropping a stone in the water) • Read the text. Show and read pages 26–27 • How are these patterns the same and how are they different? • What common function do the two patterns serve? Why is this pattern important to have? • Look at the pattern on your shoes. What happens to the pattern on the soles of your shoes once you have worn them for a while? • How would the soles on winter boots be different than the soles on these running shoes? Show and read pages 28–29 • What patterns do you see on the grater? What function do these patterns perform? Why are the openings on the sides of the grater different sizes? What foods might you grate on the two different sides? • What purpose does the pattern on the rope serve? The text says that the rope has a spiral pattern. What does this mean? Further Investigation • Show students three strands of thick twine or rope and demonstrate how you can braid the three pieces into one thicker rope. Ask what patterns you are making with your actions. 20 Patterns & Relations/Data & Probability

Materials: • Give students their own strands of rope or twine and teach them how to braid, Pattern, BLM 1: emphasizing the patterns in the actions. Chessboard, black and Show and read page 30 white pattern like on a chessboard, counters, • What patterns do you see in the spider web? What kind of pattern is it and how a knight chess piece (optional) do you know? What is repeating as the pattern grows? • Have you ever watched a spider spin its web? Where does the spider begin? How does the spider create the web without falling? Further Investigation • Show a video of a spider building its web. Have students look for the patterns in the web and the patterns in the movements of the spider. Show and read page 31 • What patterns do you see? What kinds of patterns are they? Why do you think people like to create their gardens in patterns? Follow-Up Talk • What have we learned about patterns? Let’s make a definition together. We can add to it or change it throughout the unit as we learn more about patterns. What kinds of patterns did we learn about today? Let’s put the types of patterns on the anchor chart, too (repeating, growing, shrinking). Math Talk: Math Focus: Investigating the order of a sequence of instructions to determine how it affects the outcome. Let’s Talk • Show page 4 of the book Pattern. What patterns do you see on this game board? How do you know that it is a pattern? What game is played on this board? This game is known as chess. Each player has 16 pieces that they move across the board. The idea of the game is to corner the king so it cannot escape being captured. As the players move their pieces across the board, they can capture each other’s chess pieces. An interesting part of the game is that the pieces move across the board in different ways. While some can only move one space forward at a time, others can move back and forth along the diagonal squares. Demonstrate a couple of these moves. • Show BLM 1: Chessboard and the knight chess piece. This chess piece in the shape of a horse’s head is known as a knight. It moves in a very interesting pattern that forms an L shape. It can move two squares up or down and then one square to either side, or it can move two squares to either side and then one square up or down. Demonstrate as you repeat the pattern each time. continued on next page Patterns and Relations 21

• Imagine that I put the knight on this black square near the middle of the board. Turn and talk to your partner about where the knight can move by following this pattern. Give partners a copy of the chessboard (BLM) and a counter to use as a knight. • What did you find? Let’s put a counter on each of the squares where the knight could end up. • What do you notice about all of the squares that it can move to? (e.g., All of the squares are white; the squares form a circle around the knight, which is in the middle.) • What do you think the pattern will be if the knight starts on a white square? Why? Let’s check it out. Partner Investigation • I am going to pick two squares at either end of the board and you are going to figure out a route that will take you from the beginning to the ending point. You can place a counter on each space that the knight would occupy along the way. Follow-Up Talk • Were you able to move from the beginning to the end point? Why or why not? What do you notice about the pattern created on the squares by the movement of the knight? (e.g., There is a white, black, white, black pattern.) • Do you think the order of your instructions matter? Let’s try different movements to find out. Partner Investigation • Work with your partner to see if you can create a series of instructions (code) for moving the knight so it makes a repeating pattern or loop. Where would you have to end up if it makes a repeating pattern? (e.g., on the square you started on) Use your board and some counters to mark on your moves. Follow-Up Talk • What did you find? How many moves did it take to return to the same spot? Does it always take the same number of moves? Why? Further Investigation • Explain to students that they are going to be pattern detectives over the next few days and look for patterns outdoors and in their homes. Have them take some photographs. Display some of their photos and discuss the patterns that they see. • Interested students can investigate the ways that other chess pieces move and the patterns they might make on the board. 22 Patterns & Relations/Data & Probability

2Lesson Investigating Patterns in Our Lives Teacher Possible Learning Goals Look-Fors • Recognizes and describes increasing and decreasing patterns found in our lives and explains why they are patterns • Identifies how the patterns grow or shrink and predicts how the pattern will extend • Identifies and describes increasing and decreasing patterns in our lives • Explains what growing and shrinking patterns are by giving examples • Describes the pattern using words and/or numbers • Predicts how a pattern will extend over time About the Math Talks The Math Talks are intended to further assess what your students know about patterns. Select the prompts that best meet the needs of your students. Materials: Math Talk 1: Patterns in Nature “Patterns in Nature” Math Focus: Identifying, describing, and extending patterns in nature (pages 2–3 in Patterns, Relations, Data, and Let’s Talk Probability big book and little books), Pattern Cross-Section of Tree Trunk Time: 20 minutes per day (discussing 2−3 • Show students the cross-section of a tree trunk on big book page 2. What is in images each day) this picture? What part of the tree is showing? What do you know about the state of the tree? (e.g., It is no longer living.) • What patterns do you see? Turn and talk to your partner. • What do you think? What makes it a pattern? (e.g., The colours of the rings are light, dark, light, dark; the circular rings keep getting bigger.) What kind of patterns do the colours make? (e.g., The colour pattern is a repeating pattern.) • What kind of pattern do the rings make? (e.g., The circular rings make a growing pattern.) • How are repeating and growing patterns different? The same? continued on next page Patterns and Relations 23

Teaching Tip • What do the circles on the tree tell us? (e.g., The number of rings tells us how Integrate the math talk old the tree is.) Estimate how old this tree is. Let’s count some of the outer rings moves (see page 8) together. Do you want to change your estimate? throughout Math Talks to maximize student Water Pattern participation and active listening. • Show students the water pattern on big book page 3. What is this picture about? What might have happened to form this pattern in water? What kind of pattern do you see? How is it growing? • When you drop a stone in water, the stone pushes away some of the water, which forms circular waves that keep travelling out from where the rock entered the water. As they travel, the circles get bigger and bigger. • How is this pattern like the pattern on the tree trunk? Cross-Section of a Shell • Show the picture of the snail’s shell on page 10 in the Pattern book. What pattern did we identify on this shell? What kind of pattern do you see? This growing pattern is known as a spiral. • Show the picture of the cross-section of the shell on big book page 2. This is another kind of shell. It has been cut in half so we can see what the shell looks like inside. What do you see and what do you wonder about? Turn and talk to a partner. • Discuss students’ responses. What is growing in this pattern? How can you describe how it is growing? As the animal inside the shell grows, it needs a bigger shell so the shell grows in layers, sometimes called ‘growth bands.’ • Where do you see the spiral that is like the spiral on the outside of the shell? • How is this pattern different from the tree and water patterns? How are they all the same? • What do you wonder about when you see this pattern? Fern Leaf • Show the picture of the fern leaf on big book page 2. Turn and talk to your partner about the patterns you see in this leaf. • What do you think? What kind of pattern do you see? • Look at one of the branches coming from the large leaf. This is known as a frond. What do you notice? (e.g., It looks like a miniature version of the whole leaf.) If you look closely at the tiny leaves on the frond, what do you think they look like? (e.g., like a miniature version of the frond) • This pattern is known as a fractal, which repeats the structure of the larger pattern, but as smaller and smaller versions of it. Would this be a growing or shrinking pattern? Why? Spiral Aloe • What do you think is in this picture? What patterns do you see? • This is a picture of a spiral aloe plant. Why do you think it is called a ‘spiral’ aloe? A spiral is a curved pattern that starts in the middle and then grows bigger each time it goes around the centre. How many spirals can you see in this plant? 24 Patterns & Relations/Data & Probability

Are the spirals growing clockwise, the way the hands on a clock move? Or are they moving counterclockwise in the opposite direction that the hands on a clock move? • What do you notice about the size of the leaves on each spiral as they grow outward from the middle? Why do you think this is a good example of a growing pattern? • This growing pattern is very helpful for the plant. The pattern made by how the leaves are arranged allows each leaf to get as much sun as possible because the upper leaves don’t shadow the lower leaves. Visualize rain falling on the plant. Where would the rain go? The pattern arrangement also helps to funnel the falling rain down to the roots. • Have you ever seen any other plants or animals with a growing spiral pattern? Sunflower Head • Show the picture of the sunflower head on big book page 3. What do you see in this picture? What kind of plant is it? What parts of the plant are showing? • What patterns do you see in the seeds? Look at how the seeds are organized. What kind of lines do you see as you look outward from the centre? (e.g., curved lines or spirals) In which direction do the curved lines go? If you look carefully, there are curved lines going in both directions. • The pattern in the seeds grow like this. (Print 1, 2, 3, 5, 8, 13, 21…) Turn and talk to your partner about how the numbers are growing. What did you find? This is a tricky pattern. Let’s add the first two numbers, 1 and 2. What is the sum? What is the sum of the second and third numbers? Check to see if this pattern continues. This is a famous math pattern known as the Fibonacci sequence, which is named after the man who discovered it. How can we describe the pattern rule using words? • Scientists claim that this is the best way for the seeds to be arranged so each seed gets lots of sunlight. Pine Cone • Show the picture of the pine cone on big book page 3. What is this? What is the purpose of the pine cone? Like the sunflower head, it also holds seeds. • What patterns do you see in the pine cone? The parts, or bracts, of the pine cone grow in spirals like the sunflower seeds. The number of spirals in either direction are also Fibonacci numbers. Pictures of Pink Plant and Aloe Plant • Show the pictures of the pink plant and aloe plant on big book pages 2–3. Turn and talk to your partner about the patterns in these two plants. Discuss how they are the same and how they are different. • What other pictures have similar patterns to the ones in these two plants? Green Chameleon • Show the picture of the green chameleon on big book page 3. What do you see in this picture? Have you ever seen an animal like this before? What kind of animal is it? (reptile) What is covering the outside of the animal? (scales) continued on next page Patterns and Relations 25

• What patterns do you see? Which patterns are repeating? (e.g., the colours on the scales) • What is another pattern on the chameleon? What do you notice about its tail? What kind of pattern does the tail make? Is it a shrinking or growing pattern? How do you know? • What do we call this kind of pattern? (spiral) What other pictures that we have studied have spiral patterns? • Why might it be useful for the chameleon to be able to curl its tail in a spiral? Materials: Math Talk 2: Spot the Pattern “Spot the Pattern” Math Focus: Investigating increasing and decreasing patterns in real-life situations (pages 4–5 in the Patterns, Relations, Let’s Talk Data, and Probability big book and little books) • In the last Math Talk, we investigated many patterns in nature. Turn and talk to Time: 20 minutes per day (discussing 2−3 a partner about how you can describe growing and shrinking patterns. images each day) • Discuss students’ responses. • Now, we are going to look at patterns that are made by humans. Rolled Hose • Show the picture of the rolled hose on big book page 5. What do you see? What pattern do you see? What kind of a pattern is it? How was the pattern created? • How is this similar to and different from the spiral patterns that we studied in nature, like the spiral pattern on the shell? • Why do you think the hose is rolled in this way? How long do you think this hose is when it is straightened? Why? • Visualize how else could you roll up this hose so it makes a different shape. Cobblestones • Show the picture of the cobblestones on big book page 5. What does this picture show? Where might this picture have been taken? • What patterns do you see? Turn and talk to your partner. • Do you think that there is a colour pattern? Why or why not? • How could the tiles have been laid so they do make a colour pattern? Decide on a pattern with your partner. Discuss students’ responses. • Is there a pattern that involves the size of the stones? • How is this a growing pattern? Stacked Fruit in Grocery Store • Show the picture of the stacked fruit in the grocery store on big book page 4. Where does this scene take place? What kind of store is it? 26 Patterns & Relations/Data & Probability

• What patterns do you see? Turn and talk to a partner. • What are the patterns you see in the stacked fruit? Do you see growing or shrinking patterns? Why do you think so? If you visualize making the stacks, would the pattern be growing or shrinking? • How could you show the pattern in one of these stacks using numbers? (e.g., 5, 4, 3, 2) What is the pattern rule? • If there was another row under some of these stacks, how many pieces of fruit would there be? How do you know? • Why do you think the store owner decided to have five pieces of fruit at the base of the stacks? Stacked Oranges • Ask students to look specifically at the picture of the stacked oranges in the picture of stacked fruit on big book page 4. What fruit do you see stacked in this picture? What shape is the stack of oranges? • Estimate how many oranges there might be. Turn and talk to your partner. • Do you think there are more than 50 oranges? More than 100? More than 200? • What pattern do you see? If you visualize how the pyramid of oranges was created, is it a growing or a shrinking pattern? Why? • How is this pattern the same as and different from the stacked fruit in the previous picture? • Do you think the increase in the number of oranges from the top to the bottom is the same from layer to layer? Why or why not? Bowling Pins • Show the picture of the bowling pins on big book page 4. What do you see in this picture? Have you ever bowled before? How do you play the game? • How can you describe the way the 10 pins are set up at the beginning of a turn? What patterns do you see? Turn and talk to a partner. • What did you find? (e.g., There is 1 pin in the front row, 2 in the second row, 3 in the third row, and 4 in the fourth row.) Draw a picture of the pattern and print the numbers 1–4 beside each row to indicate the number of pins. What is the pattern rule? (e.g., add one more pin each time) • How would the pattern continue for the next two rows? How many pins would there be in total? Use your mental math skills to figure this out. (e.g., There would be 21 pins.) Let’s draw in the extra rows. How does the number pattern continue? (5 more pins, 6 more pins) • What number sentence can we use to sum up all of the pins? (1 + 2 + 3 + 4 + 5 + 6) Partner Investigation • With your partner, figure out how many rows you need to have in your pattern so you have a total of 55 pins. continued on next page Patterns and Relations 27

Follow-Up Talk • What did you find? What strategies did you use to figure it out? What would be the total number of pins if we added one more row? How does this make a pattern? Pyramid of Cards • Show the picture of the pyramid of cards on big book page 5. How would you describe this structure of cards? What patterns do you see? If you visualize how this tower of cards was made, is it a growing or a shrinking pattern? • If you don’t count the horizontal cards between the layers, how are the number of cards shrinking from layer to layer as you move up the tower? • How can you show this pattern with numbers? (6, 4, 2) What is the pattern rule? (e.g., There are two less cards with every layer going up.) • If there had been another layer at the bottom of the tower, how many cards would there be? How do you know? • How is this pattern the same as and different from the pattern made with the bowling pins? Stacked Cardboard Boxes • Show the picture of the stacked cardboard boxes on big book page 5. What do you see in this picture? What do you think might be inside the boxes? Why do you think these boxes have been piled on top of each other? • What pattern do you see in the way they are stacked? Why is this a good way to stack the boxes, rather than directly on top of each other? If possible, show a pattern of bricks and how they are laid so they offset each other. Why do you think this is a popular pattern in construction? • If there was another layer of boxes underneath, how many boxes would there be? • How could you show this pattern with numbers? By how much is the pattern increasing from row to row, moving from the top to the bottom? Stacked Gold Boxes • Show the picture of the stacked gold boxes on big book page 4. Look at these boxes. Why do you think they are not stacked directly on top of each other? • Without counting, estimate how many boxes there are in this picture. Turn and talk to your partner. • What do you think? What strategy did you use to estimate? • How are these boxes stacked differently than the cardboard boxes? (e.g., The stack of cardboard boxes is only one box deep, while the layers of gold boxes are more than one box deep.) • What pattern do you see in how the boxes are stacked? • Visualize the second row from the top without any other boxes around it. How many boxes are there? (4) What shape do the surfaces of the four boxes make? (square) What shape do the surfaces of the boxes make in the third row from the top? Do all of the layers make squares? 28 Patterns & Relations/Data & Probability

• Let’s draw a top view of each layer to make sure. What do you notice about the dimensions of the squares in terms of the number of boxes? (e.g., 1 × 1, 2 × 2, 3 × 3, 4 × 4, etc.) If we added another layer at the bottom, what would be the dimensions? How many boxes would be in this layer? • How many boxes are in each layer? Record 1, 4, 9, 16, 25. These are known as square numbers because they can all be arranged into squares. Dart Board • Show the picture of the dart board on big book page 4. Have you seen this before? It is a dart board. What kind of game can you play with it? What do you think the goal of the game is? • Turn and talk to your partner and find as many different patterns as possible. • What did you find? (e.g., the colours repeat, the size of the circles grow larger from the centre to the outside) Do the circles grow in a consistent way? How would this pattern change if you started at the outside and moved to the centre? (e.g., the circles would get smaller in size) Which are repeating patterns and which are growing/shrinking patterns? • Are the numbers on the dart board in a pattern? How do you know? We refer to the numbers as being randomly placed when they are not in a pattern. Pattern in Roof of Building • Show the picture of the pattern in the roof of the building on big book page 5. What do you see? What kind of building might this be in? • What patterns do you see? Is it a growing or shrinking pattern? What is the same and what is different from row to row? • Why do you think the designer chose to use triangles as the shape for the individual panels? • Why do you think they designed a building like this? Pattern in Electrical Tower • Show the picture of the pattern in the electrical tower on big book page 4. What is this structure? Have you seen a structure like this before? What is its purpose? • What patterns do you see in its structure? • Why do you think the tower is wider at the bottom and narrower at the top? • What is similar and different about the ways in which the roof and the electrical tower were constructed? Follow-Up Talk • What have we learned that is new about patterns? We can add some of the ideas to the anchor chart that we started after reading the Pattern book. Patterns and Relations 29

Math Talk 3: Creative Patterns Math Math Focus: Investigating patterns in First Peoples art and identifying the Learning pattern rules Standards Curricular Competencies Materials: • Reasoning and analyzing: Use reasoning to explore and make connections “Creative Patterns” • Understanding and solving: Engage in problem-solving experiences that (pages 8–9 in Patterns, Relations, Data, and are connected to place, story, cultural practices, and perspectives relevant to Probability big book local First Peoples communities, the local community, and other cultures and little books) Time: 20 minutes per • Communicating and representing: Communicate mathematical thinking day (discussing 2−3 images each day) in many ways; use mathematical vocabulary and language to contribute to Math Vocabulary: mathematical discussions piccnailcrotcrtceuekalrawnsr,iisnpregea,,pttldeienaeretcnirn,oegrfao,staintge,, • Connecting and reflecting: Connect mathematical concepts to each symmetry other and to other areas and personal interests; Incorporate First Peoples worldviews and perspectives to make connections to mathematical concepts Content • Increasing and decreasing patterns • Pattern rules using words and numbers, based on concrete experiences: Share examples of First Peoples art with the class and ask students to notice patterns in the artwork Let’s Talk Select the prompts that best suit the needs and interests of your students. Seal with 2 Salmon by Trevor Husband (Gitxsan/Cree) • Look at the piece of art. Do you think it is two-dimensional or three-dimensional? Why? How do you think it was made? This is a carving by Trevor Husband. It is made from yellow cedar and carved and shaped using traditional bent knives. Visualize a bent knife. How might this be helpful when making this carving? • What images do you see in this carving? What do you think it represents? It represents the circle of life. How does the carving create this representation? (e.g., The seal is chasing the salmon to eat to survive, and the salmon are trying their hardest to survive.) • What shapes are used in the carving? (e.g., U shapes, split U shapes, S shapes) How are the shapes used to create patterns? • What kinds of patterns do you see? • Where do you see an increasing/decreasing pattern? What attribute is increasing/ decreasing? (e.g., the size of the shapes) • Where can you see a repeating pattern using colours? • How does this carving make you feel? What do you find most interesting about it? Children of the Raven by Bill Reid (Haida) • Look at this piece of art. What do you see? How does it make you feel? What emotions do you think the artist is trying to show in his art? 30 Patterns & Relations/Data & Probability

• This artwork is by Bill Reid. He was a member of the Raven clan from T’aanuu. In this art, Reid is depicting Raven, which in Pacific Northwest Coast Culture is known as both a teacher and a trickster. What do you think a ‘mischievous trickster’ is? Raven is also seen as playing an important part in changing the world. This piece of art celebrates the creation of humankind by Raven. • What patterns do you see? Turn and talk to your partner. • What repeating patterns do you see? What is the pattern rule? • What increasing/decreasing patterns do you see? How can an increasing pattern also be seen as a decreasing pattern? (e.g., It depends on your perspective and where you start with the pattern.) • Which pattern increases and then decreases? (e.g., the nine faces) What attribute is increasing/decreasing? (e.g., the size of the faces and their features) • What shapes are used in the image? (e.g., ovoids, U shapes, T shapes) Look at the red and black U shapes. What patterns do you see? • Look at the body of Raven. What do you notice about the right and left sides? (e.g., They are mirror images of each other.) If you slide the left side over to the right side do the two sides match up? Why? (e.g., No, they are reversed images.) How could you match up the two sides? (e.g., by flipping one side onto the other or folding the image in half) Where would you put the fold line? This fold line is also known as the line of symmetry. • What might Raven be thinking in this piece of art? Why do you think so? Thunderbird from Thunderbird and Man Holding Copper by Bruce Alfred (Kwakwaka’wakw) • Look at this piece of art. How does it make you feel? What emotions do you think the artist is trying to show? The artist is Bruce Alfred from Alert Bay, British Columbia, and he follows the traditional artistic methods of the Kwakwaka’wakw culture. • Is this piece of art two-dimensional or three-dimensional? How do you know? What two-dimensional shapes do you see on the sculpture? (e.g., ovoids, U shapes, split U shapes) • What patterns do you see in how the sculpture has been carved? (e.g., The left side is a mirror image of the right side.) This means that the sculpture is symmetrical. • Imagine folding the design on the sculpture so the left side matches up with the right side. Where would the fold line be? What is another name for the fold line? • What patterns do you see in the painted designs? Turn and talk to your partner. • What patterns do the colours make? • Look at the two rows of white, red, and green shapes. What role does number play in the pattern made from these shapes on one of the wings? (e.g., The pattern is increasing by two more shapes as you move down the wing.) If we were to extend the wing and add another row, how many shapes do you think there would be? Why? How can we describe the pattern rule? continued on next page Patterns and Relations 31

Burden basket (Interior Salish) • What do you see? What do you think the basket might be used for? This is known as a burden basket. What does ‘burden’ mean? Burden baskets were often used to carry heavy loads like firewood. Often, the baskets were carried on people’s backs and were attached using a tumpline. A tumpline is a strip of material that is tied to baskets when both hands are needed for climbing or collecting. The woven band is normally worn against the forehead. • What do you think the basket is made from? It is made from cedar root and cherry bark. It has a coiled construction. What do you think this means? (e.g., a material, like a root, is coiled round and round to make a shape) After the material has been coiled, the coils are stitched together. • What pattern do you see in the structure of the basket? • Look at the design. What patterns do you see? Turn and talk to a partner. • What colour patterns do you see? How do they repeat? What is the pattern rule? • Do you see any increasing/decreasing patterns? How can an increasing pattern also be seen as a decreasing pattern? (e.g., It depends on your perspective or where you think the pattern starts.) • Look at the diamond shapes in the middle. What colour patterns do you see? What is the pattern rule? • What number patterns do you see as you look at the number of squares per row? What is the pattern rule? • Describe what you see in the designs on the sides of the basket. What are the pattern rules? Storage basket (Nlaka’pamux) • Look at this basket. It is known as a storage basket. What does this mean? What kind of items might be stored in the basket? How might the construction of this basket be different than the construction of the burden basket so they both serve their different purposes? (e.g., The burden basket may be made of stronger material since it carries heavier loads.) • This basket is made from cedar root and cherry bark. How do you think it was made? It also has a coiled construction. • What patterns do you see in the designs? Are they repeating, increasing, or decreasing patterns? How do you know? What attributes are making the patterns? Is it shape, colour, number, or a combination of the attributes? • Compare the patterns on the storage basket to the patterns on the burden basket. How are they the same and how are they different? What makes them patterns? (e.g., They all have some type of rule that describes how they repeat.) Northern Lights by Susan Point (Musqueam) • What do you see in this piece of art? How does it make you feel? Why do you think it might be called “Northern Lights?” What are northern lights? Have you ever seen them? 32 Patterns & Relations/Data & Probability

• Look at the colours. Do they make a pattern? (e.g., No, overall, the colours seem more randomly placed.) Do the colours need to make a pattern? Why? (e.g., No, because patterns can be made with other attributes such as shape or number.) • What patterns do you see? Turn and talk to your partner. • What did you find? (e.g., The pattern repeats in a circular way.) If you turn the design clockwise around the centre, how many times does the segment at the top repeat onto itself until it returns to its original position? (6) What happens to the position/orientation of the arrows each time the art is rotated? Does the position of the arrows change the shape? (e.g., No, they are the same shapes but they are just turned.) • What type of pattern do you see in some of the arrow designs? (e.g., The arrow design at the top and in the other matching segments show a decreasing pattern of 5 arrows, 3 arrows, and then 1 arrow.) What is the rule for this pattern? (e.g., Each row moving inward has two less arrows.) How could you describe this as an increasing pattern? (e.g., Starting at the inside, there are two more arrows per row.) If we were to add another row of arrows to the outside, how many arrows would there be? How do you know? • What pattern do you see in the other arrows that are in pairs? (e.g., There are always two arrows in each row, but they gradually get further and further apart.) • What type of pattern do you see in the centre of the art? (e.g., a circular, repeating pattern) How many times do the shapes repeat? What do the shapes look like to you? Killerwhale Rattle by Bruce Alfred (Kwakwaka’wakw) • What do you see? Is this item two-dimensional or three-dimensional? Why do you think so? What three-dimensional object does it most closely resemble? (e.g., a rectangular prism) • What purpose do you think this item serves? It is a rattle, which is used in ceremonies. How do you think a rattle makes a noise? • What do you think the rattle is made from? Why? It is made from red cedar wood and the design has been painted with acrylic paint. • What patterns do you see on the rattle? Turn and talk to your partner. • How is colour used to make a pattern? Describe the rule for one of the colour patterns. • How is shape used to create a pattern? What is the pattern rule? • Are the eight ‘eyes’ all the same shape? How do you know? (e.g., Yes, because they match onto each other.) What is different about them? (e.g., They are in different positions.) Do their positions change the shape? (e.g., No, they are still the same shapes.) • Look at the two ‘eye’ shapes at the top of the rattle. Imagine rotating them clockwise around the centre. How many times would they match up to similar shapes until they return to their original position? (4) The shapes are making a circular pattern. • Why do you think this is called a “Killer Whale” rattle? Patterns and Relations 33

3 5LessonstoInvestigating How Patterns Increase and Decrease Math Curricular Competencies Learning Standards • Reasoning and analyzing: Use reasoning to explore and make connections; model mathematics in contextualized experiences • Understanding and solving: Visualize to explore mathematical concepts; develop and use multiple strategies to engage in problem solving • Communicating and representing: Communicate mathematical thinking in many ways; use mathematical vocabulary and language to contribute to mathematical discussions; explain and justify mathematical ideas and decisions; represent mathematical ideas in concrete, pictorial, and symbolic forms • Connecting and reflecting: Reflect on mathematical thinking Content • Increasing and decreasing patterns • Pattern rules using words and numbers, based on concrete experiences About the Primary students are naturally interested in patterns. They enjoy identifying patterns in books, rhymes, songs, and chants, and they will experiment with creating patterns as they play. Growing and shrinking patterns follow a predictable rule: Growing patterns increase in size and shrinking patterns decrease in size. These patterns can include shapes or numbers. Certain growing patterns, such as the counting sequence 1, 2, 3, 4…, will be very familiar to students (Small, 2013, p. 608). Other growing and shrinking patterns will be new to them. It is important to provide students with many opportunities to describe what they observe. Students will also need practice in representing and translating growing and shrinking patterns from one form to another (e.g., square tiles > counters, connecting cubes > actions). When students can represent the same growing or shrinking pattern, using different concrete materials or forms, they are working with the pattern’s structure and how it changes, rather than looking at what attributes change. 34 Patterns & Relations/Data & Probability

Math Vocabulary: About the Lessons idpnedeacleecrtsemtreecaerrasninbsintiern,gu,gi,ldee,gex,srtnotheetwrnirifmindyn,k,g,i,ng, Lessons 3 to 5 build on students’ knowledge of being able to describe create what they see in patterns and what attributes or operations are repeating. Students will investigate a variety of growing and shrinking patterns that they will describe and represent in a variety of ways. Students will also create their own growing and shrinking patterns using a variety of elements to represent each term (e.g., concrete materials, actions). Patterns and Relations 35

3Lesson Investigating How Patterns Can Increase Teacher Possible Learning Goals Look-Fors • Describes a variety of patterns and uses words and numbers to describe the Previous Experience pattern rule with Concepts: Students have had • Represents growing patterns using concrete materials and actions experience identifying, extending, creating, and (e.g., connecting cubes, clapping, callouts) representing patterns. • Extends patterns that increase Materials: a variety of concrete • Identifies what comes next in a variety of growing patterns objects (e.g., connecting • Describes or shows the pattern rule for a growing pattern cubes, counters, • Represents a simple growing pattern using a method of their choice square tiles, pattern blocks, etc.) (e.g., clapping, jumping, counters) Time: 45 minutes Minds On (15 minutes) • Call students to your gathering spot and begin the transition into the lesson by clapping and by stating in a soft voice, “If you can hear me, clap once. If you can hear me, clap three times. If you can hear me, clap five times,” etc. • Once students are all listening, ask them what would come next in the pattern. Ask them to explain how they know. Have them turn and repeat the pattern with a partner. Repeat the pattern with the entire class from the beginning to check for understanding. Ask the following questions: – How could you describe this pattern? (e.g., You start with one clap, then you clap three times, then five times, then seven times, etc.) – How do you know how many claps to do each time? (e.g., You do two more claps than the last time, you add two claps each time, etc.) – How many claps are there in each part of the pattern? (e.g., one, three, five, etc.) Share that each part of the pattern is called a ‘term’ or ‘element.’ • Ask, “How else might we represent this pattern? What does this mean? What could we try to make sure we understand the problem?” (e.g., We could use our math tools, connecting cubes, counters, pattern blocks, square tiles, etc.) “How many would we use to start?” (e.g., start with one, then put two, then three, etc.) Have students represent this pattern visually with whichever tool they choose. For example, they may represent it with various concrete materials or with numerals. • Draw one of their representations on chart paper and label each term of the pattern (e.g., Term 1, Term 2, etc.) so students have access to it during the Working On It activity. 36 Patterns & Relations/Data & Probability

Teaching Tip Working On It (15 minutes) Co-create an anchor • Organize students in pairs. Have each pair choose a way to represent the same chart of the vocabulary discussed in this lesson. pattern that was modelled in the Minds On (e.g., clapping hands, shapes, counters, Include examples connecting cubes, A/AA/AAA, musical instrument, etc.). They can refer to with the co-created any previous anchor charts that were created to describe patterns for ideas. definitions. • When complete, have one member of each pair ‘stay,’ and the other student ‘stray,’ to visit the other pairs’ representations. At each representation, have the ‘stayers’ describe their representation and the ‘strayers’ check that it matches the same pattern rule. Switch. Differentiation • For pairs that may be struggling representing the modelled pattern, engage them in small-group instruction and/or ask prompting questions during the Working On It section. • For pairs that may need an additional challenge, have them create their own growing pattern. Assessment Opportunities Observations: Pay attention to students’ ability to translate from the modelled pattern to their own representation. Conversations: Use the following prompts to check for understanding: – What would be the next term in the pattern? How do you know? – What is the pattern rule to get from one term to the next term? – How else could you represent the same pattern? – How might you use these counters (clap, jump, etc.) to show me the same pattern? Consolidation (15 minutes) • Discuss as a group the things students know about the ways in which patterns might grow or increase. (e.g., gets bigger from term to term; gets bigger by the same amount each time; each part of a pattern is called a term; the amount it gets bigger by is called the pattern rule) • Share some of the patterns that students created. Have the class guess and describe the pattern rule. Reinforce that it is important to know the starting term and a description of how the pattern is growing or increasing. • Challenge students to extend the pattern, describing and/or showing the next three terms. • Building Growth Mindsets: Ask students how they are feeling after learning about growing patterns. Have them identify their emotions and why they might be feeling overwhelmed or frustrated. Reassure students that they will have many experiences ahead to practise and to clear up what might seem confusing. Make a list of things that students can do if they feel frustrated (e.g., take a break; ask a friend for help; check out an anchor chart; etc.). Patterns and Relations 37

4Lesson Investigating How Patterns Can Decrease Teacher Possible Learning Goals Look-Fors • Explains how patterns can become smaller from term to term and describes the pattern rule using words and/or numbers • Represents and extends patterns that get smaller from term to term using concrete materials and actions (e.g., connecting cubes, clapping, callouts, shapes) • Identifies what comes next in a variety of patterns that get smaller from term to term • Describes or shows the pattern rule for a pattern that gets smaller from term to term • Represents a pattern that gets smaller using a method of their choice (e.g., clapping, jumping, counters, shapes) Materials: Minds On (15 minutes) Digital Slide 6: Patterns That Decrease • Review the characteristics of a growing pattern from the previous lesson Digital Slide 5: Patterns That Decrease (e.g., gets bigger from term to term; gets bigger by the same amount each 40 Digital Slide 4: Patterns That Decrease time; each part of a growing pattern is called a term; the amount it gets bigger 30 Digital Slide 3: Patterns That Decrease by is called the pattern rule). 20 Digital Slide 2: Patterns That Decrease • Project Digital Slides 1 and 2, one at a time. Pose some of the following Digital Slide 1: Patterns That Decrease 10 prompts to check for understanding: − What kind of pattern is this? 0 − How do you know? − Describe the pattern. Scholastic Canada GR3 BC Patterns & Relations 3rd Pass − How do you know how to get from one term to the next term? Digital Slides − What would be the next term in the pattern? November 9, 2021 − How is skip counting like a pattern? − How would you describe the pattern rule? Scholastic Canada GR3 BC Patterns & Relations 3rd Pass Digital Slides • Have students share their ideas about what kind of patterns they have been November 9, 2021 looking at and how they differ from growing patterns. (e.g., shrinking pattern: Scholastic Canada GR3 BC Patterns & Relations 3rd Pass it’s like a growing pattern but it gets smaller; there are less items in each term; Digital Slides the items decrease each time by the same amount) November 9, 2021 • Co-create an anchor chart to record the characteristics of a shrinking Scholastic Canada GR3 BC Patterns & Relations 3rd Pass Digital Slides (decreasing) pattern. November 9, 2021 Working On It (15 minutes) Scholastic Canada GR3 BC Patterns & Relations 3rd Pass Digital Slides • Review ‘term’ and ‘pattern rule’ with students before beginning. November 9, 2021 • Provide each pair of students with one of the four patterns found on the Scholastic Canada GR3 BC Patterns & Relations 3rd Pass Digital Slides November 9, 2021 BLM 2: Patterns That Decrease, Digital Slides 1–6: Patterns That Decrease Time: 45 minutes BLM 2: Patterns That Decrease 4 © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 Scholastic Canada GR3 BC Patterns & Relations 4th Pass Reproducibles November 9, 2021 38 Patterns & Relations/Data & Probability

second and third pages of BLM 2: Patterns That Decrease. You may wish to project these patterns using Digital Slides 3–6, so that students know the colour of each pattern. Alternatively, you could make black and white copies and have students simply represent the next term using black. • Ask students to examine and describe the pattern with their partner. (e.g., It starts with ‘#’ in term 1, then you remove/take away two from…, etc.) • Have students describe the pattern rule and identify what the next term in the pattern will look like. • Have each pair join another pair to share what they know about their pattern and how they determined what the next term in the pattern looks like. • Have students compare and contrast elements of their pattern with the other pair’s pattern. Differentiation • Pair students of like abilities so that, if needed, you can support their work during this phase of the lesson. • Strategically choose which pattern is shared with which pair of students (e.g., shrinking patterns with a pattern rule of decreasing by one will be easier for most students to identify; the first page of BLM 2 can help in this situation). • For pairs that may require an additional challenge, provide them with a more challenging pattern or have them compare and contrast two different patterns. Assessment Opportunities Observations: Pay attention to students’ ability to: – Describe the pattern in general terms (e.g., There are 8 circles and the next time there are 7 circles.) – Identify the pattern rule in order to determine the next term in the pattern (e.g., Each time you take away one more, so the pattern goes from 8 to 7, then 6 to 5, etc.) – Use mathematical language to describe what they see (e.g., term, pattern rule, shrink) Conversations: Use the following prompts to check for understanding: – What would be the next term in the pattern? How do you know? – What is the pattern rule to get from one term to the next term? Consolidation (15 minutes) • Announce to students that you would like them to come back to your gathering spot. Begin counting backwards from 20 by 1s. Ask students if they can identify the pattern rule that you just used. (e.g., shrinking pattern, starting at 20, counting backwards by 1s) Ask, “What’s another way that we could use a shrinking pattern to gather back together?” (e.g., claps, skip counting by 2s, etc.) Patterns and Relations 39

Materials: • Select two of the patterns that were used during the lesson to review with the Digital Slide 7: Describe the Pattern whole group. Ask the following prompts to ensure understanding: − What kind of pattern is this? How do you know? − Describe the pattern. How do you know how to get to the next term? − What would be the next term in this pattern? • Continue to build the co-created anchor chart to identify pattern rules of the shrinking patterns identified in this lesson. • Building Growth Mindsets: Ask students some of the following prompts to help them build their confidence when working with patterns, and have them share in the large group: − What did you notice about your pattern? − What did you notice about the pattern that the other group had? − What was the same? What was different? Have students use ‘thumbs-up’ to signal when someone else shares an idea that they had also. Further Practice • Project Digital Slide 7: Describe the Pattern. Say, “Turn and talk with your partner and your partner group to share what you notice about each pattern.” • Distribute a copy of BLM 3: Describe the Pattern as an exit pass. Have students describe the patterns. They can answer the question, “How do you know?” Scholastic Canada GR3 BC Patterns & Relations Slide 7: 3rd Pass Digital Slides November 9, 2021 Describe Digital the Pattern, BLM 3: Describe the Pattern Name: BLM 3: Describe the Pattern continued BLM 3: Describe the Pattern Repeating Growing Shrinking How do you know? Repeating Growing Shrinking How do you know? Repeating Growing Shrinking How do you know?8 © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 Scholastic Canada GR3 BC Patterns & Relations 4th Pass Reproducibles November 9, 2021 © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 7 Scholastic Canada GR3 BC Patterns & Relations 4th Pass Reproducibles November 9, 2021 40 Patterns & Relations/Data & Probability

5Lesson Creating Patterns That Increase or Decrease Teacher Possible Learning Goals Look-Fors • Independently creates patterns that increase or decrease and describes the Materials: pattern rule Digital Slide 8: My Pattern • Represents a given pattern using different materials (e.g., a similar pattern Term 1 Term 2 Term 3 Term 4 with square tiles, connecting cubes, pattern blocks, etc.) Scholastic Canada GR3 BC Patterns & Relations 3rd Pass • Creates four terms of a pattern Digital Slides • Describes patterns and explains what the pattern rule is November 9, 2021 • Extends a pattern based on the pattern rule Digital Slide 8: My Pattern, Minds On (20 minutes) variety of concrete • Project Digital Slide 8: My Pattern showing the first term in a growing/ materials (e.g., five shrinking pattern. and ten frames, colour • Explain that this is the first term in a geometric pattern. Have students turn and counters, connecting talk to a partner about what the next term in the geometric design could be. cubes, square tiles, • Ask students to share their ideas with the group. • Ask students some of the following prompts to help clarify/direct their thinking: pattern blocks, etc.), − How many red squares do you predict are in Term 2? Could there be BLM 4: My Pattern That another answer? Increases, BLM 5: My − What is the pattern rule? Can we tell what the pattern rule is from Term 1? Pattern That Decreases • Have students study the pattern and visualize that it starts at the right of the Time: 60 minutes page and progresses to the left of the page. Ask what type of pattern it is now and how the rule would change. BLM 5: My Pattern That Decreases • Together, decide on either a growing or a shrinking pattern to co-create. Name: Discuss what the pattern rule is. Ask students if there is another way to make My Pattern That DBecLreMas4es: My Pattern That Increases a pattern that increases/decreases. Draw your shrinking pattern: Working On It (20 minutes) Name: • Provide each student with a copy of BLM 4: My Pattern That Increases and a My Pattern That Increases Draw your growing pattern: copy of BLM 5: My Pattern That Decreases. Explain to students that they will be creating two different patterns on their own. In each case they need to describe Term Term Term Term the pattern, identify the pattern rule, and extend the pattern for 4 terms. Post this as Success Criteria using student-friendly language. Ask students if they Describe your pattern: have any questions. Ask what would help to make the problem clearer. Together, create an anchor chart of success criteria for the problem, for example: Term Term Term Term − I can describe my pattern. Describe your pattern: Patterns and Relations 41 What is your pattern rule? What is your pattern rule? 10 © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 Scholastic Canada GR3 BC Patterns & Relations 4th Pass Reproducibles November 9, 2021 © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 9 Scholastic Canada GR3 BC Patterns & Relations 4th Pass Reproducibles November 9, 2021

− I can identify the pattern rule. − I can extend my pattern for 4 terms. Differentiation • Some students will be more successful creating their patterns with concrete materials rather than redrawing them on their sheet. Be prepared to photograph their work digitally and provide them the opportunity to describe their pattern and the rule either on paper or orally. Assessment Opportunities Observations: Use a checklist to assess students’ ability to create, describe, 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. • Building Growth Mindsets: Have students complete a self-evaluation of their understanding of the success criteria for this task. (Use the Success Criteria in the Working On It section of this lesson.) • Collect student work to review. 42 Patterns & Relations/Data & Probability

6 7LessonsandInvestigating Patterns in Numbers Math Curricular Competencies Learning Standards • Reasoning and analyzing: Use reasoning to explore and make connections; Previous Experience estimate reasonably; develop mental math strategies and abilities to make with Concepts: sense of quantities Students have had experience identifying, • Understanding and solving: Visualize to explore mathematical concepts; describing, extending, and creating some develop and use multiple strategies to engage in problem solving increasing patterns when skip counting in grade 2. • 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: Reflect on mathematical thinking Content • Increasing and decreasing patterns • Pattern rules using words and numbers, based on concrete experiences • Addition and subtraction to 1000 • Multiplication and division concepts About the Patterns can be used to help students investigate number relationships. Due to our stable number system, many number patterns grow and shrink in a consistent manner, reflecting a repeating operation or a skip counting pattern. For example, patterns emerge as students skip count forward and backwards. Over time, they connect the rote counting they have recited to the patterns that emerge in visual representations of the counting such as hundred charts and number lines. They can visually see the repetition of an operation, such as addition (+5), subtraction (–5), or multiplication (doubling or ×2), which represents the pattern’s rule. Patterns that grow and shrink in a repetitive way can also be represented by geometric shapes, such as in the example below: 13 6 10 continued on next page Patterns and Relations 43

Math Vocabulary: Students can extend the patterns in visual representations by applying pesdraxheettrpcetieenrnerkadnait,n,,sggdirnr,eeogpisnw,rcceitrnersiebgrema,ens,,ting, their spatial reasoning skills. By physically adding another row each time with one additional object, they can describe the pattern as “add another row that has one more object than the row above it.” This is recursive thinking, which requires students to know what is in the previous row in order to continue the pattern. Eventually, students can generalize the pattern and create a rule that can determine the number of objects in any position in the pattern. About the Lessons The following two lessons offer review and build on students’ previous knowledge of patterns that grow or shrink due to repetition of an operation. Students investigate the repetitive operations of addition and subtraction, and connect them to various visual representations presented on hundred charts, calendars, and number lines. 44 Patterns & Relations/Data & Probability

6Lesson Patterns in a Hundred Chart Teacher Possible Learning Goals Look-Fors • Identifies patterns represented on a hundred chart • Describes how a pattern increases (grows) or decreases (shrinks), using the Materials: operations of addition, subtraction, or multiplication (e.g., you add 5 more “What’s My Rule?” each time, you double the number each time) (page 6 in Patterns, Relations, Data, and • Describes a variety of number patterns on the hundred chart involving Probability big book and little books), BLM 6: addition, subtraction, or multiplication Hundred Chart, coloured markers/pencils, variety • Extends a variety of number patterns on the hundred chart and explains their of white board markers for Consolidation reasoning Time: 55 minutes • Independently creates number patterns on the hundred chart and explains BLM 6: Hundred Chart their pattern rule using words and/or numbers 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 • Explains that a pattern results from a repeated operation (e.g., addition, 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 subtraction, multiplication) 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Minds On (15 minutes) 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 • Show the “What’s My Rule?” page in the big book, and direct students’ 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 attention to the calendar. Pose some of the following prompts: – What kind of chart is this? Why do we use it? What kind of pattern is this? 11 – Look at the coloured numbers (on the Saturdays). Turn and talk to your What is the starting number? partner about what pattern those numbers make. What rule can describe By how much does the pattern grow or shrink each time? the pattern? (add 7 each time) Why are you adding 7 every time? What What are all the numbers in the pattern? does the 7 represent? How can you describe the pattern if you start with What else do you notice about the pattern? the last number? (28) – Look at the other coloured numbers (on the diagonal). What pattern do © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 you see? What do you think the rule is? How do you know that adding 8 each time makes sense by looking at the visual pattern? Scholastic Canada GR3 BC Patterns & Relations 4th Pass Reproducibles • Draw attention to the hundred chart. Pose some of the following prompts: November 9, 2021 – What kind of a chart is this? How is it different from the calendar? – Look at the numbers circled in yellow. What do you know about the pattern? What do you think the pattern rule is? • Have students share their ideas. Discuss how the pattern can be increasing or decreasing, depending on the starting number. Ask students what they need to know in order to create this pattern (e.g., the starting number and how much the number is changing by). • Direct students’ attention back to the hundred chart and pose this prompt: – Look at the numbers that are in green squares in the hundred chart. What patterns do you see? Turn and talk to your partner. Patterns and Relations 45

Math Vocabulary: • Discuss students’ responses. Highlight how the pattern can be either increasing pesgsaxhruottrbetiwnetnrikrandnic,gn,t,gdido,aeendicsn,rdcmceirrtaiueiboslateniinsp,,iglni,cga,tion, doubling or decreasing, depending on the starting number. Have students clarify the pattern rules for each (e.g., for a growing pattern, start at 5 and add 3 each time). Working On It (20 minutes) • Students work in pairs. Give each pair a copy of BLM 6: Hundred Chart. Explain that they are going to create two different patterns of their choice on the hundred chart and represent each one with a different colour. They can also answer questions that are written at the bottom of the BLM. Encourage them to be creative. Differentiation • Some students may benefit from having a separate BLM page for each of their patterns so the visual representations are more obvious and less confusing. Assessment Opportunities Observations: Pay attention to how students are counting from one number to the next in the pattern: – Do they need to count from one number to the next each time or do they use the patterns inherent in the chart to help them? Conversations: Pose some of the following prompts if students are counting out the change each time: – What is your starting number? (4) – How much are you increasing by each time? (5) – What are the next three numbers? (9, 14, and 19) – What do you notice about the numbers in the ones columns? (e.g., They are all 4 and 9.) – How can this pattern help you identify the next numbers in the hundred chart? – Why does it make sense that the third number in your pattern also ends in a 4? (e.g., two jumps of 5 would be 10 and 14 is 10 more than 4) Consolidation (20 minutes) • Students can meet with another pair and take turns showing their patterns and having the other pair guess the pattern rule, including the starting number and the way the pattern increases or decreases. • Meet as a class. Discuss two or three of the patterns. • Circle 3 and tell them that the rule is ‘increase by 3’ each time. Ask what they think the tenth number in the pattern will be and why they think so. Skip count by 3 to find the tenth term. Ask how they could represent this using multiplication (3 × 10 = 30). Ask what the seventh number in the pattern would be and how they could represent it using multiplication (3 × 7 = 21). Count to the seventh term to confirm that their prediction is correct. 46 Patterns & Relations/Data & Probability

Materials: Further Practice two different coloured • Hundred Chart Pattern Game dice (one for a pattern that increases; one for a Instructions: pattern that decreases), – Each player gets a hundred chart (BLM 6), which is their gameboard. The a deck of cards with goal of the game is to cover the entire hundred chart by making different numbers 1–100, several patterns. Decide if students will play as a whole class, in small groups, transparent coloured or in pairs. (You might also provide a giant hundred chart for your class. counters, BLM 6: Make the chart on a plastic shower curtain, if you do not have a mat.) Hundred Chart – The deck of 100 numbers will be the starting point for each pattern. One coloured die represents a growing pattern, and the other coloured die BLM 6: Hundred Chart represents a shrinking pattern. 1 2 3 4 5 6 7 8 9 10 – The first player/team chooses a card from the deck of 100 cards. This 11 12 13 14 15 16 17 18 19 20 is the starting point for their pattern. They choose which die to roll, 21 22 23 24 25 26 27 28 29 30 indicating whether they are going to create a growing or shrinking 31 32 33 34 35 36 37 38 39 40 pattern. The first player/team rolls the die, which indicates how the 41 42 43 44 45 46 47 48 49 50 pattern changes. They place transparent counters on the pattern. 51 52 53 54 55 56 57 58 59 60 – The next player/team takes their turn, thinking of how they can create 61 62 63 64 65 66 67 68 69 70 a pattern that will cover different numbers. 71 72 73 74 75 76 77 78 79 80 – The game continues until one player/team has covered all or most of their 81 82 83 84 85 86 87 88 89 90 game board. 91 92 93 94 95 96 97 98 99 100 What kind of pattern is this? 11 What is the starting number? By how much does the pattern grow or shrink each time? What are all the numbers in the pattern? What else do you notice about the pattern? © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 Scholastic Canada GR3 BC Patterns & Relations 4th Pass Reproducibles November 9, 2021 Materials: Math Talk: Digital Slide 9: Hundred Chart Math Focus: Investigating patterns that involve multiplication 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Let’s Talk 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 • Let’s count by 2s aloud to 100. 41 42 43 44 45 46 47 48 49 50 • What would this pattern look like on our hundred chart? (e.g., it’s every other 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 number in each row, the columns with even numbers, every other column, etc.) 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 • What is the rule? (add 2 each time) 91 92 93 94 95 96 97 98 99 100 • What is the seventh term in this pattern? How do you know? (e.g., 14, we counted Scholastic Canada GR3 BC Patterns & Relations Slide 9: 3rd Pass by 2 seven times to 14) Digital Slides November 9, 2021 Hundred • How could you figure this out without having to count out each number? Turn Digital and talk to a partner. Chart, several colours • What did you find? (e.g., We can multiply the term number by 2 so 7 × 2 = 14.) of whiteboard This is a good conjecture, but we need to know whether it will work with all numbers. Try out a couple of numbers with your partner. markers • Let’s try some of your suggestions. Does it seem to work every time? So, this can Teaching Tip be a rule if we start from 0 and our first count is the first term. Integrate the math talk moves (see page 8) • Can this be a rule for whenever we count by 2s? throughout Math Talks to maximize student continued on next page participation and active listening. Patterns and Relations 47

• How would the counting by 2 pattern look different if I started at 1? (e.g., It would still be every second number but it would be 1, 3, 5, 7,…) • Would our rule work with this pattern? Try it with a partner. • What did you find? (It didn’t work because the correct number in the pattern was one greater because we started at 1.) • How could we write a rule that would take this into account? (e.g., We could add 1 after multiplying.) • So, the rule would look like the term number × 2 + 1. Try a couple of numbers to see if this works. • When we make a conjecture, we need to make sure that we try it out in many ways to make sure it works. In this case, we were multiplying by 2 each time, but the starting number made a difference. 48 Patterns & Relations/Data & Probability

7Lesson Patterns in a Number Line Teacher Possible Learning Goals Look-Fors • Identifies patterns represented on a number line • Describes how a pattern grows or shrinks using the operations of addition, Materials: subtraction, or multiplication (e.g., you add 5 more each time, you double the Digital Slide 10: Number Lines number each time) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 • Extends patterns represented on a number line 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 • Identifies the starting point for each number pattern, located on the number line Scholastic Canada GR3 BC Patterns & Relations 3rd Pass • Describes the rule for finding the next number Digital Slides • Identifies and describes the repeating operation November 9, 2021 • Extends the pattern by applying the rule • Moves in the appropriate direction on the number line, depending on the “What’s My Rule?” operation (page 6 in Patterns, Minds On (15 minutes) Relations, Data, and • Show students page 6 of the big book and direct students’ attention to the Probability big book and number line. little books), BLM 7: • Ask what features they notice on the number line (e.g., one end point is 0 and Number Line Patterns, the other end point is 21; the numbers increase by 1). Digital Slide 10: Number • Ask what type of pattern is represented on the number line (e.g., the pattern Lines, BLM 8: Number starts at 0 and increases by 3 each time). Lines • Ask students if they agree (e.g., no, I think it is a shrinking pattern that starts Time: 55 minutes at 21 and decreases by 3 each time until reaching 0). Scholastic Canada GR3 BC Patterns & Relations 18 © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 Scholastic Canada GR3 BC Patterns & RelationsBLM 8: Number Lines12 © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 Reproducibles Reproducibles • Discuss why both answers are correct. Ask how they could make it clear on November 9, 2021 November 9, 2021 BLM 7: Number Line Patterns a number line whether the pattern is growing or shrinking (e.g., use arrows 4th Pass 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 that proceed in the proper direction for each jump). 22222 4th Pass • Ask students what the next two numbers in this pattern would be if the 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 pattern is increasing or growing, and how they know. Ask what operation 3333 repeats in this pattern (addition). Ask what pattern repeats if it is a pattern 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 that is decreasing or shrinking (e.g., subtraction). 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 • Discuss why the numbers highlighted in the pattern are the same in the two 22222 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 patterns (e.g., addition and subtraction are opposite operations that undo each other). 3333 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Working On It (20 minutes) • Co-create an anchor chart of questions that students can think about as they analyze patterns represented on various number lines. Patterns and Relations 49

Math Vocabulary: • Below are some suggested questions: pesgsaxhruottrbetiwnetnrikrandnic,gn,t,gdido,aeendicsn,rdcmceirrtaiueiboslateniinsp,,iglni,cga,tion, doubling – Is this pattern growing or shrinking? How do I know? – What is my starting number? How do I know? – How much will I add/subtract each time? How do I know? – What numbers in my pattern do I know? – What are the next two numbers in my pattern? • Students work in pairs. Give students some of the patterns that are represented on number lines on the pages of BLM 7. (You may wish to cut out the number line patterns for students to choose.) They can use the above questions to analyze the patterns. They identify the starting point and the rule and extend the pattern by adding the next two numbers. • When finished their task, students can create their own number pattern on a blank number line up to 20 (see BLM 8: Number Lines). Differentiation • Select the patterns that best meet the individual needs of your students. • You may decide to create number lines that deal with larger numbers and larger intervals of addition and subtraction. • For students who need more of a challenge, have them create their own pattern and choose their own endpoints and pattern rule. They can also use an open number line so larger numbers can be represented. Assessment Opportunities Observations: Note whether students understand the features of a number line and can represent patterns on them: – Can students identify the starting number? – Do they count the spacing on the intervals accurately or are they counting the number they are starting on? – Do they represent their intervals with arrows to indicate how the pattern is proceeding? – Do they skip count or do they count each number? – Do they recognize the repeating operation by the direction in which the pattern proceeds? Conversations: Pose some of the following prompts if students are struggling: – What is your starting number? – Is your pattern growing or shrinking? How do you know? – By how much does your pattern grow/shrink each time? – How do you know that the numbers in your pattern are correct? Show me. – Describe your pattern on the number line. 50 Patterns & Relations/Data & Probability

Materials: Consolidation (20 minutes) Digital Slide 12: Number Lines • Students can meet with another pair. They can take turns showing the pattern Digital Slide 11: Number Lines they created on the number line and guess each other’s rules. 0 10 20 30 40 50 60 70 80 90 100 0 5 10 15 20 25 30 35 40 45 50 • Meet as a class. Strategically select some number lines to discuss based on 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 your observations as students were working. 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 • Ensure that students know how to move properly on the number line and Scholastic Canada GR3 BC Patterns & Relations 3rd Pass Digital Slides completely describe the pattern rule, including the starting number and the November 9, 2021 repeating operations. Scholastic Canada GR3 BC Patterns & Relations 11 3rd Pass • Project Digital Slide 10. Draw on a number pattern and have students identify Digital Slides November 9, 2021 and the rule. Alternatively, describe the rule and have students record the pattern on the number lines. Digital Slides Further Practice • Repeat this lesson using number lines with larger numbers. You can use Digital Slides 11 and 12 or you can create other number lines that extend up to 1000. Reinforce counting by 50s, 100s, and 200s. • Reflecting in Math Journals: Have students paste their number line pattern into their journal. Have them answer the questions from the co-created anchor chart in their journal about their pattern. 12: Number Lines Patterns and Relations 51

8 9Lessonsand Creating and Extending Number Patterns Math Curricular Competencies Learning Standards • Reasoning and analyzing: Use reasoning to explore and make connections; Previous Experience estimate reasonably; develop mental math strategies and abilities to make with Concepts: sense of quantities Students have had experience identifying, • Understanding and solving: Develop, demonstrate, and apply mathematical describing, extending, and creating a variety of understanding through play, inquiry, and problem solving; visualize to explore growing and shrinking mathematical concepts; develop and use multiple strategies to engage in patterns using concrete problem solving objects and operations (e.g., addition, subtraction, • Communicating and representing: Communicate mathematical thinking multiplication). in many ways; explain and justify mathematical ideas and decisions; represent mathematical ideas in concrete, pictorial, and symbolic forms • Connecting and reflecting: Reflect on mathematical thinking Content • Increasing and decreasing patterns • Pattern rules using words and numbers, based on concrete experiences • Addition and subtraction concepts to 1000 • Multiplication and division concepts MnscuhraemrtiahnbtkeeVi,rnongpcu,aametbtxuebtlreeanrnr,ydlig:n,reowing, About the Students can create patterns by following a given pattern rule and extending it, or by creating their own pattern and establishing their own rule. Marian Small cautions that sometimes when students are extending a pattern “there is ambiguity in terms of what you expect and what students understand or perceive” (Small, 2009, p. 571). It is important to listen to students’ explanations in order to understand how they interpreted the rule. These are good opportunities to have class discussions about what students are thinking and clear up any misconceptions. Students also learn what needs to be included in a pattern rule so there is no ambiguity. As students create their own patterns, you can evoke deeper thinking by giving them criteria to include in their pattern. It also allows you to differentiate instruction and target certain concepts that need further reinforcement. About the Lessons In the next two lessons, students create number patterns from given pattern rules and create their own patterns using a variety of representations. 52 Patterns & Relations/Data & Probability

8Lesson Creating Number Patterns from a Rule Teacher Possible Learning Goals Look-Fors • Creates number patterns when given a pattern rule described in words • Identifies and describes the repeating operation in the pattern Materials: • Follows a given rule to create and extend number patterns Digital Slide 15: Pattern Rule (3) • Recognizes patterns that increase and involve repeated addition and patterns Digital Slide 14: Pattern Rule (2) that decrease and involve repeated subtraction Digital Slide 13: Pattern Rule (1) Minds On (20 minutes) Start at 12, add 5 each time Start at 37, subtract 3 each time • Have students visualize a pattern that increases by 4 every time. They can turn Start at 0, add 4 each time and talk to a partner about what the pattern could be. Scholastic Canada GR3 BC Patterns & Relations 3rd Pass • Discuss students’ responses. Ask whether it can be represented by something Digital Slides November 9, 2021 other than numbers (e.g., 4 tiles, 8 tiles, 12 tiles, etc.). Ask how the geometric pattern can grow (e.g., up, down, to the right, to the left). Have students Scholastic Canada GR3 BC Patterns & Relations 3rd Pass demonstrate their ideas using tiles. Digital Slides November 9, 2021 • Show students the number pattern 2, 6, 10, 14…, and ask them whether Scholastic Canada GR3 BC Patterns & Relations 3rd Pass it follows the given rule. Ask whether 5 tiles, 9 tiles, and 13 tiles can also Digital Slides represent the rule. 13–16: Digital SlidesNovember9,2021 • Ask how else the pattern rule “increase by 4 every time” might be represented Pattern Rule (1–4), (e.g., using different concrete materials, sounds, etc.). BLM 9: Pattern Rules • Show students the pattern rule on Digital Slide 13. Ask whether this pattern and Number Patterns, rule can result in more than one pattern. Discuss how it is important to include the starting number in any number pattern. Ask what else is BLM 10: Pattern Rules, important to include in a rule. concrete objects or • Show students Digital Slide 14. Students can turn and talk to a partner about tools (e.g., hundred what kind of pattern the rule creates and what the first four numbers would be. charts, number lines) • Discuss their answers and show the pattern on a number line and on the Time: 60 minutes hundred chart. © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 BLM 10: Pattern Rules • If necessary, repeat this process with Digital Slides 15 and 16. Scholastic Canada GR3 BC Patterns & Relations Start at 0, add 7 Start at 0, add 12 Start at 55, subtract 10 Start at 72, subtract 10 Working On It (20 minutes) Reproducibles Start at 12, add 5 BLM 9: Pattern Rules and Number Patterns November 9, 2021 Start at 23, add 10 22 © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 • Explain to students that they will be creating patterns from a given rule. Start at 17, add 9 Scholastic Canada GR3 BC Patterns & Relations Start at 12S, taadrtda7t 0, add 3Start at 67, s3u,b6t,ra9c, t152, 15 …Start at 75S,tasrutbattra5c5t,5subtract 5 55, 50, 45, 40 … • Distribute one pre-cut card from BLM 9: Pattern Rules and Number Patterns Start at 7, add 8 Reproducibles Start at 34, add 5 November 9, 2021 Start at 13, add 5 Start at 72, subtract 8 Start at 56, subtract 8 to each student. Ensure that you have matching cards, one with the rule and Start at 12, add 2 12, 14, 16, 18 … Start at 67, subtract 2 67, 65, 63, 61 … one with the pattern. Explain that they will find a partner by discovering who has a card that matches their card (e.g., one student has the rule, and one Start at 4S5,taardt dat523, add S5tart at 17, s2u3b, t2ra8c, t313, 38 …Start at 24S,tasrutbattra7c2t,1subtract 4 72, 68, 64, 62 … student has the matching number pattern). 4th Pass Start at 37S,taardtda3t 17, add S4tart at 35, s1u7,b2tr1a,c2t 58, 29 …Start at 72S,tasrutbatrta1c7t, 8subtract 3 17, 14, 11, 8 … Start at ?, add ? Start at 42, subtract 9 Start at ?, subtract ? 4th Pass Start at 7, add 6 7, 13, 19, 25 … Start at 35, subtract 6 35, 49, 43, 37 … 23 Start at 34, add 2 34, 36, 38, 40 … Start at 49, subtract 7 49, 42, 35, 28 … Patterns and Relations 53

• Once students have found their partner, give each pair two rules, including one that involves addition and one that involves subtraction, from BLM 10: Pattern Rules. • Together, the partners create the patterns. They can represent them in any way they like and use any concrete objects or tools (e.g., number lines, hundred charts). • When they are finished, students can also create their own pattern rule and represent it in a variety of ways. Differentiation • Select the rules that best meet the needs of your students. • Some students may need more experience with creating number patterns. Meet with these students in a small group. Start with simple patterns that start at 0 and connect pattern creation to the idea of skip counting. • For students who need more of a challenge, have them represent their rules in more than one way. • Students can also create their own rules and then represent their patterns. Assessment Opportunities Observations: Pay attention to how students follow the rules to create their pattern: – Do they recognize where the pattern starts? – Do they understand whether the pattern is growing or shrinking? – Can they explain or show the way in which the pattern is consistently increasing/decreasing? Conversations: Pose some of the following prompts if students are struggling: – Is the pattern you are working on growing or shrinking? How do you know? – How did you know which number to use to begin your pattern? – How much is your pattern growing/shrinking by? How do you know? – How many terms will your pattern have? Could you show me what the tenth term would be? Consolidation (20 minutes) • Have students meet with another pair. They can take turns guessing the rule by looking at the representations. They can also give each other the problem they created and have the partners create the pattern. • Meet as a class. Co-create an anchor chart about what is important to include when creating a pattern rule. 54 Patterns & Relations/Data & Probability

Further Practice • Independent Practice in Math Journals: Ask students to choose two or three rules and create the pattern in their journal: – start at 0, add 7 each time – start at 15, add 7 each time – start at 100, subtract 3 each time – start at 71, subtract 3 each time – create your own rule, switch with a partner, and create a pattern with their rule Patterns and Relations 55

9Lesson Translating Number Patterns Teacher Possible Learning Goal Look-Fors • Translates a number pattern given on a number line and explains how the two Materials: patterns have the same structure Digital Slide 21: What’s My Pattern? What’s My Rule? (3) • Identifies and describes patterns on a number line • Describes the pattern rule by including the starting point and the way in which Digital Slide 20: What’s My Pattern? What’s My Rule? (2) it is changing Digital Slide 19: What’s My Pattern? What’s My Rule? (1) • Translates the pattern on a number line into a number pattern Digital Slide 18: Number Pattern Rule (2) • Creates patterns using self-generated rules What is missing in this pattern? What is the rule for this pattern? Digital Slide 17: Numbe6r5,Pattern, 5R1u,l4e4(,1) , 30 Minds On (15 minutes) Which number pattern shows a rule that shows62a c6h3ange of 5 each time? • Use Digital Slides 17–18 to review how to create a number pattern from 25 26 A + 14 given rules. Each slide shows a multiple-choice question. For each slide, A3 7B, 12, 17, 22–…14 have students turn and talk to a partner and then discuss which choice(s) best answer the question. Encourage them to prove that the other potential B 7C, 11, 15, 19…+ 7 answers do not follow the rules. Scholastic Canada C 77D, 72, 67, 62–…7 • While discussing Digital Slide 17, highlight why there can be more than one Digital Slides GR3 BC Patterns & Relations 3rd Pass November 9, 2021 correct answer. (e.g., The rule does not specify the beginning number; the rule D does not indicate whether the pattern is growing or shrinking.) 77, 82, 87, 92… 3rd Pass • Repeat this process with Digital Slide 18. Scholastic Canada GR3 BC Patterns & Relations • Show students Digital Slide 19 and have them turn and talk to a partner to Digital Slides November 9, 2021 discuss what the pattern is and what the rule is. Share their responses as a class (e.g., for pattern 3, 7, 11, 15, the rule is “start at 3 and add 4”). Scholastic Canada GR3 BC Patterns & Relations 3rd Pass Digital Slides • Ask students if they can create another pattern that changes by 4. Discuss November 9, 2021 their responses (e.g., patterns that grow or shrink and that start at different Scholastic Canada GR3 BC Patterns & Relations 3rd Pass numbers). Digital Slides November 9, 2021 • Ask what would be the same about the appearance of the pattern on the number Scholastic Canada GR3 BC Patterns & Relations 3rd Pass line (e.g., the intervals would all be 4) and the differences (e.g., the direction on Digital Slides the number line, the starting number, and the numbers in the pattern). glue, Digital chart paper,November9,2021 • If necessary, repeat this line of questioning with Digital Slides 20 and 21. Slides 17–18: Number Working On It (15 minutes) Pattern Rule (1–2), Digital • Students work in pairs. Cut out and give each pair one or two of the number Slides 19–21: What’s My lines from BLM 11 and a piece of chart paper. Pattern? What’s My Rule? • Have students (1) glue their number line on the paper, (2) identify the pattern (1–3); BLM 8: Number and extend it, (3) identify the rule, (4) and create another pattern that changes by the same amount. Lines, BLM 11: What Is the Pattern? What Is the Rule? Time: 50 minutes Scholastic Canada GR3 BC Patterns & Relations BLM 11: What Is the Pattern? What Is the Rule? Reproducibles Scholastic Canada GR3 BC Patterns & Relations November 9, 2021 13 14 13 14 BLM 8: Number Lines continued © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 Reproducibles 24 © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 November 9, 2021 Scholastic Canada GR3 BC Patterns & Relations 20 21 November 9, 2021 Scholastic Canada BLM 8: Number Lines continued Reproducibles Reproducibles 21 22 November 9, 2021 20 © 2022 Scholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 G©R320B2C2 PSacthteorlnasst&icRCelaantiaodnas Ltd. GRADE 3 BC: PATTERNS AND RELATION4St/hDAPTAasANsD PROBABILITY 0 2 4 BLM68: Num8ber Lin10es contin12ued 14 16 18 20 76 77 16 17 0 18Novemb©er290,2220S21cholastic Canada Ltd. GRADE 3 BC: PATTERNS AND RELATIONS/DATA AND PROBABILITY ISBN 978-1-4430-7299-1 Scholastic Canada GR3 BC Patterns & Relations10 20 30 40 BL50M 8: N6u0 mber L70 ines 80 90 100 12 13 Reproducibles 12 32 33 41 42 4th Pass 0 5 10 15 20 25 30 35 40 45 50 54 55 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 31 32 4th Pass 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 21 ISBN 978-1-4430-7299-1 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 4th Pass 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 4th Pass 19 56 Patterns & Relations/Data & Probability