<p>Students will create shape patterns. Students will:&nbsp;<br>- create shape patterns based on a rule and the description/drawing of the first element in the pattern.&nbsp;<br>- identify the obvious features of shape patterns.&nbsp;</p>

<p>- How may data be arranged and represented to reveal the link between quantities?<br>- How can mathematics help us communicate more effectively?&nbsp;<br>- How may patterns be used to describe mathematical relationships?&nbsp;<br>- How can probability and data analysis be used to make predictions?&nbsp;<br>- How may detecting repetition or regularity assist in solving problems more efficiently?<br>- How can mathematics help to quantify, compare, depict, and model numbers?&nbsp;</p>

<p>- Factor: The number or variable multiplied in a multiplication expression.&nbsp;<br>- Multiple: A number that is the product of a given integer and another integer (e.g., 6 and 9 are multiples of 3).&nbsp;<br>- Patterns: Regularities in situations such as those in nature, events, shapes, designs, and sets of numbers (e.g., spirals on pineapples, geometric designs in quilts, the number sequence 3, 6, 9, 12, . . .).</p>

<p>- one copy of Shape Pattern Examples (M-4-6-2_Shape Pattern Examples and KEY) for each student&nbsp;<br>- one copy of Modeling and Representing Shape Patterns (M-4-6-2_Modeling and Representing Shape Patterns) for each student&nbsp;<br>- one copy of the Lesson 2 Exit Ticket (M-4-6-2_Lesson 2 Exit Ticket and KEY) for each student&nbsp;<br>- copies of the Small Group Practice worksheet (M-4-6-2_Small Group Practice and KEY) as needed&nbsp;<br>- copies of Expansion Work (M-4-6-2_Expansion Work and KEY) as needed</p>

<p>- Use the Write-Pair-Share activity to examine students' understanding of shape patterns.&nbsp;<br>- During the Group Activity, assess students' comprehension levels of lesson concepts.&nbsp;<br>- Use the Matching Game to measure students' ability to create shape patterns, follow rules, and recognize patterns.&nbsp;<br>- Use the Lesson 2 Exit Ticket to quickly evaluate student mastery.&nbsp;</p>

<p>Scaffolding, Active Engagement, Metacognition, Modeling, Explicit Instruction, and Formative Assessment&nbsp;<br>W: Students will develop shape patterns based on a rule and a description or drawing of the initial element. Students will also identify the patterns' features, or attributes.&nbsp;<br>H: Students will engage with the lesson by brainstorming instances of shape patterns. The Write-Pair-Share activity enables students to get a conceptual knowledge of a shape pattern.&nbsp;<br>E: Students will brainstorm examples of shape patterns. Students will then get experience and exposure to more patterns by going through examples that provide rules, descriptions/drawings of first elements, and requests the development of shape patterns. Finally, students will get the option to engage in a matching game in which they will develop rules, descriptions/drawings of the first elements, and the final shape patterns, as well as detect pattern aspects.&nbsp;<br>R: The Write-Pair-Share activity provides an opportunity for discussion at the start of the class. Throughout the class, students will discuss ideas with their peers, prompting them to reconsider and revise their understanding. The matching game will also allow students to develop their own rules, basic elements, and shape patterns while examining their aspects.&nbsp;<br>E: Observation during the Write-Pair-Share activity can assess students' understanding. The Lesson 2 Exit Ticket will also help assess students' degree of concept mastery.&nbsp;<br>T: Use the Extension option to customize the lesson to match the needs of the student. The Routine section includes ideas for reviewing lesson throughout the year. The Small Groups section offers additional practice and instruction recommendations for those who could benefit from it. The Expansion part is meant for students who are willing to go above and beyond the requirements of the standard.&nbsp;<br>O: The lesson is structured to help students gain a conceptual knowledge of shape patterns. They'll then make shape patterns. Students will also recognize characteristics of shape patterns that are not expressly stated in the rules. This lesson focuses only on shape patterns.&nbsp;</p>

<h3><strong>Part 1: Introduction</strong></h3><p><strong>Write-Pair-Share Activity</strong><br><br>Ask students to give examples of shape patterns. Examples may include drawings and/or models of shape patterns. Give students three minutes for creating examples. Then, ask each student to share his/her examples with a partner. After about 5 minutes, the class should reconvene. One student from each group should present the examples to the class. Students should use this time to discuss, argue, and ask questions.&nbsp;<br><br>After students have brainstormed some examples, give them a reference handout on shape patterns (M-4-6-2_Shape Pattern Examples and KEY).<br><br><strong>"Check out the first pattern on the handout. Can you describe the pattern and tell us what shape will follow next?"</strong> (<i>The pattern alternates between two shapes: square, triangle, square, triangle, ... The following shape in the pattern would be a square.</i>)<strong> "Check out the second shape pattern. Explain the pattern and tell us what shape will appear next."</strong> (<i>Each shape adds a row to the right side with one more box than the preceding row, resulting in a pattern of adding 3, 4, 5, 6, etc.</i>)&nbsp;<br><br>Continue asking similar questions throughout the remaining Shape Pattern Examples. Ask students to fill out the column explaining why each example reflects a pattern. This reference sheet can also be shared to the class website.</p><h3><strong>Part 2: Generate Shape Patterns</strong></h3><p>After students have produced and evaluated examples of shape patterns, begin instruction by asking them to generate such patterns using the rules and first elements provided. Students will then examine the patterns' features.<br><br><strong>Group Activity</strong><br><br>Divide students into groups of three to four. Give students a copy of the Modeling and Representing Shape Patterns material (M-4-6-2_Modeling and Representing Shape Patterns). Each student should get six recording sheets.&nbsp;<br><br>(Note: You may want to look through additional examples. These six examples are simply samples.)&nbsp;<br><br>Students will work in groups, however each student should model on their own recording sheet while also making recording on it.<br>Directions: Students will model the shape pattern using the provided rule and describe/draw the first element in the pattern. Tangram pieces can be used for modeling purposes. Each element of the shape pattern will be modeled in a separate frame. Students will model each element within the mat's open space and in each frame of the recording sheet. Students may choose to create each diagram in the open space as well. Students will then identify the pattern's features. All of this information will be written on each recording sheet.<br><br>(Note: Encourage students to discuss and debate with their peers during group time. For Examples 3-6, you may use fewer scaffolded questions. Allow students to work through the examples with their group members before the whole-class discussion. Once students understand how to complete the sheet, it is critical that they have some initial discovery time for the next examples. Complete the projected sheet with students as each section is discussed. Following the presentation of samples, students will have the option to work on generating more shape patterns.)<br><br><strong>Example 1:</strong><br>Starting shape: <img src="https://storage.googleapis.com/worksheetzone/images/Screenshot_52.png" width="34" height="34"><br>Rule: Attach 1 square to the right side.<br><strong>"With this information, we can design a shape pattern. The first drawing is a square. Let's draw that in the first column. The rule is 'Attach 1 square to the right side.' How will we present this in the second column?"</strong> <img src="https://storage.googleapis.com/worksheetzone/images/Screenshot_53.png" width="60" height="33"> <strong>"Can anyone explain how s/he made the shape pattern in the second column?"</strong> (<i>I drew the first square. Then I added another square to the right side.</i>) <strong>"Finish the third, fourth, and fifth columns. When you're finished, compare and explain your answers to your partner."</strong> (<i>The third square will be added to the right side of the third frame, the fourth square to the fourth frame, and the fifth square to the fifth frame.</i>)<br><br>A correct drawing of pattern is presented below:<br><br><img src="https://storage.googleapis.com/worksheetzone/images/Screenshot_54.png" width="534" height="48"><br><strong>"What other observations can we make about this pattern?"</strong> (<i>The line of squares increases by 1. The perimeter increases by 2. The area increases by 1.</i>)<br><br><strong>Example 2:</strong><br>Starting shape: <img src="https://storage.googleapis.com/worksheetzone/images/Screenshot_52.png" width="34" height="34"><br>Rule: Add a triangle and a square next to the last shape.<br><strong>"Let's begin by drawing the first shape and writing the rule at the top of the paper. How can we model the pattern with the rule?"</strong> (<i>Place a square in the first column, followed by a triangle and another square in the second column, and so on.</i>)&nbsp;<br><br>A correct drawing of the pattern is presented below:<br><br><img src="https://storage.googleapis.com/worksheetzone/images/Screenshot_55.png" width="642" height="120"><br><br><strong>"What do you notice about the shape pattern?"</strong> (<i>There are an odd number of shapes in each frame. The pattern includes 1 shape in the first frame, 3 shapes in the second, 5 shapes in the third, 7 shapes in the fourth, and 9 shapes in the fifth. Additionally, every odd shape is a square, and every even shape is a triangle.</i>)<br><br><strong>Example 3:</strong><br>Starting shape: <img src="https://storage.googleapis.com/worksheetzone/images/Screenshot_56.png" width="66" height="75"><br><br>Rule: Add 1 square to the height and 2 squares to the length.<br><strong>"How would the second element look like? How will the first element change? What will the remaining frames show?"&nbsp;</strong><br><br>The pattern can be correctly drawn as follows:<br><br><img src="https://storage.googleapis.com/worksheetzone/images/Screenshot_57.png" width="595" height="314"><br><br><strong>"What do you notice about this shape pattern?"</strong> (<i>The area of each shape is a multiple of 3. The number of squares alternated between odd and even. Another element of the design is the perimeter increases by 6.</i>)<br><br><strong>Example 4</strong><br>Starting shape: <img src="https://storage.googleapis.com/worksheetzone/images/Screenshot_52.png" width="34" height="34"><br>Rule: Increase each side length of the figure by 1 square.<br><strong>"How would the second element look like? How will the first element change? What will the remaining frames show?"&nbsp;</strong><br><br>The pattern can be correctly drawn as follows:<br><br><img src="https://storage.googleapis.com/worksheetzone/images/Screenshot_58.png" width="633" height="162"><br><br><strong>"What do you notice about this shape pattern?"</strong> (<i>The perimeter increases by 4. The previous shape will fit into the corner of the current shape.</i>)<br><br><strong>Example 5</strong><br>Starting shape: <img src="https://storage.googleapis.com/worksheetzone/images/Screenshot_59.png" width="97" height="103"><br>Rule: Increase the number of shaded squares in the middle of the figure by 1. Be sure to maintain a border of unshaded squares.&nbsp;<br><strong>"How would the second element look like? What will the remaining frames show?"&nbsp;</strong><br><br>The pattern can be correctly drawn as follows:<br><br><img src="https://storage.googleapis.com/worksheetzone/images/Screenshot_60.png" width="456" height="219"><br><br><strong>"What do you notice about this shape pattern?"</strong> (<i>The circumference of the entire shape increases by 2. The area of the entire shape increases by 3.</i>)<br><br><strong>Example 6</strong><br>Starting shape: <img src="https://storage.googleapis.com/worksheetzone/images/Screenshot_61.png" width="52" height="52"><br>Rule: Add 1 isosceles triangle with a leg attached to the right edge of the previous shape.&nbsp;<br><strong>"How would the second element look like? What will the remaining frames show?"&nbsp;</strong><br><br>The pattern can be correctly drawn as follows:<br><br><img src="https://storage.googleapis.com/worksheetzone/images/Screenshot_62.png" width="635" height="60"><br><br><strong>"What do you notice about this shape pattern?"</strong> (<i>When you add triangles, the pattern changes to parallelogram, trapezoid, parallelogram, trapezoid, etc.</i>)<br><br><strong>Matching Game</strong><br><br>Have students find a partner. Ask each student to make four cards, each with a rule and a description/drawing of the first element in the shape pattern. Students will next make four more cards, each including one of the geometric patterns. Each partner will attempt to match the rules and the first element with the matching pattern. Encourage students to use different shapes.&nbsp;<br><br>Students should complete the Lesson 2 Exit Ticket (M-4-6-2_Lesson 2 Exit Ticket and KEY) at the end of the lesson to assess their level of understanding.<br><br><strong>Extension:</strong><br><br><strong>Routine:</strong> Throughout the school year, ask students to recognize patterns in real-world environments, such as tiles/ceilings and signs. Encourage students to use building blocks to create patterns and then study their characteristics. When learning about perimeter, students can explore and compare the perimeters of various shape patterns.&nbsp;</p><p><strong>Small Groups:</strong> Students who require further practice may be assigned to small groups to work on the Small Group Practice (M-4-6-2_Small Group Practice and KEY). Students can work on it together or independently, and then compare their results.&nbsp;</p><p><strong>Expansion:</strong> Students who are prepared for a challenge beyond the standard's criteria may be assigned the Expansion Work worksheet (M-4-6-2_Expansion Work and KEY). The worksheet provides several open-ended questions about shape patterns.</p>