• Use the Write-Pair-Share activity to preassess students’ knowledge of shape patterns.
• Observe during the Group Activity to determine students’ comprehension levels of lesson concepts.
• Use the Matching Game to assess students’ fluency with shape pattern creation, rule following, and pattern recognition.
• Use the Lesson 2 Exit Ticket to quickly evaluate students’ mastery.

Part 1: Introduction

Write-Pair-Share Activity

Ask students to provide examples of shape patterns. The examples may consist of drawings and/or models of shape patterns. Give students 3 minutes to create the examples. Then, have each student share his/her examples with a partner. After about 5 minutes, the class should reconvene. One member from each group should share the examples with the class. Students should discuss, debate, and ask questions during this time.

After students have brainstormed some examples, provide them with a reference handout for shape patterns (M-4-6-2_Shape Pattern Examples and KEY.docx).

“Look at the first pattern on the handout. Can someone explain the pattern and tell us what shape would come next?” (The pattern alternates between two shapes: square, triangle, square, triangle, . . . The next shape in the pattern would be a square.) “Look at the second shape pattern. Explain the pattern and tell us what shape would come next.” (Each shape adds a row to the right side that has one more box than the previous row, so the pattern is
add 3, add 4, add 5, add 6, . . .)

Continue similar questioning through the rest of the Shape Pattern Examples. Ask students to complete the column that explains why each example represents a pattern. This reference sheet may also be uploaded to the class website.

Part 2: Generate Shape Patterns

Once students have created and reviewed examples of shape patterns, begin instruction that asks students to use given rules and first elements to generate such patterns. Students will then observe features of the patterns.

Group Activity

Arrange students in groups of three to four. Provide students with copies of the Modeling and representing Shape Patterns resource (M-4-6-2_Modeling and Representing Shape Patterns.docx). Each student should receive six recording sheets.

(Note: You may wish to go through more examples. These six examples are simply samples.)

Students will work together in groups, but students should perform modeling on their own recording sheet, while also making their recordings on the sheet.

Directions: Students will model the shape pattern using the given rule and description/drawing of the first element in the pattern. Tangram pieces may be used for modeling purposes. Each element of the shape pattern will be modeled in a different frame. Students will model each element, within the open space of the mat, in each frame of the recording sheet. Students may wish to draw each diagram in the open space as well. Students will then identify features of the pattern. All of this information will be written on each recording sheet.

(Note: Encourage students to discuss and debate with their peers during the group time. For Examples 3–6, you may provide fewer scaffolded questions. Allow students time to work through the examples with their group members prior to a whole-class discussion. Once students understand how to complete the sheet, it is important that they have some initial discovery time for subsequent examples. Complete the projected sheet with students as each portion of the sheet is discussed. There will be an opportunity, following the presentation of examples for students to work on generation of additional shape patterns.)

Example 1

• Starting shape:
• Rule: Attach 1 square to the right side.

“We can create a shape pattern using this information. The first drawing is a square. Let’s draw that in the first column. The rule is ‘Attach one square to the right side.’ How will we show this in the second column?” () “Can anyone explain how s/he made the shape pattern in the second column?” (First I drew the first square. Then I attached one more square to the right side.) “Complete the third, fourth, and fifth columns. When you have finished, compare and explain your answers with your partner.” (The third frame will have a third square attached to the right side; the fourth frame will have a fourth square attached; and the fifth frame will have a fifth square attached.)

A correct drawing of the pattern is shown below:

“What other observations can we make about this pattern?” (The line of squares increases by 1.Tthe perimeter increases by 2. The area increases by 1.)

Example 2

• Starting shape:
• Rule: Add a triangle and a square next to the last shape.

“Let’s start by drawing the first shape and writing the rule at the top of the page. How can we model the pattern using the rule?” (Place a square in the first column, and then add a triangle and square next to that shape in the second column etc.)

A correct drawing of the pattern is shown below:

“What do you notice about the shape pattern?” (The number of shapes in each frame is odd. The pattern has 1 shape in the first frame, 3 shapes in the second frame, 5 shapes in the third frame, 7 shapes in the fourth frame, and 9 shapes in the fifth frame. Also, every odd shape is a square, and every even shape is a triangle.)

Example 3

• Starting shape:
• Rule: Add 1 square to the height and 2 squares to the length.

“What will the second element look like? How will the first element change? What will the other frames show?”

A correct drawing of the pattern follows:

“What do you notice about this shape pattern?” (Each shape has an area that is a multiple of 3. The number of squares alternate between odd and even. Another feature of the pattern is the perimeter increases by 6.)

Example 4

• Starting shape:
• Rule: Increase each side length of the figure by 1 square.

“What will the second element look like? How will the first element change? What will the other frames show?”

A correct drawing of the pattern follows:

“What do you notice about this shape pattern?” (The perimeter increases by 4.The previous shape will fit in the corner of the present shape.)

Example 5

• Starting shape:
• Rule: Increase the number of shaded squares in the center of the figure by 1. Be sure to keep a border of unshaded squares.

“What will the second element look like? What will the other frames show?”

A correct drawing of the pattern follows:

“What do you notice about this shape pattern?” (The perimeter of the whole shape increases by 2. The area of the whole shape increases by 3.)

Example 6

• Starting shape:
• Rule: Add 1 isosceles triangle, with a leg attached to the right edge of the previous shape.

“What will the second element look like? What will the other frames show?”

A correct drawing of the pattern follows:

“What do you notice about this shape pattern?” (After you start adding triangles, the pattern becomes parallelogram, trapezoid, parallelogram, trapezoid, etc.)

Matching Game

Have students find a partner. Ask each student to create four cards, with each card showing a rule and description/drawing of the first element in the shape pattern. Students will then create four more cards with each card showing one of the shape patterns. Each partner will try to match the rules and first element to the matching pattern. Encourage students to use a variety of shapes.

Have students complete the Lesson 2 Exit Ticket (M-4-6-2_Lesson 2 Exit Ticket and KEY.docx) at the close of the lesson to evaluate students’ level of understanding.

Extension:

• Routine: During the school year, have students identify patterns in real-world settings, such as patterns on tiles/ceilings and signs. Encourage students to build patterns with building blocks and analyze features of the patterns. When learning about perimeter, students may examine and compare perimeters of shape patterns.
• Small Groups: Students who need additional practice may by pulled into small groups to work on the Small Group Practice (M-4-6-2_Small Group Practice and KEY.docx). Students can work on it together or work individually and compare answers when done.
• Expansion: Students who are prepared for a challenge beyond the requirements of the standard may be given the Expansion Work worksheet (M-4-6-2_Expansion Work and KEY.docx). The worksheet includes more open-ended questions related to shape patterns.