## Geo Jammin' By Design - Day 2, Lesson 7: Start At Square One

### Katie KoehnemannBay District Schools

#### Description

Using manipulatives, students explore new shape possibilities by combining two and four triangles. A critical thinking approach is used to guide students' predictions and discoveries with design.

#### Objectives

The student knows congruent shapes.

The student identifies shapes that can be combined or separated (for example, a rectangle can be separated into two triangles).

The student predicts the reflection of a given two-dimensional shape.

The student identifies and demonstrates slides, flips, and turns of simple figures using concrete materials.

The student transfers patterns from one medium to another (for example, pictorial to symbolic).

#### Materials

-A substantial supply of 3x3 inch squares of colored construction paper
-Scissors for each student (or pair of students)
-Newsprint for each student
-Pencil for each student
-Glue
-A large piece of butcher paper titled Polygons. Then down the left-hand margin, and evenly spaced, place four labels: Triangle, Quadrilateral, Pentagon, and Hexagon
-Adhesive for hanging the poster and for mounting the shapes onto the poster
-Marker for adding Parallelogram, Trapezoid, Pentagon, and Hexagon to the Quilt Word Board

#### Preparations

1) Cut an ample supply of 3x3 inch squares of colored construction paper. (For this age level it is highly suggested that all the squares be the same color.)
2) Prepare an area for displaying the poster of shapes. (Butcher paper, bulletin board, white board, etc.)
3) Title the poster area Polygons and in four rows down the left side, evenly spaced write triangle, quadrilateral, pentagon, and hexagon.
4) Write on individual pieces of paper or sentence strip to add to the Quilt Word Board, the words Parallelogram, Trapezoid, Pentagon, and Hexagon.
5) Adhesive for hanging the poster and for mounting the shapes onto the poster.
6) Gather for students: scissors, newsprint, pencil, and glue.

#### Procedures

(This lesson is adapted from [Patchwork Math] by Marilyn Burns as presented by Cuisenaire)
1) Hand out one square, one sheet of newsprint, and scissors to each student.

2) Have students name the shape.
* What do you predict would happen if the square were cut through on the diagonal?
* What can you predict about those triangles?
Formative assessment occurs as students respond. Write their predictions on the board. They should predict two triangles within the square. Through reasoning they should determine them to be congruent.

3) Call on a student to demonstrate by cutting their squares on the diagonal. Students should check their predictions noting correctness/incorrectness.

4) Have all students cut their squarse into two congruent triangles by cutting on the diagonal. Give students free exploration time to manipulate the two triangles.
Challenge:
* What other shapes can be made from the two triangles? The only rule they must follow is that sides that touch must be the same length.
For each shape they discover, they are to hold the pieces in place on the newsprint and trace around the design. If they can, they are to name the shapes they make.

5) Walk around the room monitoring students. Give guidance for tracing the new shapes.

6) Call on individual students to share one of the shapes made. Make a drawing of each on the board for students to see. Formative assessment occurs as students correctly identify a square, large triangle, and a parallelogram, and as they correctly identify shapes within those shapes, such as, in a parallelogram, a square and triangles can be spotted. (See Associated File for answers)

7) Next, ask students to work with the person sitting next to them. Challenge:
* What new shapes can be made with four triangles?
* With your partner, make as many different shapes as you can.

8) As pairs of students work on the newsprint, they are to complete shapes using all four triangles, and glue them in place. Then, get two more squares, cut on the diagonal, and make a different shape, glue in place, etc. See how many different shapes they can make. (Rule: Sides touching must be the same length.) Hint: There are 14 different possibilities! (Answers in the Associated File)

9) After making as many shapes as they can with four triangles, cut all new shapes out as they are glued in place on the newsprint.

10) As students are working, monitor for understanding of assignment. Ask questions such as: What makes the shapes different from one another? What shapes are in the larger shape they made? Formative assessment is given to individuals as their shapes and responses to questions are evaluated for correctness.

11) Once all shapes are cut out, students get ready to present their findings. As they are putting scissors, glue and scraps away, hang the butcher paper poster on the wall.

12) Call students’ attention to the title ‘Polygons’ and review that a polygon is any closed figure with straight sides. Read each label down the left side of the poster and ask if students can tell you what each is. Expect them to know triangle, however probably not the others.
Challenge to students: Watch the sorting and categorizing of the shapes.
Challenge question: What determines the category a shape is placed in?

13) Call on various pairs of students to share one of the shapes they made. As they hold it up and present it ask which of the categories on the poster they think it should go in. (It would be helpful to call on a pair that is ready to share the large triangle and a pair ready to share the large square first. These will be easy to categorize and give playing field for questions that follow.)

14) Once the large triangle and large square have been placed on the poster, ask students what is different about a triangle and a square. They should know it is the number of sides. Through questioning techniques, guide students to reason that tri means three and quad means four. Lead them to use that information to help categorize the other shapes.

15) As students choose shapes to present, they must decide if the shape has already been posted, and if not, which category to place it in.
A. Guide by asking critical thinking questions such as:
* What is it that makes a triangle different from the quadrilateral square?
* Is the shape you are presenting congruent to another shape that has already been posted? (Remind them that if all they have to do is turn or flip their shape to make one that is already up there, then it is congruent to one already posted and it cannot be posted again.)
B. From the categorizing activity, students should be able to answer the challenge question (#12 above). Differentiation comes from the number of sides and angles each shape has, and that penta means five and hexa means six . . .add the gon and you have a five sided polygon, a pentagon and an eight sided polygon, a hexagon. Add these words to the Quilt Word Board.
C. Students will uncover the new shapes of parallelogram and trapezoid. Add these words to the word board.

16) Once all fourteen possibilities are added to the poster, students study the different entries and point out shapes within the shapes they recognize.
Close with critical thinking by asking students:
Where would this knowledge of shapes within a shape be important? (Designing a town, cutting sandwiches for a tea, making quilts)
Who might use this information? (Bridge designer, sign maker, etc.)

#### Assessments

Formative assessment occurs as students correctly predict and identify shapes within shapes, recognize congruent shapes, and conclude that a flip and/or a turn can make a shape look different, but it is still congruent to another. Individual students shapes and responses to questions are evaluated for correctness. Use formative assessment data to guide questioning within the Procedures.

#### Extensions

1) This is Lesson 7 – Start at Square One; math lesson
Lessons 1 – 6 are for Day 1 of the unit Geo Jammin’ By De’Sign
Lessons 7 – 11 are for Day 2 of the unit Geo Jammin’ By DeSign
Lessons 12 – 17 are for Day 3 of the unit Geo Jammin’ By DeSign
Lessons 18 – 23 are for Day 4 of the unit Geo Jammin’ By DeSign
Lessons 24 – 28 are for Day 5 of the unit Geo Jammin’ By DeSign
Lessons 29 – 32 are for Day 6 of the unit Geo Jammin’ By DeSign.
Lessons 33 – 38 are for Day 7 of the unit Geo Jammin’ By DeSign

Lessons may reflect modifications of, but are designed in conjunction with the Reading
Framework approach to classroom instruction and may be adapted to the Four Block
Classroom.
2) The Beacon Unit Plan associated with this lesson can be viewed by clicking on the link located at the top of this page or by using the following URL: http://www.beaconlearningcenter.com/search/details.asp?item=3004. Once you select the unit’s link, scroll to the bottom of the unit plan page to find the section, Associated Files. This section contains links to the Unit Plan Overview, Diagnostic and Summative Assessments, and other associated files (if any).
3) If all fourteen figures are not discovered by students in the allotted time of this lesson, inform them of how many are still missing, set up a learning center with the challenge to find the missing shapes.
4) Students become fascinated with characteristics of rectangles and parallelograms through interactive investigation and exploration at Exploring Properties of Rectangles and Parallelograms. (See Weblinks section) Critical thinking questions, various tasks and discussion are included for the teacher.
5) Students use an interactive geoboard to investigate concepts and properties at Concepts of Triangles and Properties of Polygons. (See Weblinks section)

#### Attached Files

Support Material     File Extension: pdf