# Everyday geometry: Hidden figures and polygons

A lesson plan for grade 5 math in which students use historical photographs and drafting plans to demonstrate their knowledge of mathematical figures and polygons.

**A lesson plan for grades 3–5 Mathematics**

Provided by North Carolina State University / D.H. Hill Library and Special Collections

In this lesson, students will use photographs or drafting plans to apply their knowledge of mathematical figures and polygons. These photographs and drafting plans are a collection of the Built Heritage Project at the Special Collections Research Center at North Carolina State University Libraries. The primary sources will help students assess many ways math can be used in everyday life, while examining historical documents related to dwellings from our past.

## Learning outcomes

Students will be able to answer the following essential questions:

- Where do you see shapes in the world around you?
- How do you distinguish among right, obtuse, acute, and straight angles?
- How can knowing geometric figures be helpful in real life?

Students will:

- Learn the shapes of a variety of figures and polygons
- Gain experience examining primary source documents
- Understand how mathematical figures and polygons are evident in everyday life

## Teacher planning

### Time required for lesson

- Two 60-minute blocks for the “Everyday Geometry” PowerPoint lesson, preview activity, cooperative learning activity, and review activity
- One 45-minute block for the assessment

### Materials/Resources

- Everyday geometry PowerPoint presentation (Developed with permission from Steve Conrad of The Math League.)
- One Everyday geometry PowerPoint handout per student
- White construction paper
- Document projector if available
- Internet connection
- LCD projector connected to a computer or overhead projector with premade transparencies of the photographs
- Photographs from the Built Heritage collection from the North Carolina State University Special Collections Research Center. Select one photograph per group before the lesson.
- One sheet of transparency film and wet-erase markers for each group
- Scissors
- Multiple sheets of 11 x 14 construction paper, each labeled with different geometric figures and polygons
- One “Frontier Geometry Assessment” per student
- One or more sheets per student of triangle graph paper (Triangle graph paper can be found at the Incompetech website.)

## Pre-activities

- Select images of buildings from the Built Heritage collection of the North Carolina State University Special Collections Research Center. To access the images, click on the “View all Built Heritage images” link at the bottom of the Built Heritage home page. (Make sure you have enabled your browser to accept pop-ups from the Built Heritage page.) Select one image per group of students.
- Make copies of the images to distribute among the groups of students. You should have at least one copy of a photograph for each group.

## Activities

### Preview Activity

- Use the PowerPoint presentation to review figures and polygon shapes with the students. Students will use the handout to take notes on the figures and shapes. Ask questions throughout the presentation to check for understanding.
- As an option, the teacher could insert pictures into the PowerPoint from the Built Heritage collection for students to identify figures and shapes as they learn about them.
- Use the Math is Fun website to check for understanding. Have students write their answers on notebook paper as they view the online quiz from an LCD projector connected to a computer. This will identify which students will need additional support during the lesson where they use their background knowledge of figures and polygons to identify these in drafting plans and photographs.
- Take students outside to sit in a grassy area. Give each student a sheet of white construction paper and ask them to sketch a section of the school building on it. In their sketches, have the students identify polygons and other figures they learned about in the PowerPoint presentation.
- Upon returning to the classroom, have the students share drawings in small groups. If you have a document projector, you can have the students share their drawings with the whole class.
- Ask students the following discussion question: Why is geometry essential in constructing buildings? How do you know?
- Check student’s understanding of critical vocabulary using the Polygon Quizlet online review. The teacher can modify this assignment by reducing the number of vocabulary terms the student needs to learn, based on each student’s individual ability. These modified terms will correspond with the assessment at the end of the lesson.

### Cooperative learning activity

- Project the plans or photographs selected from the Built Heritage Project either on the LCD projector or on transparencies using the overhead projector one at a time. Review the preview activity questions to help students make connections to their school building and the images they will examine from the Built Heritage Project to identify polygons and other figures.
- Organize students into groups of three. Each group will have a photocopied set of the drafting plans or photographs.
- Have groups work together to overlay the transparency sheet and use the wet erase markers to identify any polygon. Ask students to signal for the teacher to check the identified figure, and once the item has been checked, cut out the figure and place it on the appropriate poster in the room.

### Review activity

- Conduct a class discussion at the end of the activity to reveal what the students learned about the essential question: Is geometry everywhere?
- Students will use the provided word list and the triangle grid paper to identify geometric terms. They will shade in each figure with a different color and number each figure on the grid paper with the number listed on the assessment handout.

## Assessment

Assess by students’ answers to the worksheet.

## Modifications and alternative assessments

This assessment can be modified for ESL or Special Education students by reducing the number of polygons the students are required to learn.

## Critical vocabulary

Definitions for these terms can be found at the Quizlet website.

- polygon
- convex
- concave
- classification of polygons
- regular polygon
- perimeter
- triangle
- quadrilateral
- pentagon
- hexagon
- heptagon
- octagon
- nonagon
- decagon
- dodecagon
- n-gon

## Websites

Polygon Quizlet online review

Lois Terms polygon quiz

Incompetech triangle graph paper

## Supplemental Information

The following titles can be used to enhance students’ learning through reading:

- What’s your angle Pythagoras? : A math adventure by Julie Ellis and Phyllis Hornung
- Bees, snails, & peacock tails : patterns & shapes—naturally

by Betsy Franco and Steve Jenkins - Sir Cumference and the dragon of pi : a math adventure by Cindy Neuschwander and Wayne Geehan
- Sir Cumference and the First Round Table: A Math Adventure

by Cindy Neuschwander and Wayne Geehan - Sir Cumference and the Green Knight of Angleland : A Math Adventure by Cindy Neuschwander and Wayne Geehan
- Grandfather Tang’s Story by Ann Tompert and Robert Andrew Parker
- Dr. Math Presents More Geometry: Learning Geometry is Easy! Just Ask Dr. Math by Jessica Wolk-Stanley and The Math Forum

- Common Core State Standards
- Mathematics (2010)
#### Grade 3

- Geometry
- 3.G.1Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles,...

#### Grade 4

- 4.G.2Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

#### Grade 5

- 5.G.3Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.
- 5.G.4Classify two-dimensional figures in a hierarchy based on properties.

- Geometry

## North Carolina curriculum alignment

### Mathematics (2004)

#### Grade 5

**Goal 3**: Geometry - The learner will understand and use properties and relationships of plane figures.**Objective 3.01**: Identify, define, describe, and accurately represent triangles, quadrilaterals, and other polygons.