This document outlines a unit plan for an 8th grade mathematics class centered around measuring trees. The unit consists of 5 lessons applying geometric concepts like circles, similarity, the Pythagorean theorem, functions, cylinders, and cones to measure properties of trees. In each lesson, students will learn key formulas through lecture and assignments then apply them by measuring aspects of a tree they selected for a long-term project, gaining experience with geometric applications in a real-world context.

1. Trees and Geometry
An 8th-Grade Mathematics Unit Idea
Jeremiah Harrington
ED 681: Place-Based Education
May 5th, 2014

2. Overview

Draws on elements
across 8th-grade
curriculum

Ordered around a
simple, outdoor
project about trees
0 Circles & Trees
1.Similarity
2.Pythagorean
Theorem
3.Functions
4.Cylinders
5.Cones

3. Lesson 0: Circles and Trees

Time Frame: 3 days

Objectives:
– Students will
understand to
relate a circle's
radius, diameter,
circumference,
and area.
– Students will also
pick a tree for the
long-term project.
r

Standards: 7.G.4

4. Teacher will lecture on formulas for diameter,
circumference, and area. Standard
assignments will be provided.
Working in pairs, students will go outside and
choose a tree. With measuring tape or string,
students will measure the circumference of
the tree, and use this to find the diameter,
radius, and cross-sectional area at the base
of the tree.
Lesson 0: Teaching Procedures

5. Lesson 0: Teaching Procedures
(cont.)
If time provides, students will take photographs
of their trees, and then use computers or
reference sources to determine what type of
tree it is. They will also determine typical
locations for the tree, and whether or not it is
local.

6. Lesson 1: Similarity

Time Frame: 3 days

Objectives:
– Students will
understand how to
use similarity of
shapes to
measure large
objects with
models.

Standards: 8.G.4
2x
2y
2s
y
x
s

7. Teacher will provide a lecture on similarity.
Standard assignments and assessments will
be provided.
Weather permitting, students will go outside and
use shadows and similar triangles to measure
the height of their tree.
With reference sources, students will compare
the height of their tree to the typical height of
the species.
Lesson 1: Teaching Procedures

8. Lesson 2: Pythagorean Theorem

Time Frame: 3 days

Objectives:
– Students will
understand how to
use the
Pythagorean
theorem to
measure the
unknown side of a
given right
triangle.

Standards: 8.G.6,
8.G.7, 8.G.8
b
a
c
This lesson will be
standard: lecture,
assignments, quiz,
etc.

9. Lesson 3: Functions

Time Frame: 2 weeks

Objectives:
– Students will learn
how to use
functions to model
relationships
between
quantities.

Standards: 8.F.1,
8.F.3, 8.F.4
There will be a
standard lecture and
assignments.
Students will be asked
to generate functions
to model several
things.

10. Lesson 4: Cylinders

Time Frame: 2 days

Objectives:
– Students will
understand how to
use dimensions
(radius and height)
to find the surface
area and volume
of a cylinder.
There will be a
standard lecture and
assignments.
Students will use the
equations to
approximate the
amount of wood and
bark of the tree.

Standards: 8.G.9

11. Lesson 5: Cones
There will be a
standard lecture and
assignments.
Students will use the
equations to
approximate the
amount of wood and
bark of the tree.

Standards: 8.G.9

Time Frame: 2 days

Objectives:
– Students will
understand how to
use dimensions
(radius and height)
to find the surface
area and volume
of a cone.