Audrey Perry
Math
4/28/04
Lesson Plan: Geometry and Measurement
Dimensions, Area, and Perimeter
Adapted From Kennedy, Tipps, & Johnson, Activity 12.19, page 551.
Grades: 4-6
Objective: In pairs, students will construct as many rectangles as they can using sets of 36 colored tiles, and increase their understanding about the relationship between dimension, area, and perimeter as they record and discuss this data for different rectangles.
EALR: Math 1.2 – Understand and apply concepts and procedures from measurement.
Procedures: (intended for a group of ten or fewer students – adapt as necessary for larger groups)
1. Intro/Schema Activation
Draw a rectangle on the board. “Raise your hand if you know what this shape is called.” (ALL students ought to know this by now, but ask anyway just to get their attention)
“What kinds of things do we already know about this shape?” (This step not only serves to get students to recall their prior knowledge, it gives the teacher a chance to assess what information has/hasn’t been retained) Students might say any of the following:
(These last two are important. If they aren’t readily volunteered, see that they get teased out.)
2. Introduce Activity
“When I give the signal, you’re going to break into pairs, and I’ll be giving each pair a set of 36 colored tiles. Your task will be to create as many different rectangles as you can, using all of the 36 tiles for each rectangle. To keep track of your rectangles, I’d like you to record your rectangles in a table like this: (Draw this on the board)
| Diagram of Rectangle |
Length |
Width |
Area |
Perimeter |
“I’ll be collecting these tables at the end of class. Make sure each person’s name is written on the table.”
Give the signal for students to pair up and begin passing out the sets of tiles.
3. “Doing” the Activity:
After students have collected their data, ask each group to come up to the board and write in the data for one of their rectangles (request that each group add a NEW rectangle to the chart). Once each group has added one, ask the class if there are any others that were missed.
(There are only five possible rectangles that can be made with 36 tiles, unless students are counting 2 rectangles with equal dimensions different by just swapping length and width; EX: a 2x18 rectangle is considered different from an18x2 rectangle; explain that for all intents and purposes they are the same.)
The data table should end up looking something like this:
| Diagram of Rectangle |
Length |
Width |
Area |
Perimeter |
| 36 |
1 |
36 |
74 |
|
| 18 |
2 |
36 |
40 |
|
| 12 |
3 |
36 |
30 |
|
| 9 |
4 |
36 |
26 |
|
| 6 |
6 |
36 |
24 |
Once the class agrees that there are no other rectangles, ask them if they can detect any patterns among the rectangles’ data. Record all pattern suggestions on the board without evaluating, but the one you’re looking for is:
Ask: “Is this always true? How might we test to see if this rule always applies?” Let them think about this for a minute, then, if no one has suggested this, recommend that they try the same activity using only 16 tiles. As before, have them record their data in the table. When they’re finished, solicit dimensions from the class and ask, “Does the pattern still hold true?” It should!
Time permitting, this is a good opportunity to apply this concept to real life. A question you might pose is, “If we wanted to plant 36 tomato plants (that each take up a 1 foot square space) and build a fence around it to keep out animals, how could we set up the garden so that we could save money on fencing without compromising the number of tomato plants?”
In subsequent lessons, I would recommend working with the idea that perimeter is constant, and asking them to create rectangles that change dimensions in order to maximize volume. So for example, pretend you’ve got a fixed amount of fencing and you want it to enclose as large a garden as possible.