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Lesson plan In this lesson, students analyze and create rectangular patterns of squares. First they identify three stages of a pattern by coloring squares in a Microsoft Office Excel grid and quantify the information in a table. Next, they analyze the rates of growth in the three stages of the pattern, graph the formula or the points for each stage, and make predictions based on their findings. Finally, they create their own three-stage rectangular design, quantify the information, find the formulas, and share their pattern with other students. On This PageLesson plan information|
School level | | Curriculum areas | | Class time | | • | 1-2 hours, approximately |
| Software required | | • | Microsoft Math | | • | Microsoft Office Excel |
| Materials needed | |
Teacher guideGoals| • | Students will identify geometric patterns, their growth rates, and formulas, by analyzing and creating three-stage rectangular designs. |
Objectives| • | Students will organize information in a table. | | • | Students will identify number patterns. | | • | Students will write formulas and graph the relationships. | | • | Students will examine growth rates. | | • | Students will add and multiply polynomials, (for students in algebra). | | • | Students will use formulas to make predictions and create their own three-stage rectangular designs. |
Lesson procedureIntroductionIn this activity, you will learn about geometric patterns by analyzing rectangular patterns of squares. First you will identify three stages of a pattern by coloring squares in a Microsoft Office Excel grid and quantify the information in a table. Next, you will analyze the rates of growth in the three stages of the pattern, graph the formula or the points for each stage, and make predictions about other stages based on your findings. Finally, you will create your own three-stage rectangular design, quantify the information in tables, find the formulas or graph the points for three stages of your design, and share your pattern with other students.
[Note This activity can be adapted by eliminating the challenge to find the formula (the first alternative of the third activity under Step 3). Students can still graph and see the rate of growth just using the data points.]
Main activitySoftware: Microsoft Math
 Microsoft Office Excel
What to do: Step 1: Create the patterns1. |
Open the Excel Rectangle Patterns Grid (.xls, 44 KB) your teacher has saved to your classroom computer.
| 2. | On the Rectangle Patterns grid, create the rectangular patterns Stages 1, 2, and 3 shown above, using the cell fill (paint bucket) to shade the cells. Coloring in the design helps you to see the growth much more than just looking at the patterns drawn here.
If you need help shading cells in Office Excel, read How to Shade Cells in Excel (.doc 119 KB).
| 3. | Based on the patterns you observe, what do you think Stages 0 and 4 would look like? Create these two stages on the Rectangle Patterns grid. |
Step 2: Quantify the information1. | Fill out the table below with the number of squares per color in each of the stages beginning with Stages 1-3. Observe the patterns. Use the patterns to predict Stages 0, 4 and n. Stage | 0 | 1 | 2 | 3 | 4 | n | Number of Blue |
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| Number of Green |
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| 2. | Does the prediction in Stage 0 in the table match what you drew for Stage 0 in Activity 1? | 3. | Does it match for Stage 4? |
Step 3: Analyze the rate of growth1. | Which color of squares is growing at the slowest rate? | 2. | Which color of square is growing at the fastest rate? | 3. | Do one of the following: In Microsoft Math, graph the three formulas (what you got in terms of n) to get a picture of the growth of all three colors. —or— In Microsoft Math, graph the points. To graph the points, make x the stage number and y the number of colors. Observe the steepness of the lines. The steeper the line, the faster the growth.
[Note If you need help graphing, read How To Graph in Microsoft Math (.doc, 119 KB).
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Step 4: Make predictions1. | How many squares of each color will be in Stage 8 of the design? | 2. | Will the design use 42 blue squares in any stage? _____ If so, in what stage? | 3. | Will it use 102 red squares? _____ If so, in what stage? | 4. | Will it ever use 830 squares in all? _____ If so, in what stage? |
Step 5: Add some geometry1. | Fill out the table below to investigate the dimensions, areas and perimeters of the rectangles. Stage | 0 | 1 | 2 | 3 | 4 | n | Length |
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Step 6: Create your own three-stage design1. |
On square grid paper or in a fresh copy of the Excel Rectangle Patterns Grid (.xls, 41 KB) create your own design, showing at least 3 stages. The design must follow a regular numerical growth pattern. If you work in the Office Excel file, be sure to save your work.
| 2. | On a separate sheet of paper or in this document, fill in the calculations in the following tables. Stage | 0 | 1 | 2 | 3 | 4 | n | Number of Blue |
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| Number of Red |
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| Number of Green |
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Stage | 0 | 1 | 2 | 3 | 4 | n | Length |
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| 3. | Be sure to save your work. | 4. | Be prepared to exchange papers with the other students in class and figure out one another's patterns. |
Conclusion| • | Observe students as they work through lesson. | | • | Evaluate the work on the student handout. | | • | Evaluate completed assignment. | | • | Evaluate students as they explain the patterns they created to other students. |
Materials needed
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