## Numbers, Patterns, and Algebraic Thinking

### Mike RooneyBroward County Schools

#### Description

Fifth grade students use spreadsheets to help in their understanding of concepts of numbers, patterns, and algebraic thinking.

#### Objectives

The student explains and expresses numerical relationships and pattern generalizations, using algebraic symbols (for example, in the problem above, the number of calls on the nth day can be expressed as 3n+1).

#### Preparations

The teacher should review the functions of the spreadsheet application that will be used for the lesson.

Students need to be introduced to the spreadsheet function in the application that is most often used in your school. Two of the most commonly used spreadsheets are Microsoft Excel and AppleWorks Spreadsheets. This is a great time to address all new vocabulary terms as an understanding of the terms are necessary to the completion of the lesson.

Students should be given five minutes to explore entering data and moving from cell to cell within the spreadsheet.

#### Procedures

1. To produce the even numbers in column A of any spread sheet, begin by entering the first value of the sequence. Put the cursor in cell A1 one and type 2. When you press the ENTER key, the value of 2 will appear in cell A1.

2. To assign the next value in the sequence, increment the first value. Put the cursor in cell A2 and type "=A1+2." When students press the ENTER key, the value of 4 will appear in cell A2.

3. Finally, to extend the pattern, click the mouse on cell A2, and drag down to cell A10. Go to the calculate window and select FILL DOWN. The first 10 even numbers will appear in the first 10 cells of column A.

4. Spreadsheets provide a super opportunity for students to
explore mathematical possibilities. For example, what happens if they change the value of the first number? They'll find that no matter what number is selected, a pattern of counting by twos is present. My students found, if the first number was even, all numbers were even. They also found that if the first number was odd, all numbers were odd.

5. At this point, I usually suggest the idea of, what would happen if we change the assignment statement? For example, what if the assignment statement in cell A2 read "=A1+5?" Students change the value of cell A1 to a 5 and joyfully find that they've created multiples of 5.

6. Following this activity, my kids are usually able to easily create multiples of any number.

#### Assessments

Formatively assess the activity by using a checklist or printing spreadsheets from each student to find out where further instruction will be needed.
The student explains and expresses numerical relationships and pattern generalizations, using algebraic symbols in a paragraph or verbally to show understanding.

#### Attached Files

Sample pattern.     File Extension: pdf