Elementary School Algebra Lessons and Teaching Strategies

Algebra Lessons and Teaching Strategies for Elementary Students

Algebra Lessons

Greater Than, Less Than or Equal To

Kids learn to compare numbers as early as kindergarten by deciding if one number is greater than (>), less than (<) or equal to (=) another number. In kindergarten, students generally use objects to visualize the comparisons and, by first grade, students are able to compare numbers within 100.

Equations

An equation is a math sentence that has three parts:

1. A number or group of numbers
2. An equal sign (=)
3. Another number or group of numbers

Examples:
5 = 5
2 + 3 = 5
4 + 1 = 2 + 3

The equal sign shows that the number(s) on either side of it have the same value. In elementary school, the numbers in equations are mostly constants, meaning they are numbers that don't ever change. For example, three is always equal to three, 1/4 is always 1/4 of something and pi is 3.14+ without fail.

Some elementary students may solve equations with variables, which are unknown numbers. In earlier grades, it is usually represented as a question mark (?) or a box. Later, these are replaced by letters of the alphabet, such as x or y.

Examples:
2 + 3 = ?
2 + 3 = ?
2 + 3 = x, or x = 2 + 3

Linear Equations

Just as a sentence in English is made of symbols that are in a straight line, read from left to right, an equation is also presented in a straight line to be read from left to right. Often, addition and subtraction problems are written vertically to help students line up the numbers correctly. However, as your child advances, you may want to write equations horizontally to help him or her view the problem as an equation.

Examples:
x = 4 + 3 - 1
2 + y = 20 - 10 - 3

Factors and Multiples

If you have a number, such as 12, that can be evenly divided by two or more other numbers, it is a multiple. The numbers that are multiplied to get the multiple are called factors. So the multiple 12 has the following factors:

3 and 4
2 and 6
3 and 2 and 2

Order of Operations

When solving an equation with only addition and subtraction, you can do the operations in any order and get the same answer. The same is true if the equation requires only multiplication and division. However, you must do those processes in a particular sequence in order to get the correct answer if the problem involves a mixture of these operations.

Examples:
The order doesn't matter in problems like 5 + 7 - 2 = x. You can add the 5 and 7 first and then subtract 2. Or, you can subtract 2 from the 5 and then add 7. Or, you can subtract 2 from 7 ad then add 7. In all instances, the answer will be 10.

Similarly, consider this problem: 10 x 12 ÷ 2. You can divide 10 by 2, and multiply the answer by 12. Or, you can divide 12 by 2 and multiply the answer by 10. Or, you can multiply 10 by 12 and divide the answer by 2. You will always get an answer of 60.

The order does matter in problems like: 4 + 5 x 3. You can solve by doing the addition first (4 + 5 = 9). Then multiply by 3: 9 x 3 = 27.
Or, you can multiply first, 5 x 3 = 15, and then add the 4: 15 + 4 = 19.

You must do these operations in a certain sequence to find the correct answer. That sequence, called the order of operations, is:

1. Look for numbers in parentheses; do that operation first.
2. Start at the left and do the addition and subtraction operations, working towards the right.
3. Go back to the left and work towards the right, doing the multiplication and division operations.

Teaching Strategies for Elementary School Algebra

Regardless of what you're teaching, you will need to include the following:

• Motivation, or something to make the children want to learn the concept
• A concrete presentation of the concept
• Manipulatives to help students visualize the material
• Guided practice
• Independent practice
• An activity that will aid retention

Grab students' attention by asking how they would figure something out. For example: If you were very hungry, would you want to eat one slice of pizza or three slices? Why?

Alternatively, read an interesting story, such as More or Less by Stuart J. Murphy. Or play Jennifer Fixman's song Alligator Greater Than / Less Than from her album We Love Math with Miss Jenny.

For some students, numbers are vague concepts. Provide a concrete presentation of the concept by using manipulatives, such as unit cubes and rods, poker chips or buttons, dried beans or small stones. On the Internet you will find ideas for which manipulatives work best to present specific concepts.

Allow the children to also use the manipulatives. This will help them visualize and internalize the concept. At first they will likely need your guidance, but they should soon be able to practice without your assistance. Worksheets are often used for individual practice.

At the end of each lesson, you might have a discussion about what was learned and what is still fuzzy. You may have students play a game in pairs to aid retention. For example, one child thinks of a number, and the other one tries to guess the number by asking 'greater than' and 'less than' questions.