 # Teaching Algebra to Kids: Lessons and Strategies

Kids usually take a full course in algebra as ninth graders, but they begin learning algebraic thinking as early as kindergarten. Foundations of algebra are taught throughout elementary and middle school. ## How to Explain Algebra in Elementary and Middle School

### Algebraic Concepts to Introduce

#### Patterns

Finding patterns is fundamental to algebraic thinking. This process evolves into composing generalizations about numbers and representing patterns with symbols.

#### Equations

As children begin adding and subtracting in first grade, they're given the facts as 'math sentences,' or equations. Then they're shown the equations with a question mark replacing one of the parts, and taught how to determine the unknown number. In second through fourth grades, the equations are extended to include multiplication and division.

#### Factors

Factoring is important in algebra. Kids in fourth grade learn to find pairs of factors for whole numbers from 1-100. They can then find all of the factors for a number up to a certain point and order them sequentially. Fifth graders begin writing and evaluating numerical expressions using parentheses and brackets.

#### Variables

Children begin to learn about variables when equations are written in different ways, such as:

3 x 4 = ?

3 x ? = 12

? x 4 = 12

Sixth graders learn to solve equations with one variable. They also begin to use equations with letters instead of numbers or question marks.

#### Inequalities

In a sense, inequalities are what algebra is all about. Sixth graders learn to see presentations of inequality as pictures of the comparative positions of two numbers on a number line.

### Methods for Teaching Algebra

#### Pattern Recognition

Teaching patterns formally begins in kindergarten, but is often also a part of a pre-school program. Teach children to analyze and describe patterns by counting dots and shapes, and grouping them by size (larger or smaller), position (inside or outside, above or below) and whether they're the same or different. Use a number chart for skip counting by twos or tens to demonstrate a variety of patterns.

#### Multiple Routes

A basic strategy for teaching any algebraic concept is to teach more than one way to solve any kind of math problem and compare them. Demonstrate various ways of solving a problem by writing different step-by-step solutions side-by-side on the board. Follow up with a discussion of how these approaches differ.

#### Balance Bar

Draw a bar balanced in the middle on a vertical line or pivot. Beginning at the pivot, number the bar from 1-10 on each side. Draw lines representing weights on the numbers. The weights are all the same, and only one can be used on a number. Show that the total of the numbers must be the same on each side; then let the children find multiple solutions as to what weights can go on each side and still have it balance.

#### Number Line

Your students can learn the use of letters for numbers (for writing and solving equations) using a number line that goes up to 10. They can solve problems, such as:

Mary found 3 marbles in her sock drawer. Then she found more marbles in her T-shirt drawer. She kept those marbles a secret. She found 10 marbles in all. How many secret marbles did she have?

Call the 'secret' number 'x,' then show the procedure by means of an equation: 3 + x = 10, then x = 10 - 3. Point out that you subtracted the 3 on both sides of the equation; demonstrating with the number line and balance bar makes the reasoning clear.

#### Draw Shapes

Use shapes instead of numbers or letters. Show three shapes: a triangle, rectangle and circle. Give each shape a number (e.g., triangle = 6, rectangle = 16 and circle = ?).

Problems can be shown as a row of shapes followed by an equal sign and a number. The children can determine the value of the shapes. For example, a problem could read: triangle (6) circle (?) rectangle (16) = 23. Show the children that subtracting the values of the triangle and rectangle from 23 (23-22) gives you the value of the circle (1). A more complex problem might read: triangle circle triangle rectangle triangle circle triangle = 42.

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