4th Grade Pre-Algebra: Lessons and Teaching Methods

Students learn algebraic thinking from kindergarten until high school. One might say that students take 'pre-algebra' all through grade school and middle school. Below are ways to teach pre-algebra topics to 4th graders.

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Teaching Pre-Algebra to 4th Graders

Algebraic-Thinking Topics

In grades K-3, students were primarily taught the operations, which include addition, subtraction, multiplication and division. Algebraic 'sentences,' (i.e., equations) were used as one way to express these operations (e.g., 4 + 5 = 9, 8 - 3 = 5, 5 x 6 = 30, 27 ÷ 9 = 3). By 4th grade, students also know some of the properties of addition and multiplication:

Commutative property of addition - When adding two numbers, the order doesn't affect the answer. For instance, 3 + 9 = 12 and 9 + 3 = 12, which can also written as 3 + 9 = 9 + 3.
Associative property of addition - When adding multiple numbers, the grouping of the numbers doesn't after the answer. For example, 3 + (5 + 4) = 12 and (3 + 5) + 4 = 12.
Commutative property of multiplication - The order doesn't matter when multiplying two numbers: 3 x 9 = 27 and 9 x 3 = 27.
Associative property of multiplication - The way the numbers are grouped doesn't affect the product when multiplying multiple numbers together: (3 x 5) x 4 = 60 and 3 x (5 x 4) = 60.

New Topics Covered in 4th Grade

Students will understand multiplication equations as comparisons. For example, the equation 24 = 6 x 4 shows that 24 is six times as many as four and four times as many as six. They will use their knowledge of operations in word problems that take several steps to solve. In addition, 4th graders are introduced to multiples and factors. By the end of the school year, they'll be able to factor whole numbers up to 100 into pairs of numbers.

Methods for Teaching Pre-Algebra to 4th Graders

Catch Their Attention

Use multimedia to catch your students' attention. You can find a number of videos and songs on YouTube.com that will introduce factoring. Alternatively, you could read a book, such as You Can Count on Monsters by Richard Evan Schwartz, to present a visually interesting way to learn factors.


When teaching how to factor, use visuals, like a tree. You can also use blocks or squares on graph paper. For example, you can have the students give you a number between one and 50. Have them help you figure out how many types rectangles you can make with that number of blocks or squares. If they give you the number ten, you could form a rectangle of one row of ten blocks, two rows of five blocks and five rows of two blocks.

Then, demonstrate factoring with those rectangles. Show that you have divided the blocks into groups of two and five. Since two and five are prime numbers, these are the two factors of ten.


Students will remember factoring more if they have had hands-on experience with the blocks (or other manipulatives). You could divide the class into groups of two. Give each group a list of number pairs, such as 7 and 6 or 13 and 12. Have each student see how many rectangular arrangements of the blocks can be made and record them. Students should understand that you can make more types of rectangles for numbers with more factors.

Guided Practice

The first experiences the students have with doing any new concept, such as factorization, should be under your watchful eye so you can catch mistakes early and correct misconceptions before they become ingrained. Worksheets are probably the easiest and most common method for this practice. For factorization, have the students make factoring trees.

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