How To Teach Applying Distributive Property [Examples Included]

Key Concepts of Applying the Distributive Property

Students are first introduced to the distributive property in 3rd grade as a strategy to find the answer to a multiplication fact. Third graders explore this strategy of multiplication using arrays and number bonds. In sixth grade, variables get introduced. For these more complex expressions, students need to understand that the terms inside the parentheses can’t be added because they’re not like terms. 

Introduce students to the distributive property with a real-world task, like ordering different menu items at a restaurant. Coach students to draw arrows from the outside number to all of the terms inside the parentheses so they can multiply with ease. 

How do you teach the distributive property? 

Remind students of the multiplication convention groups X amount in each group = total. Explain to students that the outside number represents groups and the terms inside the parentheses represent the amount in each group. Explore a real-world context that uses variables and allow students to discover what happens when you add additional groups. Model how to write expressions in the form a(b+c) and the expanded form ab + ac. Review correct and incorrect distributing examples. 

Step 1: Model the terms inside the parentheses using an array. 

Start out labeling the outside number as groups and the terms inside the parentheses as the amount in each group. Then model one group of the terms inside the parentheses on an array. 

Step 2: Finish modeling all groups of the terms inside the parentheses using an array.

Model all of the groups of terms inside the parentheses on the array. 

Step 3: Write the expression in expanded form. 

Ask students how many groups of the first term they see. Model this relationship with multiplication. Then ask students how many groups of the second term they see. Again, model this relationship with multiplication. 

Step 4: Write the simplified expression. 

Simplify the first term with your class. Model how to use the array to count the number of squares. Repeat this process for the second term. 

Examples

Byte Learn helps students practice expanding using an area model. Step 1 requires students to multiply the partial products. Step 2 directs students to write a simplified distributed expression. 

Example 1: 8 (3x + 4)

8 (3x + 4) = 24x + 32

The digital co-teacher made with ❤️ by teachers

ByteLearn saves you time and ensures every student gets the support they need

Try for Free

Example 2: 3 (4x + 9y)

3 (4x + 9y) = 12x + 27y

Example 3: 0.25 (20 + 16r)

0.25 (20 + 16r) = 5 + 4r

Also read- How To Teach Combining Like Terms

Why teach the distributive property this way?

Using shapes and colors can help students visually see the like terms that are being separately multiplied. Focusing on groups and amount in each group helps build off of your students’ prior knowledge of equal grouping multiplication. 

Using Byte’s practice problems and virtual manipulatives will give your students the chance to practice expanding terms with a visual model. Byte gives your students feedback, and allows your students to try again until they master this essential concept!  

Vocabulary for teaching combining like terms 

Distributive Property: When a factor is multiplied by terms within parentheses, it is the same as multiplying the factor by each of the terms separately.

Expanded Form: Applying the distributive property of multiplication to rewrite a(b + c) as ab + ac.

Term: Part of an expression separated by + or – operations.

Like Term: Terms that have the same variables, raised to the same power. Constants are like terms.

Unlike Term: Terms that have different variables, or the same variables but raised to different powers.

Coefficient: A number that multiplies a variable. If there is no coefficient in front of a variable, the coefficient is 1.

Constant: A term that does not contain a variable.

Variable: A symbol (usually a letter) that is used to represent a number in an expression or equation.

Misconceptions and errors students are likely to have:

• Students might multiply the outside number by the first term only. For example, students could simplify the expression 2 (3x + 4) as 6x + 4.
  • Name for your students that they are making an error. Remind students of the multiplication convention groups X amount in each group = total. Prompts students to label the outside number as groups and the terms inside the parentheses as amount in each. Pass out colored pencils and have students model each group of 3x and 4. Have students count up the terms and compare their original answer. Ask them what they think they did incorrectly. Then explicitly model how the multiplication in expanded form. 
• Students might combine terms from left to right and disregard the variables. For example, students could simplify the expression 2 (3x + 4) as 10x.
  • Remind students of the multiplication convention groups X amount in each group = total. Prompts students to label the outside number as groups and the terms inside the parentheses as amount in each. Pass out colored pencils and have students model each group of 3x and 4 and ask them to describe the relationship between the outside number and the inside terms. Explicitly model how to write the expression in expanded form. 
• Students might combine every term inside the parentheses, regardless of the variable. For example, students might think that x + xy is the same as 2xy.
  • Try assigning a noun for each variable and ask your students if it makes sense to combine two nouns together. If this doesn’t click, try providing your students with integer tiles. It will “click” more easily for students if each set of tiles are color-coded. If this is not possible, provide colored pencils to your students and coach them to write each term in expanded form. For example, 2x + 3y is the same as x + x + y + y + y. Guide students to identify why the terms are unlike versus like. 

Resources: 

• Downloadable worksheet for practicing the distributive property 
• Quiz for assessing distributive property 

Frequently Asked Questions for How To Teach Applying Distributive Property