2 Analogies to Help Teach the Distributive Property

A Better Way to Explain the Distributive Property - with Clear, Hands-On Analogies Your Students Can Relate To

Have you ever repeatedly taught the distributive property, but the concept just doesn’t seem to stick in your students’ heads? 

​Or maybe, your students seem to grasp the concept, but after some time you realize they’ve completely forgotten the property?

It happened to me, and then I discovered that the trick was to use a relatable analogy (preferably in a hands-on way, if possible!).
 
These 2 helpful analogies will make the distributive property stick once and for all. 

Analogies are awesome when teaching, because they have the ability to make your lesson instantly relevant to your students’ interests, while also allowing your students to gain a deeper understanding of the concept.

​1.  Making Bracelets
  
A great analogy for teaching the distributive property is making bracelets with beads; this is a task that students have either done before or have the ability to easily understand! 
 
Analogy: If you are creating multiple bracelets of a certain type, you must multiply the number of bracelets being made by EACH bead type.  Just like with the distributive property, you multiply the outer term by EACH term in the parentheses.  A common mistake students make is only multiplying the first term and not distributing throughout each term in the parentheses. 
 
This bracelet analogy creates evidence to see that you must distribute throughout each term inside the quantity.  This Distributive Property Investigation Activity is perfect for getting your students to discover and thoroughly understand this bracelet analogy.
 
This set of worksheets is structured as a guided inquiry, so students are discovering the property themselves.  This helps the students to gain a deeper understanding of the distributive property.  The inquiry activity would be great for either introducing the distributive property, or a creative way to review the topic.
 
An inquiry-based approach to teaching math has many benefits for your students, including enhancing independent problem-solving skills and leading to deeper understanding of a concept.  Instead of just memorizing the property, they learn WHY it works and HOW it works.  It is important to let your students build a concept, not just follow a process.

 2.  Recipes
 
Relating the distributive property to recipes is helpful, because by this age, students tend to have a strong understanding of how recipes work, and you can create a fun, interactive lesson.  Here’s how to relate the distributive property:  Ask, “What do you do to double a recipe?”
 
Analogy: To double the whole recipe, you must be sure you remember to double EACH AND EVERY ingredient.  When using the distributive property, you have to remember to multiply by EACH AND EVERY term in the parentheses.  
 
If you forget to double one of the ingredients, the recipe won’t turn out exactly right; just like you will get an inaccurate answer if you miss a term when distributing. You must distribute to each term in the parentheses.
 
This set of doodle notes will perfectly coincide with teaching the distributive property using this analogy.  When students color or doodle in math class they activate both hemispheres of the brain. There are many proven benefits to this cross-lateral activity, including new learning, relaxation (less math anxiety), visual connections, and better memory and retention of the content!

With these doodle notes, you get sheets for students to fill in, complete the examples, and color, doodle or embellish - all about the distributive property!  Then, they can use it as a study guide later on.  They love to pull these beautiful pages back out to use as a reference throughout the year.
 

Another inquiry-based approach includes assigning students to bring in any recipe to class the day you are introducing the distributive property. Have your students work in pairs or independently to double their recipes; there are benefits to both. Working collaboratively on this is beneficial, because they have the opportunity to bounce ideas off of each other and share their recipes with each other.  Working individually enhances their independent problem-solving skills.

​If you do try this as a hands-on exploration, it really helps to limit your students to a very simple recipe with ony 3 ingredients and one container required. (for less mess, less time, and a clearer math representation.)  Simple things like punch or trail mix work well.

After they double their recipe, they can triple it, multiply it by 4, and so on.  Next, students should determine the pattern they see, and they should write a rule for the property.  Now, when you teach the distributive property, your students have already internalized this property; they have discovered it for themselves!

Another fun way to teach this is to have a pancake day in class!!  Bring just one big batch of supplies to cook pancakes for all your students, and cook them on a griddle in the front of the classroom.  

Show an expression on the board representing how many batches you'll need with each ingredient's quantity listed inside parentheses.  Talk it through and let the kids help you out when you make the "mistake" of only doubling the first ingredient in the quantity.

Sum up your work on the board with a big "Pancake Algebra Expression."
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I hope you and your students enjoy these two analogies for teaching the distributive property!  Each analogy greatly enhances student understanding, especially when paired with an inquiry-based approach or these doodle notes.  Do you have any other helpful analogies for teaching Pre-Algebra concepts in a clearer way? We’d love to hear!
 
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