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

​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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Turn-In Bin
 
Instead of allowing students to approach you at all times during the day with their make-up work, it is a good idea to have a turn-in bin in your classroom. 

It can be as simple as a paper tray the Dollar Store, or if you are feeling crafty and creative, you can add color and labels, or have separate turn-in bins for each class- instant organization!
 
 
Assigning Absent Partners

At the beginning of each grading period, assign or let the students choose absent partners.  The student will go to his or her partner for make-up work and for getting the notes.  The partner can also be responsible for getting any extra handouts.   

​This strategy works very well for some classrooms, although there can be problems that arise, such as a student being continually absent or both partners missing on the same day.  Comfortably Classic shares a great ‘What did I miss?’ bulletin board calendar idea.


Planning Ahead with a Calendar
                             
As teachers, we all know the value of those few minutes between classes or before and after school trying to get work done, and as much as we love our students, frequent interruptions can be distracting!  Keeping an up-to-date, accessible calendar is a good way to hold students responsible, while maintaining your own time.

On a calendar in the back of the room, you can list lessons, work covered in class each day, and homework assignments.  Another option is creating a digital calendar using, Google Calendar.   A digital calendar is helpful, because you can update the calendar and students can access the calendar, regardless of where you are or what time it is!
 
 
 
Absent Folders
 
An option for holding students responsible for their own makeup work is to create a specific absent folder for each class.  On any handouts, write absent students’ names on blank copies.  The students should know to check their class’ absent folder when they return to class.
 
 
 Classroom Jobs
 
Another option is to assign classroom jobs each week.  One student’s job could be to collect all of the make-up work for all absent students for a whole week.   They could be responsible for gathering handouts and work for the absent folders.
 
You can have a standard homework recording sheet that they complete for each absent student, and then they can collect  any handouts throughout the day, with each absent student’s name already written on it.
 
This method is perfect if you have separate sub-folders in a binder for each student to take upon their return, then bring back when they have caught up on all the work.  You can re-use the folders and add them back into the absent binder.
 
 
 
Rescheduling Tests & Quizzes
 
Instead of spending time emailing or chatting with each absent student in those few, precious minutes between classes or on your own personal time, you can set up a sign-up sheet to hang outside your classroom, or a digital sign-up that students can access online. 
 
On the sign-up sheet, you can list days and times before and/or after school that work for you and leave space for students to write their name to sign up.  This can also be done digitally by creating and sharing a Google Sheet with your students.  
 
When passing out tests or quizzes, immediately write any absent students’ names on blank copies, clip them on a clipboard, and then place the clipboard with the name visible.  Then when the absent students come in to take their quizzes, they can simply grab their clipboard.  There are many other benefits to using clipboards in your classroom!
 
 

​Make-Up Log
 
Meredith, at Bespoke ELA, shares a great idea for managing make-up work.  She uses her classroom’s page on her school’s website as her “Make-up Work Log.”  She uses it to write a “diary entry” of everything that went on in class, updating it every day. 
 
It only takes a couple of minutes each day, and is so advantageous!  In addition to serving as a resource for make-up work, it can also serve as a resource for students that were in class, curious parents, your principal, and you for planning next year’s curriculum!
 
As I am sure you have realized by now, sometimes planning ahead and doing a little extra work in the beginning can save you a lot of time and energy in the future, and help make your classroom smooth and efficient. 

​When it comes to managing make-up work, it is important to establish the guidelines with your students beforehand; there should be firm and clear expectations on how long they have to make up their work, quizzes, or tests, and they should understand what steps need to be taken.  I hope these ideas are helpful for you! Do you have any ideas or tips for managing makeup work?  We’d love to hear more!
 
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