Empowering Parents To Teach: Factor Trees

Do you remember making factor trees when you were younger?  You started with a number and began breaking it into factors until you reached all prime numbers.  The factor tree was a way of finding the prime factorization of a number.


It looked like this:

Empowering Parents To Teach- Factor Trees


I decided to make this idea a little more hands on by making factor trees with leaves and sticks.



  • Printable leaves (click here for the FREE printable in Green or B&W)
  • Sticks (I collected mine from outside and cut them to be roughly the same length)
  • Whiteboard marker or pencil



1. Print out the leaves in color. Or, if you are like me and have a printer that refuses to print color, print the black and white leaves on green cardstock.


2. Laminate the leaves if possible. Your child can write on the leaves with the whiteboard marker and erase when finished, allowing you to use the materials as many times as you want. If you don’t laminate the leaves, your child can simply write on the leaves with pencil, pen, or marker.  Just be sure to print enough leaves, since you can not reuse them if they aren’t laminated.


Empowering Parents to Teach- Factor Trees


3.  Take out one leaf and write a composite (not prime) number on it. For demonstration purposes, I will use 45 as the example number. On the leaf I would write 45 and place the leaf on the working surface (floor, table, or paper) with enough room underneath the number to work down.


Empowering Parents to Teach- Factor Trees


4. Have your child name two factors of the number, excluding one and itself. For example, with 45 your child might say, “9 and 5″ or “3 and 15″.  Choose only one set of factors.


5. Show your child the sticks and tell him or her to place two sticks under the 45 to show that we are splitting the 45 into two factors. In this case, we will use 9 and 5. Next, have your child take two leaves and write the factors on the two leaves. Write one factor per leaf.


Empowering Parents to Teach- Factor Trees


6. Ask your child if any of the numbers that s/he just wrote can be broken down further. Your child should notice that the 9 can be broken down into 3 and 3. Repeat the process of placing sticks and leaves.


Empowering Parents to Teach- Factor Trees


7. Once again, look at the numbers and determine if any of the numbers can be broken down into two factors. In this case, all the numbers are now prime. The process is done.  Depending on your starting number, the process may be longer.


8. Explain to your child that once they have reached only prime factors, they have found the prime factorization of the number.  Have your child list the prime numbers that s/he ended with. In our example, it would be 3,3,5.


9. Show your child how we can write that as 3x3x5.  If your child is comfortable with exponents, show him or her how to write the prime factorization as 32 x5.  Have your child do the multiplication of 3x3x5 to clearly illustrate how the prime factorization is still the same value of 45, it’s just written differently.


10. Continue the procedure with more numbers.  Keep working for as long as your child is interested. Note: If this activity is too challenging, your child may need to review factors, or prime and composite numbers. Click here for an activity to teach prime and composite numbers.


11. If your child keeps a math notebook, have him or her record one of the factor trees in the notebook.  Be sure to write out the prime factorization too. This will serve as a reference and provide practice with writing factor trees in the standard format (as seen above). Another option would be to have your child paste a stick and leaf factor tree into the notebook (substituting the sticks for pencil lines).


Have fun :)


Try these activities:


Empowering Parents To Teach- Divisibility Rules Activity

Click here for the Divisibility Rules Activity



Empowering Parents to Teach- Prime or CompositeClick here for the Prime or Composite Lesson


 Empowering Parents to Teach- Pythagorean TheoremClick here for the Pythagorean Theorem Activity

Empowering Parents To Teach- More or Less Game

Comparing Numbers With Math Bears

Comparing Number Quantities- More or Less


One of the earliest math skills children learn is the concept of more or less.  We know easily (as adults) that five is more than three, but to young ones this takes hands on experience with objects to gain this understanding.  I’ll show you one way to gain that experience through a fun game. My three year old LOVES this game! I made it up for him after he watched me and his brother play the card game, War.


More or Less game


  • Math Bears
  • Playing Cards



  • Take out any cards that are not numbers, such as the Joker,  Ace,  King,  Queen,  Jack, you only need the number cards.
  • Put the cards face down in one big pile


How to play:

1. Each player takes a card from the top of the pile and places it in front of him or herself with the number facing up.

Empowering Parents To Teach- game







2. Each player takes out the corresponding number of math bears and lines them up next to his or her card. I would do this in turns. Have the child or parent go first, then switch. That way, the child sees both numbers being constructed.


Empowering Parents To Teach-  More or Less Game







3. The child may be able to visually see that one number quantity is bigger than the other. If not, try lining them up closer to each other and matching them one to one, like this:


Empowering Parents To Teach- More or Less









4. Have the child compare which line is longer.  Remember, this only works if you line them up one to one.  Ask the child if they have more or less than you.  If the child has more, he or she wins.  If they have less, you win.


5. What if you both have the same quantity? Teach your child the term “equal”. You both have an equal number of bears.  You both win!


6. Repeat as many times as your child wants.


Teaching Tip: To extend this as your child advances with the skill, you can have your child compare how much larger a number is.  For example, using this method the child can see that five bears is bigger than three bears by two bears. 


This game is very simple, but lots of fun!  I made it up on the spot, which is why I love having my math bears handy.  You never know when they may be needed!

Empowering Parents To Teach: Adding with math bears

Adding with Math Bears

Making Math Hands On: Adding With Math Bears


Once your child has developed one to one correspondence, he or she can begin to understand addition.  There are many ways to incorporate adding into your day.  When you are playing with cars, for example, count how many cars you have.  Ask your child, “How many cars would you have if I added two more?”  Add two more cars and count them all together.  This is how I introduce the concept of adding, in the context of play with real objects.


After the child seems comfortable with the concept, I would add the number representation of the problem along with the manipulatives.   Eventually, after a lot of practice, the child can add without the aid of objects.  But there is no rush!  You want your child to add in a hands-on fashion enough times so that he or she can form mental representations in their minds.  Until then, they need the physical representation of the problem. This takes time and practice and it is very necessary.


How to show the physical representation of an addition problem:


The set up:

  • Tray
  • Math bears on the right side
  • Foam numbers 0-9 on top
  • A couple of addition problems (based on child’s level) on the left


Empowering Parents To Teach: Hands on adding with math bears


Empowering Parents to Teach: Numbers

Numbers 0-9


Step 1:  Draw a card with an addition problem.


Step 2:  Have the child put the corresponding number of bears for the top number and the bottom number. These two numbers are called addends.


Empowering Parents To Teach: Adding with math bears

Step 3:  Explain that the (+) plus sign tells us that we are to count the bears all together.  So if we have one bear and we add five more bears, how many do we have all together?  The child may begin to count all the bears.  If not, show the child how to count them all together.  Sometimes moving them together helps:

Empowering Parents to Teach: Adding with math bears

Putting them all together


I put them all together under the equal sign so that the child gets a visual image of where the answer goes.


Step 4:  Have the child find the number that corresponds to the quantity.

Empowering Parents To Teach: Adding math bears



Teaching Tip:  As your child learns the concept of addition, he or she is also learning math vocabulary.  Words like, “plus”, “all together”, “equals”, “sum”, and “addend” are great words to include in your explanation.


The more hands on practice your child has with the concept the better!  Often times, we jump too fast into paper and pencil before the child was able to form a solid foundation of the concept.  If your child comes home with addition homework and needs your help- break out the math bears!


Linked to: Montessori Monday on Living Montessori Now




Empowering Parents to Teach: Math Manipulatives

Math Manipulatives Must Haves

There are two items I always have around to help teach math- math bears and linking cubes. If I am tutoring, helping with my son’s homework, or trying to answer my preschooler’s math question, these two tools come in very handy!


Math is best learned in a hands on way. These two items allow me to do that by creating a physical representation of a math problem or concept. The best part is I can use them for so many things, I don’t have to buy a ton of different materials!


For older kids, there are a couple more items I like to keep around for more advanced concepts. I will share those in another post. You’d be surprised how much learning you can foster with just these two! If you are preparing your environment for teaching math, these are both great to have.



Math Bears

Empowering Parents to Teach: Math Manipulatives



Linking Cubes


Empowering Parents to Teach: Math Manipulatives


Both can be used for:



To order these on Amazon:

*These are affiliate links which means if you make a purchase from the links below, I receive a very small percentage of the sale at no extra cost to you.

Baby Bear Counters (102 ct.)

MathLink Cubes (Set of 100)

Snap Cubes Set Of 100 (Sorry, no picture)