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:

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

Materials:

• 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

Activity:

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.

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.

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.

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.

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:

# My Secret Weapon to Teach Early Math Skills

If you are teaching your young one early math skills, maybe you should head to the toy store!  My secret weapon for teaching kids skills such as one to one correspondence, counting, subitizing, doubling, and adding is Parcheesi!

Disclosure: This post contains affiliate links.If you make a purchase from Amazon, I receive a very small fee at no extra cost to you.

First of all, if you are unfamiliar with the game, I will very briefly describe how the game is played.  Your four pawns are at home, where you wait until you roll a five or a two dice combination of five to enter the board. The game uses two dice to indicate your spaces to move.  You can add the dice together to move one pawn or let two pawns share the dice combinations.  You have to go all the way around the board and get all four pawns to your home to win.  Along the way, you can block players and capture players.  It’s a great strategy game!

## How does Parcheesi help with all of the math skills mentioned?  Let me explain.

Counting:  When the child rolls the dice s/he can count the dots on each die to figure out the value of each one.  Your child can point to the dots while counting. This gives your child a concrete way of practicing counting with an authentic purpose (to see how far to move).

With enough practice, s/he may begin to recognize that three dots is “3” without even having to count the dots.  S/he is subitizing, or recognizing a number quantity quickly without the need to count.  With enough hands on practice counting, s/he will begin to do this automatically.  By playing this game your child is getting a lot of practice counting and subitizing.

Adding:  Since this is a game that allows two dice to be added together to determine the number of spaces to be moved, your child is also practicing adding.  With the help of the dots, your child has a visual representation of the numbers in which to count.  The more practice your child has with objects they can point to and add together (the dots), they will naturally begin to remember some of these math facts and also create a visual representation of number quantities which they will use to figure out new problems.

One to One Correspondence: This skill is practiced in two ways. First, when your child counts the dots on the dice, s/he should only count each dot once.  For example, if your child rolled a six and counts one the of dots more than once, s/he may incorrectly say there are seven dots.  Encourage your child to count again making sure s/he doesn’t count any dots more than once. With sufficient experience your child will become very good at counting each dot only once.  S/he will likely figure out a strategy that works for him or her to keep track of which dots s/he already counted to avoid over or under counting.

Another way your child is practicing one to one correspondence is when s/he moves their pawn.  Your child can advance one space per number. So, if s/he rolled a six, s/he can only move six spaces.  Young kids may skip spaces or count faster than they move.  Encourage your child to count slowly and move the pawn as she counts.  Sometimes it helps if you, the parent, point with your finger to the next space so your child doesn’t skip spaces. With enough help and practice, your child will learn to move one space per number rolled.

Doubles:  When your are working with two dice there is the chance that you roll two of the same number. You can introduce the term, “doubles”.  For example, if your child rolled two twos, you can explain that two of the same number is called “doubles”, so s/he just rolled double twos!  Not only are you introducing a new term, but you are also building a beginning foundation for multiplication.

Eventually, your child will commit the these facts to memory.  Having double facts in their memory banks gives them a reference point when figuring out new facts. For example, if your child knows that 5+5=10,  s/he can can use that knowledge plus pattern recognition to quickly figure out that 5+6=11.

Truthfully, there are many games that can also help your child practice these skills.  Any game that has a board with individual spaces and uses dice can do this!  I like Parcheesi because it tends to be a little longer in terms of play time, giving more practice! My kids also love that they can capture me and send me back to home, keeping them motivated and excited to play.  So next time your child complains about math homework, maybe taking a game break might help

To purchase Parcheesi on Amazon:

# Counting Money for Beginners

My preschooler received some Easter money from his grandmother (\$5) and found some hidden inside of an Easter egg (\$2).  Since we were headed off to Target, he really wanted to bring his money to buy a Skylander.  I told him that they cost ten dollars or fifteen dollars.  He had to count his money to see if he had enough to purchase one.

Young ones usually count the number of bills. For example, he had a five dollar bill and two one dollar bills.  Most of the time, kids that young will count the three bills and say they have three dollars. Ideally, if I had five one dollar bills I could show him that the five one dollar bills was the same as one five dollar bill.  But I didn’t have enough bills for that.  Math bears came to our rescue again!

Here’s how I would show a young one how to add bills of different denominations using readily available materials:

Step 1:

Place the bills largest to smallest in a line.

Step 2:

Have the child read the number on the first bill. Take out the corresponding number of math bears, i.e. five math bears for a five dollar bill.  Teaching Tip:  This gives the child a visual, concrete representation of the number on the bill.

Step 3:

Repeat the process of corresponding the math bears to the number on the bills.

Step 3:

Have the child count  all the math bears together.   Teaching Tip: Have the child start on the left hand side to count.  Just like reading, we typically solve math problems left to right.  It’s never too early to establish good habits!

In our case, we were not done yet.  Remember, he was counting for a purpose.  He needed to see if he had enough money to purchase a Skylander.  I asked my little guy if seven dollars was more or less than ten dollars.  He said, “Less” and immediately started to throw a tantrum because he realized he didn’t have enough money.

Once he calmed down I asked him an extension question, “If you have \$7, how many more dollars do you need to make \$10?” He responded, “\$3″.  He can mentally figure out what numbers add up to ten so I did not need to use the math bears to help him solve this. But, if he needed help, I could have put out seven math bears and we could count together how many bears we added to make ten.

Older brother came to this rescue and gave his brother his Easter money- \$5. It was super sweet.  We counted the money once again and he now had enough money for his new toy!

I love when math can be taught in context for a real purpose!  Next time your preschooler or kindergartener wants to buy something, teach him or her how to count money!  Evaluate at the end if they have enough for their purchase.

# Teachable Moments

### Education is not preparation for life; education is life itselfJohn Dewey

There are so many learning opportunities around us, naturally, everyday.  Life requires skill, knowledge, patience, problem solving, and sometimes research.  We don’t have to contrive a learning experience for our children to learn.  We need to learn to survive and survival is our basic instinct.  Your child wants to learn!  Keep your eye open to opportunities in your children’s everyday experiences.  What skills or knowledge do they need to complete a task or solve a problem?

Sometimes it is best to let your child figure it out themselves, other times your guidance with the experience is beneficial.  I truly believe finding these natural teachable moments are the best way to teach!  Why?  Simply because the child is learning the skill within the context that is actually used, is by nature hands-on, and the child has a real purpose for solving the problem or learning the skill.

I’ll show you what I mean:

My son wanted make fresh juice.  Our go to recipe is to add kale, apples, celery into our juicer.  As I was finishing the dishes in the sink I asked my son (age 3) to get the apples out for me.  He took the whole bag to the table and I hear him count- one, two, three, four, five, six, seven, eight, nine.  I walked over to him and noticed how he placed the apples. Instead of lining them up he placed them two by two with one by itself (as pictured).

By setting up his apples this way I noticed a natural occurrence of something that I knew he was learning.

A little while ago we read the book One Odd Day by Doris Fisher.  It touched on the concept of numbers being even or odd.  My little guy was catching on to the idea.  Once I realized this was a developing skill for him, I later introduced some hand-on activities to play with the concept.  He really liked it!  Knowing that this was a skill he was working on, I asked him if the nine apples were an even or odd number. We talked again about what makes a number even or odd.  We could tell that nine was odd because one apple doesn’t have a buddy (that’s our preschool language).  He looked at his apples again, he told me that four was even.  This showed me that he was continuing to think about the math concept by mentally checking other numbers to see if they were odd or even.

By taking out nine apples, we had a problem to solve.  We only needed four apples to make juice.

Other concepts he’s been working on is addition and subtraction with objects.   Since I only needed four apples for the juice I told him, “I only need four apples.  You need to take some away.  Do you know how many to take away?” At first, he insisted on putting all nine apples in the juicer.  That was really too much so I encouraged him to take away apples until there were only four left.  He took away the apples one or two a time until he only had four left.  As he took away the apples he lined them up on a different spot on the table.  Once he got down to only four apples, he counted how many had taken away to leave only four. Therefore, he realized that he had to take away five apples to get down to four apples remaining.

From nine apples, he took away five. The apple in his hand was never counted originally.

My hope is that this gets you thinking about your everyday experiences with your child and realizing their true potential.  You do not have to replicate things exactly as you see them.  A true teacher knows that every child is different and there is no script for learning. Follow your child’s lead.  Keep a mental note of what they can do, what they are learning, and what is too difficult for them.  Life will hand you teachable moments.

# 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

Materials:

• Math Bears
• Playing Cards

Set-up:

• 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.

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.

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:

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!