Division: Laying the Groundwork, Part 3

Manipulatives make learning fun.
Manipulatives make learning fun.

 Laying the Groundwork for Teaching Division, Part3

In Part 1 and Part 2 of Laying the Groundwork for Teaching Division, I discussed ways parents can begin laying the groundwork for the future teaching of division to their children.

Teaching division may seem like a complicated task but using manipulatives makes the skill easy to teach and to acquire.

For our purposes in this post, we will use recycled ice cream sticks. Family members could assist in recycling so that you have a useful amount.

Ask extended family members to save items that can be used as manipulatives to teach mathematical skills.
Ask extended family members to save items that can be used as manipulatives to teach mathematical skills.

(Another alternative would be to use tongue depressors. Just ask your doctor for a handful next time you have an appointment. If you tell him or her the purpose for your request, you may find yourself with a generous handful free of charge.)

Let’s Review Place Value First

Before we continue let’s take a moment to discuss the place value of numbers. This is just for the parents’ information.

The number 2 is a one-digit number which is made up of 2 one’s.

The number 23 is a two-digit number which is made up of 2 tens and 3 ones.

The number 234 is a three-digit number which is made up of 2 hundreds, 3 tens, and 4 ones.

In the number 2, the digit 2 is in the one’s place.

In the number 23, the digit 2 is in the ten’s place.

In the number 234, the digit 2 is in the hundred’s place.

In other words, a 3-digit number has 3 digits, one which represents the hundred’s place, one which represents the ten’s place, and one which represents the one’s place.

In the number 2, there is only one digit. This tells us we have 2 ones.

In the number 23, there are two digits. This tells us we have 2 tens and three ones.

In the number 234, there are three digits. This tells us we have 2 hundreds, 3 tens, and 4 ones.

Prepare Your Manipulatives
Choose your colors.

Back to our ice cream sticks. Choose a color you wish to use to represent the hundred’s place. For our demonstration we will use purple.

Choose another color to represent the ten’s place. For our demonstration we will use red.

Now choose another color to represent the one’s place. For our demonstration we will use yellow.

Use markers, paints, crayons, etc., per your color choices

Use markers, paints, or crayons according to your color choice to dye your assortment of ice cream sticks.  If your budget allows, colored ice cream sticks may be purchased inexpensively at various craft stores.

Teaching the Skill of Division Using Your Manipulatives

Now that you have your own manipulatives, let’s see how we can use them to continue laying the groundwork for teaching the concepts of division. You will find it much easier than you thought.

Ice cream sticks may be used to represent numbers.
Ice cream sticks may be used to represent numbers.
To represent the number 234, we will use 2 purple sticks, 3 red sticks, and 4 yellow sticks (per our color choices).

(To make this task even easier, you may decide to only use even numbers for all digits, especially if your child/student is very young.)

234/2 = ____
The example problem we will be solving is 234 divided by 2.
  • Lay the sticks out in proper order to represent the number 234.
Place value represented by manipulatives
Representing place value
Explain to your child what the colors represent.
  • Explain to your child what the colors represent. Always use the same colors to represent the same place value.
  • Tell your child to “pretend” he or she has two friends. The number 234 can represent marbles, cookies, building blocks, or whatever your child likes to play with.
  • Tell your child to divide the 234 between his or her two pretend friends equally.
Direct them through the process.

Draw attention to the 2 “hundred’s” sticks (purple). Share these two sticks equally.  They will place one stick in each pretend friend’s pile.

The “hundreds” divided.

Then direct them to divide the three “ten’s” sticks (red). They will place one stick in each pretend friend’s pile. But what will they do with the third stick? No, they cannot break it.

Problem represented thus far

Show them that they can solve this by trading the “ten” stick for ten “ones” sticks.

Now show them to place the ten “ones” sticks with the 4 “ones” sticks. How many “one” sticks (yellow) do they have now?

Ask them to divide these 14 “ones” sticks between the two “pretend” friends. 7 “ones” sticks should be placed in each pretend friend’s pile.

7 yellow sticks go to each friend
Explain the answer to the problem.

234 has now been divided into two equal but separate groups. The answer to the problem is the amount in one of the groups.

  • So, if we share 234 building blocks equally between two friends, each friend will have 117 blocks.

Therefore, 234 divided by 2 is 117.

234 divided equally between 2 friends.
234 divided equally between two friends.

This is an example of the division of a three-digit number by a one-digit number.

Where to start
  • Begin with the division of a one-digit number by a one-digit number, continue with the division of two-digit numbers by a one-digit number, and then the division of three-digit numbers by a one-digit number.
  • Go at your child’s pace.

Remember this is to be a time of enjoyment. Don’t get stressed if your child struggles at first. Eager learners will pick up on what you are requesting as you continue along.

I do hope these posts have been helpful. Parents can do a tremendous job of helping their children enjoy learning these somewhat difficult tasks.

Just take a few minutes each day to lay the groundwork for division and your child will find this task conquerable.

You may leave any questions in the comment box below.

Copyright 2017 by Peggy Clark

 

 

Laying the Groundwork for Division, Part 2

Laying the Groundwork for Teaching Division, Part 2

The process of division may seem intimidating to students and parents. However, it is not as complicated as many think.

Parents can make the passage to proficiency of this skill easier by laying the groundwork early in their child’s life.

In Part 1 of this post, two ways were discussed that parents may employ.

In this post we will discover another easy and inexpensive way to further aid in helping children develop the skills necessary to achieve mastery.

That way is through a simple technique that employs the use of manipulatives.

Manipulatives make learning fun.
Manipulatives make learning fun.

Yes, manipulatives may be costly to purchase but they can be readily made by recycling items already found in most households. One only need the imagination to come up with a variety of useful tools made from simple everyday objects that are usually thrown in the garbage.

For our purposes in this post, we will use recycled ice cream sticks.

Enlist the aid of extended family members in recycling so that you have a useful amount.

Make this a fun game. Your child will be learning concepts of division without realizing it.

Do this discovery activity.

Pile a number of ice cream sticks on the middle of a table or other flat surface. Ask a variety of questions that will engage thinking skills.

Ask extended family members to save items that can be used as manipulatives to teach mathematical skills.
Ask extended family members to save items that can be used as manipulatives to teach mathematical skills.

Change the amount of sticks. Then continue asking questions for that amount.

Adjust questions according to your child’s skill level.

Let your child discover the answers.

Whether your little one can count past ten or not is not important. Mathematical concepts such as one-to-one correspondence is being developed.

If your child is older, he or she should be able to give you a numerical answer through this discovery activity.

Some sample activities when working with one child:

Divide the pile of sticks so that you and I have the same number of sticks. How many sticks do you have?  How many sticks do I have?

Put all the sticks back in the middle of the table.

Now pretend that there are 3 people here. Divide the sticks into three equal piles. (Give the child time to complete the activity.) How many would each of us have?

Put 10 of the sticks in the middle of the table.

Divide the sticks into two equal piles.

Put 8 sticks in the middle of the table.

Divide the sticks into four equal piles or groups.  How many sticks are in each pile or group?

Use mathematical terms as you see your child progressing.

As your child progresses in understanding, begin to add in mathematical terms.

In the last question above, the word groups was added to the instruction. This is a simple but nonthreatening way for your child to begin understanding mathematical terms. Do this in a gentle way. When the child has grasped the understanding of the new term, use that term instead.

For instance, when you perceive that your child has grasped the understanding of what you are requesting when you use the word group, drop the word pile. “How many sticks are in each group?”

Don’t rush.  Just add in a new term as you see your child progressing.

Another example from above is the use of the term equal. The term equal should eventually replace the words same number.

Do a few minutes of discovery activities each day.

Adding just a few minutes of this activity to your child’s playtime each day will go far in laying the groundwork for what will not be daunting, but will actually become a welcome task of teaching the process of division.

More to come in Part 3.

Copyright 2017 by Peggy Clark.

Division: A Daunting Task

Laying the Groundwork for Teaching Division

Manipulatives Make Learning Fun Photo
Manipulatives Make Division Easy and Fun
Division is that part of math class that seems daunting to teachers and students alike.

I remember watching my older brother do long division. His homework pages had problems that seemed so long they looked as if they covered half of his paper. I assumed those problems must have been very important.  Doing that type of math looked so grown-up. It was a process that I wanted to be able to conquer. I couldn’t wait to get to that level of math.

Division is not so complicated as many think. It just needs to be taught correctly. Part of that comes with laying the proper groundwork.

Long before division class comes around, children should already be engaging in the concepts of dividing.

Those “official” concepts begin with kindergarten and continue level by level. But division has already been introduced to the child even before that “first” day of formal schooling begins.

For example, children see division at work around the supper table as they share the meal. A family of four shares four pieces of chicken equally. The pumpkin pie is divided into six or eight pieces.  A gallon of milk is poured into glasses. Rolls are shared round the table.  The last one may be divided in two parts to share between eager siblings.

So how can parents begin that formal groundwork for division?

Parents can add to what the child is observing day by day by simply adopting the usage of mathematical terms.

“Please share with your brother,” may be changed to “Please divide the roll between the two of you.”

Look for opportunities to use mathematical terms when appropriate.

Divide these sandwiches so we have two (or four) pieces each.

There’s only four cookies left. Share them equally with your sister.

Divide the candy bar equally between yourself and your brother.

Divide the last of the milk between yourself and Dad.

Divide the potato tots so that each of you get the same amount.”

Children will be alert to the methods their siblings are using because they want to be sure they are getting their “fair share.” This unknowingly draws their attention to the division process.

Another way parents can lay the groundwork is to allow their children to measure.

Mother can let the children measure the ingredients for her favorite recipes. Dad can let the children measure items for his next building or repair project.

We tend to think of measuring as adding to something that we are making; however, we also measure because we are about to subtract from something. We are taking a cup of milk from the gallon.  We are sawing a foot of lumber from six foot of lumber.

Measuring is an indirect way of preparing the child for future concepts concerning division.

This may seem odd, but division is really just a fast way to subtract the same number over and over.

A third way parents can lay the groundwork for division is to actually divide groups of items – not on paper, but with manipulatives.

I’ll discuss an easy and inexpensive way for parents to do this in my next blog post.

Copyright 2017 by Peggy Clark