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



Struggling with Addition, Part II

Strugglers who find addition to be a chore may find it a fun adventure when given the opportunity to learn with manipulatives. The use of these hands-on objects leads to purposeful learning in a stress-free manner. Allowing children time to “play” with such objects increases their imagination, stimulates brain activity, develops motor skills, and lays a foundation for learning mathematical concepts.

Cubes, dice, building blocks, building logs, buttons, beads on a string, ice cream sticks, pinto beans, even army men — what do these have in common? Each of them are wonderful tools that can be manipulated in order to accomplish learning.

The use of such tools is an inexpensive way to build upon the knowledge that a child already possesses. During play with various objects, a child learns how to build up and take down, gather together and take away, group together and take from, and sort by his or her preference. At the beginning stages, however, a child does not know the official mathematical label that we would use for such manipulation, but through play the groundwork is being laid upon which we purposefully begin to teach the foundational concepts and principles that lead to the understanding of the processes of addition, subtraction, multiplication, division, etc.

The introduction of handmade or purchased rectangular rods that are proportionally sized lead to even greater learning. Several companies have manufactured rectangular rods that are a great addition to your arsenal of manipulatives. However, knowing the limitations of household budgets, poster board or card stock can be used to create a representation of these rods, howbeit, they are not three-dimensional.

Place value is traditionally taught in some schools through the use of an abacus. Some students struggle with the use of the abacus because not all students have their own to manipulate. It is easier for a child to understand the concept when they have their own manipulatives to handle and engage in learning.

An inexpensive way to teach children place value is through the use of dried beans and ice cream sticks. Single beans are used for counting by ones, sorting into groups of equal amounts, etc. Ten beans will fit nicely onto an ice cream stick.

Using proper glue, allow the child to make his or her own “ten” sticks so he or she will realize that there are ten and only ten beans on each stick. Ten of the “ten” sticks can be placed side by side to create “hundred” sticks — just glue 2 sticks across the back to hold them together. A variety of mathematical concepts can be taught using these sticks.

So how can we use manipulatives to teach addition? By now, you probably have a variety of ways rambling through your mind, but we will give some direction in a later post. For now, begin to let your mind wander back to your childhood days when you played with blocks and logs. Yes, learning can be fun — at least some of the time.