This lesson is pretty interesting.  It is about “counting back.”  It says that it is for Prek-2nd, but I think it is pretty complex for most 4 year olds.  You might have some children who would benefit from a lesson like this.  Check it out.

I have been busy these past couple of months writing some online training modules for early childhood practitioners about young children and math.  These will eventually be available through the INCCRRA/Gateways training site and will be free of charge.  Should be cool.

One of the things I keep reading about is how certain skills and competencies develop naturally and intuitively while others are less natural and come later.  One of these is subtraction.  Once children have an established sense of number, they begin to compose (add) and decompose (subtract) numbers.  However, since we nearly always count forward with children, counting backward is much harder.

Examples:

A child is passing out instruments from the instrument box.  He gets to the bottom of the box and there are three children left without an instrument.  The teacher asks, “How many more instruments do we need so that everyone has an instrument?”  The child the counts the leftover children, “1,2,3.  We need 3 more instruments.”

or

Two children bring some dolls to school to donate to the classroom.  One child brings 3 and the other child brings 4.  The teacher asks the children, “How many new dolls do we have for our classroom?”  The children know that they can count the first set and then continue counting (we call this “counting on”) the next set until they arrive at 7. Counting from 1 to 7 is something children have been working on for a really long time, maybe even every day since they started talking.  Counting forward is a fundamental mathematical skill.

It is much less usual for children to practice counting backwards.  I’m sure there are other examples, but the only one that comes to mind, is when we count backwards from 10 when a rocket is about to take off.  But then I thought of all of those songs we sing with young children that are about “taking away.”  You know the ones I mean: 10 Little Monkeys Jumping on the Bed, 5 Little Ducks Went out One Day, 5 Little Pumpkins Sitting on a Fence, etc.

So, when you are singing these songs with the children, are you using mathematical language to highlight subtraction and take away?  Do you say, “One little duck ran away so we take away one, and we have 4 left?”  This is very important.  It is not enough to believe that simply singing the songs will instill the concept of subtraction in children as they may not even be making the connection between the number of ducks in the song at all.  To some/many children, this is just a song that they love to sing.  Explaining the song, is the grown-ups job.  The reason we sings songs like those above is because they are about subtraction.

Once your children can count forward, be sure to find opportunities for them to count backward.  This will help dramatically when they begin to subtract and take away.

Five Little Ladybugs

Five little Ladybugs climbing up a door

One Flew away then there were four

Four Little ladybugs sitting on a tree

One flew away then there were three

Three little ladybugs landed on a shoe

One flew away and then there were two

Two little ladybugs looking for some fun

One flew away and then there was one

One little ladybug sitting in the sun

She flew away and then there were none

Using one hand – five fingers – you can illustrate the idea that

5 take away 1 equals 4 and 4 take away 1 equals 3, etc.

There are several versions of this song (5 Little Pumpkins Sitting on a Fence, Way up High in the Apple Tree, 5 Little Monkeys Jumping on the Bed) that work well and my guess is that you know most of them.

Try putting a small ladybug sticker on each of your fingers or on each of the fingers of your children.  This will help them make the connection that the fingers themselves, represent the ladybugs in the song.  I also like to use a felt board when singing songs such as these. Have one child come up at a time to remove the ladybugs (they are taking away) so they can see that take-away means less or fewer. Each time there is one less ladybug until there are none.

The addition sign (+) shows that one number is to be added to the other.  If children have concrete examples of items in front of them and they are asked to count how many items there are all together, they are adding.  If you were to put 3 apples on a table top and then draw a large + sign and put 3 apples on the other side of it, the message is that the two sets of apples should be added together.  The representation of the equals (=) sign lets them know that the total number equals both sets all together.

The same is true for the minus (-) sign.  Children tend to understand the concept of take away more readily than subtraction, so I encourage you to use take away when you ask children to subtract.  You can add the word subtract so they can become familiar with it, but take away provides a concrete and visual description of the concept that supports the preoperational and the concrete operational child.

Try and add these three mathematical signs into your classroom.  When creating visual cues for children, use these signs to support the message you are communicating.   Find ways to incorporate the language of “addition,” “take away,” and “equals” into your conversations with the children.