We introduced ten-frames the other day. In Pre-K we begin by using them to tell stories. As you might read in the link above, ten-frames are frequently used when children are beginning to practice subitizing, quickly assigning a verbal number to a set of objects. This is an important mathematical skill, but at this time it is not our main focus. We are focusing on one-to-one correspondence, oral language, turn taking, working memory and basic structure of a ten-frame. Each child approaches the task at their own level, expanding their knowledge and experience.
The students start with a blank ten-frame. We call it the “garden”. They also have chosen ten glass stones known as dragon tears or dragon seeds. Mrs. Pless or I then tell them a story.
Once upon a time, a wee little [Katie] elf planted three dragon seeds in her garden.
(everyone places three stones in the squares, one for each square starting at the top left)
Along came a bird who dropped two more seeds.
(place two more seeds in their plots)
The sun shone, the rain came down, the dragon plants grew and grew. Use your fingers to show me how many dragon plants grew in the garden.
The fun begins after they have practiced a few teacher stories. Now it is their turn to tell stories to each other. One narrates while the other reenacts on their garden. Stay tuned for a recent tale…..
You might have noticed some oddly shaped “art projects” coming home this week. They seem to be shrunken boxing mitts or maybe another attempt at creating our own lungs. However, you are missing the main ingredient. Black beans.
Yes, I did say black beans, but the children wouldn’t think of them as such. In their minds, they are ants. The two larger ovoid shapes are ant chambers connected by a tunnel. These abstract pieces of ant inspired architecture are the basis for our latest math mat.
In Pre-K, we practice early addition and subtraction concepts through the use of stories, frequently using a math mat as the backdrop. By playing with manipulatives as they combine and separate groups, the children gain a strong understanding of the relationships between numbers. They are also learning to identify the vocabulary used when making and breaking sets.
Now that it is at home, you can join in on the fun. Ask your child to tell you a story using any small manipulative. It could be tiny toys or small, dried beans of your own. Now make one up for them. You can play this as a game where you move the manipulatives and find an answer when your child tells the story and vice versa.
Here are some examples to start you off:
Once upon a time, three worker ants went to check on the queen. Later, two more ants came. How many ants were there all together?
One day eight ants were walking through the tunnels. Four ants stopped in the sleeping chamber for a nap. How many ants were left?
Sometimes the tasks that seem simple and one-dimensional have much more impact than we realize. Finger counting is a good example. When our children are little, we help them practice counting to five using their fingers. As they get older, they no longer need to count each individual finger, but know the finger configurations for each of the numbers 0-5. Ask a five-and-a-half or six-year-old to quickly show you the correct number of fingers for any digit up to five and they probably won’t even think about it. They will automatically present you with the correct number of fingers. Usually, these older children can quickly use the sets from both hands to represent numbers up to ten without actually counting, either. They are so comfortable with the formation of these sets, that putting the two sets (hands) together to make a new number looks like an easy task. So how do we get a younger child to this level of creating and recognizing sets? Play and practice, of course.
In mathematical terms, seeing the quantity of a set without counting is called subititzing. We support this skill by playing games that require the children to recognize arrays of pips on dice and singing counting songs using our fingers. With experience the arrangements on the dice or on their hands become second nature. By the time they are in kindergarten, they will see and identify these sets easily. Being able to visually recognize sets of objects will help them as they move forward into double-digit addition, subtraction and even multiplication.
We’ve been using dice with our horse unit to help us get used to these patterns. In the photograph above, the child is rolling two dice to find out how many apples to feed her horse. The red die represents the red apples (or pompoms) and the green die is for the green apples. Each child in the group had a turn to roll the dice and announce the feeding requirements.
Our horses are designed using an origami type of construction. The children decorated each horse as they pleased. The folds in the head allowed the horse’s mouth to be opened and closed. With each roll, the children “picked” the correct number of apples and fed them to their ravenous equines. This activity allowed the children to practice their subitizing skills while also exploring addition.
In Pre-K, we practice early addition and subtraction concepts through the use of stories. By playing with manipulatives as they combine and separate groups, the children gain a strong understanding of the relationships between numbers. They are also learning to identify the vocabulary used when making and breaking sets.
We are keeping this project for the rest of the week so that we can use it with all of the students. However, when it comes home, you can join in on the fun. Ask your child to tell you a story using their friend puppets. Now make one up for them. You can play this as a game, “My Turn, Your Turn,” where you move the manipulatives and find an answer when your child tells the story and vice versa.
Here are some examples to start you off:
Once upon a time, three friends ran to the park. They climbed a tree. Later, two more friends came. How many friends were there all together?
One day eight friends were walking through the park. Four friends had to go home for dinner. How many friends were left?
Often, parents and grandparents wonder when we’ll start teaching Math in Pre-K. What they are really wondering is when we’ll begin using traditional equations to represent abstract mathematical data. To be honest, you won’t find many traditional equations in Pre-K. Instead, we focus on the underlying concepts needed to understand adding more to, or taking some away from, a set.
For the past week, we’ve been exploring making sets of numbers in more than one way. With our first experiment, we used two colors of links and asked the children to make a chain of 8. As the children had not yet been exposed to this type of activity, they naturally fell back on what they knew. Without any further prompting, every child made a pattern with the two colors of links. This vividly showed us that, although they had a strong understanding of patterning, they really weren’t sure what we were aiming for with our seemingly vague directions.
So, after a few Morning Meeting discussions and rearrangements of link/chain distribution over two days, the children began to see what we were practicing. Once they were able to design chains with two colors to make sets of 9 with confidence, we moved on to more complicated directions.
Our most recent attempt opened up the number of colors available. Each child was free to choose any two colors and create a set of 10. Their goal was to try to come up with a set that didn’t match any other student’s. As you can see, at this point, most of them are still focusing on the color differences rather than the quantity differences within the sets. They are just beginning to realize that some of the number sets look the same even though the color sets differ. As we continue to practice this way of thinking, the properties of sets will become more solid for them.