I’m glad the parent blogs have been so well received! If you’re an educator reading this blog you can use all of the ideals with your students in small groups. The concepts explored in today’s blog deal with the prerequisites for counting and are appropriate for Pre-K, K, and 1st grades.

Some of you asked for just a few ideas at a time. Others asked for as much as they can get. To provide for all, I’ll begin with a simple explanation of each activity and how it helps develop number sense. If you’d like a more in-depth explanation, then keep reading the rest of the blog.

If your brain starts to hurt at any point, then just stop reading and go have fun completing the activity with your child.

On Tuesday I provided a link on the FREE RESOURCES page of my website for the “Number Scavenger Hunt.” I received emails asking for more information about how to use this activity. I also received questions about counting. This activity helps with counting and helps set the stage for the understanding of number.

The “Number Scavenger Hunt” asks the child to find sets of objects between numbers which are familiar to the child. This activity helps children use the stable order rule which says the words used to count must be the same string from one count to the next. It also helps with one-to-one correspondence which requires each counting word to be paired with exactly one object being counted. If a child chooses a set of objects which are not the same, then the abstraction rule is also being cultivated by making the child aware that the objects in a group to be counted do not all have to be the same.

Scenario 1/Early Stage of Number Sense: Brooklyn and her mom decide to “hunt” for objects between the numbers 1 and 20. Together they think about how much time it might take them to find all the sets of objects and they record that estimate on the paper.

(VIN: Very Important Note: If Brooklyn is in the pre-writing stage, then her mom will do most of the recording of abstract symbols and letters Brooklyn is unable to write. The mom can let Brooklyn draw pictures of the objects to represent the amount. If Brooklyn has to do all the writing herself, then the activity becomes a hand-eye coordination lesson in penmanship instead of a time to develop a deeper understanding about mathematics.)

Brooklyn quickly finds one object—her dog. She simply counts to 1 and says it out loud. To practice her one-to-one correspondence, she touches the dog and says, “1.” Brooklyn knows how to make a straight line from top to bottom, so she writes the number 1 in the box. She can write the word dog, but it takes her a long time, so she draws a circle with ears and a nose. She also puts a few spots on the dog’s face since her dog’s name is Spot.

Brooklyn and her mom continue this process with the remaining numbers. They practice:

1. Finding a set of objects that might have that amount. (Great practice in estimation, guess and check problem solving, and relative magnitude of numbers.)
2. Touching the objects while counting out loud in a stable. They do this several times together, and then Brooklyn tries counting the objects on her own.
3. After agreeing that there are a specific number of objects in the group, then they record the number and the description or picture of the objects they counted.
4. Brooklyn’s mother encourages Brooklyn to find varied sets of objects such as a toy, a shirt, and two shoes. This is a set of 4 objects.  She wants her daughter to abstract and realize that all the objects in a set don’t have to be the same.

Brooklyn is engaged and fascinated by her ability to “think like a mathematician.” But, after about an hour Brooklyn is thirsty and hungry and her mom is hot. That’s when her mom stops for the day and comes back to it the next day. The focus is not on the completion of the scavenger hunt, but the on-going process of developing a good sense about numbers.

Scenario 2/Developing Stage of Number Sense: Casey knows how to count all the way to 100, but he gets a little confused with numbers like fifteen and all the numbers in the 40’s. It impresses family and friends when Casey can count by tens to the number 100. But, his dad isn’t sure if Casey truly understands what the numbers represent or if he has memorized the stable order of the numbers he’s repeating. Casey says the numbers like he’s chanting a rap song.

They decide to “piggy-back” on “The Number Scavenger Hunt” idea and become number detectives. Together they decide to find the tens throughout the week and devote an entire day to finding that number. They make Monday the day to find sets of 10. Tuesday is for finding sets of 20, Wednesday sets of 30, Thursday sets of 40, and Friday sets of 50.

Wherever they go and whatever they do, they look for groups of their ten for that day. Casey is going into 1st grade, so he knows how to write his numbers. He carries a clipboard with him to record what they find. On Monday, Ten Day, Casey counts the number of letters on every street sign. He is thrilled every time he finds a sign with ten letters on it. He wants to go with his grandmother to the grocery store because he knows there are sets of 10 everywhere!

By the time the week is over, Casey has developed a good “feel” for his tens. When someone asks him about the number 20 he doesn’t just try to picture the abstract mathematical symbol for 20, but he pictures the 20 different kinds of Cheerios that were on one aisle of the grocery store. He thinks about the 20 pieces of pasta that were left in his bowl when he was eating macaroni and cheese. He truly understands and can explain to others that there can be 20 goldfish crackers on his plate, 20 cars in a parking lot, and 20 different pieces of trail mix.

Brooklyn’s Mom and Casey’s dad know that one of the most powerful mathematical tools they can give their children are concrete experiences with numbers.  These simple activities did just that!

For those of you who want to jump off the “high dive” into a deeper understanding of counting…keep reading about the prerequisites.

The STABLE ORDER RULE says that the words used in counting must be the same string of words from one count to the next. This principle usually develops before the child knows the correct string of words. The child may consistently count “1, 3, 5, 64” every time she counts 4 objects in a set. Practicing the correct counting string, in an engaging and meaningful way, will help a child self-correct.

ONE-TO-ONE CORRESPONDENCE means that each counting word must be paired with exactly one object being counted. When children initially begin to count, they may skip over an object or count the same object more than once. You may want to give your children sets of objects they can move from one location to another as they count. This concrete manipulation allows more of the brain to record what is being learned into long-term memory.

When my children were preschoolers, I used setting the table to practice this prerequisite at every meal. We used paper and plastic so nothing would be broken. (As a bonus it also made cleaning up much easier.) My son would take all 5 plates and walk around the table placing them and counting, “1, 2, 3, 4, 5.” He would repeat this with the napkins, eating utensils, and cups.

THE ABSTRACTION RULE states that all the objects in a group to be counted do not all have to be the same. When you count sets of objects with your child, try to expose her to varied compositions of objects within a set or group. Have them put a book with a toy and a cup. Expose them to sets which have large objects, sets which have small objects, and sets which are mixed.

Be sure to count sets of objects left-to-right and right to left. This IRRELEVANCE-ORDER RULE stated that you can count a set in any order and still get the same result. Ask your child to count beginning on the left. When your child is sure she knows how many objects are in the set, ask her if it will be the same when she counts from the right. This rule is also vital for the beginning stages of algebraic thinking. We’ll talk more about algebraic thinking in the July blogs.

For those of you who master these activities and want more, I’m adding several more FREE RESOURCES for parents. The Place Value Mat can be used to help your child organize his counting of beans for the Bean Stick Activity. The child puts one bean at a time into the ten frame in the one’s section of the chart. When he has ten, then he puts ten dots of glue on the popsicle stick and transfers the ten beans to make a ten stick.

Band Together is a game your family can play to build on the concepts being developed by creating bean sticks. This game has players rolling a number generator (die) and taking that number of straws. When a player has 10 straws, then they ask for a “band” to make a ten and have to sing or hum part of a song to get their rubber band. Using music is a way to help both sides of your brain learn a concept. More about this in future blogs…

I can’t wait to hear from all of you who try these activities! More fun ideas on Friday…