By Cathy Lichty
Anne and Adam were twins, born the same hour of the same day. They lived with their Mother, Father and one older brother. The older brother, Benjamin was 10 years old and the twins were 6 just about to turn 7.
Every day at the dinner table their Dad liked to hold a contest. He had only started doing this a month ago but he seemed intent on continuing for some time. Dad would pose a math problem to each child to solve in their head right then. If they got it right there was a prize of money to gain. Ben got some tough problems, like subtract 21 from 534. Ben almost always got it right – he was good at math.
The twins had started by getting counting problems. Anne might have to count to 20, then Adam might have to count backwards from 10 to 0. Both twins managed the counting pretty well but sometimes they needed a bit of help.
One day Dad asked Ben to multiply 42 by 2. Ben answered 84 without any hesitation. Then Dad asked Adam to count to 20 by two. Adam looked puzzled and turned to Anne. She shook her head and had no idea of what to say. Both Anne and Adam turned to Dad, “What?” they asked. “You know,” Dad replied, “2, 4, 6 and on.” “Ok,” Adam said in a hesitant voice, “2, 4, 6” then he stopped and looked questioningly at Dad. Anne piped up “and on”. “No, no” Dad said seeming a bit frustrated “what comes after 6?” Adam and Anne shook their heads. Neither of them had any idea of what came after 6.
Mom could see that things were not going well and their nice dinner could turn into a very uncomfortable time. Adam’s face was turning red and Anne’s eyes were filling with tears. “Let’s try this another time” she suggested. “Anne and Adam why don’t you count to twenty taking turns, Adam you start with One then Anne you say Two and then back to Adam. Let’s try.” The twins immediately brightened and began to count, each taking their turn to name the next number. This they could do. Mom applauded them and gave Dad a warning look.
After the twins had gone to bed that night, Dad spoke to Mom. “I’m a little worried, the twins don’t seem to understand math.” “Well,” Mom answered gently, “ I think math just hasn’t clicked in their heads yet, but I have an idea. I am going to take them on an outing tomorrow that I think might help. We’ll see.”
So, the next day as the twins were getting ready for school, Mom explained that she would pick them up right after school and they would be going on a little adventure to a special park. She assured them they were going to really like it and have a lot of fun. This sounded good to the twins so they headed into school excited and looking forward to their adventure.
Right after school Mom was waiting at the curb to pick them up. Then they headed down the road as Mom explained a little about where they were headed. “We are going to a special park, a park that is all about numbers and counting.” The twins faces fell. This did not sound like a fun adventure at all. This sounded like school work. “No, no don’t make those faces. You are going to have fun. Trust me” Mom assured them. The twins scrunched down in their seats. They couldn’t think of any way to get out of it but this did not sound like fun to them.
After some time, Mom turned off the highway and began to drive through a neighborhood and then she entered under an archway where a sign said, Welcome to the Counting PYRAMID. The twins sat up a bit. They looked at each other. What, they wondered, was a Counting Pyramid?
Mom stopped the car and they all got out and looked around. There were trees and green grass. Yep it looked like a park all right, but just a regular park. Mom started off down a gravel path, “Come on, follow me.” So the twins followed her, passing puzzled looks between them and shaking their heads. The path led up a hill for several minutes, when they reached the top they both stopped and stared with open mouths. There in the field before them was a great big pyramid, a real pyramid. “Woah”, they both said in unison, “Look at that thing.”
Mom had a huge smile on her face. “Yep,” she said “That is the Counting Pyramid.” She put her arm around each of the twins, one on either side. “Now look at the side facing us. Do you see the steps going up to the top of the pyramid?” “Sure”,” they answered. “Well look carefully and you will see that each step has a number on it, from one to twenty. There are twenty steps up to the top of the pyramid. Why don’t you go run up those steps to the top but be sure you say the number of each step as you go. Then head back down and say the number of the step as you come down.” Adam glanced quickly at Anne and then they both took off running.
“One, two, three, four, five, . . .” they shouted as they ran up the steps to the very top of the pyramid. “Twenty!” they both exclaimed, jumping up and down like kings of the mountain. Then, they raced back down counting backward as fast as they could. Mom met them at the bottom with a big smile and a hug. “That was fun, right?” she asked. “Right,” they both answered. “Okay, now follow me to the next side of the pyramid.”
They trooped around to the next side. This side was different. Mom pointed to the steps going up this side of the pyramid. “Look at these steps, there are only ten of them and look how they are numbered. “ “Two, four, six, eight, ten, twelve, fourteen, sixteen, eighteen, twenty,” both twins called out the numbers on the steps. They turned to their Mom with a question. “Are these steps counting by two?” they asked. “Yes, yes. That is exactly right. You can see the steps are taller, each step is as tall as two of the ones on the last side. Go climb this side of the pyramid and call out the number on each step going up and going down.
She didn’t have to ask twice, both twins took off taking the taller steps and counting them off as they headed to the top of the pyramid. “Twenty,” they shouted when they reached the top. Then they headed back down, “Eighteen, Sixteen, Fourteen . . .” they counted off coming down. At the bottom Adam sat down on the grass in thought. “So this side of the pyramid is counting by twos. I get it,” Adam said with a proud smile. Anne turned and studied the steps, “Yep I get it too – two, four, six, eight. Yep got it.” She smiled, “Dad is gonna be surprised.”
“Well,” said Mom with a smile “Why don’t you climb it a couple more times to let it really sink in. Keep shouting out the number of each step.” Both twins climbed up and down the side several more times. “So”, said Mom “Are you ready for the next side?” Neither twin had given a thought to the third side of the pyramid. What was that side going to be like.
They hurried over to the third side. “The steps here are really tall, “observed Anne “and there are only four of them.” “Right, look how they are numbered, 5, 10, 15, 20. This side is counting by fives.” Mom explained. Anne and Adam studied the steps. They were a lot taller steps, each step was a tall as five of the steps on the first side of the pyramid. “You see how you get to the same place as the other sides, twenty at the top of the pyramid. But you do it by steps of five so you only need four of them.” “This is cool,” said Anne. “Does Dad know about this?” “Yes,” chuckled Mom, “I think he does. But he is going to be surprised that you know. Go on and tackle this side.”
“Wait, wait,” said Adam with his hands out. “What about the last side? I want to know what it looks like.” “Ok,” said Mom “You can come back to this side. Are you ready for side Four?” “Yeah,” both twins screamed as they raced to the fourth side. “Look at that!” gasped Adam. “How are we gonna climb that?” Anne and Adam studied this last side. This side had only two steps but each one was ten single steps high. This side counted by tens.
“Well I think you are going to need to work together. There are only two steps but you are going to have to work together to get to the top. Anne why don’t you give Adam a foot hold with your hands.” Mom demonstrated linking her hands together to offer a foot hold for Adam. Anne moved next to the first step and offered her foothold to Adam.” Once Adam managed to pull himself to the top of the step he laid down on his belly and reached his hand down to Anne. “Grab ahold Anne and pull yourself up.” Anne huffed and puffed but was finally able to scramble to the top of the step, then they repeated their moves to get to the top of the next step. “Twenty,” they both yelled. “Zero, ten, twenty. Twenty, ten, zero. Counting by ten.”
Anne and Adam spent the next couple of hours climbing the different sides of the pyramid and shouting out the number of each step as they climbed it. At the end of the time they were both plenty tired out and they had contented smiles on their faces. They couldn’t wait till dinner that night.
The family all settled around the dinner table and Dad turned to Ben, “Ben what’s 32 times 3?” Without a moments’ hesitation Ben answered, “96.” “Here you go,” and Dad slapped down a quarter in front of Ben’s plate. Dad turned to Adam. He sighed and then asked Adam “What number comes after 6?” “Dad that’s too easy, ask something harder” replied Adam. Dad got a puzzled frown on his face and turned to Mom. She nodded at him and slyly raised two fingers to her cheek. Dad got a surprised look on his face but asked Adam, “Adam can you count to ten by twos?” Both twins smiled hugely and shouted in unison, “2, 4, 6, 8, 10,“ then they took a breath and continued, “12, 14, 16, 18, 20.” They raised their hands in victory and then counted backward from twenty by twos, “20, 18 16, 14, 12, 10, 8, 6, 4, 2, 0.” Dad was amazed. Ben was amazed. Mom and the twins just smiled.
The End