Sunday, October 16, 2016

From Base 2 to Base 20 - Understanding Place Value!

Base 20? Really? And it's fun?! Read on...

In the primary math department at Seabury School, a solid foundation is laid down through lots of hands-on instruction and investigation. The students can then build upon this foundation and are able to transfer their mathematical knowledge into new situations. 

Recently the students experienced this when they applied their knowledge and conceptual understanding of base 10 place value to various bases. Using place value mats and manipulatives, the students first played a game called Race to 100

Students roll 2 dice and place the number of "units" rolled into the one's place. When there are10 units, a trade is made for a "long" in the ten's place. Trading continues until there are 10 "longs" to trade for a "flat"--a 10 X 10 manipulative that has 100 units. 

The students then played a similar game called Race to a Flat. With a solid, conceptual understanding of place value, students can understand the concept of "trading" when the maximum place value is reached.

In base 6, trades are made when there are groups of 6. 
In base 5, trades are made when there are groups of 5. 

In base 4, trades are made when there are groups of 4.

In base 3, trades are made when there are groups of 3.

We even can understand base 2, the binary system used
for most modern computer and computer-based devices.
Each digit is referred to as a bit.

We then went on to take the concept further 
and tried out some base 20 Maya Math! 

Our Maya Math Adventure:

Using sticks for 5, stones for 1 and shells for 0, 
we learned the ancient Maya method for writing very large numbers. 

We played some practice rounds at an interactive website:

And we got it!! 
First and second graders can understand and use base 20. 
Who knew!!

Lesson learned by this teacher: 
never under-estimate the potential of a child!

Sunday, October 9, 2016

Viking Math Adventure

Being a small, private school for gifted students, Seabury School has the luxury of truly differentiating in Math. To better accommodate the various students' needs, the Navigators (first graders) and the Gemstones (second graders) have Math at the same time and are given small group instruction 
from the first grade level to the fifth! 

"Education with the breaks off!" as our website says.
(I.e., there is no ceiling to how far the students can go.)

We also have the freedom to incorporate our various topics of study into Math. We purposefully do this several times a month when all the students come together for a 


Our Math Adventures are designed with some of the following in mind:
  • The students will become real life math problem solvers. 
  • The students will work collaboratively and learn from each others' ideas and each others' successes and mistakes.
  • Open-ended problem solving will stretch the students' brain muscles and increase their mathematical thinking skills. 
  • The students will learn to embrace thinking outside the box and learn how problems can be solved in a variety of ways. 
  • The students will discover that math is useful and is great fun!

Here are some pictures of our recent Math Adventure called "Viking Math Adventure."

We've been studying the Viking explorers as an introduction to our study of explorers. We began our lesson with a look at several Viking boats that have been unearthed in Scandinavia. 

We then were given the task of figuring out several things: 
(derived from

Some students worked on the strategy of "draw a picture" to figure out:
  • how many oarsmen were on the boat.
  • how many weapons were there in all if each had a sword, a spear and an axe. 

Several of them had not had multiplication before and were automatically using skip counting and repeated addition. 

Others were given more complex problems such as:
  • For every bench, there was a bow and two dozen arrows. How many bows and arrows were there on the ship? 
  • The Oseberg ship is from about the year 835 A.D. It was found in 1880. 
    • How many years old was the ship when it was found? 
    • How many years old is the Oseberg ship?
  • The ship and its equipment were made of different types of wood. It is estimated that the Gokstad ship was made of 6150 kg of oak, 880 kg of spruce and 225 kg of pine.
    • How many kilograms of wood went into the makeup of the ship and its equipment?  
    • The ships planks were fastened with 150 kg of iron rivets, the anchor weighed 100 kg and the sail and rigging weighed 1000 kg. How much did the ship weigh altogether?

They worked well collaboratively and used the math skills they have learned to figure out the answers. 

I overheard in the process:
"I don't think we need an exact answer for this. Let's estimate." 
"I think you're right. 2000-800=1200. The boat is about 1200 years old!"

This is exactly what we've been talking about in our regular math class! 

Watch out for 
the future mathematicians of America
because here we come!

Monday, October 3, 2016

Vikings Across the Curriculum

Seabury School claims to integrate subjects 
across the curriculum. 
Well, here's proof!

Be sure to read to the end to discover 
if this type of learning really works!

We read the Magic Tree House book, Viking Ships at Sunrise, for an introduction to the study of exploration and specifically Vikings. We discussed the characters, the setting, the plot, the climax and the resolution and began to discover why explorers explore. 

Using writing promps of situations the Vikings might have faced, we wrote our own Viking stories. 

Here is an excerpt: 

The Viking sailors went all the way to the North Pole. They were very cold. At least they brought a lot of shirts to stay warm. Later, they used them to make a sail. They found a polar bear. He chased them around. They repaired their sail using their extra shirts because they came across an ice storm. They ate a lot of fish.....

How did the Vikings find their way at sea? By using a sun compass. Equipped with a water bottle, three rocks, a couple sticks and the light of the sun, we constructed our own sun compasses and discovered which way is north. 

The Navigators and the Gemstones had a Math Adventure to discover how many oarsmen were on a longship and how many swords, shields and spears the oarsmen had altogether. We learned the "draw a picture" strategy for problem solving and figured out how to do multiplication (some haven't been taught it yet!)

We played a game on the computer called Viking Quest, an "epic game of loot and legend." It is a choose your own adventure type of game and we had a great time learning how to discuss the various options in an open-minded way. The kids left school still discussing what to do next! 

The next day we played the game with the 3rd and 4th grade Sphinxes and discovered the best ways to please the Chief!

We listened to the Scandinavian fairy tale called "East of the Sun and West of the Moon." There weren't pictures to go with the story so we imagined it in our minds. 


This is a picture of the troll one student imagined in his mind as he listened to the story. 

We also drew realistic pictures of Viking long ships.

Critical Thinking
What would we need to bring with us? 

Our supply lists included such things as pillow, gamer, IPod, Mrs. Towne, Mrs. West, my dog, TV, water, books, Siri, orange, rope, IPhone, underwear, maps, math, mini fridge, toothbrush, compass, perfume, brush, comb, fishing pole, bucket, crowbar, shield, socks, swim suit, Captain America video game, hot chocolate, umbrella, towel, fan or air conditioning and Xbox. 

(As you can tell, we are six and seven year olds and are still figuring out the concept of time and what it means that the Viking Age was over 1000 years ago.)

MakerSpace Collaborative Engineering 
We then made our own Viking Ship using a big, long box. We divided into groups and made the sail, the front and back parts of the boat and the wooden slats that make up the boat. 

MakerSpace Helmets
Instead of making the usual cookie cutter helmets, we each made our own unique helmet using the available supplies in the MakerSpace. To get ideas, we looked in several books and discovered that the Vikings did not have horns on their helmets. Several opted to include horns on their designs since that is how we often depict Vikings.

We will be studying maps this year and just started our Map of The World project. Here is a sneak preview of how we will map the explorers of the world:

Just plain fun
For Grandparents and Special Friends Day we had a Viking Rune treasure hunt with a real treasure to find at the end!

Play Acting and the True Test
When our Viking long boat was ready and each student had their helmet, shield and oar, we had the opportunity to JUST PLAY. And what a fine, noisy, knowledgeable bunch of Vikings we were!

Here are some of the conversations that were overheard:

"We're landing on Iceland!"
"Here's Greenland. Wait, this looks like it should be called Iceland!"
"Hey everyone, this is Newfoundland."
"Here's Italy. And Greece."
"Let's get something to eat. How about this polar bear?"
"We brought some fishing poles. Let's use them."
"Let's get some land. We need land."
"Don't forget. The Vikings weren't always mean. They became nice."

Some students started cutting out "treasures" to collect.

"Here's some gold. That's what we came here for!"
"What are other treasures we can find?"
"I know, diamonds!"
"And gemstones."
"Here's a cool book."
"Yea, books can be treasures."
"Let's get some money!"
"Vikings didn't have our kind of money."

It works! Through integrated,  project-based, hands-on, age-appropriate, engaging and fun learning, we are experiencing and learning what it meant to be a Viking explorer. 

We rented some trunks from the Nordic Heritage Museum.
The chain mail and helmets were heavy!


Saturday, September 24, 2016

Treasured People: Our Grandparents and Special Friends

What a treasured treat it was this week to host 
our grandparents and special friends. 

To show them around our classroom, we had a cryptic scavenger hunt with the hints written in Viking runes. The final prize? A treasure box full of treasures! Perfect for our concept of the year,

We then had the opportunity to take them around the school and show them all the wonderful things we treasure at Seabury--our library, our French room, our playground, our MakerSpace, our multi-purpose room, our computer lab and more. 

Be sure to check our blog throughout the year as we study world explorers, the American Colonial Era,  Native Americans, zoology, geology, botany, environmentalism and ecology, all through the lens of the treasure concept. We'll be asking:
  • what do people treasure?
  • why people treasure some things and not others?
  • what makes something a treasure?
  • how do we treat treasures?

Thank you for joining us for the afternoon and making each of us feel most treasured!!