Global Math Week Part 3: "Race to a Flat" with Different Bases

"Each digit has a place and each place has a value. That's why we call it place value."

This is such a foundational concept to understand in math. To better understand this important concept, the Navigators engaged in a game called Race to a Flat. 

Starting with base 10 using digits 0-9

Supplies:

Base ten blocks

    Units (1s)

    Longs (10s)

    Flats (100s)

Two dice

Place Value mat.

Rule: Only one digit can be in the "place". 

Roll dice, add together, and add that amount of units to your place value mat. 

Regroup (or KABOOM) if you have more than 9 units in the "place". 

Keep playing until you have reached a flat. (10 longs regrouped into 100)

Student playing Race to a Flat base 10

He has 4 "longs" (4 tens) and 0 "units" (ones)

We put the 1s, 10s, and 100s blocks into our "bank" at the top of the page, ready to regroup or KABOOM. 

We played this game until we had gained a foundational understanding of place value. 

After having played base 10 Race to a Flat, and having watched "Exploding Dots", we were ready to try Race to a Flat in different bases!

Even base 2! She played beyond a "flat" and needed lots more "places".

Base 2 (We flipped a coin marked 0 and 1)

Base 6 (We used a regular die with the number 6 covered.)

Base 4 (This die had digits 0-3)

Base 5 (this die had the digits 0-4)

Base 7 (This die is a regular die with digits 1-6)

Amazing, right?!

Global Math Week Part 2: Exploding Dots

The Navigators participated in Global Math Week by investigating different bases and these first graders GOT IT!

We talked about powers of ten and watched Cosmic Eye. Lots of conversation was generated by this video. 

Inquiry based learning: We watched the video "Exploding Dots" several times and just talked about what we noticed. 

At first we noticed:

• It was funny when it exploded. Kaboom!
• There were lots of dots. 
• The numbers changed.

Then we went a bit deeper:

• 12 is not 1100. It's wrong!
• It keeps on exploding when more dots are added.
• It explodes whenever there are two dots.

And even deeper:

• Two dots turn into one dot and goes into the next place over.
• It's like regrouping!  

Ding ding ding! We're getting it!

The Global Math Project: An Exploding Dots Puzzle

Do YOU get it?

We then went on to take the tutorials/online experience at Explodingdots.org. 

Do you see the light bulbs hovering above their heads?

 

Global Math Week Part 1: A Magical Moment with Humongous Numbers

Big numbers in first grade? Of course! Especially since gifted students LOVE THEM!

So, after we gained a solid understanding of place value, we took the opportunity to make very big numbers. 

Each student started with the digits 0-9 

and attempted to make the greatest number. 

We found a partner and put our numbers together. 

1 - 2 - 3 comma, 1 - 2 - 3 comma...

This pair turned their 6's upside down 

to make an even greater number. 

Clever!

Someone exclaimed, "Let's put all our digits together!"

We ran out of teacher generated digits and made our own!

We added lots of "Zero the Heroes!"

Some used big sheets of paper.

One student started to make more commas and announced, 

"Commas for sale! Commas for sale!"

The number twisted and twirled all around our classroom 

and so did the Navigators!

You would have thought that we had just won 

a championship  game and everyone had gone out on the field 

and was jumping up and down in celebration. 

It was a magical moment! 

And here is our number (approximately)

39,999,999,998,888,777,755,544,433,332,211,100,052,943,

108,432,985,710,674,322,100,310,528,431,975,866,547,998,

958,129,740,901,299,596,849,068,948,887,727,753,565,355,999,997,971,998,352,101,622,483,099,599,134,214,091,030,713,131,411,995,142,214,849,110,314,113,213,313,991,199,

999,119,893,086,917,633,711,999,299,399,999,994,381,999,

999,999 (not including all the extra 0's)

We then entered the digits, three at a time, into a website called Mathcat and discovered that our number was:

thirty-nine quattuoroctogintillion,

nine hundred ninety-nine treoctogintillion,

nine hundred ninety-nine duooctogintillion,

nine hundred ninety-eight unoctogintillion,

eight hundred eighty-eight octogintillion,

seven hundred seventy-seven novemseptuagintillion,

seven hundred fifty-five octoseptuagintillion,

five hundred forty-four septseptuagintillion,

four hundred thirty-three sexseptuagintillion,

three hundred thirty-two quinseptuagintillion......

and so on and so on for pages and pages!

(BTW, the first grade common core standard is place value up to 120.)

"Each digit has a place and that place has a value. That's why we call it...everyone? PLACE VALUE!"

A Quest to Discover How the Feudal System Worked

It didn't take long for the Navigators to discover that the feudal system of the Middle Ages was not fair! 

There were four main levels of the system. 

The top level: the royalty

The king ruled over all.

The next level down was the nobility and the church officials.

They pledged loyalty to the king

and were responsible for telling all what to do.

At times the two didn't agree, hence the English word feud.

The next level down were the knights. 

They provided protection for all. 

It took a long time and lots of training 

(and armor!) to become a knight.

At the bottom layer were the peasants and serfs (those who were basically slaves). 

They provided food and services for all. 

The Navigators then played a simulation game using M&M's.

Each person received 10 M&M's.

It all sounded fair and good ... until they discovered what family they were born into.

The first pyramid scheme! The peasants/serfs paid taxes and rent to knights, who in turn gave much of what they received to the nobles and church officials. They, in turn, gave much of what they received to the king.

THE KING ENDED UP WITH THE MOST BY FAR!!

The nobles and church officials each had a lot, too!

The knights had quite a lot.

And the peasants and serfs only had a few, 

enough to barely stay alive.

SO UNFAIR. 

Even with masks on we can show with our body language how we feel.

SO UNFAIR!

Here is how one student, after reading more about the feudal system, summed it up. 

 

STEAM Projects: Three Steps toward Building Collaboration

The Seabury first graders have been studying the Medieval era and have been not only doing a variety of STEAM projects, but have been learning and practicing the skill of collaboration. 

Step 1 Individual Project: Making a diorama of one of the four levels of the Feudal System

The Nobles

The peasants (with hovels in the background and a few knights to protect them)

A knight

More nobility

A king, a queen, and a knight

A pink polka-dotted dragon

Step 2 Small Group Project: Make the Tallest Tower. 

Supplies used: lots of toilet paper and paper towel tubes, scissors, two feet of masking tape, and a variety of cardboard odds and ends including a small box.

We needed to be very careful with our limited supply of tape

We needed to come up with a plan.

We needed to experiment with different ideas.

We had high hopes.

It took collaboration to use a tape measure.

A quick comparison of heights 

Adding the "Art" in STEAM

We needed to work together. 

Ta da! We reached the ceiling.

We felt proud of our accomplishments.

This group added ancient Mesopotamia and Egypt.

Can we add our dioramas? Yes! Great idea!!

We reflected on our projects as we filled out our lab reports.

A comic drawing of the project. 

Step 3 Whole Group Project: Our Classroom Castle

Stay tuned!  This project will put our collaboration skills and our engineering skills to the test!

Using Literature in Math

What do you do when Lady Di of Ameter and her husband Sir Cumference decide to throw a surprise birthday party for King Arthur and they have no idea how many people to expect? 

Well, they start to count the people as they arrive in droves!

And so we started counting. Each bean represented one person. 

What a fun way to discover a better way to count big numbers and to discover the need for place value.

 

We wrote down our strategies. 

And started counting. 1... 2... 3...

This was going to take a long, long time. 

We came up with some new strategies. This group started counting by 10's.

And then by 100's. We needed some bowls and cups to keep track.

Each group then brought their 1,000's, 100's, 10's, and 1's to our group staging area, the place value chart. 

We had to do some regrouping, and ended up with 5,614!

Here's how one student drew the activity.

We practiced on paper.

We practiced using base 10 blocks.

After literally hours of bean counting, 

place value is making sense to us. 

An example of a differentiated mini-lesson that always happen when we do Math Adventures. 

We look forward to many an adventure using the Sir Cumference book series during our year of "quest". 

Next on the agenda: who was King Arthur?

Big ideas for little people!