Operations

Flowchart

ONE operation PER material at a TIME

Operations with Golden Beads

#### Materials

For this portion, you will be leaving all your golden beads on the shelf: the thousands cubes, the hundred squares, the tens bars, and the unit beads.

You'll also keep the large number cards on the shelf. These cards will be used to record the answers.

In addition to these, you will bring out the small number cards - which come in sets of three. There are 3 sets of cards which include the numbers from 1-3000. These cards are used to create the problem, which is why each set only goes up to 3000 as we do not want our answer to exceed 9000 - we only have 9 of the thousand cubes!

It's also useful to have up to five mats. Three for the small number cards (use linen napkins for this), one for the large number cards, and one to work on.

Use this checklist to collect all your supplies:

**Small number cards 3 sets - 1-3000**(print three copies)**Large number cards 1 set 1-9000**(printable in the Golden Beads module)**Linen napkins - 3****A large mat/rug - 1 (you may choose to use the colored operations mat)****Store of golden beads**

#### A Note About This Section

These lessons are typically done with THREE children in a classroom setting, because of how large and involved it is. You probably don't have a bunch of children on the same lesson in your home, and you'll have to improvise a bit and act as both, guide and peer to your child. The setup in the following lessons is quite elaborate, so I while I do encourage you involve your child in the set up, be careful not to overwhelm them as they will then be too exhausted to do the actual lesson. I suggest that you practice this lesson and understand it thoroughly on your own before presenting it to your child so that you can be confident and calm.

#### Addition With Golden Beads

**PROBLEMS:**

#### Static Addition Problems

This file contains some ideas of problems you can use while doing the lessons below, so you don't have to stop and think about whether the numbers will add up to over 9 or not.

STATIC addition is when you add numbers without having to exchange for the next category.

#### Dynamic Addition Problems

This file contains some ideas of problems you can use while doing the lessons below, so you don't have to stop and think about whether or not there will be any exchanging.

DYNAMIC addition is when you have more than 9 in a category, and you have to exchange for the next category.

**LESSON INSTRUCTIONS:**

#### Static Addition

Lay out your mats. Three little ones on the top, one large one beneath those, and one medium one to the right side.

Bring out all the golden beads and place them to the left of the mat.

Start arranging one set of small number cards on each mat. Your number card set up may vary. If you have wooden cards that are easy to take out of the tray, you may place the tray directly on the mat without taking out the cards. But if you have paper cards that are a bit more difficult to take out of their pockets, lay them out. Just observe and see what works best for your child.

Arrange the large number cards to the right of the large mat

Now you're ready to go!

Pick a simple problem that does not require exchanging, so each combination of numbers should not add up to more than 10.

Inviting the child: you've probably already built up a lot of excitement around the lesson, just by the set up. They're probably ready to jump right in.

Tell your child you're going to show them how to do addition.

"Today, I'm going to show you how to do addition... You already know how to make numbers with the golden beads, so today we're going to add a new challenge/twist. We're going to learn to add really BIG numbers!

Now, I'm going to tell you a number, and you're going to make it with these small number cards and bring them to the big mat. Please make three thousands... two hundred... and thirty three."

*child makes the number with cards and brings them to the mat.*

Have them place the number on the left side of the mat.

"Now I'm going to make a number..." (or let the child make the number if they want.)

Make a number with the small cards (from the next mat, create only ONE number with each mat), again, keeping in mind that the combination doesn't add up to **over** 9... also keeping in mind that you will also be making another number. Bring the number to the mat and place it underneath the other number, keeping space. Read the number out loud.

"Would you like to make the next addend? Can you bring... *insert appropriate number*

Place it below the previous number, making sure to keep a gap.

You will need three addends in total.

"Now, we're going to BUILD this addend with the golden beads! So first I have three thousand, so I'm going to get three thousand cubes and put them right here (next to the first number). Then I'll get the hundreds... (place them to the right of the thousands), then the tens... then the units..."

More than likely, your child will want to step in and take over. You can ask, "Would you like to build? or "Now it's your turn to build."

"Let's build the next addend...."

Continue building until you have built all three numbers.

"Whoa! Look how many golden beads we have on the mat! Now we are going to add them up!"

Push all the beads together, category by category, starting with the units.

"Now we need to count them and find out how many we have all together! We always start counting with the units."

Start by counting the units. Once you've counted them, fetch the answer from the large number cards that are sitting patiently to the right...

"Oh we have five units, so we will need the "appropriate number" card from the large cards. Could you find that card?"

*child goes and gets the card*

Place the card beneath the unit beads.

Continue in the same way with the rest, fetching the card after counting each category and placing it beneath the quantity.

"Yay! We counted everything! Now we're going to do the magic slide with the cards so we can read the answer."

Do the magic slide with the number cards and read the number.

Tell your child, "The answer is called the sum."

You are now done.

You can ask your child if they would like to do another problem, or put everything away.

#### Dynamic Addition

Dynamic addition is when you have to exchange every time you get to ten in any category.

You will do this lesson in the same way you did the lesson for static addition, except, once you've added up all the beads and you begin counting, every time you reach ten in any category, you will exchange for the next category, just like you do in the exchange game.

So for example, you have 18 unit beads. As you're counting, and you reach ten, say, "Oh, I have 10 unit beads. I have to exchange them for a ten bar!"

You would then put the unit beads back into the bank and take a ten bar and place it with the rest of the ten bars. Then continue counting the remaining unit beads and record the answer with the large number card.

You would do this every time you have more than 10 in any category.

#### Multiplication With Golden Beads

**PROBLEMS:**

#### Static Multiplication Problems

This file contains some ideas of problems you can use while doing the lessons below, so you don't have to stop and think about whether the numbers will multiply to over 9 or not.

STATIC multiplication is when you multiply without having to exchange for the next category.

#### Dynamic Multiplication Problems

This file contains some ideas of problems you can use while doing the lessons below, so you don't have to stop and think about whether or not there will be any exchanging.

DYNAMIC addition is when you have more than 9 in a category, and you have to exchange for the next category.

**LESSON INSTRUCTIONS:**

#### Static Multiplication

Arrange your materials in the same way you did for addition.

Lay out your mats. Three little ones on the top, one large one beneath those, and one medium one to the right side. Bring out all the golden beads and place them to the left of the mat. Start arranging one set of small number cards on each mat. Arrange the large number cards on the medium mat.

Now you're ready to go!

Pick a simple problem that does not require exchanging (use the sheet provided above with sample problems), so each combination of numbers should not add up to more than 10. Use the vault above to pick a problem instead of racking your brains!

"Ooo, today, I'm going to show you something so interesting. I'm going to whisper a number in your ear and I want you to make it with the small number cards."

Whisper the number in the child's ear. Be so very secretive, as if you're on a secret mission.

*child builds number with cards and places it on the left side of the mat*

"Now I'm going to tell you to get another number."

Whisper the same number into your child's ear again. You might get some giggles.

*child builds the number with the small number cards and places it on the mat*

"Oo! Now I'm going to tell you one more number."

Whisper the same number one more time into your child's ear.

*full on laughter as your child builds the number and brings it to the mat*

"Oh my, it looks like we have the same number three times! That's called our **multiplicand**. Let's see how much we have all together."

Push all the beads together, category by category, starting with the units, getting the correct number from the large number cards for the answer.

"We counted everything! Now we're going to do the magic slide with the cards so we can read the answer."

Do the magic slide with the number cards and read the number.

"This is called multiplication. We took the same number three times and added it up. Our answer is called a **product**."

You are now done.

You can ask your child if they would like to do another problem, or put everything away and repeat on a different day if there is interest.

#### Introducing the Multiplier

In the previous lesson, we introduced the concept of multiplication: adding up the **same** number *multiple *times. But we know that we don't need to write the same number multiple times in order to do multiplication, right?

So in this lesson, you're going to introduce the **multiplier** to your child.

Have your work area set up like you've done previously, but this time you will only need two sets of number cards.

"We're going to do multiplication again. Do you remember how we did that last time? Oh yeah, it was so fun. I asked you to get the same number three times!! But today, you won't have to get the same so many times. I'm going to show you an easier way.

We are going to build the **multiplicand**, but this time we will only make it once. Let's make *insert number*."

*child brings number to mat*

"Instead of making this number soooo many times, we will use those cards *points to unit cards* to tell us how many times we will add this number. Let's multiply this number by *insert number*. This is our **multiplier**. "

*child brings multiplier to the mat*

Place it below the multiplicand.

"Let's build this number *the larger one i.e the multiplicand* this many times *the smaller one i.e the multiplier*"

Have your child build the multiplicand as many times as the multiplier.

"Now we can add them all up."

Start by counting the units and find the appropriate number from the large number cards.

Continue on in the same way as the previous lesson.

#### Dynamic Multiplication

Dynamic multiplication is when you have to exchange every time you get to ten in any category.

You will do this lesson in the same way you did the lesson for static multiplication, except, once you've added up all the beads and you begin counting, every time you reach ten in any category, you will exchange for the next category.

So for example, you have 18 unit beads. As you're counting, and you reach ten, say, "Oh, I have 10 unit beads. I have to exchange them for a ten bar!"

You would then put the unit beads back into the store and take a ten bar and place it with the rest of the ten bars. Then continue counting the unit beads and record the answer with the large number card.

You would do this every time you have more than 10 in any category.

#### Subtraction With Golden Beads

**PROBLEMS:**

#### Static Subtraction Problems

This file contains some ideas of problems you can use while doing the lessons below, so you don't have to stop and think about whether the numbers will subtract without having to exchange.

STATIC subtraction is when you have enough in the minuend to subtract from the subtrahend without having to exchange for the next category.

#### Dynamic Subtraction Problems

This file contains some ideas of problems you can use while doing the lessons below, so you don't have to stop and think about whether or not there will be any exchanging.

DYNAMIC addition is when you have more than 9 in a category, and you have to exchange for the next category.

**LESSON INSTRUCTIONS:**

#### Static Subtraction

Subtraction is a bit different from addition and multiplication. Multiplication is essentially the same as addition... You're simply adding up the same number a multiple number of times.

Subtraction is a whole different ball game and this is why we introduce it AFTER multiplication, whereas traditionally, addition and subtraction are often put together. You can think of subtraction like... reverse addition.

This lesson contains all the vocabulary of the parts of a subtraction problem. You don't need to drill them in, just gloss over them. You can skip them if you feel like it's going to be confusing for either you or your child.

You're going to start off with a large number on your large mat. You will have already built the number with the golden beads and the large number cards on the mat.

Keep the number cards to the left and build the number with the golden beads to the right of the cards.

You will need two sets of small number cards.

Point to the beads and cards you set up. "That is my subtrahend. That's how much I have."

"Now you're going to make a number with the small number cards." Have the child make a smaller number (use a problem from the vault above).

Place this number at the bottom of your mat.

"This is the minuend. This is how much I'm going to share with you. Let's see, how many units do you need?"

Have your child take the amount and place it above the small cards. Continue on with the tens, hundreds, and thousands.

"Let's see how much I have left."

Count each category and number them with a set of small cards.

"That's how much I have left! That's called the difference."

Now stack the cards for the minuend and place it under the subtrahend and stack the cards for the difference and place it underneath the minuend.

"We just did subtraction!"

#### Dynamic Subtraction

Dynamic subtraction is when you don't have enough to subtract from in a category and you have to borrow from the category before it.

You will do this lesson in the same way you did the lesson for static subtraction, except, once you get to a category where you don't have enough in the subtrahend to take from, you will go to the next category and borrow from it.

So for example, you have 4 tens in your subtrahend, but you have 7 tens in your minuend. But you can't take 7 from four.

In that case, you'll go to the hundreds, take a 100 square, break it up at the bank for 10 ten bars and bring it back.

It may go something like this:

"Oh I only have four tens, but I have to take away 7. I don't have enough! Hmm... what can I do? Do you have any ideas? *Pause* Oh! I can break up the hundred and turn them into tens. I will go to the bank and exchange a hundred square for 10 ten bars."

Now you can take 7 tens and move on. **This is how you BORROW. **

#### Division With Golden Beads

#### Static Division One Divisor

Congratulations! You're reached the division lesson. I promise you, division isn't as scary as it sounds. You might actually find that it actually starts to make sense to you while you're showing your child this lesson! The division lesson is extremely fun to do and I encourage you to get your child's favorite toys involved.

Your set up for division will be a bit different.

You'll have your large mat, the golden beads to the left side, the large number cards to the left and one set of small number cards.

You'll also need some toys. Whatever your child is into... dolls, trucks, unicorns... You'll be using these as the divisors.

Use the problems here. For the first presentation of division, you want to make sure that every number in the problem is divisible by the divisor. The task's already been done for you. You don't have to think of it, just use the problems above.

"I'm going to build eight thousand, four hundred, and sixty four..."

Build the number with the golden beads and with the large number cards. Place the large number cards to the left of the beads.

"This is how much I have, it's called a **dividend**. Wow, I have SO much! I'm going to share them with my friends..."

(I'm using the skittles from the stamp game, you can use them or who ever else will be your "friends".)

Evenly space out the skittles at the bottom of the mat.

"I have two friends. They are my **divisors**. I'm going to share all of this with them. I have to make sure that all my friends all get the same. I'm going to start with the biggest one, the thousands."

Take a thousand and give it to a friend. Place it under the skittle. Keep doing that with the thousands until you don't have anymore.

"Now I'm going to do that with the hundreds."

Do the same with the hundred squares. Continue on until you have distributed everything.

"That's it. I gave it all to my friends here. Let's see how much each friend got it."

Count how many each skittle got. You can also just count how much one friend got, and it's pretty obvious that each one has the same amount. "My answer is what each person got."

"Each one of my friends got two thousand, two hundreds, three tens... which is called thirty... two! My answer is called a '**quotient**'. My friends are so happy that I shared with them!"

#### Dynamic Division with One Divisor

Dynamic Division with One Divisor: Same as static, but when you are unable to share equally, exchange for the next category.

#### Dynamic Division with Two Divisors

Operations with the Stamp Game

#### Materials

What you need for this section

- The stamp game
- A piece of string or yarn or a stick, cut about 6 or so inches long
- Pencils or markers
- Print outs from each section

Click on the image below for the DIY stamp game file

#### Introducing the Stamp Game

For this lesson, you need the beaded thousand cube, hundred square, ten bar, a unit bead, and one of each stamp from the stamp game.

The objective is to create the connection between the stamps and the concrete golden bead material. This is the first step into abstraction. The child will no longer use the concrete beads to do operations, rather they will substitute the stamps for the beads.

Set up the golden beads starting from the right with the unit bead like you did when you introduced them.

"So, from now on, we won't really use the golden beads, but we're going to use the stamp game instead! It's just like the golden beads, but it's smaller so it will be easier to use."

Next, you'll match the stamps to the correct bead.

Place the 1 stamp under the unit bead.

"This stamp says "1" on it. It's just like the unit bead."

Place the 10 stamp under the ten bar.

"This stamp says "10" on it. It's just like the ten bar. Instead of using the 10 bar, we will use the 10 stamp."

Continue on like this with the rest of the stamps.

Once you're done with the introduction, move on to the next lesson: forming numbers with the stamp game.

#### Forming Numbers with the Stamp Game

This file contains two pages of task cards that you can use for this lesson.

One page is color coded to match the stamps and the other page is not color coded.

The second part of introducing the stamp game is to start creating numbers with the stamps. You can use the sheet above, cut it into strips and use that as a starting point.

"Today, I'm going to show you how to build numbers with the stamp game! Instead of using the golden beads, we're going to use these stamps that I showed you instead. They're a little easier to carry than the golden beads, right?"

Show your child the strips.

"Can you read this?" Encourage your child to read the number and assist them if they need help.

"So we're going to build this. We will start with the thousands. This says, one thousand..."

***Make sure you place the box so that the thousands are on the left side***

Take one thousand stamp and place it right below the thousand compartment.

"Now I need eight hundreds."

Take eight of the hundreds stamp and place it in a line beneath the hundreds compartment.

Continue on with the rest.

If you reach a number with a zero in it, tell your child, "this says zero (which ever place value the zero is in) so that means we won't put any stamps here."

If you don't want to print the number strips, you can also dictate the number to your child or write them on a piece of paper.

#### Writing Numbers

In this lesson, we're going to switch things up a bit. Instead of giving the child a number to build, you will let your child build their own number and then write it down.

"Today, you're going to make your own number with the stamps! First, I'm going to show you how I build the number."

***Make sure you place the box so that the thousands are on the left side***

Start with the thousands.

"Hmm, I'm going to take five thousands..."

Place them below the thousands compartment in a line."

"Six hundreds... four tens and seven units..." Place each category below its respective compartment.

"Now I'm going to write it down. I have five thousands."

Write a five in the thousands box.

"Six hundreds..." Write a 6 in the hundreds box. Continue on until you have recorded all quantities.

"Now I'm going to read it. Five thousand, six hundred, and forty seven!"

Now, if your child is super excited and understands the flow and wants to take over before you have finished, you can allow them to do so. Or you can also ask them to wait until you are done. You must judge this on an individual basis as every child is different. You will have to observe and make your decision and guide accordingly.

#### Addition With the Stamp Game

#### The Addition Vault

#### Blank Addition Stamp Game Paper

Click on the image below to download the file.

#### Static Addition Problems

Click on the image below to download the file.

#### Dynamic Addition Problems

Click on the image below to download the file.

#### Static Addition

Use a problem from the vault and either write it down on the dry erase board or print out the sheet to record the answer.

Tell your child that you will be doing addition with the stamp game today.

Make the first number with the stamps.

"This is the first addend."

"Now I'm going to put this string here and make the next addend."

Place the string beneath the stamps and make the next number.

"Now I'm going to add them up."

Remove the string and push the stamps up.

"Now I'm going to count how much I have after adding them up!"

Start by counting the units - and then recording. Continue in this manner until you've counted all the stamps and recorded your answer.

Point to the answer. "This is my sum. Let's read the sum"

Read the number and record it.

"I'm done! Would you like to try a problem?"

#### Dynamic Addition

Dynamic addition is when you have to exchange every time you get to ten in any category.

Use a problem from the vault and either write it down on the dry erase board or print out the sheet to record the answer.

Tell your child that you will be doing addition with the stamp game, but you're going to show them something new today: how to exchange. This work comes after you've had plenty of practice with the exchange game with the golden beads.

You will start the lesson in the same way, building the addends with the stamps and adding them up together.

Start by counting the units - once you get to 10 units, say, "Oh, I have ten units. I can exchange this for a 10 stamp."

Put the ten unit stamps back in the box and take out a blue 10 stamp and place it with the rest of the 10s. Count the remaining stamps and record the answer.

Continue in this manner until you're done with all the categories, exchanging every 10 of a category for one of the next category.

Point to the answer. "This is my sum. Let's read the sum."

Read the number and record it.

"I'm done! Would you like to try a problem?"

#### Multiplication With the Stamp Game

#### The Multiplication Vault

#### Blank Multiplication Stamp Game Paper

Click on the image below to download the file.

#### Static Multiplication Problems

Click on the image below to download the file.

#### Dynamic Multiplication Problems

Click on the image below to download the file.

#### Static Multiplication

Use a problem from the vault and either write it down on the dry erase board or print out the sheet to record the answer.

Tell your child that you will be doing multiplication with the stamp game today.

"This is my **multiplicand** *pointing to the larger number on top*. This is the number that I will build... this many times *pointing to the **multiplier***."

2321 by 3

Take out skittles to represent the multiplier.

Place them vertically, one above the other. Make sure to keep some space between them.

Now you'll build the multiplicand. Lay out the stamps horizontally. Start with the thousands, and then move on to the hundreds, tens, units... All the stamps should be in one line next to the first skittle.

"Now I'm going to make 2321 again!"

Do the same thing. Build the number with the stamps next to the second skittle.

"Now I'm going to count how much I have!"

Start by counting the units - and then recording. Continue in this manner until you've counted all the stamps and recorded your answer.

Point to the answer. "This is my **product**. Let's read the **product.**"

Read the number and record it.

"I'm done! Would you like to try a problem?"

#### Dynamic Multiplication

Dynamic multiplication is when you have to exchange every time you get to ten in any category.

Tell your child that you will be doing multiplication with the stamp game, but you're going to show them something new today: how to exchange. This work comes after you've had plenty of practice with the exchange game with the golden beads.

You will start the lesson in the same way, building the multiplicand as many times as the multiplier with the stamps and adding them up together.

Start by counting the units - once you get to 10 units, say, "Oh, I have ten units. I can exchange this for a 10 stamp."

Put the ten unit stamps back in the box and take out a blue 10 stamp and place it with the rest of the 10s. Count the remaining stamps and record the answer.

Continue in this manner until you're done with all the categories, exchanging every 10 of a category for one of the next category.

Point to the answer. "This is my product. Let's read the product."

Read the number and record it.

"I'm done! Would you like to try a problem?"

#### Subtraction With the Stamp Game

#### The Subtraction Vault

#### Blank Subtraction Stamp Game Paper

Click on the image below to download the file.

#### Static Subtraction Problems

Click on the image below to download the file.

#### Dynamic Subtraction Problems

Click on the image below to download the file.

#### Static Subtraction

Use a problem from the vault and either write it down on the dry erase board or print out the sheet to record the answer. You may also want to bring a special friend along for a ride with this lesson. A skittle, a truck, a doll... Also keep in mind that the all the mathematical terminology is just for glossing over and you don't have to drill it in in anyway... just casually mention it and let it slide.

Tell your child that you will be doing subtraction with the stamp game today.

Make the first number with the stamps.

"This is how many I have! This is called my subtrahend. And my friend skittle wants some too. She wants this many *point to the minuend and read it*... So I'm going to share with her."

Starting with the units, slide down the stamps you are taking away.

"Let's see how much I have left over."

Start by counting the units - and then recording. Continue in this manner until you've counted all the stamps and recorded your answer.

Point to the answer. "This is the **difference**. Let's read the **difference**."

Read the number and record it.

"I'm done! Would you like to try a problem?"

#### Dynamic Subtraction

Dynamic subtraction is when you don't have enough to subtract from in a category and you have to borrow from the category before it.

You will do this lesson in the same way you did the lesson for static subtraction, except, once you get to a category where you don't have enough in the subtrahend to take from, you will go to the next category and borrow from it.

So for example, you have 4 tens in your subtrahend, but you have 7 tens in your minuend. But you can't take 7 from four.

In that case, you'll go to the hundreds, take a 100 square, break it up at the bank for 10 ten bars and bring it back.

It may go something like this:

"Oh I only have four tens, but I have to take away 7. I don't have enough! Hmm... what can I do? Do you have any ideas? *Pause* Oh! I can break up the hundred and turn them into tens. I will go to the bank and exchange a hundred square for 10 ten bars."

Now you can take 7 tens and move on. **This is how you BORROW.**

#### Division With the Stamp Game

#### The Division Vault

#### Blank Division Stamp Game Paper

#### Static Division Problems

#### Dynamic Division Problems

#### Static Division

Division with the stamp game is done in a very similar way to division with the golden beads.

You will use the problems in the vault.

"Today we're going to do division with the stamp game! Remember when we did this with the golden beads?

This number is my dividend. This is how much I have. Let's build this number."

Build the dividend.

"And this is how many friends I have..." *point to the divisor*

Take the green skittles out of the box and lay them out, spacing them equally.

The reason why you will only be using the green is because we are only doing division with a single divisor and the green represents units.

"Now I'm going to share all this... *the stamps* with my friends here."

Starting with the thousands, distribute them equally... placing the stamps underneath each skittle. Continue on in the same with the hundreds, tens, and units.

"That's it. I gave it all to my friends here. Let's see how much each friend got it."

Count how any each skittle got. You can also just count how much one friend got, and it's pretty obvious that each one has the same amount.

"Each one of my friends got *insert number*. My answer is called a '**quotient**'. My friends are so happy that I shared with them!

#### Dynamic Division

Dynamic division is when you don't have enough to distribute evenly to everyone, so you'll have to break it up into the next category.

For example, if you have 4 thousands, but you're dividing by three, you will have a one thousand stamp left over. So what do you do?

"Hmmm... So I have three friends and I gave them all one one thousand stamp and I have one left... but if I give it to her, he won't like that and if I give it to him, she won't like that, and.... so I can't really give it to anyone. But I think I can break up the thousand. I can turn it into 10 hundreds!! Aha!"

Replace the 1000 stamp with 10 hundred stamps. Now you can resume the distribution. Every time you end up with "extra's", you'll do the same.

At the end, if you have a problem with remainders, tell your child, "I have 2 units left and I can't share them evenly, so I'm just going to leave them here... That's my left overs, or my remainders."

Addition with the

Dot Game

#### Materials

**What you need:**

- Dot game board or printable (look for the printable below)
- Colored pens/pencils/marker to match the hierarchies of numbers + one black writing tool.
- Lots of numbers in your head

**Dot Game Printable:**

This file contains two dot games on one page. Cut the page in half. You will also need to write the numbers for the problem on a different slip of paper.

#### The Dot Game

**When to Present The Dot Game: **

The Dot Game takes the child to the next level of abstraction in addition. It is used ONLY for addition and not for the other operations. You can present the Dot Game to a child who has already been introduced to addition with the golden beads as well as the stamp game, both static and dynamic as the game requires mastery of exchanging.

Materials List

- 55-100 golden unit beads
- 45 ten bars
- 45 hundred squares
- 9 wooden thousand cubes
- Large number cards from 1-9000
- Three sets of small number cards from 1 to 3000
- Stamp game
- Dot Game