Numbers and Counting
Flowchart
Materials
Printables
Print, laminate, and cut large number cards. Click on the button below to download the large number cards.
Lessons
Notes About the Flow Chart + Flowchart PDF
One of the most difficult and confusing things about the Montessori math curriculum is figuring out the sequencing and order of presentations, and rightfully so. It's not really a linear curriculum where you take your child from a to b to c. Everything is based on what interests you are observing in your child, and so the direction you take will vary with every child.
The flow chart here will help you make decisions on the different pathways you can take with your child, depending on what sparks their curiosity the most.
Some children absolutely love the golden beads and some don't really have a thing for it. Some may want to gloss over the golden beads and move on to something that's more interesting to them.
After you've introduced the decimal system and have done a good amount of practice, you can move on to doing golden bead operations (starting with addition) - OR move on to introduce the bead stairs and teens board from the linear counting kit. You can do these simultaneously as well depending on the interests of the child.
Addition with golden beads (found in the operations tab) and exchange game can over lap as well.
Introducing the Decimal System
For these lessons you're going to need: One cube of 1000 beads, one square of 100 beads, one bar of 10 beads and one unit bead.
- Take the child to the shelf and show him where the materials are; have the child carry the tray to the table
- With the materials on the tray from left to right being thousand, hundred, ten and unit; you will start with the unit and move to the left
- Present the child with a Three Period Lesson
The purpose of these lessons is to introduce the child to the place value of numbers and decimal system, and to illustrate in a concrete way that it is based on ten.
- Period 1
- Period 2
- Period 3
- When to Move On
Introduce the concept of the decimal system
First point the the unit and say, "This is a unit," and ask the child to repeat the word unit.
- Pick it up and feel it and give it to the child to hold, and then instruct them to place it back on the work mat.
- Next, pick up the bar of ten beads and say, "This is ten," and ask the child to repeat the word ten, then let them hold the bar of ten.
- Say to the child "let's count how many units there are in a bar of ten."
- Instruct the child to lay the bar of ten vertically on the work space.
- Pick up the unit and touch it to each of the beads in the bar of ten, while slowly counting 1 unit, 2 units, 3 units, etc. The child should count with you, encourage them to count if they don't do it on their own.
Now, place the unit bead back in its place on the work space and show the child the hundred square.
- Pick it up and say "This is one hundred," and ask the child to repeat "one hundred." Hand the square to the child and let them feel it, you'll be surprised at how interesting this is to the child!
- Say to the child, "We used the unit bead to see how many units there were in ten, let's use the ten bar to see how many tens there are in one hundred."
- Instruct the child to lay the hundred square on the mat and hold the ten bar above each row of ten on the square, vertically as you count across, "one ten, two tens, three tens," etc.
Direct the child's attention to the thousand square and say, "This is one thousand." Ask the child to repeat "one thousand."
- Pick up the thousand cube and feel it, and then give the child a turn to hold the thousand square.
- Ask the child to place it on the work space and say, "Let's count how many hundreds there are in one thousand!" Some children will have caught on and will have a guess, this is wonderful, just say, "You think there are 10? Let's find out!"
- Count the hundreds from left to right or from the bottom to the top, hold the hundred vertically/horizontally on top of the thousand cube as though you were going to slice it, and say "One hundred, two hundreds, three hundreds," etc.
This is the end of the introduction lesson. You may continue on to the second period games or place the beads back on the shelf and remind them of the language one last time. One unit, one ten, one hundred, one thousand and you place them on the shelf.
Recognition and association
In this second period, to goal is to give the child the chance to show that they recognize the units, tens, hundreds and thousands and to give them the opportunity to hear, feel and manipulate the beads. During this period, we do NOT ask the child the name of the object by asking "what is this?' or "do you do you know what this is called?" - refer to the video lesson on the Three Period Games in the Getting Started section for a refresh.
With this in mind, give the child instructions such as:
- Place the unit in my hand
- Please put the thousand here (point to a location).
- Touch the top of the hundred square with your hand.
- Hide the unit bead in your hand.
- Please give the ten bar to me.
- Play hide and seek with the objects
Get creative and come up with fun things for the child to do with the materials! When they begin to either lose interest or have mastered the concept, you many replace the materials on the shelf, once again reminding them of the names of each (one thousand, one hundred, one ten, one unit) and move on to Period Three games on a different day.
Note: Just make sure no one sticks the beads in their nose, mouth, or ears!
Recalling the Names
Once you've completed the introduction and Second Period games, you can move on to the Third Period Games.
Place the thousand cube, hundred square, ten bar, and unit bead on a mat in its correct order.
-Beginning with the thousand cube, ask the child, "what is this?"
-Repeat with each, in order, asking "what is this?" for the hundred, ten and unit.
-Next ask for the names of each out of order, you might begin with the tens, then ask about the thousand cube, and next the unit, followed by the hundred square, for example.
-For a fun twist, you can also reverse roles. You be the student and let your child be the teacher. Ask your child to teach you.
Be silly and say, "I don't even remember what this is called! Can you tell me what it's called?"
Or reverse roles from the Second Period games. Instead of you giving your child orders, have your child give you orders on what to do with the objects in front of you.
If your child says, hide this, while pointing to the object, gently ask them, "what's it's name?" or "what is it called?"
Continue playing until your child loses interest or has mastered the concept.
Once you are certain that the child understands and can name each object, move on to the next lesson - the first layout: "Tray of Nines"
First Layout - "Tray of Nines"
In this lesson, you're going to create a layout of the decimal system to show the child that once you get to nine in a category, you go to the next category.
For this lesson, you'll need to keep out nine units, nine ten bars, nine hundred squares, and just one thousand cube on a tray.
Take the tray over to your work space.
"I'm going to show you something very neat with the golden beads today. We're going to count them!"
Take out a unit bead and place it on the top right hand side. Count, "one unit."
Take out another one, lay it below the first one, with a large gap, and count, "two units."
Continue on until you get to nine.
"When I get to nine units, I'll take a 10 bar." Pick up a ten bar and place it in a new column.
Count as you lay out one at a time, "one ten, two tens, three tens..."
Once you get to nine tens, say, "Ten tens makes a hundred." Take a hundred square and start a new column.
Do the same with the hundreds.
Now you can play some fetching games while you have the layout out! This is also a "third period" lesson.
Ask for a quantity from one category. Five units, four tens, six hundreds... If you notice that your child is able to take quantities from one category with ease, start asking for quantities from two categories. Keep playing until you notice that interest in waning and come back and play more fetching games another day.
Fetching Games with Beads
In these lessons, you're going to play the fetching game with the beads. The purpose of the game is to ask for specific quantities to get the child acquainted with the categories.
Note: you don't have to complete all four parts before moving on to the next lesson: Introducing the Number Symbols. Once you've played a good amount of fetching games, you can introduce the number symbols, while continuing to play fetching games.
- Part 1
- Part 2
- Part 3
- Part 4
For this lesson, you will arrange the entire bank of golden beads on the shelf. This will be the home of the golden beads, where they will live.
Tell your child that you're going to be playing a game.
Fetch from a single category at a time - based on how much difficulty the child can handle, you have two options:
- Either ask from only ONE category per session and build up.
- Or ask from all four categories, one category at a time.
Start by asking for quantities from the unit category. (Bring me five units, four units, seven units etc.)
Once the child gets the hang of it and is ready for more (on the same day or a different day), ask for ten bars. Continue on with the hundreds and then the thousands.
If this seems too easy, you may ask for beads from all four categories, but only ask for beads from ONE category at a time. For example, you might ask for five units, then for six tens, and then two thousands, and then four tens again, and then two hundreds...and so on. You can go on to asking from two categories if you notice readiness.
Ask for beads from two categories at a time - starting with units and tens, and then moving on to ask for beads from two of any of the four categories as the child is ready.
For example, you might say, "Bring me three tens and five units."
Next, count and lay out the beads, and say the quantities while pointing to them.
"We have three tens and five units."
Finally, explain how many beads you have in total, and how to combine them.
"Three tens is also called thirty, thirty plus five units is thirty five."
Ask for beads from three categories at a time
- Start with units, tens and hundreds and then moving on to include thousands.
- For example, you might say, "Bring me two hundreds, three tens and five units."
- Next, count and lay out the beads, and say the quantities while pointing to them.
- "We have two hundreds, three tens and five units."
- Finally, explain how many beads you have in total, and how to combine them.
- "Two hundreds plus three tens--which is also called thirty, plus five units makes this number two hundred and thirty five."
Ask for beads from all four categories
- For example, you might say, "Bring me 1 thousand, 2 hundreds, 3 tens and 5 units." all at one time.
- Next, count and lay out the beads, and say the quantities while pointing to them.
- "We have one thousand, two hundreds, three tens and five units."
- Finally, explain how many beads you have in total, and how to combine them.
- "One thousand, plus two hundreds, plus three tens--which is also called thirty, plus five units makes this number one thousand, two hundred and thirty five."
Second Layout: "The 45 Layout"
The "45 Layout" is a complete layout of the decimal system, giving the child a birds eye view of all the quantities.
Let's jump straight into it. If you have a color coded mat, like the one from Branch to Bloom, it's perfect for this lesson, but if not, a regular mat works as well.
Take all your beads to your work space and arrange them in order from right to left, starting with the units.
"I'd like to show you something new today..."
Take a unit bead and place it on the top right corner of the mat.
Count out loud. "one unit..."
Take two unit beads and place it below, with a sizeable gap. "Two units."
Continue on until you read nine units, making sure to count out loud.
"After nine units... comes ten."
Take a ten bar and start a new column and continue on in the same way, making one ten, two tens, three tens, etc... until you reach 9 tens.
"After 9 tens... comes one hundred!"
Do the same with the hundreds. One hundred, two hundreds, three hundreds... etc.
Once you reach the thousands, you'll notice that you only have enough thousand cubes to make three thousands. You can point that out to your child.
"We only have enough thousand cubes to make three thousands... can you imagine what four thousands would look like? What about five thousands?Close your eyes and try to imagine!"
Once you have the entire layout, you can play some fetching games.
This is a simple lesson that makes a huge impression!
Introducing the Number Symbols: 1, 10, 100, 1000
For this lesson you're going to need the large number cards 1, 10, 100 and 1000
Period 1:
- Take the number cards for 1, 10, 100 and 1000 to a work space and place them to your left.
Show the unit card to the child and tell the child "this is how we write 1." Point out that the card has NO zeros in it and move it to the right of the work space. - Next show the child the 10 and 100 and 1000 cards in the same way, emphasizing the zeros and counting them.
Period 2:
- Take the number cards for 1, 10, 100 and 1000 to a work space and place the cards in random order in front of the child.
- Ask the child to identify the cards. Here are some examples:
- "Please point to 1."
- "Show me 10."
- "Please hand me the 100 card."
- "Which one is 1000?"
- "Put 10 on your head."
- "Hide 100 on the table."
Repeat, changing the order until you are confident that the child understands the concept.
Period 3:
- Take the number cards for 1, 10, 100 and 1000 to a work space and place them to out of your child's direct view.
- Place one of the cards in front of the child and ask the child to name it." Which number is this?"
Ask for each card several times until you are certain that the child can correctly name each number.
Number Cards Layout
For these lessons you're going to need number cards: 1-9 in green, 10-90 in blue, 100-900 in red, 1000-9000 in green. The decimal mat in your kit (only specific kits include this mat) will come in handy for this lesson as it will help keep everything in order, but it is not 100% necessary to have. If you'd like to purchase a mat, you can find it here.
The goal of these lessons is to:
- Give the child the symbol for quantities
- Introduce color coding of numbers
- Reinforce that there are no numerals beyond 9
- Show that zero gives value
Presentation one:
Choose a large, comfortable workspace to use with your child, such as the decimal mat on the floor or a large empty table. Take your large number cards to your workspace.
"Today, we're going to do something similar to what we did with the golden beads, but instead, we will do it with the number cards!"
Remove the cards, starting with the unit cards, and place them on top of their corresponding colors on the mat (or place them in their correct order if you are not using a mat).
Tell your child that you are going to count together, and begin placing each unit card in a vertical line on the right side of your work space. Count as you go along.
Repeat the process with the tens, hundreds and thousands, moving one column to the left for each place value.
Once all the cards are laid out, point out to your child that a ten has one zero, one hundred has two, one thousand has three.
You can go on to playing fetching games with the number cards if you wish to do so at this time.
Fetching Games with Number Cards
- Part 1
- part 2
- part 3
- part 4
Part one:
Tell your child that you're going to be playing a game to see if they really know what the different number cards are.
Just as with the beads, to start we will fetch cards from a single category at a time - based on how much difficulty the child can handle, you have two options:
- Either ask from only ONE category per session and build up.
- Or ask from all four, one category at a time.
Start by asking for cards from the unit category. (Bring me the card of five, four, seven, etc.)
Once the child gets the hang of it and is ready for more (on the same day or a different day), ask for cards from the tens (ten, twenty, thirty, etc.). Continue on with the hundreds and then the thousands.
If this seems too easy, you may ask for cards from all four categories, but only ask for cards from ONE category at a time. For example, you might ask for five, then for 60, and then two thousand, and then 40. You can move on to asking from two categories if you notice readiness.
Part two:
- Ask for cards from two categories at a time - starting with units and tens, and then moving on to ask for cards from two of any of the four categories as the child is ready.
- For example, you might say, "Bring me the 30 and the 5 cards."
- Next, lay out the cards, and say, "We have three tens (or thirty) and five units."
- Stack the cards on top of each other and say, "Three tens--which is also called thirty, plus five units makes this number thirty five."
Part three:
- Ask for cards from three categories at a time - starting with units, tens and hundreds and then moving on to include thousands.
- For example, you might say, "Bring the cards 200, 30 and 5."
- Next, lay out the cards, and say, "We have two hundreds, three tens (or thirty) and five units."
- Stack the cards and say, "Two hundreds, plus three tens--which is also called thirty, plus five units makes this number one thousand, two hundred and thirty five."
Part four:
- Ask for cards from all four categories.
- For example, you might say, "Bring me the 1,000, 200, 30 and 5 cards."
- Next, lay out the cards, and say, "We have one thousand, two hundreds, three tens (or thirty) and five units."
- Stack the cards and say, "One thousand, plus two hundreds, plus three tens--which is also called thirty, plus five units makes this number one thousand, two hundred and thirty five."
Number Cards and Golden Beads Layout
For this lesson you'll need:
All your golden bead materials and large number cards.
The purpose of this lesson is to help the child associate the beads with their number symbols
This is a long lesson, and some children find all the counting tedious. Remember that it's totally fine to take breaks as needed and come back to the work after doing something else. You can also be their peer and work along side, but don't do too much!
In this lesson, you are simply going to show you child to match the bead quantity to the number symbol. Choose a large workspace and take the cards and beads to your workspace.
Start by laying out and organizing the beads at the work space. Place the units box to the top right side along with the unit cards, the box with the ten bars and cards next to it, and so on so forth, like so:
Ask the child to place the cards on their mat, just as they learned earlier in the card layout lesson. If they need assistance, help only as required. It's okay for them to struggle a bit and it's also okay for you to be their peer and work along side,
Once the card layout is complete, tell your child, "now we are going to match the golden beads to the number cards."
Beginning with one unit, count out the beads and place them to the right of each numeral card. When you get to ten, remind them that once we reach 10 we must move to the next place value because there are no zeros in the units column."
Show the child that there are indeed 10 unit beads in the ten bar.
Then, beginning with one ten, count out the bead bars are place them to the right of each number card.
Tell your child that two tens are called twenty, three tens are called thirty, etc.
When you reach nine tens, "ask the child what comes next?"
Show the child that there are indeed ten tens in one hundred.
Then, beginning with one hundred, count out the hundred squares and place them to the right of each number card.
Make sure to say, one hundred, two hundreds, three hundreds, etc to emphasize that we are counting hundreds. When you reach nine hundreds ask your child "what comes next."
Show the child that there are ten hundreds in one thousand, and place the one thousand cube next to the number one thousand.
Do the same with the rest of the thousands, noting that since we don't have enough thousand cubes, we will stop at three thousands.
You can continue on to playing fetching games with the number cards if your child is excited and ready for more. Or you can come back to it on another day.
Fetching Games with Number Cards and Golden Beads
Tell your child that you're going to be playing a game with the golden bead materials.
First, you will set up by laying out the number cards as you did in the number card layout lesson.
The beads should be set up either on the shelf, or on a mat on the floor, in their respective boxes/trays.
"Now, I'm going to bring some beads, and you're going to find the number card for it!"
Bring out beads from a single category, for example, 2 units.
Ask the child to fetch the number card that matches the quantity.
Continue asking for cards from the units, tens, hundreds and thousands, one number at a time until you are satisfied that the child understands the association.
Now reverse the game!
"Now, I'm going to show you a number card, and you're going to find me the beads for it!"
Choose a number card from a SINGLE category at a time.
If you notice that fetching from one category at a time is pretty simple, move on to asking from two categories at a time, then three, then all four.
To see a more detailed overview of fetching from multiple categories, check out the tabs below.
- Part 1
- Part 2
- Part 3
- Part 4
Tell your child that you're going to be playing a game with the golden bead materials.
First, you will set up by laying out the number cards as you did in the number card layout lesson.
The beads should be set up either on the shelf, or on a mat on the floor, in their respective boxes/trays.
"Now, I'm going to bring some beads, and you're going to find the number card for it!"
Bring out beads from a single category, for example, 2 units. Place it on the work mat.
Ask the child to fetch the number cards that matches the quantity. "Find the card that match the beads."
Once they bring the card, do the magic slide and read out the number.
Now reverse the game!
"Now, I'm going to show you a number card, and you're going to find me the beads for it!"
Choose a number card from a SINGLE category at a time. It could be from any of the four categories, but it should be only ONE at a time.
Place the number card on the mat and let your child bring the quantity that matches the card.
Keep repeating combinations of both games until you're tired... I mean, until your child is done.
Once you feel like your child is comfortable fetching from a single category, move on to part 2 (this could happen within the same work period or not).
You will do the same as you did in Part 1, but instead of asking from just one category, you will ask from TWO categories at a time. For example, two tens and two units.
Set up by laying out the number cards as you did in the number card layout lesson.
The beads should be set up either on the shelf, or on a mat on the floor, in their respective boxes/trays.
Choose a quantity of beads from two categories. Lay it out on the work mat.
Ask the child to fetch the number cards that matches the quantity. "Find the cards that match the beads."
Once they bring the cards, do the magic slide and read out the number.
Now reverse the game!
"Now, I'm going to show YOU a number card, and you're going to find me the beads for it!"
Choose number cards from TWO categories at a time. Choose a number card from two categories at a time. It could be from any two categories, but it should be only two at a time.
Place the number card on the mat and let your child bring the quantity that matches the cards.
Keep repeating combinations of both games until you're tired... I mean, until your child is done.
Once you feel like your child is comfortable fetching from two categories, move on to part 3 (this could happen within the same work period or not).
You will do the same as you did in Part 1 and 2 , but instead of asking from just one or two categories, you will ask from THREE categories at a time. For example, two hundreds two tens and two units.
Set up by laying out the number cards as you did in the number card layout lesson.
The beads should be set up either on the shelf, or on a mat on the floor, in their respective boxes/trays.
Choose a quantity of beads from three categories. Lay them out on your work mat.
Ask the child to fetch the number cards that matches the quantity. "Find the cards that match the beads."
Once they bring the cards, do the magic slide and read out the number.
Now reverse the game!
"Now, I'm going to show YOU a number card, and you're going to find me the beads for it!"
Choose number cards from THREE categories at a time. It could be any three categories.
Place the number card on the mat and let your child bring the quantity that matches the cards.
Keep repeating combinations of both games until you're tired... I mean, until your child is done.
Once you feel like your child is comfortable fetching from three categories at a time, move on to part 4 during the same work cycle, or another.
You will do the same as you did in part 4 , but instead of asking from three categories, you will ask from all FOUR categories at the same time. For example, two thousands, two hundreds two tens and two units.
Set up by laying out the number cards as you did in the number card layout lesson.
The beads should be set up either on the shelf, or on a mat on the floor, in their respective boxes/trays.
Choose a quantity of beads from all four categories. Lay them out on your work mat.
Ask the child to fetch the number cards that matches the quantity. "Find the cards that match the beads."
Once they bring the cards, do the magic slide and read out the number.
Now reverse the game!
"Now, I'm going to show YOU a number card, and you're going to find me the beads for it!"
Choose number cards from THREE categories at a time. It could be any three categories.
Place the number card on the mat and let your child bring the quantity that matches the cards.
Keep repeating combinations of both games until you're tired... I mean, until your child is done.
Once you feel like your child is comfortable fetching from three categories at a time, move on to part 4 during the same work cycle, or another.
The Exchange/Bank Game
For this lesson, you're going to need a supply of units, tens, hundreds and thousands.
The goal is to give the child practice with exchanging quantities in a very concrete, hands-on way before they move on to exchanging in dynamic addition and multiplication (with carrying), and dynamic subtraction and division (with borrowing).
If your child loves a good story, or likes to pretend, you can create a storyline for these exercises. For example, create roles like banker and customer, grocery store clerk and customer, friends borrowing from one another, or shopping together.
- Part 1a
- Part 1B
- Part 1C
- Part 2A
Simple exchange of units
First prepare a tray with plenty of beads from each quantity on your shelf. Use the golden bead materials on the shelf as a bank. This will be your child's "bank." Show the child the bank on the shelf and tell them that we are going to do some exchanges with the bank.
- Take the child to a prepared work space with a second tray containing plenty of the unit golden beads in a small bowl, and one ten bar.
- Take one unit, and one bar of ten. Place the ten bar on the table vertically, and pass over each bead on the ten bar while counting, "one unit, two units, three units," etc.
- Tell the child, as soon as we reach 10 units, we must go to the bank and exchange them for one ten bar.
- Ask the child to hold out their hand and count, 1 unit, 2 units, 3 units, etc until you reach ten units.
- Tell the child "We have reached 10 units, please go and exchange them for one ten."
- The child should go to the bank, place the units in their hand on the tray, and bring back a ten bar.
- Repeat this until all the units have been changed into tens.
- Leftover units remain on the child's tray in the small bowl. Explain that these can not be exchanged because there are not enough to make ten.
You may now place the items back on the shelf, and move to Part B. Some children will need to repeat Part A several times before moving on, while others will be ready right away. Observe your child to discover their readiness. Additionally, Part B can be done directly after Part A if the child is interested, or it can be done later.
Simple Exchange of Tens
- First create a bank/supply tray on the shelf with plenty of beads in each category.
- Next, create a second tray with plenty of tens and one hundred square and take it to the work space with the child.
- Count how many tens there are in one hundred, holding the ten horizontally on the table, and moving it from left to right over the hundred square--this will cement in the child's mind that there are actually 10 tens in the one hundred square.
- Tell the child that 10 ten bars is equal to one hundred square.
- Ask the child to open their hand and count out ten, ten bars into it. (one ten, two tens, three tens, etc.)
- Once you reach 10 ten bars, tell the child "we have reached ten, now we must exchange it for one hundred." Ask the child to go to the bank and exchange the bars for one hundred.
- The child should leave the ten bars in the bank and return with one hundred square.
- Repeat until you have used all the ten bars you can use. Any left over tens remain on the child's tray and you should explain that they can not be exchanged because there were not enough to make one hundred.
When you finish, you may empty the tray and move on to Part C as the child is ready.
Simple exchange of hundreds (Part 1C)
- Create a supply tray on the self with plenty of beads in each category.
- Create a second tray with plenty of hundreds, and take it to the work space with the child.
- Count how many hundreds there are in one thousand by holding the hundred vertically above the thousand cube—as if to slice it. Say, “one hundreds, two hundreds, three hundreds,” etc. This will remind the child that there really are 10 hundreds in one thousand.
- Tell the child that when we get to 10 hundred squares, we have to exchange for one thousand.
- Carefully count out ten hundred squares on the work surface and ask the child to exchange them for one thousand from the bank.
- Exchange all of the hundred squares that you can for thousand cubes.
- Remind the child that the left over squares can not be exchanged because there were not enough left to make ten.
Empty the tray and move on to Part 2 when the child is ready.
Exchanging an entire tray: (part2)
- Create a supply tray on the self with plenty of beads in each category.
- Create a second tray with plenty of bead of each category, and take it to the work space with the child.
- Count the units to the child as in part one and have them exchange for ten bars.
- Count the tens as in Part 1B and have them exchange for hundred squares.
- Count the hundreds as in Part 1C and have them exchange for thousand cubes.
- When the exchange is complete, there will be some left in each category. Remind the child that these could not be exchanged because there were not enough to make 10.
- Some children will be interested in counting these left overs, if your child is, help them to count the number.
Materials List
- 55-100 golden unit beads
- 45 ten bars
- 45 hundred squares
- 9 wooden thousand cubes
- 10 beaded hundred squares
- 1 beaded thousand cube
- Large number cards from 1-9000