Numbers and Counting
Flowchart Notes
Materials
What you need for this portion:
For this lesson, you need the number rods. Start with placing only the first three rods on a tray and placing on the shelf.
There are lots of ways to DIY number rods.
You can use red and blue unifix cubes or even mega blocks, duplos, or legos.
The small tabletop rods are also inexpensive and work perfectly well.
Click on the image below to download a printable version of the number rods. It's best printed on heavy cardstock.
Number Rods - The What, the Why, and How to Introduce Them
The number rods are the first math materials introduced in the Montessori math curriculum. They are a set of 10 rods, segmented into red and blue - red always comes first when you're laying them down.
So now, why are these such an amazing way to teach quantity?
It's because of the amazing visual that they offer. The child can visually see the difference between each quantity and also feel the difference - one is shorter than the rest and ten is longer than the rest. They feel different and look different.
Another really cool thing about these rods is that the quantities are linked together. So two isn't two separate pieces, it's linked together, which provides a more solid and concrete depiction of the quantity than two separate parts - which actually comes a little later as we graduate from concrete to abstract.
So, are you ready to get started!?
- Period 1
- Period 2
- Period 3
- When to Move On
The second period comes directly after the first.
Once you've introduced the names of the rods, you can play some Second Period games.
We're going to start with some Show Me games.
"Show me three."
*child points to three*
"Point to one"
*child points to one*
"Pick up two."
*child picks up two*
Mix up the rods.
Repeat. Add in creative variations. Ask your child to pick up a rod and put it somewhere close by. If they're really getting into the game, take the challenge up a notch and ask them to hide it. And then ask them to find it and bring it back to the mat. Hide and seek games are a bit more advanced than just asking the child to show you the object, so make sure that the child is able to correctly point out the objects (for the most part) before attempting the hide and seek games.
So, what do you do if you're doing the second period and every time you ask for an object, your child picks the wrong one?
Don't fret. It's totally normal in the beginning.
Here's what you'll do:
"Pick up two"
*child picks up one"
"That's one! Can you find two?"
*points to three*
"That's three! Can you find two?"
*child points to the only rod left*
When you come around and do this game the second, third... tenth time, you'll begin to see mastery. Once your child has had enough of the game. Pack it away and repeat again on a different day.
Move on to the Third Period games once you see mastery.
Main purpose of the Third Period: Identify and name (recall).
Once the chid has demonstrated mastery during the Second Period, you can move on to the Third Period.
Bring out the rods that you previously introduced to the work area.
Set them out in random order.
*Ooo now we're going to play a different game with these rods. Do you remember how last time, I asked you to hide them? Well, this time, you're to tell ME where to hide them! What do you think?"
*child super excited because they get to tell you what to do now*
They might start by saying, "Hide this one" and then point to a rod.
If they do, ask, what's it called? (or if your child likes to pretend like the rods are people, use pronoun of choice.
The main purpose of the Third Period is to have the child say the name.
You can also switch roles.
"Can you show me the names of the rods? I don't remember them!"
*child proceeds to teaching you the lesson despite having doubts in your claim*
Once you've played Third Period games with your child and they are able to recognize the rods and say their names, you can introduce two new rods at a time and repeat the process.
Move on to playing games with the number rods after you have introduced all the rods and have gone through all the steps of the Three Period Game.
Main indicator of mastery: when your child is able to point out the correct rod and say its name.
Games to Play with Number Rods
In this section, you will find a variety of games to play with the number rods. By no means do you have to play ALL of them. They are simply to help master the concept. You might play a game a day, you might skip a few days... you might even skip a few games. What you are looking for is thorough understanding of one to one correspondence in your child. If they can point out a certain number rod and count it's segments with ease, they have mastered the concept. You can also move on to the next lesson as you work your way through these games.
- Game 1
- Game 2
- Game 3
- Game 4
- Game 5
Choose two areas to work with, one at a distance and one where you station yourself - try to lay out a mat in each space to define the work area.
Place the rods in order from left to right on the mat at a distance and situate yourself at the other mat.
"We are going to play a fetching game! I'm going to ask you for a number rod and you will bring it to me!"
Ask your child for the rods in order, starting with one.
"Bring me the 'rod of one'?"
*child brings the rod of one*
Place it on the bottom left edge of the mat to begin the gradation.
"Now can you bring me the 'rod of two'?"
Continue in order until you've reached the end, grading each rod as go.
Game 2 is the same as game 1, but instead of asking for the rods in order, you are going to ask for them in a random order, grading as you go.
After this, you can even reverse roles, and let your child ask you to fetch the rods.
Choose two areas to work with, one at a distance and one where you station yourself - try to lay out a mat in each space to define the work area.
Place the rods in order from left to right on the mat at a distance and situate yourself at the other mat.
"We are going to play the fetching game, but this time, it's going to be a little bit different!"
Ask for the rod of five.
*child brings the rod of 5*
Place it on the bottom left edge of the mat to begin the gradation.
Now ask for a rod larger than 5.
"Find me a rod that is larger than 5!"
Choose two areas to work with, one at a distance and one where you station yourself - try to lay out a mat in each space to define the work area.
Place the rods in order from left to right on the mat at a distance and situate yourself at the other mat.
Ask for the rod of 5.
Then ask, "Find me the rod that is one MORE than five."
They should bring the rod of six.
Then ask for, "Find me the rod that is one LESS than five."
They should bring the rod of four.
Then, "Find me the rod that is one MORE than six..."
They should bring the rod of seven.
Then, "Find me the rod that is one LESS than four..."
They should bring the rod of three.
Do you see the pattern here? Continue asking until you've asked for all the rods!
Game 5 is the same as game 4, but instead of asking for ONE more, you will ask for "the rod that is TWO more than (insert rod name)." and "the rod that is TWO less than (rod name)."
Have fun playing!
Materials
A set of green boards with numbers from 1 to 10 in sandpaper, felt, or glitter paper. These are an easy DIY.
Cut out 4 x 3.5 inch squares on green poster board. Even cardboard works!
Cut out numbers 1 - 10 with sandpaper, felt, or glitter paper. You want a color that contrasts the background. So if you're using cardboard, go for green numbers. If you're using a green background, go for tan or brown or black numbers.
Glue them on and that's all!
Sandpaper Numbers: The What, the Why, and How to Introduce Them
The sandpaper numbers create muscle memory in the child's mind, helping them to have hands-on practice with formation. The main purposes for this material are to teach the written symbols corresponding to quantity, and to help children to make the association between name and symbol. This is a key lesson to help children understand the world of written numbers.
We do not introduce this work until the child understands the Number Rod material because we want the child to understand the concept of quantity before we go on to assigning symbols.
A few notes before you get started:
Before starting this lesson, tell the child to wash their hands to help keep the sandpaper letters from getting dirt and oil on them. This will also teach them that the work is precious and special.
Show the child the material and how to carry it to the work space, slowly and carefully.
You'll begin by taking out the first three numbers to do the first of the Three Period Lessons. We begin with only the first three numerals (1,2,3). Once the child has progressed through the three period lesson with these numerals, the next set of three is introduced using the same lesson structure.
Let's get started!
- Period 1
- Period 2
- Period 3
- When to Move On
In the first period, we focus on introducing the concept.
Using the sandpaper numbers, place number card 1 in front of you.
- Say, "This is how we write '1'. I am going to show you how to trace it."
- Trace the number using your index and middle finger together, slowly, the same way that you would write it on paper.
- As you trace, say "one," and when you finish tracing say again to the child, "This is how we write the number '1'."
- Next, ask the child if they would like to try. Make sure that they trace it slowly and carefully, saying "one" while they trace it.
- When they have finished, say, "This is the number one."
- Repeat the process with numbers 2 and 3.
- Once the child has progressed through all three periods with the numerals 1, 2, 3, repeat the process with the next two to three numbers and again until you have cycled through all the numbers.
In the Second Period we teach the child to recognize each numeral.
Place numbers 1-2 on the workspace in front of the child, in order, and point to each number saying its name. Mix them up and ask the child to show you each number.
For example, say, "Can you show me the number 2?"
If the child answers correctly say, "yes this is 2!" And have them trace the number while saying "two."
Repeat for each numeral in your presentation.
Variations:
Ask the child to hand you a number instead of showing it to you.
Have the child place the number somewhere on the table that you point to.
Have them place one number on top of another.
Ask them to close their eyes while you mix the numbers.
Making the presentation fun makes it memorable!
The Third Period is for recall, we want the child to remember and name the item.
Once the child has mastered the second period, confirm that they have mastered the concepts in the Third Period.
Remove the three sandpaper numbers from the work space and place one in front of the child. Ask the child what it is. Have the child trace the number if they are correct and say the number as before.
Repeat with all three numerals, first in order and then mixed. If the child is unable to tell you the names of the numerals, return to Period Two for more practice.
When your child can recall all the numbers from 1-9, you may move on to the next lesson. This doesn't mean that they will not continue to practice with this material, only that they are ready for the next math lesson to be added!
Games to Play with Sandpaper Numbers
- Game 1
- Game 2
Place the sandpaper numbers randomly on the mat.
"Now we're going to play a 'go get me/fetching game'"
Ask for the numbers in order.
Have the child arrange them in order.
Next time, you can increase the difficulty.
Start out the same way, but instead of asking for the numbers in order, ask for them randomly.
"Find me 7, find me 4, find me 8, etc, etc..."
Attempt to have your child place them in order - if they are able to, but don't sweat it if they can't!
coming soon
Materials
Materials:
- The number rods and a set of cards on which are printed the numbers 1 to 10. Click here to download number cards.
You can also whip these up really quickly on little paper squares and write down the numbers. It really doesn't matter what color you write the numbers with.
Note: This lesson is for children when they know the Number Rods and the Sandpaper Numbers very well.
Matching Number Rods with Number Cards
Association of Rods and cards, Intro to the number 10
- Stack the number cards so that the number 10 is at the bottom of the stack, and all the others are in random order on top of it.
- Bring the stack of cards to the work space and show your child the first number. For this example, let's say it's number two.
- Ask, "Do you know what this number is?" Your child should say yes it is number two. (If they do not know, go back to reviewing the sandpaper numerals.)
- Now ask the child to go and get the rod of two from the number rods and bring it to the work space.
- When your child comes back have him place the rod on the work surface, touch it, and count it the way that he did when learning the number rods.
- Place the card at the end of the rod on the last section and say the name of the number, in this case "two."
- Repeat this process until your child has all the cards except 10 on the work surface.
- Ask him "is there a rod left on the shelf?" When he answers that there is, ask which rod it is. When the child says "ten" ask them to bring it to the work space.
- When the 10 rod is set on the work surface, show him the number 10 card and say "This is number 10," and have him place the number ten at the end of the rod.
Games to Play with Number Rods and Tablets
- Game 1
- Game 2
- Game 3
Place the rods on a mat in sequential order.
Place the cards on another in sequential order.
Ask your child to choose a rod.
And then ask for the corresponding number card.
"Go to the mat and choose a rod."
*Child chooses the rod of five*
"Okay, now find the card for the rod of five!"
*Child finds the card of five"
"Okay now put the rod with the card on that mat (the one with the cards)."
Place the rods on a mat in sequential order.
Place the cards on another in sequential order.
Ask your child to choose a number card.
And then ask for the corresponding rod.
"Go to the mat and choose a number card."
*Child chooses the card that says '5'*
""Okay, now find the rod for the card!"
*Child finds the rod of five"
"Okay now put the card with the rod on that mat (the one with the rods)."
Place the rods on a mat in sequential order.
Place the cards on another mat in sequential order.
Ask your child to choose the rod AND number card together.
"Find me the rod and the number card for 6!"
*Child chooses the rod and number card for 6*
"Okay, now lets put them on the mat together."
*Place on the mat together*
Continue asking for the rods in random order.
Materials
Spindle mat/box with 45 spindles in a container
OPTIONAL: 9 ties or rubbers for tying the spindles
Playing the Zero Game
The Zero Game is a fun game used to introduce the idea of zero - of nothing. The best part? You need no special material for this game.
"I'm going to show you the zero game today."
"Clap two times. Now clap four times. Clap three times... Clap zero times."
*child wondering what on earth!?*
"There you go! Zero means nothing. So you clapped zero times!"
------
Collect a few objects and make several groups of one, two, three, four, etc... It doesn't have to be a lot, just a couple.
*point to a group*
"How many are here?"
*child answers*
Point to another group.
"What about here?"
*child answers*
Then point to a space that has nothing."
Maybe the child says there's nothing... or is confused.
Be silly and say, "It's zero! Zero means nothing!"
Introducing the Spindle Mat/Box
Take the spindle mat and spindles to your work space
- Make sure you have set out only just enough spindles in the box. There should be no extras.
- Point to and trace zero and ask the child which number it is. When he answers "0", say, "zero means nothing, so we will leave this empty."
- Trace 1. "This says 1." Pick up one spindle and dramatically place into your palm and count, "one!". Wrap your hand around it. Place it into the pocket labeled '1'.
- Continue on the same way with the next number.
- Now invite your child to do the same for the remaining empty sections (continue with the second mat if the child demonstrates mastery during the first mat), they must count out loud for each spindle!
Materials
For this lesson, you need the number cards from the previous lessons.
If you're DIYing and you already have sandpaper numbers, use them for this lesson. It works perfectly well... If not, then all you need to do is write down the numbers 1 through 10 on cardboard (use those Amazon boxes!) or some stiff paper.
Additionally, you'll need 55 items to count with. The kit comes with glass marble counters. It's great if you have matching items, but it's not necessary. Use things that you already have around your house... things that your child is already interested in. Cars, farm animals, dolls....
You can get really creative with counters, whether you buy them or make them yourself. If you want to make them, you can cut out squares from felt (I say square instead of circles, because 55 circles would be a pain to cut out.) How about some cheerios? Those make AMAZING edible counters! And fairly easy to put together too!
Introducing the Cards and Counters
Materials List
- Number rods
- Number cards
- Sandpaper/felt numbers
- 55 counters
- Spindle box/mat
- 45 spindles
