Linear and Skip Counting
Flowchart
Flowchart
Printable Material
Teens and Tens
Print on cardstock and cut. Set scale to 100%
Arrows for Short Chain
Print on card stock (laminate if you wish) and cut them out. Sort them out into little color coordinating organza bags.
Arrows for Long Chain
Print on card stock (laminate if you wish) and cut them out. Sort them out into little color coordinating organza bags.
Colored Bead Stair
Introducing the Colored Bead Stair
For this lesson, you're going to bring out the colored bead bars. You will need one of each color. You will need to pull this out of the decanomial bead box which has 55 of each color, but for the upcoming lessons, you will ONLY need ONE of each color 1-9.
You will also need some number cards labeled 1-9. Use the small number cards that you used for the cards and counters lesson or you can even use sandpaper numbers.
Place them on a bowl or tray and leave on the shelf.
This is a simple lesson to just introduce the colored bead stairs and show the child that the beads are similar to the rods, golden unit beads, and the counters that they have used previously.
Show your child the one bead. "This is one." Put it at the bottom of the mat.
Now show your child the two bead, which is green. "This is two." Count the beads. "One, two."
Place it above the one. Continue doing this with the rest. Chances are, your child will catch on pretty quickly and understand.
Now lay out the number cards in random order at the bottom of the mat.
Pick up the one bead bar, place it at the top of the mat, and find the card that says one. "This is how we write one." Continue on like this with the rest.
They are now free to play around with the beads and build the stair.
Games to Play with the Bead Stair
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Extension
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Teens
Introducing Teen Numbers with Colored Beads
Materials:
For this lesson you'll need 9 ten bar and one set of bead stair.
Introducing the Number Symbols for Teens
Working with the Teens Board
Materials:
For this lesson you'll need the teens mat, board, or cards (whatever you use, the idea is the same).
If you have the mat, use the cards from large number cards set.
*If you already have a teens board, it should already have the number cards in the box*
Or you can DIY one yourself or use the printable in the printable library above.
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For the next part of this lesson, you'll mix up the numbers on the board (instead of placing them in order) and build the quantities with the beads. Allow plenty of time for repetition and practice to let everything sink in.
Extensions and Games for Teens
Tens
Introducing the Tens with Their Names
Your child has already been exposed to the concept of tens when you introduced the golden beads.
When you are doing linear counting, you reintroduce the tens, but this time, we are going to reinforce their traditional names. Previously, we've always counted 1 ten, 2 ten, 3 ten, etc...
For this lesson, you'll need 9 ten bars and 10 unit beads. This will be the control of error for the child.
Working with the Tens Board
The Passage of Tens
In this lesson, you will show your child how to count in between the tens, which is basically linear counting, something the child hasn't done directly yet.
For this lesson you'll need: the tens board/mat/cards. For the purpose of this lesson, I'll be using the word "cards" since that is what is included in your kit. You'll also need 9 ten bars and 10 unit beads.
Lay out the cards vertically in order starting with 10. If you have the boards, the first board goes up to 50 so it all depends on what has already been previously introduced. Remember that Montessori math does not follow a linear progression so you could introduce 10-50 and go through the previous two lessons and reach this one without having introduced 60-90 just yet.
Put the beads to the left of the boards/cards and the cards from 1-9 in a stack to the right of the board.
Show your child the first card. "This says 10." Put a ten bar to the left of the card (leave a little bit of space since we'll be putting unit beads to the right of the ten bar).
Take the "1" card and put it over the 0 on the 10. "This is how we write eleven. Now I'll build 11."
Put one unit bead to the right of the 10 bar. "This is eleven."
Remove the "1" card, flip it upside down from the short edge and put it to the side.
Put the "2" card over the zero now. And repeat...
"This says 12. Now let's build 12..."
Add another unit bead to the right of the ten bar.
Invite your child to continue. Continue on until you get to 19.
Once you're done with 19, notice that there is still one more unit bead left in the cup.
"If we take this unit bead and add it here, we'll have 10 units... I can now exchange these 10 units for a 10 bar.
Exchange the 10 unit beads for a ten bar and slide both 10 bars down to "20".
"Now we have 20!!"
Take the stack of cards and flip them over to the right side.
From here on, you will continue the process of counting through twenty and inserting the cards one at a time. You will repeat the same process for 30, 40, 50 etc...
Now, this is a long work and it's more than likely that your child will not get through everything all in one sitting. They may get tired after going through 20 or 30, and that is okay. Put the work away and continue on from where you left off on another day.
Linear Counting
Linear Counting with the 100 Bead Chain
For this presentation you will need:
- Short bead chain of 10
- One hundred square
- Arrows for the short 10 chain
Show your child how to carry the 10 chain, hanging it over your fingers gently, and bring it to the work space.
"Today, we're going to count this very long chain! But first, I'm going to show you how it turns into a square, just like this!" *point to the 100 square.
Fold the chain into a square on the work surface and take the one hundred square, place it on top of the folded chain, next to it and above it.
"Wow, that looks pretty cool!"
Unfold the chain and make it into a straight line.
"Would you like to try?"
Ask the child to fold the chain as you did, and then lengthen it again as you did.
"Now I'm going to count..."
Start counting from left to right, making your way to one hundred.
Place the one hundred square at the end of the chain and take the labels out of their pouch.
"Now it's your turn! Would you like to try? This time we're going to use the arrows."
Start your child off by counting, "one", and place the one green arrow label below the first bead, continue with 2, 3, 4, 5. Allow your child to finish the units to ten if they are able and want to.
When you reach ten, place a blue ten arrow label above the bead chain.
Continue counting, "11, 12, 13, 14..." until you reach 20.
Tell your child, "Let's find the arrow that says 20 and put it right here."
At this point your child may catch on that you are counting by 10's, if so, allow them to skip count by tens with the labels, adding 10 each time. If not, continue with linear counting for each ten, placing the next multiple of ten until you reach 100.
Once all the beads have been counted, go back to the beginning of the bead chain and say, "Let's count all of our arrows." Count 1-10, and then by tens to one hundred.
Tell the child, "Ten tens makes 100. That was a pretty long chain!"
Gather the labels back to their container and fold the bead chain again into a square. Transpose the 100 square on top of the folded bead chain.
Say, "Ten tens makes the 100 square!"
Linear Counting with the 1000 Bead Chain
For this presentation, you will need:
- Long thousand chain
- Arrows for the long chain
- 10 hundred squares
- One thousand cube.
It is important to spread out the chain to its full length for this exercise. You can make it zig zag if you don't have enough space to lay it out from one end to another.
Ask the child if they remember when you counted out the 100 chain. Say "We are going to do the same thing, but this time with the 1000 chain!"
Carry the bead chain and other materials to the work space.
Fold a square with the first hundred beads and take a hundred square off of the stack you have carried to your work space. Place it above your folded square.
Show the child how to fold the next section of chain, and take another hundred square and place it above the newly folded section.
Ask your child to continue folding the chain as you have, and when your child is finished, gather all of the hundred squares that were placed above the folded chain into a stack.
Compare the stacked hundred squares to the thousand cubes and point out that they are equal.
Have your child hold onto the left end of the folded chain while you take hold of the end at the right and slowly draw the chain out to its full length.
Place the thousand cube at the right end of the chain.
Tell the child, "Now we are going to do a BIG work, we are going to count all the way to 1,000!"
Some children will be excited because it's such a big number, and others will feel overwhelmed. You can do this in sections throughout the day if it becomes tedious. Another fun way to do it is by having a small toy or figure (like a LEGO figure) count along with the child. Try to make it exciting and fun, play makes learning stick!
Ask the child to count the beads and place the labels below the
numbers 1-10.
When they reach 10, place the ten label below the chain.
Have the child continue to count to 20, and place the 20 label below the chain. Continue you this for the multiples of ten until reaching 100.
When you reach 100, place the 100 label above the chain and place a 100 square above the label.
Allow the child to continue counting until they reach 200. When they reach 200, have them place the 200 label above the chain and a second 100 square above the label.
Be certain that the child is saying, "one hundred, two hundreds, three hundreds," we want them to understand that they are literally counting hundred squares.
When they reach 1000, have them stretch out the 100 chain above the thousand chain to compare the two. Emphasize that there is such a big difference between 100 and 1000!
Stack the 100 squares and count them again to show that 10, 100s makes one thousand.
Return the work to the shelf. Congratulate your child on their accomplishment. This is big work!
Skip Counting
When should you start presenting these lessons?
You may present the following lessons to your child once you've:
- Introduced the decimal system
- Worked with the teens and tens
- Completed the teens and tens lessons and started the ten chain lesson in the Linear Counting module.
These lessons give the child a multi sensory experience priming them for a faster way of counting: skip counting! It also introducing the idea of squaring and cubing numbers in a concrete way. Hey, you might even have an aha! moment or two while you work through the following lessons with your child! Perhaps the squares and cubes of numbers will actually come to life with these gorgeous bead materials!
This module looks short, but there is a lot of work involved with the chains because there are ten of them! Also note that this is a sensorial introduction to squares and cubes of numbers. You will dive in way deeper in elementary.
Introducing the Short Chains for Skip Counting and Squares of Numbers
When introducing for the first time: "Look what I brought out today! This is the short chain of 5 and the square of 5. Wow... I think it's so pretty, what do you think? I'd like to show you this lesson today."
Ask your child to take the short (square) chain of 5, one square of 5 and the labels to the work area.
- Take the short chain (square chain) and fold it into a square. Compare the square of five to the folded square. Gasp with some excitement as you do this. "Whoa!"
- Place the square of 5 at the top of the folded square and lengthen the chain out again.
- Say, "Now it's your turn!" Instruct them to fold the chain into a square and lengthen it again just as you did.
- Place the square at the right end of the short chain and have your child count the square chain of five, and label it with the labels at each interval of 5.
- Count by fives, using the labels as a guide, from the beginning to the end of the short chain.
This is the end of the lesson. You may repeat this lesson with another short chain if your child is fascinated by this lesson, as many children are, on the same day or continue on a different day depending on the interest of the child!
Introducing the Long Chains for Skip Counting and Cubes of Numbers
Take the long chain of 5 (cube chain), five squares of 5, one cube of 5 to the work space.
Fold the first five, 5 bars in the long chain of 5 into square, and place a 5 square above the folded square.
Ask the child to fold the rest of the chain into squares just as you have done with the first five, five bars in the chain. Tell them to place a five square above each of the folded sections just as you have done.
Now tell your child to lengthen the chain back out again. and gather the squares of 5 in a stack. Show your child that the stack of 5 squares is the same as the cube of 5.
Say,"Now we are going to count this long chain of 5!" Have them remove the labels and count the beads, and place the labels just as they did in the linear counting lessons.
When they have finished, congratulate them on their effort and perseverance!
Read with them all of the labels of the long chain... if both of you can last that long!
Repeat this lesson with all of the cube chains.
Using the Short Chain for Long Chain Skip Counting
It is possible to do skip counting all the way to the cube of a number without the long chain.
The kit does not include the long chain for a reason: it's not a work with much longevity and there are alternatives.
So here's the solution to doing this lesson with just the short chain:
Bring out all the squares and the cube of the number you will be working on and set up all the arrows for the long chain.
Start skip counting with the short chain as usual, placing the square at the end. Now, flip the chain and continue counting and once you get to the end of the chain, place the next square at the end. You'll do this as many times as there are squares.
For example, the cube of 3 is 3x3x3, so you'll have to flip the chain twice for a total of 3 chains.
You can tell your child, "we counted the chain of three, three times... Can you imagine how long it is!?"
You can also put something at the beginning of the chain when you begin counting so you can have some sort of idea of how long the chain is when you're done.
At the end, take the squares and stack them up and compare to the cube.
Materials List
- One set of colored bead stairs
- 9 ten bars
- Teens board/mat/cards
- Tens board/mat/cards
- Short bead chains
- Arrows for short bead chain
- Arrows for long bead chain
- Colored squares
- Colored cubes
- Long bead chain (optional)
- Arrows for long bead chain