Amounts 7, 8, & 9
When your child has mastered counting and identifying amounts 4, 5, and 6, start Three Step Lessons using amounts 7, 8, and 9.
Encourage counting to identify amounts. Use different kinds of identical objects for different lessons.
Ten
Learning the numerals 0-10
As your child works on amounts 0-10, he can also learn the
numerals 0-10. Soon, she will be ready to match the amounts and the numerals. For these activities, you will need a set of Montessori Sandpaper Numerals ($7.95, Montessori Outlet).
To teach your child a numeral, trace it carefully with your first two fingers while you look at it and say its name. Then your child does the same. Encourage your child to trace (two fingers, tactile), look at (visual), and say (auditory) the numeral all at the same time.
If you will be using tablet apps to teach your child the numerals, then Intro to Math (iPad) is one of the best. It also has activities for identifying amounts and matching amounts and numerals.
Take time to review 10 thoroughly. 10 is a really important number. Use ten coins, a gold bead ten bar (p.361), and different numeral depictions, as shown at left. Have your child count to ten frequently. Fingers and toes are perfect for this.
You can use the amounts and the numeral 10 together, as shown in the photo.
Do Three Step Lessons with the numerals, three at a time. Encourage practice.
Video: Sandpaper Numerals Three Step lesson.
Step 1: Identification Step 2: Recognition Step 3: Recall
“This says one.”
Trace and say
“One”
“Show me the (three, one, two).” Switch positions
“What number is this?”
“This says two.”
Trace and say
“Two”
“Which one is (two, one, three)?” Switch positions
“What does this say?”
“This says three.”
Trace and say
“Three”
“Where is the (one, three, two)?”
“What numeral is
this?”
When your child masters 1-3, do 4, 5, & 6. When she masters those numerals, do 7, 8 ,&
9. Do 10 by itself.
Writing Numerals
It will probably take multiple lessons and up to a few weeks to learn all these numerals. A shallow pan with a thin layer of cornmeal makes a great numeral and letter writing practice tool. The tray here was used to trace the letter C. Numerals work the same way. Your child can use all the resources on pages 405 - 408 for numeral writing practice. Worksheets and practice writing the numerals is what it takes.
Here is a graphic representation of the process your child is working through:
Learn amounts 0-10
Match Amounts Learn amounts Match Amounts & Numerals 0-10 11-13 & Numerals 11-20 Learn Numerals
0-10
Matching Amounts & Numerals 0-10
When your child has mastered amounts and numerals 0-10, it is time to match them up. This may seem like a long process, especially with so many tablet apps that appear to offer instant, easy results. It is really important that your child has a thorough understanding of these first steps. This is the all-important foundation for everything else. It pays to take time and make sure your child really masters 0-10. Once your child has these numbers down, all the rest will come easier. This process is why Montessori math works so well.
Cards & Counters
For this activity you use a set of numeral cards and 55 pennies. There is a 0-10 numeral cards printable on p. 469. You can also use the sandpaper numerals, or easily make your own set just by writing the numerals on small cards with a marker, one numeral to each card. Put the cards and pennies in a nice tray.
Free Cards & Counters Template at Montessori For Everyone (third down on the left) Take pictures and make a big deal out of this accomplishment! Now we'll do the same activity a different way to reinforce what your child has learned. At least two different layouts will insure that your child truly understands these concepts. There are obviously many ways you can match amounts and numerals. You can do candy corn at Halloween, little turkeys at Thanksgiving, etc. Our goal here is to master the concept and move on.
It helps to do the above activity the first few times using identical items like other identical coins, beans, identical beads, etc. Using objects that are all the same isolates quantity as the feature of the experience. In the next activity you will introduce the concept that
objects that are different can still belong to the same group. The final step in this process is to make groups of objects that differ greatly from one another.
Have your child lay out the numeral cards as shown at left.
Then he can lay the correct number of pennies under each card, as at right. A layout like the one shown clearly shows the even and odd numbers. The even numbers have all pairs.
Straws and cups
Introduce the Montessori Bead Bars
You will need 12 small cups, 55 pennies, 55 colored straws cut in half, and a small tray. Multi-colored straws introduce the idea that objects in a group can differ from each other, in this case by their color.
Attach labels with the numerals 0-10 on the cups, or just write the numerals on with a marker.
Have your child lay out the cups in one or two lines, from 1-10 or 0-10, just as with the numeral cards. he can then count out the correct number of straws into each cup. When she is done, have her check her work by removing groups of straws and counting them out. When your child has done the activity with the straws, she can use the pennies.
Intro to Math (left, iPad) has a number of good amount and numeral matching activities.
Kindergarten Kids Math (middle, android) is a pretty good app for android users, with a number of matching, sequencing, and other activities. Dominoes Easy Match (right, iPad) requires careful counting of small dots, but is a decent amounts & numerals app.
Get a Montessori Teen Bead Bar Box, around $7. These are a must-have item for doing Montessori math at home. At right: a 0-10 amounts & numerals matching activity using the 1-9 beads.
Amounts & Numerals 11-20
In the next step of the Math Sequence, we do the same sequence of activities we just finished, but with amounts and numerals from 11-20. The number eleven and the 'teens' have unique names that are not used anywhere else in our ten based number system, so we make learning them a separate step. Once we are past 20 it gets quicker up to 100.
From now on, the Montessori Bead Bars shine:
A 10 bar + a 4 bar = 14
Try doing this with pennies and you will see why Montessori created bead bars! When you first introduce the bead bars, let your child practice counting the beads and identifying each bar. Let her use a pencil or other pointed object as a pointer to carefully count each bead. Make sure he can accurately count the beads before you continue. She will have it down pretty soon.
The 1-10 Counting Cards, (left) and the free 0-10 Number Cards & Counters (right) from Montessori Print Shop are used to match amounts and numerals 0-10 in different, interestingways.
+ =
When you introduce your child to the bead bars, let her do another 0-10 amounts and numerals matching layout with them so that she gets very familiar with each bar.
Video: Matching amounts & numerals 1-10 Number Matching Printables at 1+1+1=1
When your child is familiar with the bead bars, start Three Step Lessons using amounts 11, 12, & 13:
Step 1: Identification Step 2: Recognition Step 3: Recall
"This is eleven"
(child counts)
"Where is eleven ?"
(then 12,13)
“How many are
there?”
"This is twelve"
(child counts)
"Where is thirteen ?"
(then 11,12)
“How many is
this?”
"This is thirteen"
(child counts)
"Where is twelve?"
(then 11,13)
“How many are
there here?”
When your child masters these, do lessons with 14, 15, & 16; and then 17, 18, & 19.
Video: A Montessori School Teen Bead Bar Presentation
Matching Amounts & Numerals 11-20
If you will be using coins for the 11-20 activities, take time to show your child the equivalent amounts at left: 10 pennies = 1 dime = one gold ten bead bar. If your child practices exchanging ten pennies for a dime and a ten bead bar and really understands that they are all the same, you may be able to teach the larger numbers using dimes and pennies. The bead bars are best because the beads are separate objects.
Print the numeral cards on pages 470- 471. The single numeral cards are laid over the zeros on the 10 cards to make the numerals 11-19. 20 has its own card.
Once your child knows the amounts 11, 12, & 13, you can match them right up with their numerals without a separate step of teaching just the numerals:
Video: Doing this activity with the Montessori Teen Boards
Lay out the ten bars above three 10 cards on the left, and the 1, 2, & 3 bars above their numeral cards on the right. Start with 11. Bring the bead bars together as you say, "Ten and one makes eleven." Then move the 10 card to the middle and set the 1 card over the zero as you say, "Ten and One says
eleven." Now your board will look like the photo. Repeat with 12 & 13. Return the board to the original layout and have your child do it. Help as needed.
Left: If your child is very clear that one dime = 10 pennies, you can substitute coins for this activity.
Right: The Teen Beads, Boards, and Worksheets from Montessori Print Shop
are nice, inexpensive printables for more abstract work with these numbers.
When your child knows 11, 12, & 13 well, add 14, & 15 (left).
Continue until your child has practiced amounts and numerals 11-19 enough to really understand them. This takes time, so allow for lots of practice.
Bitsboard (iPad) has boards for counting 0- 20 objects and learning numerals 0-100 and beyond. These boards are great for practice.
Pocket Chart Pro (iPad) has a board for counting up to 20 objects and matching the numerals, and many other boards as well.
Just as with the number 10, we make extra fuss over 20. Make twenty objects many different ways. Let your child make patterns with the pennies. If she really understands that one dime = 10 pennies, let her use 2 dimes to represent 20.
Amounts & Numerals 21-100
Have you guessed what we do from 21-100? That's right, more of the same activities we just finished. On pages 472-477 you will find the printouts for the cards from 20 - 90 &
100. Use your numeral cards with these to make all the rest of the numerals from 21- 100. Do 21-30, then 31-40, 41-50, 51-60, 61-70, 71-80, 81-90, and 91-100.
Laying out all the amounts from 91-100, for example, takes 91 golden bead ten bars, still more than the 54 you will have after you buy the box above and add it to your other ten bars. If the box of bars above just isn't possible budget-wise, get the $2.95 100 Golden Bead Chain and use it, along with your ten bars from the Teen Bead Bar Box
and do as many numbers at a time as you can. It will all work out.
As the amounts increase, you will run out of gold bead ten bars. No worries, get a box of 45 Golden Bead Ten Bars. You should also get the cool, $3 100 Golden Bead Chain. Total for both is around $16
If your child truly understands that 1 dime = 10 pennies, you are in luck! You can do all the amounts and numerals from 21-100 using these coins, as shown at left with 31-35. You can also use the 1-9 bead bars instead of the pennies to make it easier. Be sure your child counts by counting the dimes as "Ten, twenty, thirty".
Do all the amounts and numerals in sequence up to 100. Make a special activity out of 20, 30, 40, 50, 60, 70, 80, and 90. Check before each activity to see if your child remembers the numbers she learned the last time you did math work.
Working with 100
After probably a good length of time getting here, making it to 100 is a big deal! Your child has come a very long way. We now do activities to help your child reinforce her new understanding of numbers up to 100, including how they break into groups of ten, skip counting, and other activities. This is all leading up to learning about the Decimal System.
Left: Count to 100 using the 100 Golden Bead Chain, and skip count to 100 by tens with the chain bars and with dimes (help as needed), Middle: Print out the 100 Golden Bead Chain Pointers (another set is on p. 478), cut them out, and have your child count the 100 Golden Bead Chain, placing the 10,20,30,40,50,60,70,80, 90, and 100 pointers in their correct places as he goes. Right: Count the 100 Chain to 50, group those 5 bars together, and point a 50 pointer at them. Show your child how 50 + 50 = 100.
Practicing 0-100
Once your child is working on amounts and numerals 21-100, you can start doing Operations with Numbers (p. 373), Telling Time (p. 381), Money (p.385), and Fractions (p. 379). This will provide variety and reinforce what
your child is learning about larger numbers.
Now we do some work practicing with amounts and numerals 1-100, to reinforce your child's new skills. Lay out the 100 Golden Bead Chain. Write a numeral on a small card and let your child count left to right that many beads. Do many different numbers.
Work on amounts and numerals 0-100 this way until your child is very familiar with them, and can make and identify any number in this range.
The Hundred Board
The Hundred Board is a classic math material. It shows relationships between numbers in our ten-based system very clearly. Children can learn skip counting, addition and subtraction, multiplication, exchanging coins, and other skills with this material. If you can afford the Montessori material, it is very nice. Printed materials will work at home if printed on heavy card stock and stored safely. On pages 479-480 you will find more
hundred board printables.
Free Hundred Board printables at Donna Young
When you do larger numbers, angle the sections until you get to the chain that has the number on it. Now your child can skip count the bent chains by tens - "Ten, twenty, thirty..." - until he gets to the last chain, and count that one by ones to get to the number.
Use 10 bars and 1-9 bars to make amounts for your child to identify. Make numerals and let your child put together the amounts. Then reverse and give your child amounts so he can make the numerals. Use the tens and unit numerals from the printouts on pages 472-476.
Left: The Montessori Hundred Board. Very nice, around $26.
Right: The 1-100 Math Series from
Montessori Print Shop has a full set of charts, boards, number cards, and lessons, for only $3.
The usual first activity is to start with 1 at the top left and build the board one number at a time to 100. Points of interest:
• The vertical rows all end in the same number
• Skip counting down the tens row vertically from the top by tens (10, 20, 30, etc), and down the other rows.
• Skip counting by 2,3,4,5,etc. Lay out just the numerals for each amount (2,4,6,8...5,10,15,20, etc)
Exchanging Coins
Left to right: (1) Counting out 100 pennies to fill the board. (2) Placing a nickel on every 5th space as the board is counted. (3) Placing a quarter on every 25th space. (4) Placing dimes at the end of each row and showing that 10 dimes = 1 dollar.
• Have your child fill up the board with pennies. Show her that 100 pennies = 1 dollar.
• Have her pick up the pennies five at a time, placing a nickel on every 5th space, as in the second photo from left above. Show her that 5 pennies = 1 nickel.
• When all the nickels are placed, have her count them to see that 20 nickels = 100 pennies = 1 dollar.
• With the nickels still on the board, count from 1, emphasizing the count at each nickel to teach your child how to skip count by 5's ("Five, ten, fifteen", etc). At every 5th nickel, place a quarter, so the board looks like the third photo from left when you are done. Show your child how 5 nickels = 1 quarter.
• Count the board again, leaving a dime at each ten space on the ends of the rows.
Remind your child that 1 dime = 10 pennies. When finished, have your child pick up the dimes, starting at the top, while skip counting by tens to 100 ("10, 20, 30, etc"). Show your child that 10 dimes = 1 dollar
Extend these activities to your shopping trips. Point out prices and talk about how much money different things cost. Give your child $1-3 to spend at the small toys rack and require him to figure out how to stay within his 'budget'.
For more challenge, give your child numeral tiles at random and have him figure out where they go on the board. Help only if needed. Remind your child that in each vertical row the numerals all end with the same number.
Online Hundred Board Games
Find and paint numerals on a Hundred Board A good skip counting board
Say numbers, find, and 'splat' them
'Mend' the board by placing numerals correctly Find the correct number from a verbal cue Finding dog bones on the board
Type in numbers to fill in the blanks on the board Hundred Board puzzles and worksheets
Hundred Board & Skip Counting Apps
Bonus Step: Going from 100 - 1000
The Hundred Square
The Hundred Square, around $3, is another great Montessori material to have at this point. It reinforces the relationship between 100 objects in a concrete way for moving beyond 100, and leads into Decimal System work. To move beyond 100, use the 100 Square, your Teen Bead Bar Box, and Hundred Squares
from the printout on page 481.
Now we will do amounts and numerals activities as we did to get to 100. This will probably be a faster process as your child continues and sees the sequences repeat.
Left to right: Hundred Board (iPad) is a decent app, but should offer more - like a free work option - for $2.99, IMO. 100's Board (iPad) is another basic hundred board app that provides good practice. Skip Counting (iPad) provides practice in this important number skill. Montessori Bead Skip Counting (iPad) offers another way to skip count.
At The Education of Ours, They made a Hundred Board layout on
kitchen floor tiles.
Now, it is just a matter of doing the games and activities you did to reinforce numbers 1-100, and these layouts above, with numbers from 101-200. This continues with 201- 300, 301-400, 401-500, etc., all the way up to 1000 if your child shows the interest.
Print out Gold Hundred Squares from the printout on page 481 as you need them.
Staple 10 of them together to represent 1000. As you get higher, the process becomes quicker because your child gets used to seeing repeating number patterns.
Review with your child that the Hundred Square
and your printed 100 squares (p. 481) each have 100 on them. Lay a ten bar over successive vertical rows, going left to right, as your child counts, "Ten, twenty, thirty", etc., up to 100.
The Hundred Board 101-200 (iPad) app can be used to help your child learn the numerals 101-200. You still need to work with amounts first for real understanding.
Use a ten bead bar to do 110. "100 plus ten makes one hundred and ten." Go right into using two ten bars to make 120, three to make 130 and so on, up to adding ten 10 bars to make 200, where you exchange the bead bars for a 100 Square.
Lay a square and the 1 bar out. As you put them together, say, "100 plus 1 makes one hundred and one." Repeat with the 2 - 9 bead bars to do 102 - 109.
Make a 101-200 Square by laying out the numerals on a blank hundred square board. You will find a numerals printable for this on page 482.