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Help me pick next year's math


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We are using Montessori math materials right now. I have all the manipulatives needed for the 3-6 age range. This was a huge investment, and we don't have any complaints.


However, as I look forward into 1st grade...I'd need to make another decently large purchase for more materials. 1) we're running out of room! 2) some days I am thinking about the grass is greener on the workbook side...


I do love, love, love the idea of Montessori math however. And the same manipulatives can be used (or derivations that are color-coded) for quite some time.


I'm thinking of moving toward a leveled workbook approach, while still using the materials we have on hand. We've put so much time and money into them!


I also would really, really like this to be the last change we make in the elementary years. I've read too many stories of people switching around too much in math and really regretting it.


The pressure is on to find the perfect fit now!


My child:


Likes math

Likes manipulatives and workbooks

Enjoys working on math "discovery" on his own time



Here are some options I'm considering:


-Full Montessori


-Miquon using Montessori beads (possibly making more Montessori material purchases as I see fit)


-Singapore Math using Montessori beads (possibly making more Montessori purchases as needed)




Are either of those two specifically designed for c-rods? We don't own them, and I'd prefer to stick with the manipulatives we already own and have worked with.


Thanks, if you made it this far! :)

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Miquon would be great for you IF you feel like you can understand how to teach it. I've read it and still have no clue where to start. I just do better myself with something more straightforward. You may not be like me though. ;)


I use Singapore Essential Math K right now, and will likely try out Singapore Standards Edition grade 1 next year (I'm using grade 4 with my older son now - just switched recently and really like it). I use C-rods with Singapore. C-rods are cheap - about $15 for the bucket of 155 rods. That's the only manipulative we are really using right now. I'm also a bit manipulative-adverse though and am a Rightstart dropout. :lol: I still have the entire RS level A manipulatives kit, and we NEVER use any of it.


The child I'm using SM EM K with right now likes workbooks and manipulatives, so this combo is working very well. My oldest didn't need manipulatives and gets too distracted by them (preferring to build things than use them for math), so he went a different route (Math Mammoth was excellent for him, since he was accelerating in 1st grade).


You can add manipulatives to any math program you choose.

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One thing I would consider is what type of child you have.


I have one kid who wants school to be as straight forward as possible, "git r done" type, and then leave him alone do his own creative play. MM is perfect for him as it is pretty cut and dried with minimal pictures (and when they are present, they are illustrations related to the problem).


I have another one who wants everything to be a game, including school, and he wants it to go on for as long as possible. RightStart or Singapore is better for him and I'm fairly certain MM would cause fits and tears.


How does your dc like to learn? Rightstart might be a good one for you to consider given that it is based on Montessori math and you probably have most of the manipulatives already (although I can't think of any hs curriculum that uses beads like those in ds's Montessori Pre-K/K).

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I'm an RS evangelist anyway, but even if I weren't I think I'd recommend it for your situation. The author is a Montessori teacher herself and the curriculum blends Montessori methods and manipulatives with those used in Asian elementary schools. It's very similar to Singapore, but with more manipulatives, and while the script doesn't always tend toward discovery-based instruction (though that is a defined focus of the program), if you feel comfortable with the material you can use the script as a jumping-off point and make it discovery-based.

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The pressure is on to find the perfect fit now!


My child:


Likes math

Likes manipulatives and workbooks

Enjoys working on math "discovery" on his own time



Here are some options I'm considering:


-Full Montessori


-Miquon using Montessori beads (possibly making more Montessori material purchases as I see fit)


-Singapore Math using Montessori beads (possibly making more Montessori purchases as needed)



The good news is you have good choices. One potent option is to use both Miquon and Primary Mathematics 1A/B and perhaps some MEP.


Miquon would give you the discovery aspect you seem to desire and it is an amazing way to get a child ready for whole-parts math programs like Singapore in child friendly ways that are open to modification and the use of your preexisting manipulative. You would need some C Rods but at less than $20 this should not be a deal-breaker.


Miquon could not be your last program, however, as it (as written) covers 1st-3rd (although I like starting it earlier).


Miquon is also less "workbooky" and less open and go than Singapore. Is this good for you or not? It actually takes more parent time to create a Math Lab style leaning environment and to facilitate discovery learning scenarios than it does to open a workbook/textbook. But the rewards are huge. With Miquon I felt like my son "owned it" (and so did he) this strongly promoted a sense of autonomy and competence that "lessons" directed my me could not have.


Singapore is great for building a math model. But it is less hands on than Miquon and lacks the explicit discussion of mathematical laws (in a form children grasp) that one finds in Miquon.


They are strong in different areas. When you put them together there is synergy.


Going to the trouble of creating a hybrid approach that included Miquon, MEP, Singapore and RightStart elements was one of the best moves I've ever made with my math loving son.


Best wishes!



Edited by Spy Car
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I'm currently in training to get my AMI Elementary Montessori certificate / M.Ed, and while I *adore* Montessori math at the elementary level, I cannot imagine creating (or buying) all that you'd need. It would be a tremendous investment of time and/or money.


One thing you may need to think about is where your child is in relation to traditional scope and sequence. My five year old is in Montessori school this year and he is very comfortable doing four digit addition and subtraction and is doing a lot of work with large number multiplication and division as well. The approach is so different that it would be hard to imagine placing him in SM or RS.


If you can work placement out, I think the general approach of RS is as close to Montessori as anything else I've seen, and it is what I used with my older ds before he transitioned into Montessori.


If you want to do a little elementary math the Montessori way, I would highly recommend the multiplication checker board and division racks and tubes. They are expensive of course. Montessori Outlet has the best prices I have seen, but you could easily make a checker board and, with a little thinking, racks and tubes too.

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I had copied this from somewhere.


· Our students are typically introduced to numbers at age 3: learning the numbers and number symbols one to ten: the red and blue rods, sand-paper numerals, association of number rods and numerals, spindle boxes, cards and counters, counting, sight recognition, concept of odd and even.


· Introduction to the decimal system typically begins at age 3 or 4. Units, tens, hundreds, thousands are represented by specially prepared concrete learning materials that show the decimal hierarchy in three dimensional form: units = single beads, tens = a bar of 10 units, hundreds = 10 ten bars fastened together into a square, thousands = a cube ten units long ten units wide and ten units high. The children learn to first recognize the quantities, then to form numbers with the bead or cube materials through 9,999 and to read them back, to read and write numerals up to 9,999, and to exchange equivalent quantities of units for tens, tens for hundreds, etc.


· Linear Counting: learning the number facts to ten (what numbers make ten, basic addition up to ten); learning the teens (11 = one ten + one unit), counting by tens (34 = three tens + four units) to one hundred.


· Development of the concept of the four basic mathematical operations: addition, subtraction, division, and multiplication through work with the Montessori Golden Bead Material. The child builds numbers with the bead material and performs mathematical operations concretely. (This process normally begins by age 4 and extends over the next two or three years.) Work with this material over a long period is critical to the full understanding of abstract mathematics for all but a few exceptional children. This process tends to develop in the child a much deeper understanding of mathematics.


· Development of the concept of "dynamic" addition and subtraction through the manipulation of the concrete math materials. (Addition and subtraction where exchanging and regrouping of numbers is necessary.)


· Memorization of the basic math facts: adding and subtracting numbers under 10 without the aid of the concrete materials. (Typically begins at age 5 and is normally completed by age 7.)


· Development of further abstract understanding of addition, subtraction, division, and multiplication with large numbers through the Stamp Game (a manipulative system that represents the decimal system as color-keyed "stamps") and the Small and Large Bead Frames (color-coded abacuses).


· Skip counting with the chains of the squares of the numbers from zero to ten: i.e., counting to 25 by 5's, to 36 by 6's, etc. (Age 5-6) Developing first understanding of the concept of the "square" of a number.


· Skip counting with the chains of the cubes of the numbers zero to ten: i.e., counting to 1,000 by ones or tens. Developing the first understanding of the concept of a "cube" of a number.


· Beginning the "passage to abstraction," the child begins to solve problems with paper and pencil while working with the concrete materials. Eventually, the materials are no longer needed.


· Development of the concept of long multiplication and division through concrete work with the bead and cube materials. (The child is typically 6 or younger, and cannot yet do such problems on paper without the concrete materials. The objective is to develop the concept first.)


· Development of more abstract understanding of "short" division through more advanced manipulative materials (Division Board); movement to paper and pencil problems, and memorization of basic division facts. (Normally by age 7-8)


· Development of still more abstract understanding of "long" multiplication through highly advanced and manipulative materials (the Multiplication Checkerboard). (Usually age 7-8)


· Development of still more abstract understanding of "long division" through highly advanced manipulative materials (Test Tube Division apparatus). (Typically by age 7-8)


· Solving problems involving parentheses, such as (3 X 4) - (2 + 9) = ?


· Missing sign problems: In a given situation, should you add, divide, multiply or subtract ?


· Introduction to problems involving tens of thousands, hundreds of thousands, and millions. (Normally by 7yrs.)


· Study of fractions: Normally begins when children using the short division materials who find that they have a "remainder" of one and ask whether or not the single unit can be divided further. The study of fractions begins with very concrete materials (the fraction circles), and involves learning names, symbols, equivalencies common denominators, and simple addition, subtraction, division, and multiplication of fractions up to "tenths". (Normally by age 7-8)


· Study of decimal fractions: all four mathematical operations. (Normally begins by age 8-9, and continues for about two years until the child totally grasps the ideas and processes.)


· Practical application problems, which are used to some extent from the beginning, become far more important around age 7-8 and afterward. Solving word problems, and determining arithmetic procedures in real situations becomes a major focus.


· Money: units, history, equivalent sums, foreign currencies (units and exchange). (Begins as part of social studies and applied math by age 6.)


· Interest: concrete to abstract; real life problems involving credit cards and loans; principal, rate, time.


· Computing the squares and cubes of numbers: cubes and squares of binomials and trinomials. (Normally by age 10)


· Calculating square and cube roots: from concrete to abstract. (Normally by age 10 or 11)


· The history of mathematics and its application in science, engineering, technology & economics.


· Reinforcing application of all mathematical skills to practical problems around the school and in everyday life.


· Basic data gathering, graph reading and preparation, and statistical analysis.





· Sensorial exploration of plane and solid figures at the Primary level (Ages 3 to 6): the children learn to recognize the names and basic shapes of plane and solid geometry through manipulation of special wooden geometric insets. They then learn to order them by size or degree.


· Stage I: Basic geometric shapes. (Age 3-4)


· Stage II: More advanced plane geometric shapes-triangles, polygons, various rectangles and irregular forms. (Age 3-5)


· Stage III: Introduction to solid geometric forms and their relationship to plane geometric shapes. (Age 2-5)


· Study of the basic properties and definitions of the geometric shapes. This is essentially as much a reading exercise as mathematics since the definitions are part of the early language materials.


· More advanced study of the nomenclature, characteristics, measurement and drawing of the geometric shapes and concepts such as points, line, angle, surface, solid, properties of triangles, circles, etc. (Continues through age 12 in repeated cycles.)


· Congruence, similarity, equality, and equivalence.


· The history of applications of geometry.


· The theorem of Pythagorus.


· The calculation of area and volume.

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I should add that I made many of the Montessori math and language manipulatives for my dd earlier. We used some of them (such as the bead stair), but then I bought C-rods and she liked those better. Now she doesnt need the rods either. The golden bead material is the only thing we still use occasionally, but I think she is outgrowing that too. The only thing we may keep using is the abacus because with that we can do addition/subtraction upto a million.



Found this sequence in my notes that I had made up to work with my dd (when I was planning to do Montessori maths only). Hope it helps you.


1. Finding 1s on the 100-board

2. Finding 2s on the 100-board

3. Finding 3s...

4. Number bonds to 10 and 20 (using 2 colours of beads)

5. Teen boards - cycle through 11 to 20.

6. Ten Boards - cycle through 21 to 99 (one decade at a time)

7. Ten Boards - Making numbers at random upto 99

8. Making numbers upto 999

10. Making numbers upto 9999


7. Static Addition upto 99

8. Static Subtraction upto 99

9. Static Addition upto 999

10. Static Subtraction upto 999

11. Static Addition upto 9999

12. Static Subtraction upto 9999

13. Dynamic Addition upto 9999

14. Dynamic Subtraction upto 9999

15. Multiplication Board

16. 10s table

17. 100s table

18. Division Board

19. Multiplication using bead bars - 1s, 2s, 3s, etc

20. Skip counting on 100 board

21. Fractions - operations

Edited by nansk
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