Math Mammoth User Guide, Grade 2
The Light Blue Series

This document has the following sections:

Basic principles in using Math Mammoth Complete Curriculum
How to get started
Pacing the curriculum
Using tests
Using cumulative reviews and the worksheet maker
Frequently asked questions
Contact the author

Basic principles in using Math Mammoth Complete Curriculum

Math Mammoth Complete Curriculum is not a scripted curriculum. In other words, it is not spelling out in exact detail what the teacher is to do or say in a specific lesson. Instead, Math Mammoth gives you, the teacher, various tools for teaching:


How to get started

Simply start out by printing the first lesson from the student worktext. Study the teaching part (within the blue boxes) together with your child. Go through a few of the exercises together, and then assign some problems for your child to do on his/her own. You can also let the child study the lesson completely on his own if you feel he/she is capable.


Pacing the curriculum

The lessons in Math Mammoth complete curriculum are NOT written to be done in a single teaching session or class. Sometimes you might be able to go through a whole lesson in one day, but more often, the lesson itself might span 3-5 pages and take 2-3 days or classes to complete.

Therefore, it is not possible to say exactly how many pages a student needs to do in one day. This will vary. However, you should calculate yourself a general guideline as to how many pages per week you should cover in the student worktext in order to go through the curriculum in one school year (or some other span of time you want to allot to it).

You can check below how many pages there are to do for your particular grade level. Fill in how many days of school you have in mind. Also allow several days for tests and cumulative reviews - at least twice the number of chapters in the curriculum. Then, to get a count of "pages/day", divide the number of pages by the number of available days. This number will be between 1 and 2, assuming you do school 5 days a week, about 40 weeks a year. Then, multiply this number by 5 to get an approximate page count to go through in a week.

Example:

Grade level Lesson
pages
Number of
school  days
Number of days
for tests
and reviews
Pages to study
per day
Pages to study
per week
2-A133 95 5 1.48 7.4
2-B148 105 5 1.48 7.4
Grade 2 total 281 200 10 1.48 7.4

The one below is for you to fill in.

Grade level Lesson
pages
Number of
school  days
Number of days
for tests
and reviews
Pages to study
per day
Pages to study
per week
2-A133        
2-B148        
Grade 2 total 281        

Now, let's assume you determine that you need to study about 1.5 pages a day, or about 7.6 pages a week in order to get through the curriculum, based on the number of school days in your school year. As you study each lesson, keep in mind that sometimes most of the page might be filled with those blue teaching boxes, and very few exercises. You might be able to "cover" two full pages on such a day. Then some other day you might only assign one page of word problems. Also, you might be able to go through the pages quicker in some chapters, for example when studying the clock, because the large clock pictures fill the page so that one page does not have many problems.

When you have a page or two filled with lots of similar practice problems ("drill") or large sets of problems, feel free to only assign 1/2 or 2/3 of those problems. If your child "gets it" with less amount of exercises, then that is perfect! If not, you can always assign him/her the rest of the problems some other day. In fact, you could even use these unassigned problems the next week or next month for some additional review.

In general, 1st-2nd graders might spend 25-40 minutes a day on math. 3rd-4th graders might spend 30-60 minutes a day. 5th - 6th graders might spend 45-75 minutes a day. If your child finds math enjoyable, he/she can of course spend more time with it! However, it is not good to drag out the lessons on a regular basis, because that can then affect the child's attitude towards math.


Using tests

There is a test for each chapter, which can be administered right after studying the chapter. The tests are optional. Some homeschooling families might prefer not to give tests at all. The main reason I have provided tests is for diagnostic purposes, and so that homeschooling families can use them for their record keeping. I have not provided any grading system for the chapter tests. You can grade them however you want.

These test files are located in their own folder. They are provided as PDF files and as editable html files. You can open the html files in most any word processor (such as Microsoft Word) for editing. Then you can edit the test and change the numbers or problems in it. However, remember to save the edited test files under a different file name, or you will lose the original test file.

The end-of-year test has a suggestion for grading. This test is best administered as a diagnostic or assessment test, which will tell you how well the student remembers and has mastered the math content of the entire grade level.


Using cumulative reviews and the worksheet maker

There is a cumulative review matched for each chapter, except for chapter 1. For example, the review titled "Cumulative Review, Chapters 1 - 4" means that the problems in that review cover topics from chapters 1-4. These cumulative reviews are available as PDF files and as editable html files. You are welcome to edit the html files for the purpose of providing a slightly different review for your student. For example, you can easily change the numbers in the problems.

Use the corresponding cumulative review some time after you are done studying a particular chapter. For example, you could use the "Cumulative Review, Chapters 1 - 4" right after or before administering chapter 4 test. Or, you could use it 1-2 weeks after finishing chapter 4.

There are no "hard and fast" rules when it comes to cumulative reviews. It is not necessary to use all of them within a school year; however I do recommend that you use at least 1/2 of them.

One of the main reasons for the cumulative reviews is to spot any areas that the student has not grasped well or has forgotten, and thus needs additional practice. When you find such a topic or concept, you have several options:

  1. Check if the worksheet maker lets you make worksheets for that topic (for example, conversions between measuring units or equivalent fractions).

  2. Check for any online games in the Introduction part of the particular chapter this topic or concept was taught in.

  3. You might also be able to simply reprint the lesson from the student worktext and have the student restudy that.

  4. Or, maybe you only assigned 2/3 of the exercise sets the first time through, and can now use the remaining exercises.

  5. Occasionally a lack is not of concern. This is true if the topic either is going to be taught in-depth or can safely be delayed to the next grade level.

    Such topics in grade 2 include: regrouping in subtraction with three-digit numbers and multiplication. Even clock reading may be delayed to the end of 2nd grade or beginning of 3rd. If you decide to delay a topic, just don't forget to study it thoroughly later on.

Another sign that the student has not grasped a necessary concept is if he/she cannot do WORD PROBLEMS in the subsequent chapters that require past knowledge or concepts. If your child has great difficulty with those kinds of word problems, then it might be time to use the worksheet maker, online games, or restudy the concept using the worktext. I have always striven to make the word problems progressively so that they involve concepts and skills studied in earlier chapters.


Frequently asked questions

1. Do you have placement / diagnostic tests?

2. Is there a teacher's manual?

3a. Are there printed versions available?

3b. Can we buy the downloads and then take them to a Kinko's or Staples type place to have the book printed up and bound nicely?

4. Can I buy it on a CD?

4b. Is there any advantage for buying the curriculum on a CD?

4c. Does it work on a Mac or Linux?

4d. Can the PDF be filled in on the computer or tablet device (iPad or similar)?

5. What is a worktext?

6. What is the difference between the Blue Series and Light Blue series?

7. How does the complete curriculum (Light Blue books) compare with Singapore math,
    Math-U-See, or other popular homeschool math curricula?

8. Are earlier concepts reviewed in later levels?

9. Do the books have review problems that continue to review previous concepts?

10 Are tests included?

11. What about kindergarten math? At what age is it appropriate to start your 1st grade books?

12. Will you be writing more grade levels?

13. How far can I use the Light Blue series? Will it cover pre-algebra or algebra?

14. For drilling the addition and subtraction tables should we just go over each lesson
    over and over until she memorizes her tables?

15. Is Math Mammoth aligned with any state standards?

16. Does Math Mammoth curriculum encourage the use of manipulatives?

17. How and when to use the 100-bead abacus?

18. My son is having trouble with the word problems. I'd like him to get more practice with them. Is there a place to get more worksheets for word problems?

19. Is Math Mammoth a spiral or mastery curriculum (horizontal or vertical math)?

20. Some graphics are missing from the PDF file. Why?

21. What is the origin of this curriculum?

22. Does the author have any mathematics or education credentials?


 

1. Do you have placement / diagnostic tests?

Yes. Simply click here for placement tests for all the grade-levels.


 

2. Is there a teacher's manual?

No. This curriculum does not contain a separate teacher's manual nor scripted lessons. The student worktext contains in the text itself explanations of the concepts, and I've tried to create a text that is as self-explanatory as possible. Students will often be able to read and study through the lessons on their own. The parent can "get it" at the same time as the student, if they have not understood math concepts before.

Also, in the beginning of each chapter there are some general notes and helps for the teacher (Introduction).

If you have previously used a scripted curriculum and are worried about your ability to teach with Math Mammoth, I would encourage you to try it out by purchasing one of the Blue Series topical books.


 

3a. Are there printed versions available?

Yes. The books are available as softcopies (printed books) through Lulu.com and at Rainbow Resource. The inside pages are black-and-white (or grayscale) (not full color) because full color publishing is fairly costly.


 

3b. Can we buy the downloads and then take them to a Kinko's or Staples type place to have the book printed up and bound nicely?

Sure. Just remember the copyright notice: the person who owns the book(s) is allowed to make copies (whether by Kinko's printer or some other printer) to HIS / HER students, but not to other teacher's students. You can also use online printing services such as Mimeo.com or Bestvaluecopy.com. However, color printing can be expensive no matter where you do it.


 

4. Can I buy it on a CD?

Yes. At Kagi, you can purchase each of the Light Blue grade levels separately on a CD or all six grade levels on single CD.  Rainbow Resource sells the CD for all six grade levels.


 

4b. Is there any advantage for buying the curriculum on a CD?

Usually no, because the CD just contains the same files as the download, and if you purchase a download, you may always make a backup copy of the files on a CD or on a memory stick (flash drive).

However, a CD is helpful if you know beforehand that you cannot download large files. Or, some people may prefer a CD so as to not lose track where the files are stored. Even if you purchase a CD, I recommend a backup copy be made. CDs do not last forever.

 

4c. Does it work on a Mac or Linux?

Yes. The actual files you get are PDF or html files. You will need to install Adobe Acrobat Reader for Mac or for Linux to view the PDF files correctly. I've had customers tell me that Mac's native PDF viewer shows black boxes in the files, or that lots of the graphics are missing. In Linux, if you use other PDF viewers, some images will likely be missing or messed up, so again, you need to install Acrobat Reader version for Linux.

Also, it won't matter whether you get a download or a CD.

The only thing that does not work in Mac or Linux is the bonus software "Soft-Pak".
 


4d. Can the PDF be filled in on the computer or tablet device (iPad or similar)?

On the computer, definitely yes. The PDF files are enabled for annotating. This means that if you prefer, the student can fill them in on the computer, using the typewriter and drawing tools in Adobe Reader version 9 or greater.

On a tablet device (iPad etc.) sort of yes - BUT: 1) Other PDF viewers don't necessarily show all the images in my PDFs, and 2) the annotating tools will depend on the PDF app you are using. There exist several PDF apps for iPad that have annotating tools (neu.AnnotatePDF, PDF Expert, iAnnotatePDF, Goodreader, Notability). The tools will vary; most should have the ability to handwrite or use a stylus to write.

Unfortunately at this time I don't have a solution to the problem where all the images would show in these alternative PDF viewers. Only Adobe Reader app seems to do a perfect job with images. However, while Adobe Reader app does have annotating tools as of spring 2012, those are disabled in protected PDF files (such as I have to use with Math Mammoth). So, you could not write into the PDF on your iPad with Adobe Reader.


5. What is a worktext?

Worktext means that the book contains both the "text" (= the explanations) and the "work" (= the problems). Simply put, the textbook and problems are in the same book. This is especially useful for homeschooling and for any kind of independent study.


 

6. What is the difference between the Blue Series and Light Blue series?

These two series have practically the same lesson material. Comparing with the Light Blue series, there are only a few lessons here and there that are in one series but not in the other.

The MAIN difference is in how the material is organized. The Light Blue Series goes by grades, and being a complete curriculum also includes tests & cumulative reviews. The Blue Series just consists of worktexts for various topics, and the material in each book usually spans 2-3 grade levels.

So, which you would choose depends mostly on your goals: Do you wish to have a complete curriculum for a given grade level? Go Light Blue. Do you wish to review/reteach certain topics only? Go Blue. Do you want to cover all topics as in a full curriculum but without mentions of grade levels? Blue Series can work there as well.


 

7. How does the complete curriculum (Light Blue books) compare with Singapore math, Math-U-See, or other popular homeschool math curricula?

Please read comparisons of Math Mammoth with other homeschool math curricula here.


 

8. Are earlier concepts reviewed in later levels?

To some extent, yes, but not so much as in a typical spiral curricula. For example, I often introduce somewhat difficult topics in two grades. A few topics are "introductory" in one grade and "in focus" in the next. For example:

Some elementary mathematics topics are covered over several years in a spiraling style, such as place value (with increasing digits), measuring units, geometry vocabulary (pentagon, octagon, parallel), reading clock, coins, and money problems.

The following topics are NOT reviewed in any great depth, but mastery is expected: single digit addition/ subtraction after 1st grade, double-digit addition/subtraction after 2nd, clock reading or coins after 3rd. Multiplication tables and basic division receive a quick review in 4th grade but not after that. I cannot list every single concept and its progression in this short space though.


 

9. I am concerned that there won't be enough review. Do your books have review problems that continue to review previous concepts?

The program includes cumulative reviews meant to be used after each chapter. These have various kinds of problems, including word problems. When you notice that your child needs additional review of any kind of calculation topic (such as after using the cumulative reviews), you can use the worksheet maker included in the downloadable curriculum, and generate additional worksheets with it.

This worksheet generator requires an Internet access. If you don't have Internet at home, you can use it in an Internet cafe or public library or a friend's house, and save the generated worksheets on a memory stick to print later.

Also, the major concepts, such as addition, subtraction, multiplication and division, or fractions, actually get reviewed in a sense because they get used all the time. For example, a child who learns their multiplication tables will keep using them all the time in division and multidigit multiplication. Addition and subtraction strategies are used in word problems about money or measuring, or again when studying place value and large numbers. Division facts are used in long division.

I never make word problems to exactly match the lesson. By this I mean that a word problem found in a multiplication lesson might require both multiplication and addition to solve. Similarly, word problems in the other chapters will include multiplication. So, the word problems dealing with various topics (money, measuring, division, fractions) include the usage of all operations all the time (once the operation has been studied), and thus review these operations. The word problems in this curriculum constantly use important concepts that have been already learned.


 

10. Are tests included?

Yes. There is a chapter test after each chapter and an end-of-year test to be used after each grade level.


 

11. What about kindergarten math? At what age is it appropriate to start your 1st grade books?

There are no Math Mammoth books for kindergarten, but I've written a fairly comprehensive article about kindergarten math to use as a guideline. You can start 1st grade once the child can write and recognize numbers, count to 20 (preferably to 30 or beyond), has mastered basic concepts of equivalence, more, and less; and has a basic idea of addition.


 

12. Will you be writing more grade levels?

I intend to write a prealgebra curriculum in late 2012 - early 2013. I have written an article for algebra 1 recommendations.
 

13. How far can I use the Light Blue series? Will it cover pre-algebra or algebra?

After completing Math Mammoth 6th grade, most students should be able to continue directly to pre-algebra. Also, the whole series emphasizes algebraic thinking and thus prepares students for algebra. But Math Mammoth Light Blue Series does not cover algebra 1 topics.

In the Golden Series, you will find worksheet collections for 6th, 7th (pre-algebra), and 8th/9th (algebra 1). These are useful as supplements but unless a parent or teacher is supplying the instruction, they could not be used as a full curriculum.
 


14. For drilling the addition and subtraction tables should we just go over each lesson over and over until she memorizes her tables?

First of all, you should go through the books and check that she knows all the concepts related to addition and subtraction.

To learn the facts, go carefully over those lessons that present fact families and number rainbows. These provide the structure and a context for learning the facts so that they are not learned as separate, random things.

Then, once she thoroughly understands fact families and the pattern in the number rainbow, you can move on to other math topics such as place value, geometry, etc. but keep up the facts practice a few minutes a day with games, worksheets, and flash cards.

These basic facts are also used a lot even when studying place value and other topics, so that helps kids remember them too.


 

15. Is Math Mammoth aligned with any state standards?

Grades 1 and 2 are aligned to Common Core standards as of April 2012. I will be working on the other grades to align them to these standards during 2012.


 

16. Does Math Mammoth curriculum encourage the use of manipulatives?

For the most part, the curriculum does not specifically emphasize manipulatives but visual models. The exercises with visual models COULD be done equally with manipulatives (beans/counters, base ten blocks, fraction manipulatives, etc.)

The exception is the 100-bead abacus, which I feel is needful for first grade. (The other option would be base ten blocks.) I feel that it's essential that kindergartners and first graders have the opportunity to learn tens and ones (place value) using some manipulative.

Here is a list of manipulatives that are needed or recommended for grade 1:
  1. A 100-bead abacus (for 1-A and 1-B; especially in chapter 3 and chapter 7)
    Please read more about the 100-bead abacus here.
  2. An old-fashioned alarm clock or other analog clock where you can turn the minute hand and the hour hand will turn as it is supposed to (for 1-B).
  3. A ruler that measures in inches (for 1-B).
  4. A ruler that measures in centimeters (for 1-B).

 

Here is a list of manipulatives that are needed or recommended for grade 2:
  1. An old-fashioned alarm clock or other analog clock where you can turn the minute hand and the hour hand will turn as it is supposed to (for 2-A).
  2. A ruler that measures in inches (for 2-B).
  3. A ruler that measures in centimeters (for 2-B).
  4. A bathroom scales. It is best if you can have one that measures in pounds and kilograms, or one with pounds and another with kilograms; however I realize most people wouldn't normally buy two bathroom scales, so if you decide not to get both kinds, it means you will just need to skip some activities in the measuring chapter (for 2-B).
  5. A quart jar and a pint jar (for 2-B).
  6. A measuring cup that measures 1 cup (for 2-B).
  7. A measuring cup that measures in milliliters (for 2-B).
  8. Base ten blocks to illustrate place value with hundreds (optional). The 2-B worktext has pictures that are just like base ten blocks, and most kids can understand the concepts from the visual representation, without a physical manipulative; however for some kids the actual blocks can be beneficial (for 2-B).
  9. A 100-bead abacus (optional)

 

Here is a list of manipulatives that are needed or recommended for grade 3. Measuring tapes, scales, and measuring cups are only used in the measuring chapter.

  1. An old-fashioned alarm clock or other analog clock where you can turn the minute hand and the hour hand will turn as it is supposed to (optional; for 3-A).
  2. A ruler that measures in inches (for 3-B).
  3. A ruler that measures in centimeters (for 3-B).
  4. A measuring tape that measures in feet (for 3-B).
  5. A measuring tape that measures in meters (for 3-B).
  6. A kitchen scales that measures in ounces (for 3-B).
  7. A kitchen scales that measures in grams (for 3-B).
  8. Measuring cups that measure 1 cup, 1/2 cup, 1/4 cup (for 3-B) of which at least one has markings for ounces.
  9. A measuring cup that measures in milliliters (for 3-B).
  10. A thermometer that uses Fahrenheit degrees (optional; for 3-B).
  11. A thermometer that uses Celsius degrees (optional; for 3-B).
  12. Fraction manipulatives. The curriculum contains printables to make your own fraction manipulatives. The text uses visual pie models extensively, and students even learn to draw them themselves for the exercises, therefore making or buying the manipulatives is entirely optional (optional; for 3-B).

 

17. How and when to use the 100-bead abacus?

The only way the abacus is used in my books is where each bead counts as one. Nothing fancy. It is NOT used like Chinese, Russian, or any of the other abaci where one bead might count as 5, 10, or 100.

A 100-bead abacus or school abacus simply contains 10 beads on 10 rods, a total of 100. In the school abacus, each bead simply represents one. The 100-bead abacus lets children both "see" the numbers and use their touch while making them.

First and foremost, the abacus is used in the place value section in 1st grade where children learn about tens and ones (numbers up to 100). We use it to show clearly how 45 is made up of 4 tens and 5 ones, for example.

Secondly, you can use the abacus with addition and subtraction problems in 1st and 2nd grades. For example:

The purpose is mainly to help children to visualize two-digit numbers, and to add and subtract two-digit numbers.

The goal in my books is to drop the abacus by 3rd grade. Even before that, students use visual models, and from those go on to the abstract. The quicker the child can use visual models, and then do the math problems without any models, the better.

See also these abacus-related articles on my blog.
 

At Amazon you can find Melissa & Doug Classic Wooden Abacus at Amazon for around $12. An abacus where the beads alternate colors by fives is even more useful.

Browse Amazon's abacus selection here. Other stores carry abaci as well.

You can also use this virtual abacus. Or, make your own abacus. Just don't make it exactly like they show on that web page but instead use 10 bamboo skewer with 10 beads in each so you get a 10 x 10 abacus.


 

18. My son is doing 4-A and having trouble with the word problems. I'd like him to get more practice with them. Is there a place to get more worksheets for word problems?

The issue here is probably that the student has not had enough word problems before, or the ones he has done have not been complex enough.

Whether you look at the Blue or Light Blue series, the child gets to do many word problems from the very beginning. At first, these are just either addition or subtraction one-step problems. But already in second grade level, most of them take at least two steps. That might be what your son hasn't done --multi-step word problems.

I don't know any gold nugget that would make children suddenly learn word problems. I do know if they get to do them from early on, with an increasing difficulty, they won't be that difficult later on.

Please also read Problem with Word Problems and Which operation should you use in word problems? to help you understand the issue.

To remedy, you could simply use the earlier grades of Light Blue series. Go to 2nd grade, and do the word problems with him from addition and subtraction chapters. Then go to 3rd grade, and do all the word problems with him. You could either do several problems a day alongside your regular math, or take a break and just do word problems for a few weeks.


 

19. Is Math Mammoth a spiral or mastery curriculum (horizontal or vertical math)?

Math Mammoth is basically a mastery-based curriculum. Some topics are studied till mastery within one and the same chapter. Example of such include regrouping in subtraction for 2-digit numbers (2nd), multiplication tables (3rd), or long division (4th).

However, often the topic is present in two (or even three) neighboring grades. Examples include: equivalent fractions (both 4th and 5th grade), percent (5th and 6th), area of triangle (5th and 6th). Some topics are "developed" to mastery over several grades, going from simple to more complex; for example reading the clock (grades 1-3), counting coins (grades 1-3), adding like fractions (grades 3-5), decimal arithmetic (grades 4-5).

So, you could call Math Mammoth a mastery-oriented program with some spiraling over the grades. It does NOT employ a "tight" or "short" spiral where the same topic would be present, say, every 10 lessons, or dozens of times within the same school year.

 


20. Some graphics are missing from the PDF file. Why?

This is a common problem in Mac computers. If it seems that some images or graphics are missing (such as number lines, bar graphs, diagrams, etc.), you need to use Adobe Acrobat Reader to open Math Mammoth PDFs, and not in some other PDF viewer. Download and install Adobe Acrobat Reader for Mac from this link, and open the PDFs in it.

 


21. What is the origin of this curriculum?

Math Mammoth books had their start at around 2002, when I (Maria Miller) was tutoring homeschooling children, and noticed the difficulties their parents had in explaining mathematics.

I initially wrote books for certain topics, and later those books gave rise to the Blue Series books currently sold on this site.

I always designed the lessons in the books so that they would teach BOTH the parent and the child the processes and concepts of elementary math. Thus, the books contain very clear explanations, lots of visual exercises and pattern exercises that help children see the structure of mathematics and clearly understand the concepts of mathematics, instead of just memorizing rules.

Ample practice for computation is not forgotten either. Word problems abound.

The complete curriculum had its start in 2007, when I was asked to combine my books into material that could be sold by grade levels.


 

22. Does the author have any mathematics or education credentials?

Yes. I have a master's degree in mathematics (1997) after studying 5 years in in university of Joensuu, Finland, and one term in the University of Nottingham, UK. My degree includes minors in physics and statistics, and the educational studies required to become a teacher (as required in Finland).


CONTACT THE AUTHOR

In case of any questions about this product, you can fill a form at www.mathmammoth.com/contact.php

I wish you success in your math teaching!
Maria Miller