The Light Blue Series

This document has the following sections:

Basic principles in using Math Mammoth Complete CurriculumHow to get started

Pacing the curriculum

Using tests

Using cumulative reviews and the worksheet maker

Concerning challenging word problems and puzzles

Frequently asked questions

Contact the author

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:

**The two student worktexts**(parts A and B) are the most important part of the curriculum. These contain all the lesson material and exercises, and INCLUDE the explanations of the concepts (the teaching part) in blue boxes. The worktexts also contain some advice for the teacher in the “Introduction” of each chapter.

The teacher can read the teaching part of each lesson before the lesson, or read and study it together with the student in the lesson, or let the student read and study it on his own. If you are a classroom teacher, you can copy the examples from the “blue teaching boxes” to the chalkboard and go through them on the chalkboard.

- The “Introduction” part of each chapter (within the student worktext) has a
**link list to various free online games**or other resources on the Internet. These games can be used to supplement the math lessons, for learning math facts, or just for some fun.

- There is one
**Cumulative Review**for each chapter, excluding the first chapter. These cumulative reviews are supplied as separate PDF files.

- Each chapter has a
**Chapter Test**, again supplied as a separate PDF file.

- The
**Worksheet Maker**allows you to make additional worksheets for most calculation-type topics in the curriculum. This is a single html file. You will need Internet access to be able to use it.

- Some grade levels have
**cutouts**to make fraction manipulatives or geometric solids.

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.

The lessons in Math Mammoth complete curriculum are NOT intended 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 for 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 whatever span of time you want to allot to it).

You can check below to see how many pages there are to do for your particular grade level. Fill in how many days of school you intend to take. Also allow several days for tests and cumulative reviews - there will be 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 of pages 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 the approximate page count to cover in a week.

Example:

Grade level |
Lesson pages |
Number of school days |
Number of days for tests and reviews |
Number of days for studying the student book |
Pages to study per day |
Pages to study per week |
---|---|---|---|---|---|---|

5-A | 170 | 99 | 10 | 89 | 1.91 | 9.55 |

5-B | 176 | 101 | 10 | 91 | 1.93 | 9.67 |

Grade 5 total | 346 | 200 | 20 | 180 | 1.92 | 9.61 |

The table below is for you to fill in.

Grade level |
Lesson pages |
Number of school days |
Number of days for tests and reviews |
Number of days for studying the student book |
Pages to study per day |
Pages to study per week |
---|---|---|---|---|---|---|

5-A | 170 | |||||

5-B | 176 | |||||

Grade 5 total | 346 |

Now, let's assume you determine that you need to study about 2 pages a day, or about 10 pages a week in order to get through the curriculum. As you study each lesson, keep in mind that sometimes most of the page might be filled with blue teaching boxes and very few exercises. You might be able to “cover” 2 1/2 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 graphs, because the large 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, first and second graders might spend 25-40 minutes a day on math. Third and fourth graders might spend 30-60 minutes a day. Fifth and sixth 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.

There is generally a test for each chapter (with a few exceptions), 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 wish. These tests are not aligned or matched to any standards.

These test files are located in their own folder. They are provided as PDF files and html files. Backup files are also provided. If you print the html files from your web browser, set the margins to 0.6 inches in the Page Setup. You can also set your header and footer in the Page Setup of your browser.

You can open the html files in most any word processor program 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. If this happens anyway, and you wish to go back to the originals, backup files are provided in a folder called /backup-copies/.

The end-of-the-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 for the entire grade level.

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 htm and pdf files. You are welcome to edit the htm 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
the 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,
so he/she needs additional practice**. When you find such a topic or concept, you have several options:

- Check if the
__worksheet maker__lets you make worksheets for that topic (for example, conversions between measuring units or equivalent fractions). - Check for any
__online games__in the*Introduction*part of the particular chapter in which this topic or concept was taught. - You might also be able to simply
__reprint the lesson__from the student worktext and have the student restudy that. - Or, maybe you only assigned 2/3 of the exercise sets the first time through, and can now
__use the remaining exercises__. - Occasionally a lack or a mistake 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 5 include exponents, mean (average), and introduction to ratios.

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 tried to make the word problems progressively so that they involve concepts and skills studied in earlier chapters.

While this is not absolutely necessary, I heartily recommend supplementing Math Mammoth with challenging word problems and puzzles. You could do that once a month, for example, or more often if the student enjoys it.

The goal of challenging story problems and puzzles is to **develop the
student’s logical and abstract
thinking and mental discipline**. I recommend starting these in fourth grade, at the latest.
Then, students are able to read the problems on their own and have developed mathematical knowledge in many different areas. Of course I am not discouraging students from doing such in earlier grades, either.

Math Mammoth curriculum contains lots of word problems, and they are usually multi-step problems. Several of the lessons utilize a bar model for solving problems. Even so, the problems I have created are usually tied to a specific concept or concepts. I feel students can benefit from solving problems and puzzles that require them to think “out of the box” or are just different from the ones I have written.

You can use the resources below for some problem solving practice. You can find more puzzles online by searching for “brain puzzles for kids,” “logic puzzles for kids,” or “brain teasers for kids.” Choose something that fits your budget (most of these are free) and that you and your students will like.

**Problem Solving Decks from North Carolina public schools**

Includes a deck of problem cards for grades 1-8, student sheets,
and solutions. Many of these problems are best solved with calculators. All of
these problems lend themselves to students telling and writing about their
thinking.

http://www.homeschoolmath.net/teaching/problem-solving-decks.php

**Math Stars Problem Solving Newsletter (grades 1-8)**

These
newsletters are a fantastic, printable resource for problems to solve and their
solutions.

http://www.homeschoolmath.net/teaching/math-stars.php

**A+ Click**

A+ Click features a graduated set of over 4700 challenging problems for students
in grades one through twelve, starting from the very simple to the extremely
difficult. No fees, no ads, no calculators, and no sign in. The questions
concentrate on understanding, spatial reasoning, usefulness, and problem solving
rather than math rules and theorems. The tests adapt to student ability.

http://www.aplusclick.com

**Problem Solving from MathWire.com**

Neat and creative problems to solve for K-8.

http://www.mathwire.com/problemsolving/probs.html

**Challenge Math For the Elementary and Middle School Math Student
**by Edward Zaccaro

http://www.amazon.com/Challenge-Elementary-Middle-Student-Edition/dp/0967991552/?tag=mathmammoth-20

**Mathematics
Enrichment - nrich.maths.org**

Open-ended, investigative math challenges for all levels from the UK. Use
Stage 3 problems for 7th grade.

http://nrich.maths.org/

http://nrich.maths.org/public/themes.php
lets you find problems organized by mathematical themes.

**Figure This! Math
Challenges for Families**

Word problems related to real life. They do not always have all
the information but you have to estimate and think. For each problem, there is a
hint, other related problems, and interesting trivia. Website supported by
National Council of Teachers of Mathematics.

http://figurethis.nctm.org/

**MathCounts School Handbook (PDF)**

This handbook contains 300 creative problems for grades 6-8. All problems are
mapped according to topic, to difficulty level, and to the Common Core State
Standards.

http://mathcounts.org/resources/school-handbook

**Noetic Learning Challenge Math**

This is a program with weekly assignments, designed to hone young students’ mathematical problem solving skills and logical reasoning skills. The problems are non-routine problem solving questions that are adapted to many math competitions. Price is about $20 for a semester
(10 weeks).

http://www.noetic-learning.com/gifted/index.jsp

**“Problem of the Week” (POWs)**

Problem of the week contests are excellent for finding
challenging problems and for motivation. There are several:

**Math Forum: Problem of the Week**

Five weekly problem projects for various levels of math. Mentoring available.

http://mathforum.org/pows/

**Math Contest at Columbus State University**

Elementary, middle, algebra, and “general” levels.

http://mathcontest.olemiss.edu/

**Math Olympiads**

A math problem solving competition for teams (groups of students) from schools or home schools. For grades 4-8.

http://www.moems.org/

**American Mathematics Competitions**

America’s longest-running math contests. There is one for middle school students and two for high school students.

http://www.maa.org/math-competitions

**Grace Church School’s ABACUS International Math Challenge**

This is open to any child in three different age groups.

http://www.gcschool.org/page/Shortcuts/Abacus

See even more word problem and problem solving resources at

http://www.homeschoolmath.net/online/problem_solving.php

You can also use puzzles from the Internet:

Search in Google for “brain puzzles for kids”

Search in Google for “logic puzzles for kids”

Search in Google for “brain teasers for kids”

1. Do you have placement / diagnostic tests?

2. Is there a teacher’s manual?

3a. Are there printed versions available?

3c. I hesitate to buy MM because I cannot print in color. Any suggestions?

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)?

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

8. Are earlier concepts reviewed in later levels?

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

11. Is Math Mammoth aligned with any state standards?

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

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

14. What is the origin of this curriculum?

15. What do you recommend for high school math?

16. 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 have 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 Introduction of each chapter I have included some general notes and
helps for the teacher.

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 Light Blue series books are available as paperbacks in two stores:

- Lulu.com sells spiral-bound student texts, insides are grayscale (b&w).
- Rainbow Resource Center sells perfect-bound copies, both with black-and-white inside pages (cheaper) and with full-color pages.

On the page for each grade of Light Blue series at MathMammoth.com you will find direct links to purchase printed copies for that grade level in these two stores.

**3b. Can we take the download version to Kinko’s, Staples,
or similar to have the book printed up and bound nicely?**

Yes. The copyright notice that is printed on page 2 specifically *allows* the person who
purchases the book(s) to make copies — whether by Kinko’s or their own printer —
for __his__ or __her__ students, but not for other teacher’s students. You can also use online
printing services such as Mimeo.com or Bestvaluecopy.com. Keep in mind color
printing can be expensive no matter where you do it.

**3c. I hesitate to buy MM because I cannot print in color.
Any suggestions?**

1) Print in black and white, but let the child color the boxes the problems are in, using crayons.

2) Utilize the online games recommended in the introduction of each chapter for the “color” (so to speak). It works for some!

Yes. You can purchase each of the grade levels of the Light Blue series on a
CD at
Kagi store or at
Rainbow Resource. You can buy all available grade levels on one CD at
Kagi,
Rainbow Resource Center, or at Homeschool Buyers Co-op or Educents (at
special sales).

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

Usually no, because the CD contains the exact same files as the download. Also, if you purchase a download, you may make a backup copy of the files on a CD or on a flash drive.

However, a CD is a good option if you cannot download large files. Some people may prefer a CD so they can resell it or so as to not lose track of where the files are stored. Even if you purchase a CD, I recommend you make a backup copy, because CDs do not last forever.

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

Yes. The actual files you get (whether from a download or on a CD)
are PDF or html files so Math Mammoth is compatible with Macs and
Linux machines. However, you will need to install
Adobe Acrobat Reader for Mac or Linux to view the PDF files
correctly. I have had some customers tell me that Mac’s native PDF
viewer shows black boxes in the files or that many of the graphics
are missing. Similarly in Linux, some images will likely be missing
or messed up if you use other PDF viewers, so again, you need to use
Acrobat Reader version for Linux.

Please note that the bonus software “Soft-Pak” is Windows software only. However, Soft-Pak is not a part of the actual curriculum and is not needed when using Math Mammoth — it is only an additional bonus.

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

Yes, it can. The PDF files are enabled for annotating. This means that if you prefer, the student can fill the math books in on the computer or tablet device using annotating tools in a PDF application.

On a computer, use Adobe Reader version 9 or greater. It has typewriter and drawing tools.

For iPad, there exist several PDF apps that have annotating tools and work well for Math Mammoth files: PDF Expert ($9.99), Goodreader ($2.99), iAnnotatePDF ($9.99). You can add text, lines, and shapes, or use a stylus to write. The apps neu.AnnotatePDF ($1.99) and Notability ($2.99) work also, but are not as user-friendly as the other three.

Adobe Reader app for iPad (free) unfortunately does not allow annotating protected PDF files (such as I have to use with Math Mammoth). So, you cannot write into the PDF on your iPad with Adobe Reader (Adobe Reader for PC and Mac works great though.)

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 lessons. 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 and cumulative reviews. The Blue Series consists of topical worktexts, and the material in each book usually spans 2-3 grade levels.

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

**7. How does the complete curriculum (Light Blue Series) 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 as much as in a typical spiral curriculum. For example, I often introduce somewhat difficult topics in two grade levels. A few topics are “introductory” in one grade and “in focus” in the next. For example:

- Addition where the result goes over 10 (such as 6 + 8) is included in the last half of first grade and first half of second grade.
- Regrouping in subtraction is studied both in second and third (mostly in second).
- The concept of multiplication is introduced in the very end of second grade but studied in depth in third.
- Multi-digit multiplication is studied in length in fourth grade, and studied once more in fifth (5-A).
- Similarly, long division is studied both in fourth and fifth.
- Decimal numbers are introduced in fourth grade, then studied in-depth in fifth, and reviewed in sixth.
- Fractions are introduced in second and third grades, and studied some more in fourth. In fifth grade, they are in “focus”. Then they are reviewed in sixth grade.

Topics such as place value, measuring units, geometry, clock, and money are covered over several years in a spiraling style.

The following topics are not reviewed much in later levels (mastery is expected): single-digit addition and subtraction after first grade, double-digit addition and subtraction after second, and reading the clock and counting coins after third grade. The multiplication tables and basic division facts receive a quick review in fourth 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 will not be enough review. Do your books have
problems that continue to review previous concepts?**

The program includes mixed review lessons (one near the end of each chapter) and additional (separate) cumulative review lessons that you can use when needed. Both of these cover a mix of topics that have already been studied.

You can also use the worksheet maker to generate additional worksheets for practice. This worksheet generator requires an Internet access. If you do not have internet at home, you can use it in an Internet cafe, public library, or at a friend’s house, and save the worksheets on a flash drive to print later.

Also, all the major concepts, such as addition, subtraction, multiplication, division, decimals, and fractions get reviewed in a sense because they are used all the time. For example, a child will keep using the multiplication tables when studying division and multi-digit multiplication. The student will use various addition and subtraction strategies in word problems about money and measuring and when studying place value. Division facts are used in long division.

I never make all the word problems to match the lesson exactly. 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 (such as money, measuring, division, or fractions)
will include the usage of multiplication. The word problems in the curriculum constantly use important
concepts that have already been learned.

**10. Are tests included? And should I score every
assignment or just tests? **

Yes. There is a test for each chapter and an end-of-the-year test to be used after each grade level. Each test includes a grading rubric. However, you do not have to follow the grading rubrics -- they are provided for you just in case you want to use them.

Personally, I feel that grading needs to be done in such a manner that **it does not discourage the child.** So it really depends on the child. Some children do better if they only receive feedback about where they need to work more, how to fix errors, etc.

All grading is best accompanied with notes such as, “You worked hard and I appreciate that!” “Here you show you have learned this topic and worked hard on it,” so that the **emphasis is on the appreciation of the hard work and on giving feedback on specifics**, and not on the actual percent score.

On the other hand, if a child is getting a “big head” (proud) over their accomplishments, you could find a really hard test so they can learn they have room to improve. But this is not nearly as common as the opposite situation where children are discouraged and think they “cannot do math”.

I don't recommend grading the day-to-day work with percent scores or letter grades. Of course you need to find if the student made errors, but that should be sufficient.

Also, when you assign a final mark for a whole grade, do not look *only at* the tests but also at the overall accomplishments, the effort, etc. I like to give my children assignments outside of tests that count towards the final mark.
For example, in math, it could be a neatly written solution to a hard word problem, a set of definitions for geometry terms accompanied by drawings, or a description or exact instructions for a math game. Then
those can go to their portfolio if you use such.

Most children in our society tend to get the idea that math is all about “speed” and getting correct answers, so math test scores become really important to them. We need to discourage that line of thinking. See also: Timed tests and how it damages students learning of math.

**11. Is Math Mammoth aligned with any state standards?**

Grades 1-7 meet and exceed the Common Core standards. Please see this FAQ for more information.

**12. 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. Examples of such topics include regrouping 2-digit numbers in subtraction (2nd), multiplication tables (3rd), and long division (4th).

Often the topic is present in two (or even three) neighboring grade levels. Examples include: equivalent fractions (both 4th and 5th grade), percent (6th and 7th), the area of a triangle (6th and 7th). Some topics are “developed” to mastery over several grades, going from simple to more complex. For example, we learn reading the clock (grades 1-3), counting coins (grades 1-3), adding like fractions (grades 3-5), and 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.

**13. Some graphics are missing from the PDF file. Why?**

This is a common problem in Mac computers. If it some images are missing , download and install Adobe Acrobat Reader for Mac from this link, and open the PDF files in it, instead of in Mac’s native PDF viewer.

Another possible problem is that some graphics/images will not print on a
Mac. Try select "print image" in the advanced section of the printer window, and
see if that helps.

**14. What is the origin of this curriculum?**

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

I initially wrote books on certain math topics, and later those books gave rise to the Math Mammoth Blue Series books.

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.

**15. What do you recommend for high school math?**

Please read my advice for high school math here.

**16. Does the author have any mathematics or education credentials?**

Yes. I have a master’s degree in mathematics (1997) after studying 5 years in the 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).

In case of any questions about this product, you can fill out a form at www.mathmammoth.com/contact.php or just email me at maria_miller@mathmammoth.com

I wish you success in teaching math!

Maria Miller