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 lessons and exercises, and include the explanations of the concepts. The worktexts also contain some advice for the teacher in the introductions for each chapter.

The teacher can read and study the teaching part of each lesson together with the student or let the student read and study on his own. If you are teaching in a classroom, you can simply copy the examples from the blue teaching boxes onto the board.

- The introduction part of each chapter (in the student worktext) has a
**list of useful Internet resources**matching the topics of the chapter. These games, activities, quizzes, and other resources can be used to supplement the lessons, for review, or just for some additional fun.

- There is a
**test**for each chapter. These tests are supplied as separate PDF files and located in the folder titled “2 - Tests”.

- I have included one
**Cumulative Review**for each chapter, excluding the first chapter. These cumulative reviews are supplied as separate PDF files and are located in the folder titled “3 - For review”.

- The
**Worksheet Maker**(located in the folder “3 - For review”) allows you to make additional worksheets for many topics in the curriculum. The worksheet maker is an html file. You need to be connected to the Internet in order to generate the worksheets.

Simply start out by printing the first lesson from the student worktext. You might read the lesson before presenting it to the student so you can be familiar with it. Study the teaching part of the lesson together with the student. You can also go through some of the exercises with the student. Then assign some problems for the student and monitor his/her progress. You can also let the student study the lesson completely on his own.

The lessons in Math Mammoth complete curriculum are *not *written for a single teaching session or class.
It is common for the lessons to span 4-7 pages and take 2-4 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
can calculate *approximately *how many pages the student should complete
each week (or each day) in order to finish the curriculum in one school year.
Use that number as a guideline, but do not become bound by it.

In the table below you can check how many pages the student worktexts contain. Fill in how many school days you are planning to have. Remember to allow several days for tests and cumulative reviews.

To get a measure of “pages/day”, divide the number of pages by the number of days. This number will be between 2 and 3, assuming you do school 5 days a week, about 40 weeks a year. Then, multiply this number by 5 to get an approximate weekly page count.

Examples:

Grade level | Page
count |
Number of school days (total) |
Days for tests and reviews |
Days for the lessons |
Pages to study per day |
Pages to study per week |
---|---|---|---|---|---|---|

7-A | 202 | 89 | 10 | 79 | 2.56 | 12.78 |

7-B | 253 | 111 | 12 | 99 | 2.56 | 12.78 |

Grade 7 total | 455 | 200 | 22 | 178 | 2.56 | 12.78 |

The table below is for you to use.

Grade level | Page
count |
Number of school days (total) |
Days for tests and reviews |
Days for the lessons |
Pages to study per day |
Pages to study per week |
---|---|---|---|---|---|---|

7-A | 202 | |||||

7-B | 253 | |||||

Grade 7 total | 455 |

Let’s say you determine that your student needs to study about 2.6 pages a day, or about 13 pages a week on average in order to finish the curriculum in a year. As the student studies each lesson, keep in mind that sometimes most of the page might be reserved for workspace to solve equations or other problems. You might be able to cover more than the average number of pages on such a day. Some other day you might assign the student only one page of word problems.

When you see large sets of similar exercises, feel free to **only assign 1/2 or 2/3 of those**. If your
student masters the concept with those exercises, that is perfect! If not, you can assign the student the rest. You can also use these unassigned problems later for additional review.

In general, students in first to second grade might spend 25-40 minutes studying math in a day. Students in third through fourth grade might spend 30-60 minutes, students in fifth through sixth grade should spend about 45-75 minutes, and seventh graders 60-90 minutes a day. If the student finds math enjoyable, he/she can spend more time with it! However, it is not good to drag out the lessons on a regular basis, because that can affect the student’s attitude towards math.

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
to not give tests at all. The main reasons for tests are for diagnostic purposes and for
record keeping.

The tests are located in their own folder. They are provided as both PDF files and html files. You can edit the html versions of the tests in a word processor (such as Microsoft Word). Remember to save the edited test under a different file name, or you will lose the original test file.

The PDF versions of the tests are of course easy to print. You can print the html files from your web browser. If possible, set the margins to 0.6 inches in the Page Setup of your browser. You can also set a header and footer there.

The end-of-year test is best administered as a diagnostic or assessment test. It is a long test so allow several sessions or days for it. It will tell you how well the student remembers and has mastered the math content of the entire grade level.

There is one cumulative review lesson 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. So, use the cumulative review some time after the student has finished the particular chapter (chapter 4).

These cumulative reviews are available as html and PDF files. You can edit the html files in any word processor for the purpose of providing a slightly different review for your student.

There are no hard and fast rules when it comes to cumulative reviews. It is not necessary to use all of them; however I do recommend the student complete about half of them within a school year.

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

- Check if the
__worksheet maker__lets you make worksheets for that topic. - Check for
__online resources__in the*Introduction*part of the particular chapter in which the topic was taught. - You can simply
__reprint the lesson__from the student worktext and have the student restudy it. - If you assigned only 1/2 or 2/3 of the exercises the first time through, you can now
__assign the remaining exercises__.

Another sign that the student has not grasped a concept is if he/she cannot do word problems in the subsequent chapters that require that concept. I have always tried to make the word problems progressive so 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 in a form at www.mathmammoth.com/contact.php or email me at maria_miller@mathmammoth.com

I wish you success in teaching math!

Maria Miller