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

Concerning challenging word problems and puzzles

Frequently asked questions

Contact the author

How 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.

I need to note at this point that Math Mammoth Grade 7 is, in a sense, a hybrid course — it can work as a complete 7th grade curriculum that meets the Common Core Standards, or as a traditional pre-algebra course. The difference between the two has to do with the chapter on the Pythagorean Theorem. If your student(s) will be tested based on the Common Core Standards or your student(s) will be going on to an 8th grade curriculum that is based on the CCS, then you can safely omit the chapter on the Pythagorean Theorem. That theorem will be studied in all algebra 1 and geometry courses anyway, but it also traditionally studied in pre-algebra, so that is why I included it — for those people who wish their students to study it before an algebra 1 course.

On the other hand, if you need a pre-algebra course for your student(s), and if time does not allow, you can omit the chapter on statistics. (That chapter deals with random sampling and comparing two populations informally. High school courses deal with more sophisticated methods for comparing two populations or two samples.) You can also do a combination of your own also.

So, I provide you THREE different tables below for you to plan the pacing: one where the chapter on Pythagorean Theorem is omitted, the second where the statistics chapter is omitted, and the third is for the entire curriculum. Fill in how many school days you are planning to have. Remember to allow several days for tests and cumulative reviews.

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:

**(1) Omitting the chapter on the Pythagorean Theorem:**

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 | 96 | 10 | 86 | 2.35 | 11.7 |

7-B | 223 | 104 | 10 | 94 | 2.37 | 11.9 |

Grade 7 total | 425 | 200 | 20 | 180 | 2.36 | 11.8 |

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 | 223 | |||||

Grade 7 total | 425 |

(2) Omitting the chapter on statistics:

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 | 98 | 10 | 88 | 2.3 | 11.5 |

7-B | 213 | 102 | 10 | 92 | 2.32 | 11.6 |

Grade 7 total | 415 | 200 | 20 | 180 | 2.31 | 11.5 |

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 | 213 | |||||

Grade 7 total | 415 |

(3) Doing it all:

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 | 90 | 10 | 80 | 2.53 | 12.6 |

7-B | 250 | 110 | 12 | 98 | 2.55 | 12.8 |

Grade 7 total | 452 | 200 | 22 | 178 | 2.54 | 12.7 |

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 | 250 | |||||

Grade 7 total | 452 |

For comparison, here is a table for all the seven grades (the decimals are rounded):

Grade level | Page count | Number of days in school year |
Number of days for tests and reviews |
Pages to study per day |
Pages to study per week |
---|---|---|---|---|---|

1st grade | 248 | 200 | 16 | 1.3 | 6.7 |

2nd grade | 277 | 200 | 20 | 1.5 | 7.7 |

3rd grade | 306 | 200 | 20 | 1.7 | 8.5 |

4th grade | 337 | 200 | 16 | 1.8 | 9.2 |

5th grade | 363 | 200 | 16 | 1.97 | 9.9 |

6th grade | 314 | 200 | 20 | 1.74 | 8.7 |

7th grade | 425 | 200 | 20 | 2.4 | 11.8 |

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

**Problem Solving from MathWire.com**

Neat and creative problems to solve for K-8.

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

**Step-by-Step Problem Solving, Grade 4**

A problem-solving workbook that provides step-by-step instruction, problem pages at varied levels of difficulty, a math strategies overview, and a complete answer key. The book utilizes bar models just like Math Mammoth and Singapore Math. Other grades available also.

www.amazon.com/Step-Problem-Solving-Carson-Dellosa-Learning/dp/1609964799?tag=mathmammoth-20

**Challenge Math For the Elementary and Middle School Math Student**

Over 1,000 math word problems for children in grades 4-8. Answers are included in the back of the book. ISBN
978-0967991559.

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.

https://www.mathcounts.org/resources/school-handbook

**“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://themathcontest.com/

**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.

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

**Paul Erdös International Math Challenge**

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

http://inside.gcschool.org/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”

Please read the FAQ at the Math Mammoth website.

In case of any further questions (but please first check the FAQ!) about the curriculum, you can contact me at www.mathmammoth.com/contact.php.

I wish you success in teaching math!

Maria Miller