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 revisions 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 revisions 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**(part A and B) are the most important part of the curriculum. These contains 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 on his own. If you are a classroom teacher, you can copy the examples from the “blue teaching boxes” to the board and go through them on the board.- There are hundreds of videos matched to the curriculum available at https://www.mathmammoth.com/videos/ . You can simply have the author teach your child or student!
- The “Introduction” part of each chapter (within the student worktext) has a
**link list to various free online games**and other resources on the Internet. These games can be used to supplement the math lessons, for learning math facts, or just for some fun. - The student books contain some
**mixed revision lessons**, and the curriculum also provides you with additional**cumulative revision****lessons**. - There is a
**chapter test**for each chapter of the curriculum, and a comprehensive end-of-year test. - 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. - You can use the free online exercises at https://www.mathmammoth.com/practice/
- Some grade levels have
**cutouts**to make fraction manipulatives or geometric solids. - And of course there are answer keys to everything.

Have ready the first lesson from the student worktext. Go over the first teaching part (within the blue boxes) together with your child. Go through a few of the first exercises together, and then assign some problems for your child to do on their own.

Repeat this if the lesson has other blue teaching boxes. Naturally, you can also use the videos at https://www.mathmammoth.com/videos/

Many children can eventually study the lessons completely on their own — the curriculum becomes self-teaching. However, children definitely vary in how much they need someone to be there to actually teach them.

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, it is helpful to calculate 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).

The table below lists how many pages there are for the student to finish in this particular grade level, and gives you a guideline for how many pages per day to finish, assuming a 180-day school year.

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 |
---|---|---|---|---|---|---|

4-A | 168 | 88 | 8 | 80 | 2.1 | 10.5 |

4-B | 177 | 92 | 8 | 84 | 2.1 | 10.5 |

Grade 4 total | 345 | 180 | 16 | 164 | 2.1 | 10.5 |

The table below is for you to fill in. First fill in how many days of school you intend to have. Allow several days for tests and for review lessons before tests — at least twice the number of chapters in the curriculum. For example, if a particular grade has 8 chapters, allow at least 16 days for tests & review. Then, to get a count of “pages/day”, divide the number of pages by the number of available days. Then, multiply this number by 5 to get the approximate number of pages to cover in a week.

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 |
---|---|---|---|---|---|---|

1-A* | 168 | |||||

1-B | 177 | |||||

Grade 1 total* | 345 |

Now, let's assume you determine that you need to study about 2 pages a day, 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
revision.

In general, 1st-2nd graders might spend 25-40 minutes a day on math. Third-fourth graders might spend 30-60 minutes a day. Fifth - 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 maths.

The curriculum generally includes working space directly on the page for students to work out the problems. However, feel free to let your students to use extra paper when necessary. They can use it, not only for the "long" algorithms (where you line up numbers to add, subtract, multiply and divide), but also to draw diagrams and pictures to help organize their thoughts. Some students won't need the additional space (and may resist the thought of extra paper), while some will benefit from it. Use your discretion.

Some exercises don't have any working space, but just an empty line for the answer (e.g. 200 + _____ = 1 000). Typically, I have intended that such exercises to be done using MENTAL MATHS.

However, there are some students who struggle with mental maths (often this is because of not having studied and used it in the past). As always, the teacher has the final say (not me!) as to how to approach the exercises and how to use the curriculum. We do want to prevent extreme frustration (to the point of tears). The goal is always to provide SOME challenge, but not too much, and to let students experience success enough so that they can continue enjoying learning maths.

Students struggling with mental maths will probably benefit from studying the basic principles of mental calculations from the earlier grades. This article gives you a few such principles, but to study all of them, one would need to go through all the earlier grade levels of Math Mammoth curriculum, and find the lessons that list mental maths strategies. They are taught in the chapters about addition, subtraction, place value, multiplication and division.

For each chapter, there is a **chapter test**, which can be administered right after studying the chapter. **The tests are optional.** Some 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. These tests are not aligned or matched to any standards.

In the digital version of the curriculum, the tests are provided both as PDF files and as html files. Normally, you would use the PDF files. The html files are provided so that you can edit them (in a word processor such as Microsoft Word or LibreOffice), and change the numbers or he problems in it, in case you want your student to take the test second time.

Remember to save the edited file under a different file name, or you will lose the original file.

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

The student books contain mixed revision lessons which revise concepts from earlier chapters. The curriculum also comes with additional cumulative revision lessons, which are just like the mixed revision lessons in the student books, with a mix of problems covering various topics.

These cumulative revisions are optional; use them as needed. They are named indicating which chapters of the main curriculum the problems in the revision come from. For example, the revision titled “Cumulative Revision, Chapters 1 - 4” includes problems that cover topics from chapters 1-4.

In the digital version of the curriculum, the cumulative revisions are provided both as PDF files and as html files. Again, the html versions are editable.

Both the mixed and cumulative revisions allow you to spot areas that the student has not grasped well or has forgotten. Another sign that the student has not understood a concept or skill is if he/she cannot do word problems in the curriculum that require that concept or skill.

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 and resources__in the Introduction part of the particular chapter in which this topic or concept was taught. - If you have the digital version, you could simply
__reprint the lesson__from the student worktext, and have the student restudy that. - Perhaps you only assigned 1/2 or 2/3 of the exercise sets in the student
book at first, and can now
__use the remaining exercises__. - Check if our online practice area at https://www.mathmammoth.com/practice/ has something for that topic. We are constantly adding more exercises and games to this.
- Khan Academy has free online exercises, articles, and videos for most any maths topic imaginable.

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 your math teaching!

Maria Miller