Author Archives:

WEST Math for the Middle Grades

Most of us learned to divide fractions.  We wrote the problem as it was presented in our math books:

3/4 ÷ 1/2

Then we were instructed to rewrite the problem changing the division to multiplication and flipping the second fraction:

3/4 x 2/1

At this point we could cancel, or we could multiply and reduce later.  Let’s multiply:


We can reduce to by dividing the numerator and denominator by 2:


And if necessary, we can change this to a mixed number:

1 1/2

Does this answer make sense?  It’s hard to tell.  We’ve followed a procedure, an algorithm, but do we understand what just happened?  For most of us, understanding the connection between the original division and the answer was missed.  Maybe your elementary teacher didn’t explain it.  Maybe he did and you didn’t understand or remember.

In Math for the Middle Grades we use a wonderful curriculum called Math Mammoth.  Math Mammoth is written by a Maria Miller, a homeschool mom who was born and educated in Finland and now lives in the U.S.  According to her website (click here), she was tutoring homeschooled children and saw that there was conceptual understanding missing from the children’s math education.  In her books she provides lessons in understanding math concepts, followed by lessons that teach the traditional algorithms for those concepts.

Students who join us for Math for the Middle Grades get a good start on understanding of operations with whole numbers, fractions, decimals, and percents.  This understanding provides some great advantages:

  1. Greater ability to calculate mentally.  This is a great time saver when solving long, complicated algebra trigonometry equations.
  2. Increased recognition of sensible answers.  When following an algorithm to divide decimal numbers or add fractions it’s helpful to have a rough estimate of what the answer should be.  That estimate can be made quickly by mental calculation when the operation is understood.
  3. More easily connect real world problems with the math that represents them.  Solving real world problems can be difficult to solve when the process starts with picking the right algorithm.  Making a connection between the algorithm for multiplying decimal numbers and calculating the sales tax on a particular purchase seems arbitrary.  Understanding the concepts of decimal part of a number or percent of a number has a more direct connection to the problem.

Math for the Middle Grades help students in grades five and up with understanding the concepts described in this post and lots more.  In this worktext-based class we also study basic math facts, geometry, and graphs.  Most weeks also include a game that provides practice of math skills.

Join us!  Find more information at WEST.


Years ago, one of my children attended a charter school where she received lots of special education.  After the first year there, summer was a welcome relief from the early morning drive to school and I was thrilled to have my baby home all day!

At the end of the second year of school, I met with her teachers.  They wanted my daughter to attend summer school so that the gains made during the school year would not be lost.  I mentioned that my daughter had not attended summer school the previous year and did just fine.  One of the teachers looked through the child’s records and saw that test scores indicated that the child had made progress over the previous summer.  A wave of disbelief washed through the room. Then one of the teachers mentioned my background as an educator and everyone assumed I had taught my daughter all summer.  At that point, I decided to keep quiet and not reveal that our summer had been completely aimless and recreational.

Besides my own daughter’s gains over a lazy summer, many of my math students have made similar gains.  Over and over again I’ve seen students struggle with math concepts in the spring, avoid math all summer, and suddenly grasp concepts in the fall.  I think of summer as a time to digest learning.  All year we fill our students’ brains.  In the summer their brains sort, store, and process the information they’ve had poured into them for months.

Some years I have looked at June, July, and August as a perfect chance to get some academic work done.  My children were behind, so I thought they should catch up. Now I’m older, and maybe wiser. For some students, sometimes, summer is a good time for formal learning, but I believe summer can be put to better use.

Summer is a great time for field trips, travel, and lazy afternoons at the swimming pool.  Long conversations, reading to each other, and good movies can all be enjoyed any time.  Cooking, cleaning, laundry, and home organization can be explored at a leisurely pace during the long days of summer.  I think I’ve just written my family’s plan for the summer!

Homework Due 4/18 and 4/19

If you haven’t scheduled your annual testing, consider the Peabody Individual Achievement Test.  It is administered individually, takes about an hour, and scores are available immediately after testing. Contact WEST for scheduling at WEST.  If testing at WEST doesn’t work for you, let me know and we can schedule outside of WEST.

If you need to turn in work after April 19, here are some options:
I’ll be at WEST Tuesday, Wednesday, and Thursday, April 25-27.  Drop off your work then.  Look for a box in the hall with my name on it. You may also scan and email, or snail mail your work to me.  No work will be accepted after May 31.

In math classes on 4/18 and 4/19, each class will have a final exam. It’s part trivia and fun, part spelling (math words), and part math.


Math for the Middle Grades – In class we played with polygons, protractors, and patterns!  Try to finish lesson 88.  That’s it.

Math 76 – lesson 116.  Any problems in that are from lesson 115 are optional.  Continue working on tests.

Algebra 1/2 – lessons 121-123 and tests.

Algebra 1 – lessons 118-120, tests.

Algebra 2 – lesson 122, tests.

Personal Finance – review!  We’ll have a final exam in class on Wednesday.  Your activities for chapter 12 have been emailed. Another option for chapter 12 homework is to listen to a series of messages by Andy Stanley. Click here to access the messages:  Your Move.  Or download the Your Move app and listen on your phone or tablet.  Pick any series, or single message, that has something to do with money, listen, write at least half a page of response.  Be sure to include the name of the message or series.  Some suggestions: “What Makes You Happy”, “See the World”, “Crazy Like Us”, and “Breathing Room”.

Homework Due 4/11 and 4/12

Planning for fall?  Let me know if you would like my input on which math class might be a good fit for your child for next year.  Also, if Personal Finance and/or Geometry are in your plans for 2017-18, it’s a good time to buy the books.  Both classes use consumable worktexts.  Here are the links:

Geometry:  This link is to the 10 Lifepac set plus teacher’s guide.  The teacher’s guide is required for the class.

If you already have the teacher’s guide, here’s the link to the set of 10 Lifepacs:

Personal Finance:

Next, this week’s homework:

Math for the Middle Grades – Lesson 90 and Homework 28.

Math 76 – Lesson 112, all the problems.  Be sure to complete the next test this week.

Algebra 1/2 – Lessons 118-120.  Tests 24, 26, and 28 are due by 4/18.

Algebra 1 – Lessons 113-115 practice and odds.  Lesson 119:12-14. Work each problem twice, once using the quadratic formula and once by completing the square.  Keep working on tests.

Algebra 2 – Lesson 120 practice and odds, read Lessons 123 –  128. Keep working on tests.

Personal Finance – Your activities have been emailed.  Also, begin a list of your achievements, at least one per year for the past four or five years, as part of preparing to make a résumé.


When my first son was born we lived in a townhouse. It seemed easy to keep track of my son as he scooted around the tiny house.

One day when the baby was five months old he was playing happily with some toys and my husband and I were talking not far away. It was a lovely, peaceful scene. The quiet moment was interrupted by a loud pounding sound. It sounded like the neighbors in the adjoining unit were pounding on an upstairs wall. My husband and I looked around and were surprised to see the baby was gone.

We ran up the stairs toward the pounding. Upstairs we found the baby standing next to the toilet pounding on the lid.  Once the shock wore off we quickly completed all the baby-proofing projects we thought we had months to complete.

On the flip side, only one of our six children lost baby teeth at about the times doctors say it should happen.  The rest of the children had baby teeth well into their teens.  And why are they called twelve-year molars when they don’t show up until you’re fifteen years old?

We accept differences in child development.  Everyone is one his or her own schedule.  That is until the child turns five.  Then it becomes ultimately important to be on track with the academic schedule of the school.  Great harm can be done when skills and knowledge are taught according to the age of the child, and not the child’s development.

I’ve seen this over and over in math.  Students who were expected to understand and apply principles of math before they were ready can end up believing they are something less than smart, or that math is just too hard.  Even students who are old enough to understand algebra and are unable to get past the emotions surrounding earlier failure in math.  These failures were not caused by the child’s lack of effort, but by teachers trying to make them do something they were developmentally unable to do.

I could go on and on about the hazards of early formal instruction, but I’ll give my solution:  wait.  Wait until the student asks for instruction.  Wait until learning is a treat, not torture.  And when the student gets stuck it’s time for a break.  It could be a day, a week, or a few months before the student is ready to begin again.  In the meantime, do what’s productive.  Learn what the student is ready to learn.  If we wait and take breaks, and if we work on what students are developmentally ready for,  learning can take much less time and effort.



Homework Due 4/4 and 4/5

Math for the Middle Grades – Lessons 85 and 86, homework 27.  We started lesson 87 in class and we’ll continue to work on it in class next week.

Math 76 – Lessons 108-111 practice and odds, Test 20.

Algebra 1/2 – Lessons 115-117, practice and odds.

Algebra 1 – Lessons 110-112, practice and odds; lessons 118-119, practice and problems 8-11 all.

Algebra 2 – Lessons 116-119, practice and odds.

Personal Finance – your activities have been emailed to you.  Start reviewing for the final exam which will be given in class on the last day of class.

Homework Due 3/28 and 3/29

Just a few weeks left!  As we approach the end of our math books, there will be a few lessons that are more complex.  A little extra effort will pay off in greater understanding!  It’s time to renew your commitment to the practices of successful students:  get to class on time (3-5 minutes early), have supplies ready to use, pay attention in class, take notes, start homework as soon as possible, contact the teacher with questions frequently.

Math for the Middle Grades – This is a change from the syllabus!
Lessons 83-84 and continue working on Homework 27.  If you have finished Homework 27, check your work.  Homework 28 will be optional.

Math 76 – Lessons 104-107 evens.  Any problems that don’t have answers in the key may be skipped.  Check to see if you are missing any tests.  This semester the following tests were are assigned: 10, 11, 13, 14, 16, 18, 19, 20, and 22.  Test 26 is on the syllabus, but we have moved at a more reasonable pace through the book, so we’ll skip that one.

Algebra 1/2 – Lessons 112-114.  Check to see if you are missing any tests.

Algebra 1 – Lessons 107-109.  Check to see if you are missing any tests.

Algebra 2 – Lessons 112-115 and test 24.  Check to see you are missing any tests.

Personal Finance – Your activities have been emailed.

Finishing Well

With only a few weeks left of classes at WEST, I’m thinking about how to finish well.  The first few weeks of a new school year seem strong, powerful, and effective.  A lot of energy is generated and used in starting a new thing.  I want the end of the year to feel like that.  The end of the year has the potential to be as productive as the beginning.  Here are a few things I’ve been thinking about:

The big picture, the goal, has to be in front of me.  I need to know what I’m working toward and how to know when I’ve finished. The finish line is not just a date.  It might not be a date at all.  The finish line is when I’m done with the work.

The goal is achieved by making many small choices. Sometimes there are many decisions in a day that could have a cumulative effect on whether or not I reach the finish line.

Patient endurance is key.  The initial excitement got me going, but patiently looking toward the goal and enduring through occasional, or sometimes frequent, discouragement will get me to the goal.

Sometimes I’ll need help from others.  It’s much better to ask for help than to miss the opportunity to achieve.

How can you finish well?  How can you keep the big picture in mind, make small choices, patiently endure, and ask for help today?

Homework Due 3/21 and 3/22

There are just a few weeks of WEST classes left.  Let’s finish well!

And the winners are

Math for the Middle Grades – Mia T.
Math 76 – blank ticket
Algebra 1/2 – Ben
Algebra 1 – Jerilynn
Algebra 2 – Lilly

Email me at to claim your prize!

On to homework!

MMG – lesson 79-81 and homework number 26.

Math 76 – lessons 104-106.   Also, read lessons 107-108.

Algebra 1/2 – lessons 108-111 and test 24.

Algebra 1 – lessons 103-106

Algebra 2 – lessons 108-111 and test 24.

Personal Finance – your activities have been emailed to you.  Also, you are encouraged to do some research on different ways to invest for retirement.




Homework Due 3/14 and 3/15

Wednesday was an interesting day at WEST for a few of us.  There was no power in one of our classrooms, so some math classes met in rooms some of us didn’t even know existed.  I’m going to blame this for my forgetting to collect everyone’s tickets!  We’ll try again next week!

Pi Day is March 14.  Celebrate!  A Google search will give you more ideas than anyone needs.  Be creative, document your celebration, and get extra credit!

Math for the Middle Grades – homework 25 and lessons 76-78.

Math 76 – If you haven’t done test 17 yet, it has become optional. For next week do the following:  Test 18.  Lessons 99, 101-103, practice and odds.  For lesson 100, complete the project described in the book, or any other project that demonstrated the relationship between diameter and circumference of a circle.  Turn in documentation of your project.

Algebra 1/2 – Lessons 104-107.

Algebra 1 – Lessons 100-102 and test 22.  We have also started working with the quadratic formula in class.

Algebra 2 – Lessons 104-107.  Remember to look up “British Factoring Method” if you need help factoring trinomials with a non-unity lead coefficient.

Personal Finance – Your homework has been emailed.