Math: Mastery, Spiral, or Confused?

Math is one of those subjects that tends to cause struggles for homeschool families.

The sheer number of math curriculum companies and titles out there don’t help. It may seem “everyone” is using a particular curriculum and it is producing such gifted, wonderful scholars, and isn’t that just what you want your kids to be? Don’t beat yourself up. Math is the leading cause of insanity in homeschool moms.

You knew that, right?

Math: Mastery, Spiral, or Confused?|HSBAPost

Changing to a certain curriculum almost never is THE answer. It’s just not that easy. So what’s the difference in these math programs, anyway? There are two main sequencing styles among curriculum publishers:  Mastery and Spiral.


Mastery-based programs tend to focus on a topic or a set of topics for a period of time, and then move on to others. Some programs break them into chapters. Others break them into worktexts, where they complete 10 worktexts in a school year and each focuses on a different topic. One in particular takes on a topic for the entire school year.

Throughout these programs there is some review, possibly a “Cumulative Review” toward the end of each unit, but the main focus is on moving forward through the topics. Mastery-based programs include:

  • Alpha Omega Lifepacs
  • Bob Jones Math
  • Keys To…
  • Math Mammoth Blue Series
  • Khan Academy
  • Math-U-See
  • Modern Curriculum Press
  • Developmental Math


Spiral teaching programs have review built into the daily lessons. The lessons will have a focus of one or two new concepts, and there will be problems for students to work out from the current lesson. There will also be other problems pulled from previous lessons so that there is constant review. No topic is left alone for long.

Spiral programs include:

  • Abeka
  • Christian Light
  • Saxon
  • Horizons
  • Teaching Textbooks

Which method is best?

That depends entirely on your students. Some kids need to have time to focus on just one concept at a time, until they fully grasp it. Once they do, they are ready to move on.

The nice thing about math is that it is progressive.  One concept builds upon another, and another, until they have reached higher math and are using all of the previous concepts to work at a higher level.

The struggle comes in when the program moves too fast through the concepts.  This is where you need to know your child’s learning style.

Does she take a long time to understand concepts? She may do better with a program that works through with mastery in mind. Does she require a lot of review? A spiral method may be just the thing.

On the other hand, some kids struggle with “jumping around” from concept to concept so much and some just don’t like so much review.

Sometimes you have a child that needs both.

When working with a child that needs lots of time to master concepts, but tends to forget things if left too long, there are practice books and online programs you can use to keep her skills sharp in between. When used for a short time but consistently each day, there should be no loss of skills between units that use them. Xtra Math is one of our favorite sites for skill practice.

What about gaps?

Honestly, there will always be gaps, no matter which curriculum you use, or what school they go to. Gaps are invitable because there is no way to teach EVERYTHING that is available to be learned. The key is to be consistent.

Here’s the thing. It doesn’t matter what curriculum you use. (Gasp! Blasphemy!) Pick one and stick with it. Eventually they all cover everything your kids will need to learn. It’s the moving from one program to another that leaves the biggest holes.

How many math programs have YOU used?

The Momma Knows

Dawn (24 Posts)

Dawn is still happily homeschooling after 16 years. She teaches her two sons, 13 & 11, enjoying every minute of "the second time around". She lives in Eastern Washington with her husband, the youngest 2 of their 6 kids, and an assortment of barking, squeaking, and clucking critters. She writes at her homeschool/parenting blog The Momma Knows and her new chapter, Dawn Marie Perkins. You can also find her on Twitter @DawnMPerkins, , and Pinterest.

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Pumpkin Patch Math

We had a great field trip with our Homeschool Co-op today!  I jotted down some activities before we left to makes sure I incorporated some math in our trip since we’d all be tired once we got home.  Here are some of my ideas.  Hopefully you can use them too!

homeschool post


1.  Measure the Circumference of a Pumpkin.  Although this is a bit beyond the math level my oldest is on, it’s never too early to learn something new!


2.  Measure Pumpkin Height/Width.  This is easy and can be perfect for preschoolers and school aged kiddos!



3.  How Many Pumpkins Tall Are You?  Teach non-linear measurement by having your child lie down and measure how many pumpkins tall they each are.  If you have several kiddos (and Mom too) do everyone!  Then, create a chart with tallest to shortest!



4.  Label the parts of the pumpkin.  Well, this isn’t math, but it’s fun and educational!  You can use toothpicks and labels to actually label a real pumpkin, or just draw a model and write down the parts.  Either way, the kids will ‘get it’ and retain it!


5.  Bake the Pumpkin Seeds!  Preheating the oven, counting how many seeds there are, estimating how many seeds, how many minutes should they bake?  All of these simple activities are an easy way to incorporate math into your pumpkin patch trip.  These hands on moments will have a greater impact than any worksheet!


6.  Estimate how fast the hayride is going.  How many MPH do you think the tractor is going?  After you estimate, ask the driver and see who was closest!



7.  Take a compass into the Corn Field Maze to incorporate Geography!  My boys love using a compass.  Directions are not my forte!  However, they got a kick out of it!  If you have more than one school aged boy, I’d recommend bringing more than one compass.  Don’t ask me how I know ;)

8.  Find the heaviest and lightest pumpkins.  Unless you bring along a scale (which, hey why not!), you couldn’t be certain, but for a preschooler, you could use obvious pumpkins to teach this lesson.


Taking a few minute to think of ways you can extend the learning while on field trips is a great way to make your day more successful!  Have a great fall y’all!


Liz (5 Posts)

Liz was a cheerleader swept off her feet by the football player back in high school. They’ve been married nearly ten years and are the proud parents to four young boys. She’d always envisioned working and sending her kiddos off to school so she could live the ‘normal’ American dream. However, life and the Lord surprised her and she’s learning to ‘redefine having it all’ while being a debt free homeschooling housewife. She enjoys finding strength from God’s word, the Today show, talking on the phone with friends, and being real about finances and parenting.

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Keeping Math Fun with Games

Keeping Math Fun

My favorite subject is math (I’m now ducking behind my computer screen)!  My son’s favorite subject is not math!! He isn’t terrible at it, but he gets discouraged.  Things that require memorization are hard for him; because of this, I make an effort to plan fun games to play.

Sammy loves games.  He doesn’t feel the same need to be perfect while playing them as he does while doing his book work.  This allows for some great math review, learning and fun!  Many of the first grade math review games that I have planned could be easily adapted for higher grades.  Some of the things I want to work on for this year are addition facts, subtraction facts, greater than and less than, skip counting, and telling time.

5 Fun Addition Fact Games

  1. Sum match – Place flashcards on the ground like you are playing memory.  Then make matches with the answers (i.e. 2+2 and 1+3 would be a match)
  2. Sum Swamp- I got mine at our convention’s used curriculum sale, but you can get it on Amazon – This game provides practice for both addition and subtraction.
  3. Flip 10 – Using Uno cards, you can work on addition facts to add up to 10.
  4. Fiddle Sticks – You can play this game for a wide range of repetitive learning facts (sight words, math facts, foreign language words, etc.)
  5. Dart addition – Write some numbers on your white board, have your child shoot darts at the numbers and add them together.  This was a huge hit for my nerf gun loving boy!

5 Greater Than Less Than Math Games

  1. Lego Compare
  2. War (classic, but still fun – you can use this with addition facts by flipping two cards and adding them together.)
  3. The Cup Game – We played this game early on in the school year and it was a lot of fun!
  4. Make 10 – Another big hit at our house.  It seems like such a simple game, but Sammy really enjoyed playing it and has asked to play it since then!
  5. Hungry Alligator – using a toy alligator, Sammy decides what number is bigger and eats the bigger number.

5 Skip Counting Activities

  1. Hopscotch skip counting
  2. Skip Counting  Memory- I created some basic memory cards for 2’s, 5’s, and 10’s to help Sammy work on his skip counting.  Flip over 2 cards skip count the objects (shoes – 2’s, tally marks – 5’s, and $10 bills – 10’s) and see if it matches the written number.Skip Counting Memory
  3. Skip Counting Mazes
  4. Skip Counting Online Game
  5. Speed – We don’t have this yet, but we will hopefully be adding it to our collection soon.  This game was created by a homeschool mom, and is a wonderful way to practice skip counting and multiplication facts!
Lindsay BytesOfMemory (7 Posts)

Christian, wife, mom, knitter, reader, and wearer of many hats (literal and figurative). I am also a computer geek, homeschool mom, sock sorter, and a blogger. I like coffee, tea, chocolate, Mexican food (not together), and lists!

***See the Light Christmas special for HOMESCHOOL POST readers: 25% off BIBLE STORIES 5 DVD Boxed set + FREE SHIPPING. Over 17 hours of content including 15 stories and 15 complete step-by-step art lessons. Code to use: HSP
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