In 2014 my district purchased the Envision Math program. Now to be honest, I haven’t actually used a math book in my classroom since the years started with 19-. That said, I always take a good look at every series we get and try to take the best of what they provide — games, worksheets, manipulatives, etc. Typically, math series all looked pretty much the same.
What I noticed right away was that the new Pearson Envision Common Core edition really flipped the script on sequence of instruction a little bit.
It lists the first 4 topics in 4th Grade Envision Math as:
- Topic 1: Multiplication and Division: Meanings and Facts
- Topic 2: Generate and Analyze Patterns
- Topic 3: Place Value
- Topic 4: Addition and Subtraction of Whole Numbers
- Topic 5: Number Sense: Multiplying by 1-Digit Numbers
The sequence of topics made me scratch my head a little bit. An explanation of the choice for this sequence is probably buried in the documentation somewhere, but couldn’t find it easily. So, I’m left to wonder why they decided to place multiplication concepts ahead of addition and why place value has suddenly be moved to third.
Personally, I always liked starting with Place Value for a few reasons. First off, it is a skill introduced in 2nd grade and 3rd grade that we are building off, just moving as far as the millions place. Secondly, I always felt that place value helped me better understand the student who really “get” what math is about. Unlike learning algorithms in multiplication of subtraction, place have tests a student’s understanding of numbers.
This is no slam on Envision, as I think was the best math series we had purchased at that point. I do use some of the worksheets and center activities from time to time and will use the online tools on occasion. But other than that, the student books remains on my shelf. Knowing the cost of the book, I felt really guilty about that. But I believe that the textbook was not a tremendously effective instructional tool.
When I started teaching, the Math manual was very useful to me to help plan my Math lessons from day to day. It was common to assign questions to be completed on loose-leaf paper from the book. But after having four Math series and buying and creating so much of my own math “stuff” over 30+ years of teaching, I really don’t need it anymore.
And though I use the textbook as a general guide, I rarely follow the sequence of the topics/chapters in a Math series anyways. Other than a few exceptions, the sequence of the topics is not as important as the sequence of your daily lessons in my opinion. For example, I used to teach a unit on graphing (topic 17 in the book) right after addition and subtraction (second). Why? I taught it there for a couple reasons. First, it tied in well to a lot of the graphing that we did to show results of Science experiments. And second, it gave my students more time to gain mastery of their basic multiplication facts that they needed to learn before we started to multiply greater numbers.
All this being said, you could probably ask ten Math teachers and get ten different opinions on the best sequence of instruction. So, if you’d ask me: does the sequence of instruction matter? I’d answer, if it does matter, it’s not much. What matters most is building upon the student’s current understanding each day and making connections between new and old concepts a little bit at a time.
A few general observations
A few things jump out once you line these four programs up side by side. The first is simply how much they disagree. They’re all built for the same Grade 4 standards, yet division shows up as early as Eureka’s third module and as late as the sixth unit in both Everyday Math and Desmos. Place value is the very first thing three of the four programs teach — and the fourth, Desmos, waits until its fourth unit. Same standards, wildly different running order.
The differences usually aren’t random, though. The programs that introduce multiplication and division early tend to lean on them for much of what follows; the ones that hold them back spend those first units shoring up place value and addition instead. Neither approach is wrong — they’re just different bets about what students need underneath them before they build.
Fractions might be the most telling row of all. Eureka gives them one dedicated block, enVision stretches them across three straight topics, and Everyday Math spirals them across the entire year. That spiral-versus-mastery split says far more about how a program thinks kids learn than whether place value comes first or third.
Which brings me back to where I started: none of these orders is the “right” one. Every publisher can defend its sequence, and students have learned math well under all of them. What the chart really shows isn’t which program is best — it’s that the running order is a choice, not a rule. Which is exactly why I’ve never felt too guilty about teaching topics in whatever order made the most sense for my own classroom.
So what do you think? Feel free to leave your opinion in the comments below.
This is a personal blog, so it should be assumed that I could preface everything I say with the phrase “in my opinion.” Feel free to agree or disagree (respectfully) if you like in the comments section.