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Mathematics scope and sequence suggestion in chart form

Different math curricula utilize different scopes and sequences. If you're piecing together your math curriculum from several sources, or for some reason not following any curriculum exactly to the "tee", it is helpful to have

I have made the following chart as a rough guideline approximately when and in which order one should study various math topics. It gives you a general idea of a "basic" mathematics scope and sequence through elementary and middle school (grades 1-7 or 8). Don't read too much into it. For example, it is not telling you in which order to study the topics during any grade, and it doesn't include every single topic.

The chart aims to show that certain mathematics topics are IN FOCUS in certain grade levels, and then "fade away" into the status of occasional review only. As explained in my coherent curriculum article, you do not need to study basic arithmetic topics in each and every grade till 8th grade. It is better to focus, aim for mastery, and then move on.

Note also that most math curricula have algebra in 9th grade and pre-algebra in 8th grade. This chart is assuming algebra starts in 8th grade, but children and situations are different: for some, it works better to start algebra in 8th, while for others it is better to wait till 9th.

Mathematics scope and sequence chart
Mathematics scope and sequence chart


The red 'strand' is addition, subtraction, and place value. These tie together. In first grade, children start with the addition and subtraction concepts, place value till 100, basic addition and subtraction facts within 10, and some easy additions and subtractions within 100.

Regrouping in multi-digit addition and subtraction is introduced in second grade, and is studied with bigger numbers in grades 3 and 4. Mental addition and subtraction are important, too. As years pass, students study bigger and bigger numbers: up to 1000 in 2nd grade, and up to one million in 4th.

After fourth grade, a child should have mastered addition and subtraction of whole numbers so that it is no longer the center of study. From then on, topics such as fractions, decimals, integers, square roots, and irrational numbers expand the student's concept of number.

The yellow 'strand' is multiplication and division of whole numbers. Multiplication as a concept can be introduced in late 2nd grade. Single-digit multiplication and the times tables are in focus during 3rd grade, as is division with single-digit divisors. In fourth grade, students study multi-digit multiplication and long division, and are introduced to factors and primes.

Then the focus switches to fractions and decimals for fifth and sixth grades.

The concept of percent ties in with ratios, proportios, and decimals. All of these are topics for 6th-7th grades with lots of real-world applications.

Geometry and measuring are important from first grade on, tying in with other elementary math concepts, such as multiplication, area, fractions, and decimals.

Graphs (or statistics) and probability are present a little from first grade onward, but in the early grades, students only study some simple graphs.

See also:

Common Core Standards
The new standards that are being implemented in most of the US states from 2012 onward.

Online math assessment tests from Texas
Online mathematics tests for student assessment for grades K-11. Multiple choice. The tests are Texas Assessment of Knowledge and Skills (TAKS) and the State-Developed Alternative Assessment (SDAA).

Math Mammoth placement tests
For grades 1-6; you can use these as generic math assessment tests or for placement into Math Mammoth curriculum.