Mathematics scope and sequence suggestion in chart form
Different math curricula utilize different scopes and sequences. This article gives you a general idea of a "basic" mathematics scope and sequence through elementary and middle school (grades 1-7 or 8), which is helpful if you're piecing together your math curriculum or for some reason not following any curriculum exactly to the "tee".
The following chart is a rough guideline showing you approximately when and in which order one should study various math topics. 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.
Notice that certain math topics are IN FOCUS in certain grade levels, and then "fade away" into the status of occasional review only. As explained in my article on coherent curriculum, you don't need to study basic arithmetic topics in each and every grade until the 8th grade. It is better to keep a good focus, aim for mastery, and then move on.
Note also that many math curricula present algebra in 9th grade and pre-algebra in 8th grade. This chart is assuming that algebra starts in 8th grade, but children and their 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
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, students should have mastered addition and subtraction of whole numbers so that it is no longer the focus 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 for fifth and sixth grade, the focus switches to fractions and decimals.
The concept of percent ties in with ratios, proportios, and decimals. All of these are topics for 6th-7th grade with lots of real-world applications.
Geometry and measuring are important from first grade on. They tie 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.
Common Core Standards
The new standards that are being implemented in most of the US states from 2012 onward.
Math Mammoth placement tests
For grades 1-6; you can use these as generic math assessment tests or for placement into Math Mammoth curriculum.