The placement tests below are "end of the year" tests for Math Mammoth complete curriculum. In other words, the tests are meant to be taken AFTER studying the particular grade.
You can also use these tests as general math diagnostic tests, to help you find if your student has any gaps or has not learned specific topics, because the tests group the questions by topic. Just look at the test results per "sections" of similar problems (addition, multiplication, measuring, geometry, place value, problem solving). You can always email me your child's test results if in doubt.
Placement into Math Mammoth: The goal is to find a test that the child passes or nearly passes, which means that the score is approximately in the 6585% range. That test will then indicate the general placement of the child in Math Mammoth. If the child scores better, consider administering the next test up. If the child does worse than 65%, consider administering the next lower level test.
I recommend that in order to start with Math Mammoth complete curriculum for grade level X, the student should score 80% or more in the previous year's "end of year" test. Children scoring between 70 and 80% may also continue with the next grade, depending on the types of errors (careless errors or not remembering something, vs. lack of understanding). Use your judgment.
Tip: If you notice your child has problems with one or two concept areas in a particular test, but otherwise does fine, you can use Math Mammoth Blue Series books to "fill in those gaps". You can also email me with your test results if you have trouble deciding which Blue Series book you should use for such remedial work.
Math Mammoth gradelevel review workbooks can also be used to pinpoint areas of weakness or to review a whole grade level of topics.
Here is an example of one student's test results and the placement advice I gave to the parent of this student.
Background: the student began homeschooling the same year as the tests were taken and is technically in 7th grade. She had started doing Teaching Textbooks Algebra 1. However, the parent noticed that she didn't know some basic fraction information, decided to look for a supplement, and came across Math Mammoth.
The student took three endofyear tests: for grade 6, grade 5, and grade 4. She did not do very well in the grade 6 test, but you can see her work for grade 4 and grade 5 tests in the links below. If you decide to send me your child's test results, it is not necessary to send me the complete test like this person did, but it makes a good example. Most people send me only the point counts for the various test items.
And here is my assessment and recommendations:
Hello,
I think it's a good idea to have her start at grade 5 in Math Mammoth.
Additionally, I feel she should study these books from the Blue series.
 Early Geometry, because she doesn't seem to understand the concepts of area and perimeter – which are of paramount importance. This book is for grades 13 so some topics in it are too easy and she can skip them.
 Geometry 1 – meant for grades 45. She will need to study the lessons that are in 4th grade level first (angles, quadrilaterals, triangles, etc.) Please note some of the content here overlaps with MM grade 5. She can study the overlapping lessons from either source.
 Measuring 1 – it is for grades 13 but she may need to review everything from the beginning when it comes to measuring units. Some lessons may be too easy and can be omitted  use your judgment on that.
 Measuring 2 – for grades 46. Please note some of the content here overlaps with MM grades 5 and 6. She can study the overlapping lessons from either source.
 Decimals 1
She has not grasped the basics of how fractions and decimals tie together – which, once again, is a very fundamental concept. She should study Decimals 1 book before starting the decimals chapter in grade 5.
Other than those few areas (geometry, measuring, decimals), she can be placed into MM 5.
By the way, don't assign all the problems that have to do with calculations (large exercise sets) in any of the materials. It's enough to assign maybe 1/3 of those at first. If she has difficulties, then use the rest (and that may be the case when it comes to, say, perimeter and area).
And, she did really well with the first two sections of grade 5 endofyeartest, which means she could perhaps skip the first two chapters in MM5. You could let her study the chapter reviews and/or tests from those 2 chapters. Check and see how she does with them, and then use your judgment if she'd need to study any of the lessons from those chapters.
Thankfully, she also understands many things of fraction arithmetic, which will make things go quicker in part 5B.
I'm really glad her 'gaps' are not in general problem solving! It's far easier to deal with topics such as measuring units, area, and perimeter, than to fix a general lack of not being able to solve word problems (which is the case with many children).
Sincerely,
Maria Miller
Student attempted 2nd grade endofyear test:
Add & Subtract 2A, Add & Subtract 2B, and half of Add & Subtract 3.Student attempted 3rd grade endofyear test:
(possibly Add & Subtract 2A) Add & Subtract 2B, Add & Subtract 3, Multiplication 1, and Division 1.Student attempted 4th grade endofyear test:
Add & Subtract 3, Multiplication 1, Division 1, Multiplication 2, and Division 2.
Area of lack  Remedial book 

Addition and subtraction facts within 010  Subtraction 1 
Addition and subtraction facts within 018  Add & Subtract 2A 
Place value of tens and ones  Place Value 1 
Place value of 3digit numbers  Place Value 2 
Place value of 4digit numbers  Place Value 3 
Mental math  addition and subtraction strategies for 2digit numbers  Add & Subtract 2B 
Mental math  addition and subtraction strategies for 3digit numbers  Add & Subtract 3 
Multiplication concept, multiplication tables, or simple multiplication word problems (grade 3)  Multiplication 1 
Multidigit multiplication and related word problems (grades 45)  Multiplication 2 
Prime factorization, LCM, GCF (grades 46)  Multiplication & Division 3 
Basic division concept (singledigit divisors) and related word problems (grade 3)  Division 1 
Long division and related word problems (grades 45)  Division 2 
Reading the clock, telling time, or elapsed time  Clock 
Any measuringrelated difficulty within grades 13, including not knowing metric units  Measuring 1 
Geometric concepts within grades 13  Early Geometry 
Geometry (grades 47)  Geometry 1 and Geometry 2 
Fraction concepts within grades 24  Introduction to Fractions 
Fraction topics within grades 56  Fractions 1 and Fractions 2 
Basic concept of decimals (grades 34)  Decimals 1 
Decimal arithmetic (grades 56)  Decimals 2 
Ratios and proportions (grades 67)  Ratios, Proportions & Problem Solving 
Percent (grades 67)  Percent 
Integers (grades 67)  Integers 
Statistics (grades 57)  Statistics & Probability 
By Maria Miller
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