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Placement in Math Mammoth Blue Series

For placement in the complete curriculum series (Light Blue), click here.

Use these questions to guide you which of the Blue Series books your child should study.

For some books, such as Clock, Money, Measuring, Geometry 1, and Fractions 1 & 2, it will be quite easy and obvious (I hope!) to know if the child should study those, so that is why this page concentrates on the add/subtract/multiply/divide books.

Maybe your child has studied such-and-such curriculum, then switched to this-and-that curriculum, maybe been in this school, using that book. After such a hodgepodge it can be difficult to determine where the child is at in their math studies.


Addition 1

  • Can the child confidently add two numbers when the sum is between 0 and 10?
  • Can he find the missing addend in similar problems ( such as 4 + __ = 6) ?
  • Can he make a list of number pairs that add up to 7, 8, 9 or 10?
    (for example, 0 + 7, 1 + 6, 2 + 5, and 3 + 4 all add up to 7).

Subtraction 1

  • Can the child confidently and quickly subtract two numbers less than 10? (no negative answers though)
  • Does he understand the connection between addition and subtraction, using small numbers?
  • Does he understand to use subtraction in these situations:
    • "how many more" situation
    • "taking away" situation
    • "Two parts - one whole" situation (e.g. There are 9 kids and 2 are boys. How many are girls?)
  • Is he able to use the concept of fact families to solve addition and subtraction problems? (For example, the problem 6 − ___ = 3 can be solved by remembering that 3 + 3 = 6.)
  • Can he solve simple word problems that involve either addition or subtraction?

Add & Subtract 2-A

  • Does the child comprehend the concept of completing the ten in addition, and going over?
  • Does your child add confidently any two numbers less than 10? (Such as 6 + 8 = 14 or 9 + 9 = 18)
  • Does he know by heart the corresponding subtraction facts? (Such as 14 − 6 = 8)
  • Does he know the concept of "difference of two numbers"?
  • Is he able to add and subtract mentally whole tens?
  • Is he able to add a single-digit number to a two-digit number when the sum does not go over the next whole ten? (such as 55 + 4 = __)
  • Is he able to subtract a single-digit number from a two-digit number when the difference does not pass to the previous whole ten? (such as 46 − 5 = __)
  • Is he able to solve simple word problems that involve difference, "how many more", or situations where something is first added then something is subtracted or vice versa?

Add & Subtract 2-B

  • Is your child able to add two-digit numbers in columns, with or without carrying?
  • Is your child able to subtract two-digit numbers in columns, with or without borrowing?
  • Is your child able to use the memorized addition facts to solve other addition problems mentally (especially this type: knowing that 6 + 7 = 13, the child is able to solve 56 + 7 or 86 + 7.)
  • Is the child able to add or subtract whole tens mentally?
  • Is he familiar with mental math strategies such as subtracting in parts, or adding up the difference when subtracting? (for example: solve 65 − 7 this way: 65 − 5 − 2. Or, solve 65 − 61 by thinking of the difference of 61 and 65.)

Multiplication 1

  • Does your child understand the concept of multiplication?
  • Has he memorized the times tables?
  • Is he able to use multiplication to solve word problems that involve addition, subtraction, or multiplication?
  • Does he understand basic properties of multiplication: multiplying by 1 or 0, the order does not matter?

Add & Subtract 3

  • Can the child add and subtract in columns 3-digit numbers, including borrowing or carrying two times?
  • Can the child add and subtract without writing numbers in columns, using known addition and subtraction facts and strategies to help? For example:
    • 700 + 300 or 340 + 400 or 609 − 500 (add hundreds to hundreds)
    • 560 + 30 or 182 − 50 = (add tens to tens, or subtract tens from tens)
    • 540 + ___ 600 (think of 40 + __ = 100)
    • 677 + 9 = __ (think of 77 + 9)
  • Is he able to understand and use the connection between addition and subtraction when the word problems involve 3-digit numbers
  • Is he able to round numbers to the nearest ten, and estimate sums or difference using rounding?
  • Is he aware of mental math strategies such as adding/subtracting in parts, adding up to find the difference, or using easy, nearby numbers ?

Division 1

  • Does the child understand the concept of division?
  • Does the child understand the connection between multiplication and division? Can he solve divisions by his knowledge of multiplication facts?
  • Can he write fact families of two multiplication and two division facts?
  • Does the child understand basic properties of division, such as dividing by 1 and 0, and division as repeated subtraction?
  • Does the child understand concept of remainder?
  • Does the child understand concept of divisibility?
  • Is he able to check division results with remainder?
  • Does he understand that finding 1/2 of a number is the same as dividing the number by 2 (and similarly for other small divisors)?

Multiplication 2

  • Can the child multiply mentally by whole tens and whole hundreds?
  • Can the child multiply in columns by a single-digit number?
  • Does he understand the basic principle behind why multiplication in columns works (= multiplying in parts)?
  • Can he multiply in parts without multiplying in columns? (For example, write 2 × 54 as 2 × 50 + 2 × 4)
  • Does the child know the order of operations for expressions including addition, subtraction, and multiplication?
  • Can he use rounding to estimate products, including in word problems?

Division 2

  • Can the child divide 3- and 4-digit numbers using long division?
  • Can the child solve word problems that involce the usage of long division, including the concept of average?
  • Does he know how to check long division results, including if there was a remainder?
  • Can the student find a fractional part of a number, using division and multiplication (e.g. find 2/5 of 385)
  • Does he understand the concept of divisibility? (e.g. solve if 548 is divisible by 8)
  • Does he know how to quicly know if a number is divisible b 2, 5, or 10? (e.g. 778 is divisible by 2 since it ends in 8, but not divisible by 5 or 10)

Multiplication Division 3

  • Can the child multiply in columns a 3-digit number by a two-digit number?
  • Can the child use long division with a two-digit divisor?
  • Does he know the basic divisibility rules (by 2, 3, 4, 5, 6, 9, and 10)?
  • Does he understand the concepts of a prime and composite number?
  • Can he factor (factorize) small numbers into their prime factors?
  • Can he factor (factorize) 3-digit numbers into their prime factors, using the knowledge of divisibility rules?

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