*Relearning to Teach Arithmetic, Susan Jo Russell. 1999.
    Everett Public Schools, 2005
    Subtraction and Division – Mental Math or
    Procedure/Strategy Examples
    Division:
    •
    Subtracting groups of the divisor*
    159 ÷ 13
    159
    29 OR Use the Big 7 method of recording (see below)
    10 x 13 = 130 -130
    -26
    2 x 13 = 26
    29
    3
    12 r3
    •
    Breaking the problem into parts*
    150 ÷ 48 = (50 ÷ 48) + (50 ÷ 48) + (50 ÷ 48) = 3 r 6
    (There is one 48 with 2 left over in each 50)
    OR
    159/13
    Break into 130 + 29, 130 divided by 13 is 10; 29 divided by 13 is 2 with 3 remaining
    •
    Transferring the problem into an equivalent problem that is easier to solve.*
    1400 ÷ 35 = 200 ÷ 5 (divide both numbers by 7)
    928/16 = 464/8 = 232/4 = 116/2 = 58
    •
    Solving and easier related problem, then compensating*
    247 ÷ 13
    Solve 260 ÷ 13 (There are 20 thirteens in 260, but 247 is 13 less than 260. So there are only 19
    thirteens in 247)
    •
    Dealing out into groups*
    159/13
    Give 10 to each group; that uses up 130; 29 is left
    Give 1 more to each group; that uses up 13; 16 is left
    Give 1 more to each group; 3 is left.
    The result is 12 in each group, remainder 3
    Subtraction: 465 – 129
    •
    Subtract one number in parts from the other.*
    465 – 100 = 365 OR
    465 – 125 = 340
    365 – 20 = 345
    340 – 4 = 336
    345 – 5 = 340
    340 – 4 = 336
    •
    Change one number, then compensate for the change.*
    465 – 130 = 335
    OR
    460 – 129 = 331
    335 + 1 = 336
    331 + 5 = 336
    •
    Add up from the number being subtracted.*
    129 + 1 = 130
    OR
    129 + 130 = 429
    130 + 300 = 430
    429 + 1 = 430
    430 + 35 = 465
    430 + 35 = 465
    1 + 300 + 35 = 336
    300 + 1 + 35 = 336
    •
    Transform the entire problem to an equivalent problem that is easier to solve.*
    465 – 129 = 466 – 130
    466 – 130 = 336
    *Relearning to Teach Arithmetic, Susan Jo Russell. 1999.
    Everett Public Schools, 2005
    •
    Subtract each column and record each difference, whether it is positive or negative.*
    400 – 100 = 300
    60 – 20 = 40
    5 – 9 = -4
    300 + 40 +(– 4) = 336
    Please note that students may use larger numbers or chunks once they are more confident with their
    understanding with number. Also, the recording of the numbers is to explain how they solved the
    problem and can look tedious. Many of the steps can be done mentally with some keeping track on
    paper if necessary.
    It is important that students eventually learn to read all common notations, including both vertical
    and horizontal notations for addition, subtraction, and multiplication, as well as the various notations
    for division. However, they need to be secure enough to interpret these notations correctly while still
    relying on their own mathematically sound procedures to solve problems notated in any of these
    ways.*
    For example:
    2 + 4 = 6
    32 – 27 = 5
    5 = 32 - 27
    2
    32
    12
    12 x 7 = 84
    +4
    - 27
    x 7
    6
    5
    84
    6
    24 ÷ 4 = 6
    24/4 = 6
    4)24
    Big 7 - looks like a big 7 (method of recording to keep track of subtraction and multiplication)
    7)293
    -70
    7 x 10 = 70
    223
    -140
    7 x 20 = 140
    83
    -70
    7 x 10 = 70
    13
    -7
    7 x 1 = 7
    6
    41 R 6

    Back to top