Grade 4 Mental Math Strategies

					                                    Grade 4
                             Mental Math Strategies

Skip Counting: Children should review counting by 2’s, 5’s, 10’s, 25’s and 100’s.

SCO: N3: Demonstrate an understanding of addition of numbers with answers
to 10 000 and their corresponding subtractions (limited to 3 and 4-digit
numerals) by
         • using personal strategies for adding and subtracting
         • estimating sums and differences
         • solving problems involving addition and subtraction

Some strategies to consider: using benchmarks, rounding, front-end addition and
subtraction (left-to-right calculations), and clustering of compatible numbers.

    benchmarks: 207 – 126 would give an answer between 75 (200 - 125), and 85
     (210 - 125)
    rounding: 439 + 52 is approximately 440 + 50.
    front-end: 138 + 245 = 370 (200 + 100 is 300, 30 + 40 is 70 for an estimate
     of 370). Some students may include the ones in their estimate making their
     answer 380.
    front-end subtraction: 476 – 348 = 130 (400 – 300 is 100, 70 – 40 is 30, 6
     and 8 are about the same so I’ll ignore them; my estimate is 130.
    clustering: cluster the 29, 35, and 42 together to make 100.
    compatibles: 225 + 68 + 75 = (225 + 75) + 68 = 368


See also Mental Math in the Middle Grades
Lessons 10, 11, 13, 15 to 18, and 21

SCO:N5: Describe and apply mental mathematics strategies, such as:
    skip counting from a known fact
    using doubling or halving
    using doubling or halving and adding or subtracting one more group
    using patterns in the 9s facts
    using repeated doubling to determine basic multiplication facts to 9 × 9 and
     related division facts.
    doubling, e.g., for 4  3, think 2  3 = 6, so 4  3 = 6 + 6
    doubling and adding one more group, e.g., for 3  7, think 2  7 = 14, and
     14 + 7 = 21
    use ten facts when multiplying by 9, e.g., for 9  6, think 10  6 = 60, and
     60 – 6 = 54; for 7  9,
    think 7  10 = 70, and 70 – 7 = 63
    halving, e.g., if 4  6 is equal to 24, then 2 × 6 is equal to 12
    relating division to multiplication, e.g., for 64 ÷ 8, think 8   = 64.
    multiplying single-digit numbers by 10 and 100

SCO:N11: Demonstrate an understanding of addition and subtraction of
decimals (limited to hundredths) by:
      • using compatible numbers
      • estimating sums and differences
      • using mental math strategies to solve problems.

Use estimation strategies including:

    Compatible numbers: e.g., 0.72 + 0.23 are close to 0.75 and 0.25 which are
      compatible numbers so the sum of the decimal numbers must be close to 1.

    Front-end addition: e.g., 32.3 + 24.5 + 14.1; a student might think “30 + 20 +
      10 is 60 and the ones and tenths clustered together make about another 10
      for a total of 70.”

    Front-end subtraction: e.g., 4.76 – 3.48; a student might think “4 ones – 3
      ones is 1 and 7 tenths – 4 tenths is 3 tenths for a difference of
      approximately 1 and 3 tenths.”

    Rounding: e.g., 4.39 + 5.2 is approximately 4+ 5 for an estimate of 9.
Use mental computation strategies including:
   Compatible numbers: e.g., 3.55 + 6.45 or $3 and $6 would be $9 while 55
     cents and 45 cents would make another dollar, for a sum of $10 or 10.

    Front-end strategy: e.g., 7.69 – 2. 45 A student might think “7 ones subtract
     2 ones is 5 ones, 6 tenths subtract 4 tenths is 2 tenths and 9 hundredths
     subtract 5 hundredths is 4 hundredths, so the difference would be 5.24”

    Compensate: e.g., $4.99 + 1.98 + 0.99 could be calculated by finding the sum
     of 5 + 2 + 1 and then subtracting 0.04 or 4 cents. The sum would be $7.96.

    Counting on/ counting back: $2 – 1.48; a student might think, “2 more pennies
     would make $1.50 and 50 cents more makes $2 so the difference (change) is
     52 cents

    Renaming: think of 3.2 + 0.9 as 32 tenths + 9 tenths.

				
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