Grade 5 Mental Math Strategies SCO : N2 : Use estimation ...

[Pages:3]Grade 5

Mental Math Strategies

SCO : N2 : Use estimation strategies including:

? front-end rounding ? compensation ? compatible numbers in problem-solving contexts

Rounding There are a number of things to consider when rounding to estimate for a multiplication calculation. If one of the factors is a single digit, consider the other factor carefully. For example, when estimating 8 x 693, rounding 693 to 700 and multiplying by 8 is a much closer estimate than multiplying 10 by 700. Explore rounding one factor up and the other one down, even if it does not follow the "rule". For example, when estimating 77 by 35, compare 80 x 30 and 80 x 40 to the actual answer of 2695.

Compensation In this case, compensation refers to increasing one value and decreasing the other. For example, 35 + 57 might be estimated as 30 + 60 (rather than 40 + 60) as this is a more accurate estimation.

Compatible numbers

Clustering compatible (or near compatible) numbers is useful for addition. For example, to solve 134 + 55 + 68 + 46, the 46 and 55 together make about 100; the 134 and 68 make about another 200 for a total of 300. Look for compatible numbers when rounding for a division estimate. For 4719 ? 6, think "4800 ? 6". For 3308 ? 78, think "3200 ? 80".

SCO: N3: Apply mental mathematics strategies and number properties:

? skip counting from a known fact ? using doubling or halving ? using patterns in the 9s facts

? using repeated doubling or halving to determine answers for basic multiplication facts to 81 and related division facts.

In grade 4, students will have become proficient at doubling (4 x 3 = (2 x 3) x 2).

This idea is extended in grade 5 to include repeated doubling. For example, to solve 8 x 6, students can think 2 x 6 = 12; 4 x 6 = 24, so 8 x 6 = 48.

The same principle applies to halving and repeated halving. For example, for 36 ? 4, think 36 ? 2 = 18; so 18 ? 2 = 9.

Skip counting up or down from a known fact reinforces the meanings of multiplication and division as students must be thinking about the addition or subtraction of "groups".

For example, for 8 x 7, think 7 x 7 = 49 and then add another group of 7; 49 + 7 = 56.

SCO: N4: Apply mental mathematics strategies for multiplication, such as:

? annexing then adding zero ? halving and doubling ? using the distributive property. ? Annexing then adding zero

For multiplication by 10, 100 and 1000 and multiplication of single-digit multiples of powers of ten (e.g., for 30 400, students should think "Tens times hundreds is thousands. How many thousands? 3 4 or 12 thousands.")

Halving and doubling For example, to solve 4 16, students can change it to 2 32 or 8 8. Or, to multiply 18 x 35, a student can think 9 x 70 = 630

Distributive property The ability to break numbers apart is important in multiplication. For example, to multiply 5 43, think 5 40 (200) and 5 3 (15) and then add the results.

This principle also applies to multiplication questions in which one of the factors ends in a nine (or eight or seven).

For such questions, one could use a compensating strategy Multiply by the next multiple of ten and compensate by subtracting to find the actual product. For example, when multiplying 39 by 7 mentally, one could think, "7 times 40 is 280, but there were only 39 sevens so I need to subtract 7 from 280 which gives an answer of 273."

Also see Mental Math in the Middle Grades Lessons 22, 23 and 24

Multiplying by 11 For example, to multiply 36 x 11, think (36 x 10) + (36 x 1) = 360 + 36 = 396

SCO: N10: Compare and order decimals (to thousandths), by using

? benchmarks

? place value

? equivalent decimals

By using number lines with benchmarks such as 1 (0.25), 1 (0.5), 3 (0.75) we can

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help to create a visual for students.

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