Grade 5
Mental Math Strategies
SCO = Specific Curriculum Outcome
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."
 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
help to create a visual for students.
1
4
(0.25),
1
2
(0.5),
3
4
(0.75) we can