Download Mental Math in the Middle Grades

1
Grade 4
Mental Math Strategies
Addition
(SCO B15)
1. Front-end Strategy
Start from the left and add the hundreds first then the tens
and the ones.
525 + 245 = 500 + 200 + 20 + 40 + 5 + 5 = 770
Also see « Mental Math in the Middle Grades »
Lesson #10
2. Compensation
Add a nice number and subtract the difference
347 + 18 = (347 + 20) – 2 = 365
change 18 to 20 then subtract 2
Also see « Mental Math in the Middle Grades »
Lesson # 13
3. Partner Numbers (Compatible numbers)
Numbers that go together to make multiples of ten.
40 +60
300 + 700
25 + 75
250 + 750
64 + 36
72 + 28
Students must be able to recognize the partner numbers
225 + 68 + 75 = (225 +75) + 68 = 368
Also see « Mental Math in the Middle Grades »
Lesson #15, 16, 17, 18
Revised April 2004
2
Subtraction
(SCO B15)
1. Front-end Strategy
The only problems that you can subtract from the left are
those that do not need regrouping. These problems can be
calculated from either end.
Also see « Mental Math in the Middle Grades »
Lesson #11
2. Compensation
Subtract a nice number and then add the difference.
722 – 197 = 722 – 200 = 522 and add 3 = 525
Also see « Mental Math in the Middle Grades »
Lesson #21
3. Counting on / Counting back
Count on from a number (like giving change back in $)
243 – 197 = Start at 197 and add 3 to 200 then add 43 to 243
(3 + 43 = 46)
4. Partner Numbers (Compatible numbers)
Numbers that go together to make multiples of ten.
100 – 30 = 70
200 – 80 = 120
100 – 53 = 47
Also see « Mental Math in the Middle Grades »
Lesson #15
Revised April 2004
3
Multiplication
(SCO B9)
1. Multiplication facts
Multiplication facts to 9 x 9 using strategies
 Doubles for the 2 times table.
Example: 2 x 7 = (double 7 or 7 + 7)
 Double and add a set for the 3 times table.
Example: 3 x 7 = (2 x 7 + 7 more = 21)
 Double the 2 times tables for the 4 times table.
Example: 4 x 8 = (double 2 x 8 = 2 x 16 =32)
 Minutes on the clock for the 5 times table.
Example: 5 x 8 = 40 (the minute hand on 8 is 40 minutes)
 Double the 3 times table for the 6 timetables.
Example: 6 x 7 = (double 3 x 7 = 2 x 21 = 42)
 Multiply by 10 and subtract 1 set for the 9 times table.
Example: 7 x 9 = (7 x 10 and subtract 7 = 63)
 In the 9 times table, the digits in the answer add up to 9
(from 1 x 9 to 10 x 9) and the answer is always 1 less than
the other factor in the tens place and the missing addend to
make 9 for the ones place.
Example: 7 x 9 = (1 less than 7 is 6 for the tens place and
6 + 3 = 9 so 3 for the ones place) = 63
 When multiplying by 9, make a finger fold. Lay both
hands in front of you on the table. Fold the number you
want to multiply by 9. The number of fingers on the left of
the folded finger represents the tens place and the number
of fingers on the right of the folded finger represents the
ones place.
Revised April 2004
4
Example: 9 x 7 Fold the 7th finger (You show 6 fingers on the left
and 3 fingers on the right) = 63
 To multiply any two numbers from 6 to 10, you can use the
slick fingers method.
Place your hands on the table palm down. Number your fingers
from six to ten. – Starting at your thumbs on each side – (Or use
paper cutouts)
To multiply: touch the fingers representing each factor. Count all
the fingers starting at the thumbs including the two touching
fingers. These represent the tens place. Then multiply the number
of fingers above the touching fingers (one hand X the other hand).
This is your unit place.
10
10
9
8
7
6
9
8
7
6
Example: 9 x 8 = (7 fingers starting at the bottom counting the
touching fingers.) 1 x 2 = 2 to multiply fingers of both hands above
the touching fingers.
Answer: 72
Revised April 2004
5
Example: 8 x 7 = (5 fingers from the bottom). 2 x 3 = 6 to multiply
the fingers above.
Answer: 56
It works every time.
Note: For 6 x 6 you have 2 fingers touching which means 20 and 4
x 4 = 16 to multiply the above fingers. You have to add 20 + 16 =
36.
Revised April 2004
6
(SCO B16)
1. Multiply 2-digit numbers by 10 and 100
Before you give the rule of adding zeros, take the time to use
base-ten blocks to show that multiplying by 10 is the same as
counting rods and multiplying by 100 is the same as counting
flats. Check a few examples to show consistency.
Example: 23 x 10 = 23 rods … if you count by ten 23 times, you
will have 230 therefore adding one zero to the number.
Similarly: 34 x 100 = 34 flats give you 3400.
After the students understand why we add the “trailing zeros”,
then give them the rule and have them practice.
Also see « Mental Math in the Middle Grades »
Lesson # 22, 23, 24
(SCO C3)
1. Multiply a 2-digit number by 11
When you multiply a 2-digit number by 11, you move the
digit in the tens place to the hundreds place. Add the 2 digits
and place the answer in the tens place.
Example: 26 x 11 = 2_6 (add 2 + 6 = 8 for the tens place) =
286
Show the students why this works and what would happen if
the 2 digits add up to a number greater than 9.
This works because when you multiply by eleven, the
number is added to the same number lined up one place value
to the left.
26
x 11
26
+26_
286
Revised April 2004
7
When the 2 digits add up to a sum greater than 9, all you
need to do is add 1 to the first digit (the hundred place) and
place the unit digit of that sum as the tens place. The students
are able to do this very well with practice.
Revised April 2004