Download Mental Math - Mrs Steeves

Mental Math “PLAN” for Grade 6
Week 0: Quiz each day first thing to pre-test kids to find out what math facts they know. (5 pre-tests, 20 questions each, 5 mins, 012)
Week 1: (Harry Boen’s stuff could be done Days 1, 2, & 3 for one strategy and Day 4, 5 & 6 for the next strategy, instead of one
per week)
Here is our task, to learn one-hundred multiplication facts. Let's set up a game plan to get
this accomplished!"
At the time this activity is commenced, students should have a solid understanding of the
concept of multiplication based on the manipulation of concrete materials using array
patterns. A main thrust of this activity is to help bridge the gap from the concrete stage
(building arrays) to the symbolic stage (memorization of the facts). Mark off an eleven by
eleven grid on a bulletin board using square decimeters. Use a strip of paper to cover up
the first two columns and the bottom two rows of the grid as shown below. Place a dot in
the square in the lower left-hand corner.
The Twos: (Mental Math: Doubling)
Because students already know facts like 2 fours make 8, the twos are a good starting
point. Prepare a grid to be placed on the overhead. Provide students graph paper with
squares the
same size as those on the grid. Have them cut out as many different array patterns as they
can in which one side is two units long and no more than eighteen total squares are
included. Several
examples are pictured here.
Some interesting discussions can take place as to whether the number of arrays that fit the
conditions will be even or odd (odd because of the 2 by 2 array) and what the total
number will be(17) As students begin to cut out such array patterns the questions will
usually arise as to whether
the common shaded arrays above (4 by 2 and 2 by 4 and 1 by 2 and 2 by 1) are the same
or different. Discuss the pros and cons of this issue. Decide (temporarily) to consider
such pairs as being different...one showing the problem 2 x 4 = 8 and the other that 4 x 2
= 8. To help
distinguish between them, have students place a dot in the lower left hand corner of each
array.
Have students continue cutting out array patterns until all seventeen have been found.
Have a student hold up on of the arrays. "What are the dimensions of your array pattern?"
(4 x 2)
"How many squares in a four by two array pattern?" (8) Say, "Four twos make eight.
Four times two equals eight." Have the student place the array pattern on the overhead
grid with the dot on the dot, fold back the corner opposite the dot, and write the numeral
8 in that square as you say, "Four twos make eight. Four times two equals eight."
Have another student hold up a different array pattern. "What are the dimensions of your
array
pattern?" (2 x 5) "How many squares in all?" (10) "Five twos make ten. Two times five
equals ten." Have the student hold this array pattern on the grid with the dot on the dot.
Fold back the corner opposite the dot and record the numeral 10 as you repeat,
"Five twos make ten. Two times five equals ten." Continue until all possible arrays have
been utilized, then fill in the facts on the permanent board. The finished product appears
below on the left.
Say, "We have started today to fill in the multiplication tables. Remember the addition
tables you had to learn?" Show a picture of the addition table. Return to the bulletin board
and say, "We sure have a lot of facts left to learn, don't we? Was there a big idea that
helped make it easier to learn the addition tables?" By studying the addition tables, lead
the class to a verbalization of the commutative property of addition ... that 3 + 4 = 4 + 3,
8 + 6 = 6 + 8, etc. Show how this property cut the number of addition facts we had to
learn almost in half.
Ask, "Do you think this idea also works with multiplication?" Show that it does work
using
array patterns. Have students demonstrate on the grid how the same array pattern could
be used to show both 2 x 4 and 4 x 2. Repeat for several other array patterns. Say, "This
idea will also cut the number of multiplication facts we have to learn almost in half."
Place a large sheet of colored paper over the lower part of the table as shown below.
Leave this partially completed bulletin board up for students to use to practice on the
twos. Emphasize the fact that they really know facts like 2 x 7 because they know 7 + 7.
Be sure to cover the permanent bulletin board when fact mastery work is in progress.
Note: All facts should be taught in context, i.e., presented in verbal problems made up by
teacher and students alike.
Your FIRST QUIZ WILL BE 20 FACTS FROM THE 2s!!
Mental Math Test #1
Name:__________________
1. 2 X 2 = __________
2. 3 X 2 =____________
3. 4 X 2 = ___________
4. 5 X 2 =____________
5. 6 X 2 =____________
6. 7 X 2 = ____________
7. 8 X 2 =____________
8. 9 X 2 =____________
9. 10 X 2 =___________
10. 11 X 2 =__________
11. 12 X 2 = __________
12. 13 X 2 = __________
13. 14 X 2 = _________
14. 15 X 2 = __________
15. 16 X 2 = __________
Week 2:
The Fives (Mental Math: use the minutes on the clock)
Many teachers next work on the fives. This is probably because they can be easily
attained by skip-counting. Have students cut out array patterns in which one side is five
units long using no more than 45 total squares. Remind the class that we now think of the
two arrays below as being the same. Show with several examples how one can be rotated
to look like the other.
Ask, "How many different arrays can we come up with?" (9) Do not put dots in the
corners from this point on. Have a student hold up one of the arrays. "What are the
dimensions of your array pattern?" (5 by 6) "How many squares in all?" (30) "What
multiplication problem does it show?" (6 times 5 = 30) Place the array pattern on the
bulletin board, fold back the appropriate corner, and say, "Six fives make 30 - six times
five equals 30." If the student places the array on the grid so the square under the turned
down corner is black, have them rotate the array the other way.
Continue until all of the fives have been placed on the grid. Various games should be
used to make the twos and fives automatic
WEEK 2: QUIZ will be on the FIVES and the TWOS!!
Mental Math Test #2
Name:______________________
1. 2 X 2 = _______________
2. 2 X 3 = _______________
3. 5 X 3 = _______________
4. 5 X 2 = _______________
5. 5 X 5 = _______________
6. 5 X 7 =_______________
7. 2 X 4 = _______________
8. 2 X 16 = _______________
9. 5 X 8 = _______________
10. 5 X 9 =_______________
11. 5 X 1 = _______________
12. 2 X 17 = _______________
13. 2 X 5 = _______________
14. 5 X 6 =_______________
15. 5 X 10 =_______________
Week 3:
The Fours (Mental Math: Double the 2 times tables for
the 4 times tables)
Next, the fours should be attacked. The fours are attainable by using prior knowledge of
the twos and doubling twice. For example, 4 x 7 is twice as much as 2 x 7. This should be
shown concretely as pictured below. Since 2 sevens make 14, 4 sevens should be twice as
much or 28.
This basic strategy can be applied any time one of the factors is even. Although they have
already covered 4 x 5, a helpful strategy is to use the perfect squares as below.
For some reason, students seem to find the perfect squares easier to remember. Have
students cut out arrays for the fours and add them to the multiplication table.
Week 3’s quiz will be on the twos, fives, and fours.
Mental Math Test #3
Name:_________________
1. 2 X 18 = _______
2. 4 X 3 = ________
3. 5 X 5 = ________
4. 5 X 9 = ________
5. 4 X 10 =________
6. 4 X 6 =_________
7. 4 X 9 =_________
8. 2 X 20 = ________
9. 5 X 20 =_________
10. 4 X 8 = _________
11. 5 X 2 = ________
12. 4 X 2 = ________
13. 4 X 4 = ________
14. 4 X 5 =_________
15. 4 X 30 = ________
Week 4:
The Threes (Mental Math: Double and add a set)
The threes are also usually introduced using skip counting. However, since skip counting
by threes is not as easy for students as is skip counting by twos and fives, some of the
thinking strategies below might be utilized. All such situations are free rides, i.e., using
what you do know to get at what you do not know.
Splitting a Product Into Known Parts
This strategy, which has several sub-categories, can be used to get any unknown fact
from a
known fact using the free ride strategy. As at the right, you might use prior knowledge of
2 x 3 to make sense out of 3 x 3. Provide a 2 by 3 array and add a third column of 3. "If 2
threes are 6, what would 3 threes be?
In this example, knowledge of 3 x 5 can help make sense of 3 x 6. "If 5 threes make 15,
what would 6 threes be?"
This same strategy can be used in reverse by starting with the known fact, in this case 4
x3 and eliminating a column. "If 4 threes make 12, what would 3 threes be?"
Here, some students might get at 7 x 3 by thinking, "If 5 threes are 15 and 2 threes are 6,
then 7 threes should be 15 + 6 or 21." As in the examples above, one should start the
thinking with manipulatives and move on to doing the same thinking mentally.
The threes should now be added to the table and included in the various fact games and
activities. Each time a new set of facts is added to the chart, be sure to stop and point out
how the number of facts left to be learned has decreased. (We are now down to 15.)
Week 4s test will be on the fours, fives, threes, and twos.
Mental Math Test #4
Name:_____________________
1. 4 X 3 = ________
2. 5 X 5 = ________
3. 3 X 7 =_________
4. 2 X 7 = _________
5. 3 X 9 =__________
6. 3 X 10 = ________
7. 3 X 6 = ______
8. 3 X 5 = ________
9. 3 X 4 = _________
10. 5 X 7 = ________
11. 4 X 4 =__________
12. 4 X 20 =_________
13. 5 X 30 = ________
14. 2 X 120 = _______
15. 2 X 70 = ________
Week 5:
The Ones
At this point, the ones may be added to the table. Although the ones are very easy, it is
not a good idea to include them until the concept of multiplication has been established.
Array patterns including the ones should be used to place these products on the table.
Now only ten additional facts remain.
Table With 3's and 4's Added---------------Table With 1's Added
Week 5s test will be the threes, twos, fours, fives, and ones.
Mental Math Test #5
Name:______________________
1. 1 X 31 = _______
2. 2 X 40 = _______
3. 3 X 5 = ________
4. 4 X 8 =________
5. 5 X 6 = ________
6. 3 X 7 = ________
7. 5 X 20 = ________
8. 4 X 40 = ________
9. 3 X 70 = ________
10. 1 X 1000 = _______
11. 2 X 8 = _______
12. 3 X 8 = _______
13. 4 X 9 = _______
14. 5 X 8 = ______
15. 1 X 9 = _______
Week 6:

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.)
The Nines (Mental Math:
Because of some interesting patterns, the remaining nines should be covered at this time.
Write the nines that have already been covered on the chalkboard as shown below. Allow
students to study this information looking for patterns.
Some of the patterns usually quickly discovered include:
1. The sum of the digits of each product is nine.
2. As the ones digit of each product is decreasing by one, the tens digit is increasing by
one.
3. The tens digit of each product is one less than the number by which nine
is being multiplied.
Discovery of and discussion about these patterns should lead students to the finding the
products of the remaining nines. The discussion should center around why these patterns
exist. Some of the explanations develop from knowing how to multiply by ten (10 x 3 =
30 so 9 x 3 should be in the twenties. 10 x 3 = 30 so 6 x 3 should be 3 less or 27.).
Although multiplication by ten has not been discussed, it should follow from place value
work (3 tens make 30).
Discussion should also lead to a method for determining a fact such as 7 x 9 without
having to list all of the combinations. If 7 tens is seventy, then 7 nines should be in the
sixties. If the answer is sixty-something and the sum of the digits must be nine, then the
product must be sixty-three. Array patterns should be used to add the new nines to the
table. Now only six facts remain!
Week 6s quiz will be on the nines, fives, fours, threes, twos, and ones.
Mental Math Test #6
Name:______________________
1. 9 X 3 = ____
2. 5 X 4 = ______
3. 4 X 4 = _______
4. 3 X 2 =
_______
5. 2 X 80 = _________
6. 1 X 500 = ________
7. 9 X 9 = ________
8. 9 X 4 = _________
9. 9 X 1 = __________
10. 9 X 50 = ___________
11. 4 X 60 = ___________
12. 3 X 8 = _________
13. 2 X 9 = _______
14. 4 X 9 = ________
15. 5 X 80 = ______
Week 7:
The Perfect Squares
Next, the remaining "doubles" should be added to the table (6 x 6, 7 x 7 and 8 x 8). These
facts can be covered using the "splitting a product into known parts" and "twice as much
as a known fact" strategies discussed earlier.
7x7=?
Since 5 x 7 = 35,
and 2 x 7 = 14
7 x 7 should = 49
6x6=?
Since 5 x 6 = 30,
6 x 6 should be 6 more
or 36.
8x8=?
Since 4 x 8 = 32,
8 x 8 should be
twice that or 64.
Any of this type of reasoning is a free ride, using what you do know to solve a problem
you don't know. Students should be given the opportunity to make such math connections
on their own. Adding the doubles to the table leaves only three facts to be covered!
Week 7s test will be on perfect squares, nines, twos, threes, fours, fives, ones.
Mental Math Test #7
Name:___________________
1. 4 X 4 =_______
2. 5 X 5 = ______
3. 3 X 3 = _______
4. 2 X 2 = _______
5. 1 X 1 = _______
6. 9 X 9 = _______
7. 8 X 8 = _______
8. 7 X 7 = ________
9. 6 X 6 = _______
10. 10 X 10 = ________
11. 11 X 11 = __________
12. 12 X 12 = ________
13. 9 X 2 = ________
14. 3 X 9 = _______
15. 5 X 1 = _______
Week 8:
The Last Three
Mental Math: Double the 3 times table for the 6 timetables
To fill in the remaining three facts (6 x 7, 6 x 8, and 7 x 8) in addition to "splitting" and
"twice as much" strategies used earlier, students can also make use of the doubles. These,
of course are all free rides.
6x7=?
Since 6 x 6 = 36,
so 7 x 6 should 6 more
or 42
7x8=?
Since 5 x 8 = 40,
and 2 x 8 = 16,
so 7 x 8 should be 56
6x8=?
3 x 8 = 24,
so 6 x 8 should be
twice that or 48
Week 8s test will be on the twos, fives, threes, sixes, sevens, eights, nines, ones.
Mental Math Test #8
Name:___________________
1. 1 X 1 = _______
2. 2 X 5 = _______
3. 3 X 6 = _______
4. 4 X 6 = _______
5. 5 X 9 = _______
6. 6 X 7 = _______
7. 7 X 10 = ______
8. 8 X 8 = _______
9. 9 X 4 = _______
10. 10 X 2 = ______
11. 6 X 3 = _______
12. 6 X 5 = ______
13. 7 X 8 = _______
14. 8 X 4 = _______
15. 8 X 6 = _______
Week 9:
Multiplying by Zero
Finally, multiplication with zero as a factor can be covered. Although these facts may
actually be dealt with earlier, it is better not to put them on the chart until all other facts
have been covered. Now the strips covering the first two columns and rows can be
removed to reveal a completed multiplication table.
Week 9s test will be on the zeros, ones, twos, threes, fours, fives, sixes, sevens, eights, and nines.
Mental Math Test #9
Name:________________
1. 0 X 99 = __________
2. 1 X 99 = __________
3. 2 X 5 = __________
4. 3 X 8 = __________
5. 4 X 4 = ________
6. 5 X 5 = ________
7. 0 X 9 = ________
8. 6 X 7 = ________
9. 7 X 7 = _________
10. 8 X 10 = __________
11. 9 X 5 = _________
12. 1000 X 0 = __________
13. 8 X 9 = ________
14. 9 X 1 = ________
15. 10 X 8 = _______
Week 10:
Multiplication by 10, 100, and 1000.
Show students by using manips (base-ten) why you can add “trailing zeros” (See
Mental Math grade 4)
For example: 41 x 100 = 4100
Week 10’s quiz will be on multiplication facts 0-10, 100, and
1000.
Mental Math Test #10
Name:_________________
1. 1 X 100 = _________
2. 2 X 25 = __________
3. 3 X 1000 = __________
4. 75 X 10 = __________
5. 4 X 80 = __________
6. 5 X 7 = _________
7. 2 X 17 = _______
8. 8 X 9 = ________
9. 88 X 100 = ________
10.
9 X 8 = _________
11.
0 X 67 = __________
12.
9 X 9 = __________
13.
12 X 12 = ________
14.
76 X 1000 = __________
15.
75 X 2 = __________
Week 11:
Multiplication of two single-digit numbers in powers of 10.
Break the numbers so to separate the multiples of ten. Then rearrange the factors to show
how multiplication can be done easier.
Ex. 30 x 400 = [(3 x 10 x 4 x 100) ] = [3 x 4 x 10 x 100] =
12 x 1000 = 12000
After the students see where it comes from, then we can tell
them to multiply the digits and place the “trailing zeros”.
Week 11’s test will be on multiplication facts 0-10, 100, 1000, and
this strategy.
Mental Math Test #11
Name:______________
1. 0 X 990 = _________
2. 80 X 20 = _________
3. 30 X 50 = _________
4. 40 X 40 = _________
5. 80 X 20 = _________
6. 40 X 90 = _________
7. 50 X 70 =_________
8. 20 X 10 = _________
9. 60 X 50 = _________
10.
11 X 100 = _________
11.
12 X 10 = _________
12.
1 X 44 = _________
13.
9 X 4 = _________
14.
2 X 14 = _________
15.
70 X 30 = _________
Week 12:
Multiplication by 25
Divide by 4.
If no remainder add 00
If remainder = 1 add 25
If remainder = 2 add 50
If remainder = 3 add 75
Ex 25 x 36 = (36 ÷ 4) = 9 R 0 place 00 at the end = 900
25 x 27 = (27 ÷ 4) = 6 R 3 place 75 at the end= 675
25 x 33 = (33 ÷ 4) = 8 R 1 place 25 at the end = 825
25 x 42 = (42 ÷ 4) = 10 R 2 place 50 at the end = 1050
Week 12’s test will be on all ‘mental math’ stuff we’ve learned so far and THIS.
Mental Math Test #12
Name:_______________
1. 25 X 4 = ________
2. 25 X 100 = _________
3. 25 X 6 = __________
4. 14 X 10 = ___________
5. 3 X 7 = __________
6. 7 X 8 = _______
7. 8 X 9 = ________
8. 0 X 100 =_______
9. 28 X 10 = ________
10.
9 X 10 = _________
11.
25 X 8 = ________
12.
25 X 3 = _________
13.
30 X 60 = ________
14.
6 X 6 = _________
15.
5 X 25 = ____________
Week 13:
Double / Halving
You double one number and half the other. ** It works well
when you can double the 5 to a 10.
Ex. 4 x 16 = 2 x 32 = 64
24 x 5 = 12 x 10 = 120
Week 13’s test will be on all strategies learned up to this point,
including this one.
Mental Math Test #13
Name:______________
1. 4 X 16 = _______
2. 24 X 5 = ________
3. 48 X 5 = ________
4. 5 X 1000 = _______
5. 80 X 60 = _________
6. 4 X 18 = __________
7. 9 X 9 = _________
8. 71 X 10 = _______
9. 25 X 6 = _________
10.
8 X 4 = ________
11.
5 X 84 = ________
12.
2 X 81 = _______
13.
9 X 7 = _______
14.
5 X 8 = _______
15.
50 X 40 = _______
Week 14
Front-end solving
When the numbers are easy to multiply with no or very few
regroupings. You do the multiplication from left to right. You
can add the numbers as you go.
Ex. 3124 x 3 = 9000 + 300 + 60 + 12 = 9372
A student should say 9000 …300… 60.. 72 (avoid saying
the “plus”)
Mental Math Test #14
Name:___________________
1. 25 X 9 = _______
2. 4 X 80 = ________
3. 541 X 3 = _______
4. 3124 X 3 = ___________
5. 80 X 20 = ___________
6. 524 X 5 = __________
7. 313 X 4 = ___________
8. 8000 X 0 = ________
9. 2 X 90 = ________
10.
24 X 4 = ________
11.
51 X 0 = _______
12.
1 X 13 = ______
13.
5 X 7 = _______
14.
6 X 8 = _______
15.
7 X 3 = __________
Week 15
Compensate Strategy
Multiply by a multiple of 10 and subtract the extra.
Ex. 4 x 29 = Think 4 x 30 = 120 then subtract 4 = 116.
Multiply by one- or two-digit numbers ending in 8 or 9
Multiply by a multiple of 10 and compensate.
Ex. 29 x 6 = Think 30 x 6 is 180 but this is 1 extra group of
6 so you need to subtract 6. 180 – 6 = 174.
Ex. 49 x 24 = Think 50 x 24 or 100 x 12 (Double half) =
1200 but this is an extra group of 24 so you need to take
away 24. 1200 – 24 = 1176.
Mental Math Test #15
Name:_________________
1. 0 X 989 = ________
2. 1 X 87 = ________
3. 2 X 45 = _________
4. 3 X 60 = _________
5. 4 X 29 = _________
6. 5 X 900 = _________
7. 310 X 3 = _________
8. 6 X 9 = _________
9. 7 X 100 = ________
10.
80 X 50 = ________
11.
9 X 701 = _______
12.
10 X 623 = _______
13.
3 X 49 = ________
14.
4 X 50 = _______
99 X 6 = __________
Week 16
Multiply by 11
Write the first digit and the second digit with a space inbetween. In that space write the sum of the 2 digits.
Please note that if the sum of the 2 digits is more than 9, you
have to increase the first digit.
Ex. 11 x 23 = 2 (2+3) 3 = 253
11 x 48 = 4 (4+8) 8 = 528
The 4 changes to 5 because 4+8 = 12.
Show the students why this will always work. Use a vertical
multiplication by 11.
Mental Math Test #16
Name:______________
1. 0 X 11 = ______
2. 1 X 11 = ______
3. 2 X 91 = _______
4. 11 X 56 = _______
5. 11 X 32 = ________
6. 79 X 4 = _______
7. 9 X 60 = ________
8. 5 X 5 = _______
9. 11 X 99 = _________
10.
24 X 4 = _________
11.
8 X 3 = ________
12.
80 X 60 = _________
13.
32 X 100 = _________
14.
25 X 7 = __________
15.
70 X 40 = _________
Week 17
. Division involving facts
Division of a two-digit number by a single digit divisor:
Think multiplication!
Ex. 56 ÷ 8 = think “ 8 x what number = 56”
75 ÷ 3 = think “3 groups of what number = 75”
try: 18 ÷ 6 or 84 ÷ 4
Mental Math Test #17
Name:_____________
1. 56 ÷ 7 =_________
2. 72 ÷ 9 = ____________
3. 8 X 9 = _____________
4. 4 X 25 = __________
5. 16 ÷ 4 = ___________
6. 100 ÷ 4 = __________
7. 63 ÷ 7 = __________
8. 75 ÷ 1 = ________
9. 45 X 4 = __________
10.
11 X 61 = ________
11.
569 X 10 =________
12.
31 X 4 = ________
13.
301 X 9 = _______
14.
24 ÷6 = _______
15.
50 ÷ 5 = _______
Week 18
Divide by 10, 100, 1000
Use base-ten to show the sharing or grouping for division.
Students will see that in a two-digit number, the digit in the
tens place is the number of rods I can have so if I divide by
10, this digit has to be the whole number and the unit place
will be only a part of a rod, therefore creating a decimal.
Ex. 45 ÷ 10 = 4 rod and 5 units left = 4.5
567 ÷ 10 = 56 rods and 7 units left = 56.7
1240 ÷ 10 = 124 rods and 0 units left = 124
The same thing happens when you divide by 100.
Ex. 394 ÷ 100 = 3 flats and 94 units left = 3.94
2865 ÷ 1000 = 28 flats and 65 units left = 28.65
63 ÷ 100 = no flats and 63 units left = 0.63
After all this practice and seeing the pattern, the students should
understand the short cut and why it
works. Moving the decimal to the left the same number of spaces
as there are zeros in the divisor.
Technically and on my paper I say that I move the decimal to the left. In some of
our resources you will find that on the place value chart to show the students, they
say that you move the entire number to the right. Therefore changing the value of
each digit.
Example:
Hundred
3
Tens
Ones
9
4
3
Mental Math Test #18
Name:______________
1. 72 ÷ 9 = ______
2. 78 ÷10 = ________
3. 11 X 33 = _______
4. 70 X 20 = _______
5. 3 X 3 = _______
6. 8900 ÷ 100 = _______
7. 25 X 7 = _______
8. 789 ÷10 = _______
9. 24 X 4 = _______
10.
23 ÷100 = _______
11.
88 ÷11 = _______
12.
8 X 9 = ______
13.
8X8 = _______
14.
334 X 2 = _________
15.
501 X 3 = _______
Tenths
9
Hundredths Thousandths
4
Week 19
Multiply whole numbers by 0.1, 0.01 and 0.001
1. Show the students how these multiplications relate to divisions by 10, 100,
and 1000. Use manipulatives and comparison to other examples of the same
concept.
Example: When you multiply a number by 2, you have 2 of that
number. When you multiply a number by 0.1, you have 0.1 (one
1
tenth) of that number. When you divide by 10, you have
(one
10
tenth) of that number.
2 x 8 = 16
0.1 x 8 = 0.8
8
8 ÷ 10 =
= 0.8
10
2. Use patterns.
Mental Math Test #19
Name:________________
1. 89 X 0.1 = ________
2. 85 X 0.001 = __________
3. 7 X 7 = ___________
4. 3456 X 0.01 = _______
5. 11 X 88 = __________
6. 20 X 60 = _________
7. 602 X 3 = _________
8. 56 X 0.01 = _________
9. 61 X 4 = _________
10.
64 ÷ 8 = _________
11.
54 ÷ 6 = __________
12.
895 ÷10 = __________
13.
3 X 4 = _________
14.
6 X 7 =_________
15.
90 X 20 = ________
Week 20
SCO B9: Estimate products and quotients involving whole
numbers only, whole numbers and decimals, and decimals
only.
Facility with basic facts and mental computation skills are required
for estimation. Estimation should not be considered an exercise
one does only when called upon to do so, but an integral part of
doing any computation, whether it is with a calculator or with
pencil and paper.
Strategies that may be used for estimation include:
1. Rounding:
Multiplication - Change the problem to one that is easier to
work with mentally by substituting “nicer numbers” of similar
magnitude (Multiples of 10).
For example: 213 x 48 = 210 x 50 = 10 500 or
213 x 48 = 200 x 50 = 10 000
Mental Math Test #20
Name:______________
1. 0 X 78956 = _______
2. 1 X 97 = _______
3. 2 X 65 = _______
4. 3 X 3 = _______
5. 4 X 9 = ________
6. 5 X 8 = _______
7. 8 X 9 = ________
8. 9 X 3 = ________
9. 10 X 9989 =_________
10.
4567 ÷ 100 = _________
11.
34 X 0.1 = __________
12.
11 X 74 = __________
13.
25 X 2 = _______
14.
27 X 4 = ________
15.
60 X 50 = ______
Week 21:
Estimation continued…
Division – Change the problem to one that is easier to work
with mentally by substituting “nicer numbers” of similar
magnitude (Multiples of 10).
For example: 789.6 ÷ 89 = think 90 for the divisor and 800
for the dividend. Then use a multiplication with a missing
factor to help with estimation: 90 x ? ≈ 800 The estimation
would be 9.
Mental Math Test #21
Name:________________
1. 30 X 90 = _________
2. 77 X 0.01 = ___________
3. 88 X 0.1 = __________
4. 81 ÷ 9 = __________
5. 3 X 7 = __________
6. 30 X 70 = __________
7. 123 X 3 = __________
8. 98765 ÷ 1000 = __________
9. 20 X 40 = __________
10.
1000 X 67 = __________
11.
70 X 4 = _________
12.
528 X 10 = _________
13.
11 X 44 = _________
14.
11 X 33 = _________
15.
1 X 987 = _________
Week 22:
Front-end strategy:
Multiplication - Perform operations from left to right.
Because these are decimal numbers, the fraction part is not
multiplied but estimated.
For example: 6.1 x 23 Front: 6 x 20 =120 End: 6 x 3 = 18
For the decimal part, since these are low numbers, we add a bit more and round up the
product.
Total estimation is 120 + 18 and a little more = 140
Week 12s test will be on estimation, multiplication facts 0-9, and
front-end strategy for multiplication.
Mental Math Test # 22
Name:______________
1. 25 X 5 = ________
2. 11 X 55 = _________
3. 10 X 94 = __________
4. 7 X 204 = __________
5. 8 X 321 = __________
6. 0 X 65 = _________
7. 8 X 3 = __________
8. 76 ÷100 = ________
9. 3 X 0.01 = ____________
10.
6 X 702 = __________
11.
64 X 2 = __________
12.
54 X 5 = __________
13.
70 X 30 = __________
14.
98 X 1000 = __________
15.
45 X 0.01 = ___________
Week 23:
The Front-end strategy for Division
Division – You need to do front-end estimation to do paper
pencil division problems but before they start, students should have
an idea of the quotient.
Example: 8 424.53 The first estimation is 8 x ? = 400. They need to
know that the quotient will be between 50 and 60 therefore the first
digit in the quotient will be 5 tens.
Mental Math Test #23
Name:______________________
1. 0 X 5 = _______
2. 1 X 23 = ________
3. 2 X 75 = _______
4. 3 X 21 = ________
5. 4 X 14 = _________
6. 5 X 15 = ________
7. 6 X 7 = ________
8. 7 X 81 = _______
9. 8 X 93 = _________
10.
9 X 53 =_______
11.
10 X 88 = ________
12.
11 X 73 = ________
13.
14 ÷ 7 = __________
14.
560 ÷8 = _________
15.
100 X 34 = ________
Week 24:
SCO B10: Divide numbers by 0.1, 0.01, and 0.001 mentally.
N.B. The document reminds us that students usually expect the
division process to result in a quotient that is smaller than the
dividend, and it is important they understand why this is not the
case with decimal numbers and fractions.
1. Thinking Fractions: Students need to realize that 0.10 =
0.01 =
1
,
100
and 0.001 =
1
,
10
1
1000
This should lead to an understanding that:
1
25 ÷ 0.10 = 25 ÷
= 25 x 10 = 250
10
Similarly 14 ÷ 0.01 = 14 ÷
1
100
= 14 x 100 = 1400
The question you should ask to explain the division of fractions
or decimal numbers is: “How many groups of one tenth (0.1
1
or ) are there in the dividend?” There will be 10 for every unit
10
therefore increasing the dividend by a factor of 10(ten times the
number). This explains the larger quotient and why the decimal
will move to the right when you divide by a decimal.
Similarly: 56.9 ÷ 0.01 = (56.9 divided into hundredths). When
we divide by hundredths it is like multiplying by 100 so the
decimal moves 2 places to the right. Therefore 56.9 divided into
hundredths = 5690.
When we divide by 0.001 (thousandths) we move the decimal 3
places to the right. Example: 76.3 ÷ 0.001 = 76300.
Mental Math Test #24
Name:______________
1. 76.3 ÷ 0.001 = _______
2. 35 ÷ 0.01 = _______
3. 7 X 9 = ________
4. 99 X 4 = ________
5. 0 X 5678 = ________
6. 70 X 60 = ________
7. 45 X 4 = _______
8. 25 X 6 = _________
9. 100 ÷ 2 = __________
10.
785 ÷ 0.1 = __________
11.
87 X 0.01 = ____________
12.
332 X 0.1 = ________
13.
8 X 8 = __________
14.
1 X 785 = ___________
15.
122 X 4 = __________
~Approximately 37 weeks in a school year….last 13 weeks will be review of year.
Week 25
SCO A6
Develop and apply divisibility rules for 3,4,6, and 9.
Knowledge of the divisibility rules will provide a valuable tool for
mental arithmetic and general development of operation sense.
The divisibility rules are as follows:
A number is divisible by
 2 if it is even
 3 if the sum of the digits is divisible by 3
 4 if the number formed by the last two digits is divisible by 4




5 if it ends in a 5 or a 0
6 if the number is divisible by 3 and even
9 if the sum of the digits is divisible by 9
10 if it ends in a 0
Mental Math Test #25
Name:___________________
1. 12 divided by 2 = _________
2. 30 divided by 3 = _________
3. 25 divided by 5 = _________
4. 11 X 44 = _________
5. 25 X 40 = _________
6. 1200 X 3 = ________
7. 500 X 20 = ________
8. 31 X 3 = _______
9. 500 divided by 2 = _______
10. 370 divided by 100 = _______
11. 3700 divided by 10 = _______
12. 0.81 divided by 0.9 = _______
13. 7500 divided by 0.1 = _______
14. 0.42 divided by 0.7 = _______
15. 0.56 divided by 0.8 = _______
Week 26
N.B. Divisibility tests for 7 and 8 are not as simple as the tests for
the other numbers from 1 through 10. Just go ahead and do the
division.
Example: Try 360 - The number 360 ends in 0, the sum of its digits
is 9, and the number formed by its last two digits is 60. The
divisibility rules tell you that 2,3,4,5,6,9, and 10 are some of the
factors of 360.
Try 175: The number 175 ends in 5, the sum of its digits is 13
and the number formed by its last two digits is 75. The divisibility
rules tell you that 5 is a factor of 175 and 2,3,4,6,9, and 10 are not.
Try this one: There will be 138 people at a party. Can the
host fill tables of 5? No, 138 is not divisible by 5. Can the host fill
tables of 6? Yes, 138 is divisible by 6.
Week 27
Strategies that may be used for estimation include:
1. Rounding: Change the problem to one that is easier to work
with mentally by substituting ‘nicer’ numbers
(multiples of 10) of similar magnitude;
For example, 213 x 48  210 x 50 = 10 500
Week 28
2. Front-end strategy: Perform operations from left to right:
For example: $2.39 + $4.56 + $2.97 + $2.28 + $5.78 =?
Front 2+4+2+2+5 = $15
End 39 + 56  $1 97  $1 28 + 78  $1
1+1+1 = $3
Total = $15 + $3 = $18.00
Week 29
3. Special number strategy: turn one of the numbers into 1, 10,
100, etc., for easy multiplication or division
For example: 324.4  0.97 = ?
Since 0.97 is almost 1 then the estimate would be 324  1= 324.
Another strategy is to double both the dividend and divisor if
dividing by 5
Week 30
4. Clustering strategy: round a quantity of numbers to the same
number and multiply the quantity by the rounded number
For example:
$389.22 + $420.27 + $396.45 + $403.67 + $395.50, think: all of
these numbers are about $400.00 so 5 x $400.00 = $2000.00
Week 31
5. Compatible Numbers: Look for number combinations that
result in 10, 100, 1000, etc.
For example,467+281+241+325, think: 467 + 241 is close to 700 and 281 + 325 is
close to 600, 700 + 600 = 1300.
Week 32
Use mental math strategies for calculations involving
integers and decimal numbers.
Many of the strategies for estimation can be used in mentally
calculating exact answers.
1. Front-end Strategy: For example, –46 + (-38):
Add the tens and ones separately and combine.
-40 + (-30) = -70 -6 + (- 8) = -14 -70 +(-14) = -84
Week 33
Compatible Numbers:
Analyze the numbers to see if
compatible sums resulting in 10, 100, 1000, etc. are present.
For example,
-28 + 63 + 37 + 33 +(-72) = [-28 + (-72)] + [63 + 37] + 33
= -100 + 100 +33
= 33
Week 34
3. Compatible Factors: Analyze the numbers to see if
compatible products resulting in 10, 100, 1000, etc. are
present.
For example,
-8 x 137 x 125 = (-8 x 125) x 137 = -1000 x 137 = -137 000.
Week 35
4. Working by Parts: Break a number into two parts and find
the missing factor; one (or both) of the parts would be a
multiple of 10, 100, 1000, etc.
For example, 5472  9,
Think: 5472 is 5400 + 72, 5400 = 600 x 9 and 72 = 9 x 8;
so, 600 +8 = 608.
Week 36
5. Double and Halve: Double one factor and halve the other.
(Half as many groups, which are twice as large, result in the
same product.)
For example: 486 x 500 is the same as 243 x 1000 = 243 000.