Download For the next Math Unit, your child will need to know: Sample

Higher Multiplication and Division
Study Guide
For the next Math Unit, your child will need to know:
1. Higher level multiplication. Ask your child what strategy they use. (Multiplication
problems will not be higher than 3 digit x 2 digit. Ex. 342 x 82)
2. Higher level division. Ask your child what strategy they use. (Division problems
will have only a one-digit divisor and a three-digit dividend. Ex. 879 ÷ 9)
3. Word Problems using multiplication and division.
4. Multiplication and Division estimation. See examples below.
**** If would like a sample of Mult and Division strategies, please send a note in to
your teacher, and she will be happy to send home a guide to these strategies!
Sample Problem
The solution to 563 x 34 is closest to –
A. 180
C. 1,800
B. 18,000
D. 180,000
Misha has 4 piggy banks. Each piggy bank
has 391 pennies in it. About how many
pennies does she have?
Explanation/Answer
Since the problem doesn’t specify what
place to round, you round to the front
number. Therefore:
563 x 34 is rounded to
600 x 30
which is equal to 18,000.
Since this problem doesn’t specify what
place to round, you child can round to the
front number. Therefore:
391 x 4 is rounded to
400 x 4
The solution to 573 ÷ 8 is closest to –
A. 7
C. 700
B. 70
D. 7,000
which is equal to 1,600.
In this case, your child can estimate by
using their multiplication skills. They
should think. . .
“8 times what number will get me closest
to 573?”
Since I know that 8 x 7 is 56, then I know
that 8 x 70 is 560. Therefore, B is the
correct answer.
Larger Number Multiplication
Study Guide!
You can use a number of methods to multiply larger numbers.
Three are shown below for different problems.
Vertical (old-fashioned)
11
245
x 73
735
+ 17150
17,885
New Vertical
Move to the seven (in the tens place) and repeat
what you did above.
Multiply the ones, tens, and hundreds but write each product one
under the other. Then add them all together. Here’s an example
for 415 x 5.
These are just a guide so
+
Horizontal
(Same as the Vertical,
just written in a
different way.)
Multiply by the ones.
Carry any tens that you have.
Multiply by the tens and add in anything
that you carried.
Repeat for any other digits in the top number
415
x 23
15
30
1200
100
200
8000
9,545
you can see where the
numbers on the left came
from.
<3x5
< 3 x 10
< 3 x 400
< 20 x 5
< 20 x 10
< 20 x 400
Use place value to break apart the bigger number. Multiply each
part of the bigger number by the other number. Then add all of
the answers together.
Here’s an example with 415 x 23
400 x 3 = 1200
10 x 3 = 30
5 x 3 = 15
400 x 20 = 8000
10 x 20 = 200
5 x 20 = 100
9,545
Add all 6 numbers up.
This uses the same idea as horizontal multiplication, but you use
array boxes. Here’s an example for 415 x 23.
Array boxes
400 + 10 +
5
20
8000
200
100
3
1200
300
15
Then, add up all the numbers in the box to get 9,545.
Division Strategies
(with and without Remainders)
Inverse
Use your multiplication facts to help you divide!
(Think of
Multiplication) Example: 56 ÷ 8 = _____
Think . . . 8 x ____ = 56
Oh! 8 x 7 = 56, Therefore, the answer is 7.
Close
Estimate
Get as close to the answer as possible.
Example: 66 ÷ 3
1) Think of landmark numbers to get you close to 66 (the dividend).
2) I know: 3 x 10= 30 (I can get closer)
3 x 20= 60 (I’m close! Now, I can count by 3s—the
divisor)
3 x 21=63 (almost there)
3 x 22= 66
So, my answer is 22.
Close
Estimate
(with
remainder)
Example: 72 ÷ 5
I know: 5 x 10= 50 (I can get closer)
5 x 20= 100 (too high, I’ll try in the middle)
5 x 15= 75 (too high, but closer!)
5 x 14= 70 (too low, but I can’t add 5 more or I’ll go over
72! So, there will be a remainder of 2.)
So, the answer is 14 with a remainder of 2. Or 14 R2.
Bubble
Estimate
Example: 72 ÷ 5
1) Put the dividend in the big bubble, then your estimate in the
small bubbles. The number of small bubbles is the divisor or 5
in this case. (Since there are ten in five bubbles below, then this
estimate is 50. Therefore, we have 22 left to divide evenly
among the bubbles . . . 72 – 50=22)
2) Now, start divvying out the remaining 22 to each group equally
until you reach 72.
3) If you can’t add equally, like this example, then there will be a
remainder.
72
10
10
2
2
10
10
2
2
2
2
2
2
10
2 (60)
2 (70)
Since we got to 70, we’re only 2 away from 72. But, 2 is not enough to
give to each group (they must all have an equal number). Therefore,
they are leftovers (remainders). Our whole answer will include how
much is in each group: 10 + 2 + 2, which is 14. Don’t forget the
remainder though! So, the answer is 14 R2.
Another child might estimate the same problem differently, but get the
same answer. This child knew 12 x 5= 60, so this would get them
closer to 72.
72
12
12
2
2
12
12
2
2
Answer: 14 in each group and 2 extra. Or 14 R2.
12
2 (70)
Ladder
Method
72 ÷ 5
or 5 72
In this method, the student again estimates how many times the divisor
(in this case 5) can go into 72. They put their estimates on the right
side of the bar. So, this child knew that there were at least 10 sets of
five in 72. Once he recorded that on the right, he subtracted the 10
sets of five (or 50) from the original number.
Estimates
5 72
- 50
22
- 20
2
10
4
+____
14 groups of 5
The 2 above is a remainder
22 was left. So, the student tried to find out how many groups of five
were in 22. He knew four sets of 5 were twenty, so he recorded that
and subtracted. With two left over, the student knows that there is not
a group of 5 in the number 2, so that is a remainder. The student adds
the total groups of five to get his answer. Therefore the answer is 14 R2.