Partial Products
What is Partial Products?
Breaking apart each factor in a problem into place values and multiplying each place value to get "partial products" then multiplying them to get the entire product.
When multiplying using the standard algorithm do we multiply least to greatest place value? Or greatest to least?
Least too greatest.
Start with ones, then tens, then hundreds, etc.
What is the Distributive Property?
The Distributive property is when you break apart multi-digit numbers apart by their place value to help you multiply numbers.
How does the number of zeros in the product relate to the number of zeros in the factor? Use the example of 6 X 20 to explain your reasoning.
The number of zeros in the factor gets added into the product. For example: In the problem, 6 X 20, the factor 20 has 1 zero. That zero will be added into the product. 6 X 2 = 12, 6 X 20 = 120.
What are the steps to rounding numbers.
1. Underline P.V
2. Look at # next door.
3. 4 or less let underlined P.V rest
4. 4 or more add one more to Underlines P.V
5. Everything to the right turns to zeros ( lesser P.V's). Everything to the left stays the same (Greater P.V).
Solve 182 X 6 using partial products.
1,092
Multiply 12 X 5
60
Solve 14 X 4 using the Distributive Property. Be prepared to "teach" this process to the class.
14 X 4
(10+ 4) X 4
(4 X 10) + (4 X 4)
(40) + (16) = 56
Continue the pattern.
3 X 2 =
3 X 20 =
3 X 200 =
3 X 2 = 6
3X 20 = 60
3 X 200 = 600
Round the number below to the hundreds place
543
500
Solve 542 X 16
8,672
Multiple 23 X 12
276
Solve 26 X 5 using the Distributive Property. Be prepared to "teach" this process to the class.
26 X 5 =
(20 + 6) X 5 =
(20 X 5) + (6 X 5) =
(100) + (30) = 130
Complete the pattern.
8 X 7 =
8 X 7, 000=
8 X 70, 000 =
8 X 7 = 56
8 X 7, 000 = 56,000
8 X 70,000 = 560,000
Round the following number to the ten thousands place
537, 234
540,000
Solve 523 X 234
122,382
Multiple 532 X 261
138, 852
Solve 5 X 15 using the Distributive Property. You will need to draw a model.
15 X 5 =
(10+ 5) X 5 =
(10 X 5) + (5 X 5) =
(50) + (25) = 75
56 X 3,000 =
56 X 3 = 168
56 X 3,000 = 168, 000
What are the three different ways to represent numbers? Please come up with an example to present to the class.
* A new person needs to present each way to represent numbers.
Expanded 10 + 2
Standard 12
Written Twelve
Solve 342 X 231
79,002
Multiply 167 X 225
37,575
Solve 6 X 15 using the Distributive Property. You will need to draw a model.
15 X 6=
(10+ 5) X 6 =
(10 X 6) + (5 X 6) =
(60) + (30) = 90
72 X 5, 000 =
72 X 500,000 =
** Commas must be in the correct place***
72 X 5 = 360
72 X 5,000 = 360, 000
72 X 500,000 = 36, 000,000
Please solve both problems.
971 - 659 =
346 + 275 =
971 - 659 = 312
346 + 275 = 621