Standard Algorithm
What is the standard algorithm for multiplication?
Breaking down numbers into their place values, multiplying each digit of one number by each digit of the other number.
Multiply 12 by 10.
12 x 10 = 120
Round 34 to the nearest ten and multiply by 3.
34 rounded to the nearest 10 is 30. So,
30 x 3 = 90
If a box contains 24 apples and there are 5 boxes, how many apples are there in total?
24 x 5 = 120.
There are 120 apples in total.
What is a pattern you notice when you multiply by 10?
When you multiply any number by 10, you simply add a 0 at the end of the number.
Multiply 23 and 45 using the standard algorithm.
23 x 45 = 1,035
102 x 5 = 510
Estimate the product of 17 and 84. Round each number to the nearest tens place.
17 x 84 rounded to the nearest tens place would be 20 x 80 = 1,600
A car travels 70 miles each hour. How far does it travel in 11 hours?
70 x 11 = 770. In 11 hours the car travels 770 miles.
What happens when you multiply any number by 0?
The answer is 0.
What is the product of 56 and 34?
56 x 34 = 1,904
What is the product of 245 x 31?
245 x 31 = 7,595
If you multiply 45 by 6, what is a reasonable estimate?
Possible answers:
50 x 6 = 300
50 x 5 = 250
If a farmer has 32 rows of corn with 18 plants in each row, how many plants are there?
32 x 18 = 576. There are 576 plants total.
Describe a pattern when multiplying by 5.
How do you check your work when using the standard algorithm?
A couple of ways: find an estimate or you can divide the answer by one of the factors to see if you get the other factor.
Find the product of 714 x 25.
714 x 25 = 17,850
Estimate 181 x 913 rounding each number to the nearest hundreds place.
181 x 913 rounded to the nearest hundreds place is 200 x 900 = 180,000
There are 413 books on each shelf and 34 shelves. How many books are there in total?
413 x 34 = 14,042. There are 14,042 books in total.
Purpose: Indicates that you are multiplying by a multiple of ten
Example: When multiplying 23 by a two-digit number, you would place a zero below the ones digit of the partial product.
Importance: Helps maintain place value.
Explain why the standard algorithm is effective for multiplication.
It is more of a shorthand way of multiplying in parts, while doing some of the addition at the same time as multiplication
Find the product of 134 x 182.
134 x 182 = 24,388
Is 2,601 a reasonable answer for the multiplication problem 321 x 81?
No, 2,601 is not a reasonable answer because when you round 321 to 300 and 81 to 80 and multiply, 300 x 80 = 24,000. Or, when solving 321 x 81 = 26,001.
A bakery makes 4,521 cupcakes each day. How many cupcakes will they make in 14 days?
4,521 x 14 = 63,294. They will make 63,294 cupcakes in 14 days.
How can you tell how many partial products you will need when using the standard algorithm?
The total number of digits in the bottom factor is the total number of partial products you will have. For example 145 x 67 will require two partial products, one for when you multiply 7 x 145 and one for when you multiply 60 x 145.