Find the value of each product mentally.

Here are two algorithms that represent finding the value of .

multiply. four hundred thirteen times 21. 9 rows. First row: four hundred thirteen. Second row: multiplication symbol, 21. Horizontal line. Third row: 3, step 1. Fourth row: 10, step 2. Fifth row: four hundred, step 3. Sixth row: 60, step 4. Seventh row: 2 hundred, step 5. Eighth row: plus 8 thousand, step 6. Horizontal line. Ninth row: 8 thousand six hundred seventy three, step 7.

step 1

step 2

step 3

step 4

step 5

step 6

step 7

multiply. four hundred thirteen times 21. 5 rows. First row: four hundred thirteen. Second row: multiplication symbol, 21. Horizontal line. Third row: four hundred thirteen. Fourth row: plus eight thousand two hundred sixty. Horizontal line. eight thousand six hundred seventy three.

1. How are the 2 algorithms alike? How are they different?
2. Explain or show where you see each step from the first algorithm in the second algorithm.
3. How are the final steps in the 2 algorithms alike? How are they different?

Use the standard algorithm to find the value of each expression.

4. Diego finds the value of . Why doesn’t Diego’s answer make sense? Explain your reasoning.

   

   multiply. three hundred one times 24. 5 rows. First row: three hundred one. Second row: multiplication symbol, 24. Horizontal line. Third row: one thousand two hundred four. Fourth row: plus, six hundred two. Horizontal line. Fifth row: one thousand eight hundred six.