Estimate multi-digit products

Round the factors to estimate the product.

Now, before you estimate 13,205 × 880, compare this to the problem we just did. What do you notice is different?

What do you think that will do to our estimate?

Let’s test that prediction. Round and find the estimated product.

Was our prediction correct?

Note: Accept any reasonable estimates of the factors. The most important thinking is how the properties are used to arrive at a product. Ask students to justify their choice of place value for rounding.

S: I used 1,300 × 90, so I multiplied 13 × 9, then multiplied that by 1,000. This gave me 117,000. I used 1,000 × 90 and got 90,000.

S: The factors are greater. 13,205 is about 10 times as large as 1,320, and 880 is exactly 10 times as large as 88.

S: It should increase the product. The product should be about 100 times as large as the first one

NOTE: Accept any reasonable estimate of the factors. The important thinking is the properties and the comparison of the relative sizes of the products.

S: 13,205 → 10,000 and 880 → 900. So, 10,000 × 900 = (9 × 1) × 10,000 × 100 = 9,000,000.

S: Yes. 9 million is 100 times as large as 90,000.

Repeat the sequence for 3,120 × 880 and 31,200 × 880.