1. 6.1.2.2 Judge the reasonableness of the results of rational number estimates and/or computations.

2. Let’s review rounding!

3. Simple Steps to Estimating whole numbers 1. Find whatever place value you are looking to estimate to 2. look at the digit to the right. If the digit to the right is "5 or higher" the place value INCREASES by 1. 4. If the digit to the right IS NOT "5 or higher" the place value STAYS as it is. 5. All the rest of the numbers to the right of the place value become ZEROS.

4. Example 1: Estimate 1,754 to the nearest thousand. 1,754 >>> 1 is in the thousands place. Look to the right of the 1 and notice that there is a 7. 7 is "5 or higher", so the 1 increases by 1 and becomes a 2. All the other numbers to the right of the 2 now become Zeros. Meaning: 1,754 rounds UP to 2,000

5. Example 2: Estimate 32,795 to the nearest ten-thousand 32,795 >>> 3 is in the ten-thousands place. Look to the right of the 3 and notice that there is a 2. 2 is NOT "5 or higher", so the 3 STAYS as it is. All the other numbers to the right of the 3 now become Zeros. Meaning: 32,795 rounds DOWN to 30,000

6. Remember! ~ If the number to the right of the place value you're looking to estimate is "5 or higher", increase the place value number by 1. ~ If the number to the right of the place value you're looking to estimate is NOT "5 or higher", the place value number STAYS as it is.

7. Rounding is one way to estimate products. Now that we have determined that rounding can be used to estimate results we can also justify the reasonableness of rounding products as well.

8. For instance, let's take a look at the cost of a six pack of soda. We know that a six pack of soda cost about $2.99. So, if we round $2.99 to the nearest dollar, it would be $3.00. Saying a six pack of soda costs $3.00 would be reasonable. Saying a six pack of soda costs $10.00 would not be reasonable.

9. Let's take a look at how to round numbers to multiply … Round to the greatest place value to estimate products. Estimate 2 x 258 = ? You need to round 258 to the greatest place value. Step 1 Compare. The 2 in 258 means 2 hundreds. So 258 is between 200 and 300. Step 2 Round to the closer hundred. The halfway point between 200 and 300 is 250.

10. Step 3 Use the rounded number to estimate. 2 x 258 rounds to about 2 x 300 = 600 2 x 258 is about 600. 258 is closer to 300 than 200.

11. Estimate to the nearest ten. 16 20 x 2 x 2 ? 40 Use the rounded number to estimate. 16 rounds to about 20 2 x 16 is about 2 x 20 = 40. 40 is a reasonable answer.

12. Estimate to the nearest hundred. 157 200 x 2 x 2 ? 400 Use the rounded number to estimate. 157 rounds to about 200 2 x 157 is about 2 x 200 = 400. 400 is a reasonable answer.

13. Estimate to the nearest thousand. 6400 6000 x 2 x 2 ? 12,000 Use the rounded number to estimate. 6400 rounds to about 6000 2 x 6400 is about 2 x 6000 = 12,000. 12,000 is a reasonable answer.

14. Use compatible numbers to estimate the quotient 446 Round 44 to the closest product of 6. 6 x 7 = 42 and 6 x 8 = 48 42 is closest to 44, so the answer would be 7.

15. Estimate the quotient: 85 ⌯ 7 Since 7 x 12 is 84, that is the closest product of 7. So the estimate of 85 ⌯ 7 = 12

16. Round to the greatest place value to estimate products. Round to compatible numbers to estimate quotients. Use the rounded number to justify the reasonableness of estimating.

17. Justify Reasonableness Answer the following questions dealing with estimation. Make sure your answers are reasonable.

18. Alyssa wants to fill her swimming pool. It holds no more than 23 gallons of water. If her bucket holds 2 gallons, how many will she need to fill without overflowing the pool? 22

19. If there is complete sunshine for a total of 470 minutes, ‘About’ how many hours of complete sunshine was there? 8

20. Dan is doing yard work for his dad. He is working for about 50 minutes a day. If he works for 3 days, 'about' how many hours will he work altogether? 3

21. Mike has math homework. He has to do 4 rows of problems. There are 9 problems in each row. If he can do 10 problems every 15 minutes, 'about' how long will it take Mike to finish his homework? 1 hour

22. There are 9 groups at the beach. The groups have an average of 18 people each. If the beach is supposed to have 2 lifeguards for every 150 people, how many lifeguards should be on duty? 2

23. Courtney is painting a sunset. She uses five colors, and 2 tubes of each color. If each tube of paint costs $4.50, about how much will she spend on the paint? About $50

24. Now, let’s do some practicing!