1 Lesson Estimation

2 Lesson Estimation California Standard: Mathematical Reasoning 2.3 Estimate unknown quantities graphically and solve for them by using logical reasoning and arithmetic and algebraic techniques. What it means for you: You’ll practice working out an approximate answer when you can’t find, or don’t need, an exact one. Key words: estimate compare exact answer

3 Lesson Estimation Estimation means “making a good guess.” You can use it if you don’t need to know an exact answer, or if a question has no exact right answer. “How far is the Sun from the Earth?”“How much wallpaper do I need?”“How many books will fit on the shelf?”

4 You Can Estimate When There’s No Exact Answer Lesson Estimation Sometimes in math there is no exact right answer. You can use the information you do have to make an estimate. “How old is the Earth?”“How long does it take to drive from San Francisco to Eureka?”

5 Example 1 Solution follows… Lesson Estimation Carla has a tall bookshelf and a short bookshelf. When full, the tall bookshelf can hold about 60 books. Estimate from the picture how many books the small bookshelf will hold. Solution There is no exact number of books you can fit on a bookshelf, because not all books are the same size. To estimate the answer, compare the bookshelves. Solution continues…

6 Example 1 Lesson Estimation Carla has a tall bookshelf and a short bookshelf. When full, the tall bookshelf can hold about 60 books. Estimate from the picture how many books the small bookshelf will hold. Solution (continued) So estimate that the small bookshelf will hold about 40 books. All the shelves are the same size, so the small bookshelf will hold around two-thirds the number of books. The tall one has 3 shelves, and the small one only 2.

7 Guided Practice Solution follows… Lesson Estimation 1. This crate is partially filled with 18 apples. Estimate the total number of apples the crate can hold. The crate appears to be about one-quarter full, so could probably hold around 18 × 4 = 72 apples. Estimates of between 70 and 80 apples are reasonable. 2. Mr. Lawrence is loading rolls of carpet of varying thickness into his van. He has put 5 in so far. Estimate how many rolls he will get in the van in total. The van appears to be close to half full, so could probably fit around 5 × 2 = 10 rolls in total. Estimates of between 10 and 12 are reasonable.

8 Guided Practice Solution follows… Lesson Estimation 3. Jermaine collects seashells, and gets two new cases to display some of them. He has filled the smaller one with 19 shells. Estimate how many will fit in the larger case. The larger case appears to be about twice the size of the smaller case, so could probably hold around 19 × 2 = 38 seashells. Rounding this estimate to 40 seashells is reasonable.

9 You Can Estimate If You Don’t Need an Exact Answer Lesson Estimation You don’t always need to use an exact figure. Sometimes an estimate is enough. “How much gas will I need?”“What is the population of California?”

10 Solution continues… Example 2 Solution follows… Lesson Estimation The manager only wants a rough idea of how many visitors there were each day. Estimate the total number of people who visited the park over Friday and Saturday. Number of visitors Day of the week MTWThFSunS 25,000 20,000 15,000 10,000 5,000 0 This graph shows how many people visited a theme park last week. Solution The value for Friday is about halfway between 15,000 and 20,000 on the vertical axis. So a good estimate for Friday would be about 17,500 people. A good estimate for Saturday might be 21,000, because the value for Saturday is just above 20,000.

11 Example 2 Lesson Estimation The manager only wants a rough idea of how many visitors there were each day. Estimate the total number of people who visited the park over Friday and Saturday. Number of visitors Day of the week MTWThFSunS 25,000 20,000 15,000 10,000 5,000 0 This graph shows how many people visited a theme park last week. Solution (continued) This gives an estimate of 21, ,500 = 38,500 for the total number of people visiting the park over Friday and Saturday. Friday = 17,500 people Saturday = 21,000 people

12 4. Use the graph from Example 2 (shown below) to estimate the number of theme park visitors on: (i) Monday (ii) Tuesday (iii) Wednesday (iv) Thursday (v) Sunday. Number of visitors Day of the week MTWThFSunS 25,000 20,000 15,000 10,000 5,000 0 Guided Practice Solution follows… Lesson Estimation About 14,000 About 12,000 About 10,000 About 13,000 About 14,500

13 Guided Practice Solution follows… Lesson Estimation 5. This car is 20 feet long. Estimate the length of the bicycle. The bicycle is around a quarter of the length of the car. So would be about 20 ÷ 4 = 5 feet long. 6. The house in this picture is 30 feet tall. Estimate the height of the tree. The tree is around twice the height of the house, so a reasonable estimate would be 30 × 2 = 60 feet tall.

14 Guided Practice Solution follows… Lesson Estimation 7. Carlos spent a total of 50 minutes doing his English and math homework. The circle graph shows how much of the time he spent on math and how much on English. Estimate how many minutes Carlos spent doing his math homework. Carlos spent a bit more than half of the time on his math homework. 50 ÷ 2 = 25, so a reasonable estimate would be 30 minutes.

15 Guided Practice Solution follows… Lesson Estimation 8. This bar graph shows the number of points scored by four students in a math test. Alex scored 40 points. Estimate the number of points scored by: (i) Lupe (ii) Aisha (iii) Joe Alex’s score shows that each increment represents 10 points. Lupe scored between 20 and 30 points, so estimate 25 points. Aisha scored between 50 and 60 points, so estimate 55 points. Joe scored between 45 and 50 points, so estimate 47 points.

16 Independent Practice Solution follows… Lesson Estimation 1. George has two sunflowers in his garden. The taller flower is 62 inches tall. Estimate the height of the shorter sunflower. About 40 inches 2. Casey is baking cookies. She has put 9 cookies on the cookie sheet as shown. Estimate the total number of cookies Casey can fit on this tray. About 26–30 cookies

17 Independent Practice Solution follows… Lesson Estimation 3. Ms. Marquez is putting up pictures the students in her art class have painted. Her display boards are shown below. She has put up 7 pictures on the smaller board. Estimate how many pictures she can fit on the larger board. About 10–12

18 Independent Practice Solution follows… Lesson Estimation The bar graph shows the number of 6th grade boys and girls who went on a trip to the museum. 4. Estimate how many girls went to the museum. 5. Estimate how many boys went to the museum. About 20 GirlsBoys About 24

19 Independent Practice Solution follows… Lesson Estimation 6. The circle graph shows how many soccer balls, footballs, and basketballs a sports store has in stock. The total number of balls in stock is 60. Estimate how many of each type of ball are in stock. About 15 soccer balls, 20 basketballs, 25 footballs

20 The graph below shows the sales of sunglasses from one store for six months of the year. Use it to answer Exercises 7–9. 7. Estimate the number of pairs of sunglasses sold in April. 8. Estimate the total number of pairs of sunglasses sold in June, July, and August. 9. Estimate the average monthly sales for the period. Independent Practice Solution follows… Lesson Estimation About 90 About 1100 About 280 Number of sales Month of the year AprMayJunJulAugSep

21 Lesson Estimation Some estimates are better than others, but remember there’s often no exact answer when you’re giving an estimate. Make sure you always check your answer to make sure the estimate is reasonable. Round Up