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Summer Mathematical Enrichment Class for Girls 2012 Model Solar System Author(s): John Quintanilla Date/Time Lesson to be Taught: July 2, 2012 Technology Lesson: Yes No Course Description: Name: Summer Mathematical Enrichment Class for Girls 2012 Grade Level: Mostly 3rd graders Honors or Regular: Honors Lesson Source: JQ Objectives: SWBAT identify a scale from a map. SWBAT multiply and divide by powers of 10, moving the decimal point as necessary. SWBAT make conversions involving kilometers, meters, centimeters, and millimeters. Texas Essential Knowledge and Skills: §111.16. Mathematics, Grade 4. (b) Knowledge and skills (6) Patterns, relationships, and algebraic thinking. The student uses patterns in multiplication and division. The student is expected to: (B) use patterns to multiply by 10 and 100. (11) Measurement. The student applies measurement concepts. The student is expected to estimate and measure to solve problems involving length (including perimeter) and area. The student uses measurement tools to measure capacity/volume and weight/mass. The student is expected to: (A) estimate and use measurement tools to determine length (including perimeter), area, capacity and weight/mass using standard units SI (metric) and customary (B) perform simple conversions between different units of length, between different units of capacity, and between different units of weight within the customary measurement system Materials List and Advanced Preparations: Maps that show a scale (like 1:2,000,000) in the legend. My experience is that AAA/CAA maps work well for this; not all road maps have a scale pre-printed, unfortunately. It’d be nice to have maps (possibly insets of a big map) over a range from a city to a state to a country, so that scales are quite different. Globe that shows a scale (like 1:43,000,000). The scale and legend of a globe is usually printed somewhere in the south Pacific. Worksheet for multiplying and dividing by powers of 10 Page 1 of 9 Summer Mathematical Enrichment Class for Girls 2012 Worksheet for metric system Worksheet for solar system Calculators (optional) Tape measure that measures in metric Transparent tape Pencil Accommodations for Learners with Special Needs (ELL, Special Ed, 504, GT, learning styles, etc.): None provided below, though this could be added. 5Es Page 2 of 9 Summer Mathematical Enrichment Class for Girls 2012 ENGAGEMENT What the Teacher Will Do Time: 3 Minutes Probing/Eliciting Questions On the table, you will see a whole bunch of maps. Please pick one. [Also use insets of maps if they show a scale.] [Teacher has a map also.] In the corner of my map is something called the legend. Student Responses and Misconceptions [Students select a map.] What place(s) are shown in your map? [Answers vary.] Can you find the legend of your map? [Students find the legend.] Evaluation/Decision Point Assessment All students have maps and have found the legend. Student Outcomes None yet. Page 3 of 9 Summer Mathematical Enrichment Class for Girls 2012 EXPLORATION Time: 15 Minutes What the Teacher Will Do Probing/Eliciting Questions In the legend is something called the scale. For my map, the scale is 1:2,000,000 [or whatever it is… write on the board]. That means that every inch on this map represents 2,000,000 inches in real life. What is the legend of your map? Student Responses and Misconceptions [Answers vary --- all answers are written on the board.] Which number is the smallest? [Students identify.] Who had the map with that number? [Student raises hand.] And what place does that map show? [Student answers, probably a city.] Now, which number is the largest? [Students identify.] Who had the map with that number? [Student raises hand.] And what place does that map show? [Student answers, probably a country.] Why do you think different scales are needed? Countries are a lot bigger than cities! What is this? A globe! And what does the globe represent? The whole world! Very good. And what kind of scale do you think this needs? A big number! How big? [Students guess.] That’s right. For something like a map of the whole country, we need a big scale. But for something smaller like a city, we need a small scale. [Shows globe.] It turns out that the scale of this globe is 1:42,000,000 [or whatever the number is… writes on board] Wow. And why is the scale so big? Because the world is big! Page 4 of 9 Summer Mathematical Enrichment Class for Girls 2012 OK, let’s find that place on the map. Good. Now, has anyone here ever been on vacation to an island (like Hawaii) or another country, maybe in Europe? [Hopefully somebody has. Canada or Mexico probably won’t work for this question --- it needs to be an island or else a “small” country.] Did you have your vacation in a teeny, tiny spot like this? No, it was bigger than that! So why do you think it looks so small on this globe? I guess because Hawaii [or other place] is small compared to the whole world. That’s right. Hawaii [or other place] is a big place, but the whole world is much, much bigger. So on a globe, Hawaii [or other place] looks really small, even though it’s not that small. Today, we’re going to make our own model. It’s going to be a model of the entire solar system. That means the sun and all of the planets. Whoa. What kind of scale do you think we’ll need for the entire solar system? Well, the model that we’re going to make will be about 1:14,000,000,000 [change the number if the handout is changed.] Evaluation/Decision Point Assessment Students have an intuitive understanding of scales. [Students guess.] Whoa. Student Outcomes The students can identify the scale on a map and know that big scales are needed for big places. Page 5 of 9 Summer Mathematical Enrichment Class for Girls 2012 EXPLANATION 1: Multiply/Divide by Powers of 10 What the Teacher Will Do Probing/Eliciting Questions Time: 20 Minutes Student Responses and Misconceptions Before making the solar system, we need to go over the rules for multiplying and dividing by powers of 10. [Go over the first Warm-Up page, one problem at a time. Expect real difficulty when decimal points are introduced for the first time. These can be explained monetarily… if 100 people have $54.34, then the total amount of money that they have is $5,434. Another difficulty for students will be placing the commas correctly for big numbers, like writing 12,000,000 instead of 120,000,00. In other words, there could be a tendency to start from the left when counting groups of three digits instead of the right. Likewise, if $89 is evenly divided among 100 people, then each person gets $0.89.] Evaluation/Decision Point Assessment Students are comfortable with moving the decimal point when multiplying and dividing by a power of 10. Student Outcomes Students are able to correct multiply and divide by powers of 10, including working with decimals. Page 6 of 9 Summer Mathematical Enrichment Class for Girls 2012 EXPLANATION 2: Converting Units in Metric What the Teacher Will Do Probing/Eliciting Questions [Next, go over the second Warm-Up page, one line at a time, on the metric system. Students may be unfamiliar with the metric system. Emphasize that the civilized universe switched to metric a generation ago, but we’re stuck with customary units in the U.S. Also, emphasize that it’s far easier to multiply and divide by a power of 10 than by 12, 36, or 5280.] Evaluation/Decision Point Assessment Students are comfortable with moving the decimal point when converting units of distance within the metric system. Time: 20 Minutes Student Responses and Misconceptions Student Outcomes Students work with kilometers, meters, centimeters, and millimeters. Page 7 of 9 Summer Mathematical Enrichment Class for Girls 2012 ELABORATION What the Teacher Will Do Time: 75 Minutes Probing/ Eliciting Questions Student Responses and Misconceptions [Finally, divide students into groups to perform calculations for the model solar system. Each group only does 2 or 3 of the pages. If time is an issue, here’s the order of importance: Sun, eight planets, Moon Voyager 1, speed of light, Alpha Centauri system Dwarf planets The scale of about 1:14,000,000,000 was chosen so that the eight planets would fit on a straight section of sidewalk about 350 meters long. Obviously, the scale should be modified to fit the space that’s available. Another reasonable choice would be to build the solar system only to Saturn and then ask the class roughly how much further Uranus and Neptune would be. This has the desirable effect of making the planets a bit larger and hence easier to build. After the calculations, the class builds the Sun, planets, and other objects. Rolling up bits of paper will do for most of them. For the inner planets, it might be easiest to toast some bread, shake off some crumbs, and then select crumbs of appropriate size. All objects are taped to pieces of paper. (The Earth and Moon should be taped on the same piece of paper at the appropriate distance apart.) Finally, using the metric tape measure, the class goes outside and places the objects at the appropriate distances from the Sun. If the tape measure is 5 meters long, it’s best to have a team of students measure distances from the Sun in 5-meter increments, rather than having to walk all the way back to the Sun after each planet is placed. Fun things to discuss as the solar system is built: Look at the model Sun after the Earth/Moon system is placed, and then ask the class if the Sun in the sky appears that big. Page 8 of 9 Summer Mathematical Enrichment Class for Girls 2012 Mention it took about three days for astronauts to travel to the Moon. Walk at the speed of light… in the 1:14 billion model, that’s a very slow walk of about 1.3 meters per minute. Give commentary about the number of years it took Voyager 2, travelling over 20,000 kilometers per second and one of the fastest manmade objects ever built, to reach the outer planets (launched 1977, Jupiter 1979, Saturn 1981, Uranus 1985, Neptune 1989.) Look at the model Sun after Neptune is placed… from that distance, the Sun appears to be just a bright star and not a circle. ] EVALUATION What the Teacher Will Do Time: 10 minutes Probing/Eliciting Questions Student Responses and Misconceptions Post-Assessment Page 9 of 9