Larger Distances

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Objective

SWBAT sequence numbers in the thousands.

Big Idea

Common Core standards expect second graders to be able to work with numbers to 1,000. This lesson introduces larger numbers (even beyond 1,000) to extend student understanding of the patterns in numbers.

Warm Up

15 minutes

I begin today by writing 3 numbers, 871, 258,  469 on the board. I ask students to write the numbers in order from least to greatest in their math journals. 

I ask for a student to come up and write the numbers on the board in order. We read the numbers aloud together to practice reading 3-digit numbers. 

I put 3 more numbers on the board, 29, 902 and 219 on the board and ask students to do the same thing. We repeat the process several more times as I circulate around the room to check on student understanding. I want to make sure that students understand the structure of numbers to 1000 - that they are made up of hundreds, tens and ones. The examples I use become more and more similar, in that the numbers to be compared contain the same digits - such as 409, 904, 914 and 419.

 

Teaching the Lesson

30 minutes

Students have been reading about planets during reading time. They have taken notes on important facts about planets, including size of the planets. We discuss how the world globe we have in the room is only a model of earth. It is way smaller than earth really is. I tell them that we can think of the planets in a similar way. We look at the sizes of the planets in distance around by using the numbers that students researched,  and together we organize them from smallest to biggest. 

Next I hand out paper in different sizes. I ask students why they think that some people are getting small paper and some are getting large paper to draw their planets on? (some planets are bigger than others based on the sizes we just figured out from our research).  I ask students to make a drawing of the planet they have researched. I tell them that we will hang up the planets in order once we are done. We do not use an exact scale here because of the size of the numbers, and that is why I have chosen to hand out different sized paper so we end up with relative sizes for our planets.

Students complete the drawings in partners so we have one of each planet, and a sun.

Hanging the Planets

20 minutes

Next I put the following distances on the board in mixed order. I write the name of the planet and the distance in million kilometers on the board. I ask students what a kilometer is close to that we might be more familiar with? (a mile). So today we are going to talk about measuring in kilometers which are close to, but a bit smaller than a mile. I ask about how far the middle school is from our school (you can pick a land mark in your area that is about a mile away) Yes, it is about a kilometer or a mile away so we would want to think about a million of those distances. and for each one even more than 1 million so we are talking about huge distances. (I ask students if they think Florida is more than a million or less than a million kilometers from Maine because many of the students have visited Florida. (right, it is much less than a million so we are talking about further than a trip to Florida, or California.

Next I discuss how each of these is not just the number, but a million of that number so that the 60 becomes 60,000,000, but that to make our job easier, we will just use the 60 because they are all in the millions. 

I ask students to order the planets from closest to the sun to furthest from the sun by ordering the numbers. 

When students are done, we write the planets in order and distance. I then tell students that we will now make the numbers even more manageable so we can hang up the planets. We will turn 60 into 6, 110 into 11, etc. We make all the numbers into smiley face numbers (ending in zero) and compute the distance in centimeters.

Next I hang the sun from the ceiling at the end of the room and place a small piece of masking tape below it on the floor to mark my starting point. I ask a student to measure 6 cm from the point I am marking so I can hang Mercury up. I remind students that our planets are not to the same scale (1 centimeter = 10 million kilometers ) because then our planets would be so small we wouldn't be able to see them so while they are relative in size to each other, they would be much smaller if we used the same measurements as we are doing for distance from the sun. It is like our maps of the whole earth and the map of the United States. On the world map the US is much smaller than it is on the map just of the US. in the same way our planets and our distances are much smaller than the real thing, but our planets need to be big enough to see and our distances need to be small enough to fit in the room. 

After I have hung the first planet, I ask a student to measure 11 cm from the sun mark on the floor so I can hang the second planet. 

I remind students that they need to be very careful as they measure and attend to the correct measurements so our planets will be the correct distances from the sun (MP6). They must also be careful to measure in centimeters and not inches (MP5). As the planets go beyond the length of the ruler, students will need to choose a meter stick or tape measure to carry out their measurement tasks. I let students choose the appropriate tool for the measurement they are making.(MP5)

I hang the planets from the ceiling as students measure the distance on the floor using a ruler. 

 

Mercury  - 60m km

Venus - 110 m km

Earth - 150 m km

Mars - 225 m km

Jupiter - 778 m km

Saturn - 1425 m km

Uranus - 2900 m km

Neptune - 4500 m km