Materials Needed: DN Worksheet, Example problem on chart paper, white board, dry erase markers, and IND Practice Worksheet. NOTE: teacher will need to draw “maps” for GP and IND practice worksheet.
Vocabulary: map scale, atlas, key
Do Now (2 - 3 min): The teacher passes out the DN worksheet with one question about total cost to review the lesson from the previous day.
Opening (2 -3 min): Teacher opens by reviewing the answers to the DN. The teacher then states the objective, “Yesterday we learned how to solve for the unit cost and then calculate a new total cost. Today, we are going to continue focusing on proportional relationships, only we are going to focus on map scales. By the end of the lesson, you will be able to solve for the total distance given a map scale.”
Direct Instruction/Guided Practice (15 - 20 min): Teacher explains, “Ok, does anyone know what a map scale is? Has anyone looked at an atlas before? A scale on a map represents the distance on the map as it corresponds to the actual distance on the ground. All maps have a scale to let the reader know the actual distance. Let’s look at this example so you can all see a scale. Then we will move into solving proportional relationship problems that in scales on maps.” The teacher shows the example visual and focuses on the 1 inch = 15 miles. The teacher should make a reference to the key on a pictograph if it has already been introduced covered. The teacher should explain that each inch on the map/drawing represents 15 miles on the actual island.
The teacher then continues, “We will need to know how to solve proportional relationship problems that involve scales on maps. So now I want you to watch as I solve a problem that includes a scale from a map. Let’s look at the same map but now read the problem with it.” The teacher reads the problem and then continues, “Ok. I’ve read the problem now I have to ask myself what the question is asking me to do, so I know that I understand what I am supposed to do. Well, they want to know the actual distance between the two points on the map. Ok, so now I have to figure out the relevant information in the problem to help me solve this problem. I know that on the map it 3 inches from Standford to Hillcrest. I see the key telling me that 1inch = 15 miles. I think that is all the relevant information in the problem, so I am going to write it down. Ok, now I have to set up my problem. Setting up proportional relationship problems using a scale on a map isn’t the same as setting up a number sentence. There are actually two ways I can set it up. The first looks like this: In order to solve this problem I need to make an equivalent fraction, which is a fifth grade standard! I need to figure out what I multiple 1 by to get 3 and then I multiple my denominator by the same number and I have my answer = the actual distance.
1 * 3 = 3
15 *3 = X = 45
The other way I could solve this problem, if I am not comfortable setting up the fractions, would be to use repeated addition. I need the same relevant information as before. I would set my problem up this way.
1 inch = 15 miles.
2 inches = 30 miles
3 inches = 45 miles -or- 15+15+15 = 45
The teacher continues, “Ok, so what is the answer to this problem? . Did everyone see as I solved the problem with two different strategies? You can use the fraction model or you can use repeated addition to solve proportional relationship problems that involve a scale on a map. Ok, now we are going to do one together. We all watched as I solved one problem. Now I want to work as a class to solve another before independent practice. First, who can come to the board and show me one way to set up a proportional relationship problem with a scale from a map? [student comes to board to answer question.] The teacher repeats questioning to get other strategy on the board. Then the teacher reads the second problem. The teacher should be sure to tell the students that nothing changes even though the scale is based on 2 inches instead of 1 inch, the problem is still set up the same way.
GP Question: A map has a scale of 2 in: 10 mi. If Baltimore and Washington, DC are 10 in apart on the map then how far apart are the real cities?
Strategy 1: Strategy 2:
2*5= 10 “Do we add 10,10 times? No! We need to look at out our scale. This
___ ____ scale is based on 2 inches, which means we need to count by 2s to
10, or divide 10 by 5 to find out how many times we need to add.
10*5= 50 We need to add it 5 times, because 2 goes into 10 5 times, so our
problem will look like” 10+10+10+10+10 = 50
Independent (10 min): The teacher hands out the IND worksheet, which mimics Guided Practice. Students are asked to complete the worksheet independently and turn it in.
Closing (2-3 min): Teacher calls the attention of the students back toward the front of the class to quickly review the answers to the Independent Practice worksheet/ ask what we learned about.