Scale Drawings

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Objective

SWBAT use proportions when given scale to determine an unknown length or width in scale and actual drawings.

Big Idea

Students work in pairs and individually to solve scale problems using quadrille paper and real life examples including enlargements and reductions.

Do Now

15 minutes

Students enter silently according to the Daily Entrance Routine. A timer is set with 6 minutes for students to complete the Do Now assignment. It includes one question where students must graph a table of values to determine if the graph describes a proportional relationship. With this example, I hope to review the concepts that a proportional relationship is described as linear graph that goes through the origin. When reviewing this answer, I ask the following question:

Consider the equation we use to describe proportional relationships: y = kx. Why does it make sense that the graph of the line must go through the origin? Consider the coordinate pair at the origin and how it relates to the equation when answering.

We began this discussion in lesson 11 of this unit. The graph of the lines should go through the origin because if we plug in a value of zero for x, then the y value is also zero. No matter what the constant of proportionality (k) is, when you multiply it by zero in the equation y = kx, the y value will be zero.

The second question in the Do Now prompts students only to annotate the reading. I am giving students a longer problem to read for various reasons:

  • Common core requires closer reading of word problems and we need the practice!
  • This is an opportunity to see how rates connect to the real world
  • I want to assess how students read problems in math, whether or not they know how to weed out the unnecessary information and focus on the necessary information.

As I walk around the room during the independent portion of the Do Now, I am looking for students who underline everything. These students will need more guidance finding only the necessary information. I’m also looking for students who are not annotating. These students will be completing this task at lunch, with a fair warning. If students need quick guidance about what to annotate, I state, “underline or highlight the important fact that will help us answer the main question.”

I find that my struggling readers often do not know what the word “determine” means within math questions. Identifying a singular verb such as “determine” as the root of the cause for misunderstanding many questions reminds me to check in with my struggling readers anytime that questions are using verbs assumed to be understood by most. In this category I would also include the following verbs often used in lessons and questioning:

  • Compare
  • Distinguish
  • Prove
  • Interpret
  • Apply
  • Analyze
  • Synthesize

For most of these words, simplifying the context and then using the word in question is enough to allow students to identify what the question requires them to do. For example, when reviewing this particular question about mileage, it is a good idea to have an expert summarizer tell us what the problem is most about, and a couple of other students to write the necessary facts on the board. Then I can restate the question in simpler terms:

We need to determine if we will make it to the gas station OR if we will run out of gas and NOT make it to the gas station. So we need to write our answer one of two ways, either, “yes, they’ll make it to the gas station because….” Or “no, they won’t make it to the gas station because….” After the word because… we will need to prove our yes/no answer with the calculations and facts we took from the problem.

Class Notes

15 minutes

Next I distribute class notes to students. These are not Cornell Notes style. While that is my preferred way of taking notes for students, I also like to expose them to distinct ways to take notes so that they may choose the best strategy in high school.

I use the powerpoint to review the definition at the top of the paper. Each time, before showing what goes in the blank, I ask one student to try and fill in the blanks, awarding extra points on their paychecks if they can quickly locate a definition in their notes. This vocabulary section should take no longer than 5 minutes.

The next vocabulary section should also take no longer than 5 minutes. In it, I will be using disproportionate enlargements and reductions of pictures to prove why pictures have a scale and to illustrate the distortions that results when a picture is not kept to scale. We also define the words enlargement and reduction.

After reviewing this vocabulary I turn off the ppt and work to get students started on the back of the class notes on the SmartBoard. They will have 5 minutes to complete this section. I also let them know that if they do a good job completing the back of the class notes paper with a partner I have a “funny” picture to show them in the power point. This is a picture of myself when I was around their age and it is meant to be made fun of. This picture is included in the last three slides of the ppt and should be replaced with an embarrassing picture of whatever teacher is using the ppt. Let hilarity ensue. 

Task

15 minutes

After letting hilarity ensue, I distribute the class work paper. A timer is set up displaying 10 minutes of silent work time. During this time I will be selecting students to solve on the board so that we can have work available for struggling students to refer to. The first problem’s graph and table should be displayed on quadrille graph paper or the smart board. All other answers may be shown on the black board. After 15 minutes, whether students are finished or not, time must be stopped. The last 10 minutes of class should be prioritized and given to student presentations of the work that was put up on the board.

Closing

10 minutes

All students must stop working, get a pen of a different color out, and check the answers that have been provided on the board. All students must show engagement in the discussion and presentation of answers. I expect that not all students, or very few, will complete the class work during the previous section of class. Anything not completed during class has been planned to be given for homework.

Prioritizing MP3 in this section, as well as other lessons, is important because it drives student understanding of complex concepts. Students learn best from each other and I am freed up to walk around the room to provide extra support to those who need it as well as maintaining high expectations for quality discussion.