Lesson: Proportional Relationship Problems: Guess and Check Strategy

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Lesson Objective

SWBAT use guess and check to solve proportional relationship problems

Lesson Plan

Materials Needed: paper, pencil, Example Image, GP worksheet, IND practice worksheet
Vocabulary: relational numbers, proportion, guess, check, equal, addition, subtraction
Do Now (6 min): Teacher writes the following on the board:
Teacher says, “I want you all to take five minutes and think about the two numbers I just wrote on the board. I want you to think about the different numbers that you can add, subtract, multiply or divide in order to get one of these numbers as the answer. For example, I can add 5 and 10 to get 15. Ok, ready….go!”
Opening (2 -3 min): Teacher reviews the student’s answers to the Do Now. Keep in mind that there are many answers; teacher should just check that every answer makes sense and that it does not equal a number other than 15 or 20. Teacher says, “Today, we are going to talk about the relationship between numbers. We are going to use some mathematical models to help us understand the relation between different shapes and values. By the end of the lesson you will be able to guess and check to solve proportional relationship problems.”
Direct Instruction (10 - 12 min): Teacher says, “You heard me say some words that might be unfamiliar just a minute ago, does anyone want to guess what a proportional relationship is? [Answers will vary] A proportional relation is when several different combinations of numbers equal the same thing. In the Do Now, you made sets of proportional relationships to the numbers 15 and 20.”
Teacher writes the following on the board:
Teacher says, “In math, we sometimes use models to talk about proportional relationships. You will more than likely see these models when you are answering questions on the DC-CAS.” Teacher draws an image based on the Example Image 1 and says, “When you look at these models, you can assume that all of the boxes have the same weight and that all of the cylinders have the same weight. We are given two total weights, but we are not told what each model actually weighs on its own. We want to know what each model weights on its own so that we can understand their proportional relationship. To figure this out, we need to do a math strategy called guess and check. I always recommend starting with the least complicated set. In this case, we know that one box and one cylinder equal 6 pounds. We can tell that the box weights more than the cylinder because it is bigger. I am going to guess that the cylinder weights 2 pounds and the box weights 4 pounds. 4+2 is 6, so it is possible that this is the weight for each object.” Teacher writes the following on the board:
Guess #1: box=4 pounds, cylinder=2 pounds
Teacher continues, “Ok, now I have made a guess, so I need to check my guess. You know that these models have a proportional relationship, so the box and the cylinder will always be the same weight no matter which box or cylinder you are looking at. Now lets look at the model that equals 13. There are 2 boxes and 3 cylinders. I have guessed that a box weights 4 pounds and a cylinder weights 2 pounds.” Teacher writes the following on the board:
Check #1: 4+4+2+2+2=14
Teacher continues, “Ok, based on my guess, this side of the model would equal 14, not 13, so that means that my first guess in incorrect. But that is ok, because this means that I get to guess again! This time I am going to look at the side of the model that equals 6 and change my guess so that the box weights 5 pounds and the cylinder weighs 1 pound. Then I will check my answer using the other side of the model.” Teacher writes on the board:
Guess #2: box=5 pounds, cylinder=1 pound
Check#2: 5+5+1+1+1=13
Teacher says, “Now, this time my guess was right because I got the total of 13. So now I know that the box is 5 pounds and the cylinder is 1 pound. To make sure you really understand the concept, I am going to have you break into small groups, solve a similar problem and then answer some questions. Before we break into groups, does anyone have some questions for me?
Guided Practice (10 -12 min): Teacher gives each math group a GP worksheet and circulates the room to answer any questions. When most students are finished, the teacher reviews the answers to the problem by modeling the whole guess and check process on the board, making sure to highlight the importance of understanding the proportional relationship of the objects/models. 
Independent Practice (10 min): The teacher hands out the IND Practice worksheet. 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.

Lesson Resources

IND lesson 9   Classwork
GP lesson 9   Classwork
EX lesson 9   Exemplar


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