Making the Steps
Lesson 4 of 6
Objective: Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit.
These Are The Steps
In this lesson, I want students to understand that multi-step problems must be worked out fully in order for them to get a correct answer. I pose the following problem on the board.
Danny and 3 of his friends are going camping for the weekend. The are taking 3 gallons of water along with them. They need to have cups of water a day per person. Will they have enough water? How much, if any, will be left over?
I explain the steps in the problem. I begin by explaining what it is that the question is asking. First off, Danny, with his friends included makes 4. Now, I have to convert gallons to cups. There are 16 cups in a gallon. Since there are 3 gallons, I need to multiply 3 by 16 to get 48. Four people times 8 cups of water per day is 32. They will have enough water to last them throughout the trip. They will also have 16 cups left over which can be converted back to 1 gallon.
I wait to see if students need clarification, then I erase the board and have the students to explain the steps again to make sure that they understand.
This lesson will focus on the following Mathematical Practices:
MP.1. Make sense of problems and persevere in solving them.
MP.2. Reason abstractly and quantitatively.
MP.4. Model with mathematics.
MP.5. Use appropriate tools strategically.
MP.6. Attend to precision.
Walking In Stride
I display the following question on the overhead after placing students in groups of four.
Marie ran for 2 hours on Monday, 1 1/2 hours on Tuesday, and 30 minutes on Wednesday and Thursday. What is the total number of minutes ran on all four days?
I explain to students that each step must be included in order for them to get a correct answer. I transition throughout the room and ask students questions as they are working. What is the first that you will take in answering the question? I will convert all of the hours to minutes. Ok How many minutes are there in an hour? 60. How about 2? 120. Ok. When you get to 1 1/2, what will you do? There are 60 minutes in 1 hour and there are 30 minutes in a half-hour. I am going to add 60 and 30 together to get 90. Ok. What will you do next? I know that she ran 30 minutes on the other two days, so I will add that together to get 60. What's your next step? I will add 120 plus 90 plus 60 to get 270. Great! Now, can you convert the time back for me into hours and minutes.
I go on and allow this to be a bonus activity since the question only asked for the total minutes.
After we have finished working together, I ask students to fill out a Problem-Solving Step Card. I explain that this card can be referred to when solving additional problems.
How Many Steps Did You Take
Material: note taking paper.pdf
Students are asked to create their own multiple step problem to exchange with their classmates to work. Each problem/question must contain at least 3 steps.
Students will work independently to answer questions that contain multiple steps. All questions will involve conversion from feet to inches, ounces to pounds, cups to pints, addition, subtraction, multiplication, and division. I want students to feel comfortable completing such tasks. Not only will they work out the problems, but they will be asked to write an explanation for how the problem was solved.