¿Ya llegamos? (Velocidad y tiempo distantes) Problemas de palabras incluidos

How will students learn? 

There will be several ways to interact with me in an online class: through synchronous interaction and asynchronous interactions.

Here are some examples of ways I will engage in synchronous interactions:

Live course orientation. 

Synchronous online meeting. 

How will the students learn?

*The students will be able to discuss what makes word problems challenging. Explain that one strategy for solving
word problems effectively are to identify “keywords” which indicate a mathematical operation. 

How will they interact with myself and each other?

I will use the gradual release method of teaching: " I do, we do, you do" 
- First, I demonstrate how to do it (using several examples).  
- Next, the students do some problems along with me.
- Finally, they complete some problems on their own that I will check for accuracy and give more guidance if needed. 

How is class time structured?

The material taught in an online course follows a structure. Just like a traditional course, students start at the beginning of the education objectives and progress through the coursework. They move from the most introductory topics the class covers to the most advanced.

What topics will be covered?

introducing Distance, Rate, Time (D=rt) word problems to Grades 5-8

Standards Addressed:

Algebra and Functions
1.1 Use variables and appropriate operations to write an expression, equation, inequality, or system of equations or inequalities which represent a verbal description (e.g., three less than a number, half as large as area A)

4.2. Solve multi-step problems involving rate, average speed,
distance and time, or direct variation

Measurement and Geometry
1.1 Compare weights, capacities, geometric measures, times and
temperatures within and between measurement systems (e.g., miles per hour and feet per second, cubic inches to cubic centimeters)

Mathematical Reasoning
1.1 Analyze problems by identifying relationships, discriminating relevant from
Irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns
3.1 Evaluate the reasonableness of the solution in the context of the original situation


Students will be able to master the following in this lesson: 

Listed below are some of the questions that you may ask during this lesson and what they need to master. The questions I will ask will depend on the students' responses. My focus in this part of the lesson is to have students try and picture the problem in their head and creating a graphic organizer template to make sense of what is happening in any given Math problem. Students will come up with a variety of answers. Some example questions I could ask include:

1) What do you notice about this word problem? (answers may vary: there are 8 zebras and 5 monkeys, it has animals, it has numbers, etc.)
2) What is different in the problem? (answers may vary: there are different animals, numbers are different, there's more zebras, there are fewer monkeys, etc.)
3) What are we trying to find out? (how many less monkeys there are than zebras)
4) How can we represent this part of the story? (draw, write a number, use manipulatives)
5) What would help us organize our thinking and our work? (answers may vary: draw it out, act it out, write an equation, etc.)
6) What strategies can we use to solve this problem? (we can match up 5 zebras and 5 monkeys then see how many zebras are left, that will tell us how many fewer monkeys we have than zebras.)

Class break down per day of instruction. Note *(instructional minutes may vary depending of skill set of students/groups)

Introduction and Rationale
  Learning Objectives: What should students know and be able to do as a result of this lesson?

    The student will be able to use the distance, rate, time, formula (d=rt) to solve real world problems.
    The student will use a graph to represent and interpret data regarding speed versus time at a constant rate of speed.
    The student will use a graph to represent and interpret data regarding speed versus time at varying rates of speed.

Prior Knowledge: What prior knowledge should students have for this lesson?

    The students should know how to graph points in quadrant one in the coordinate plane.
    The students should know how to measure to the nearest tenth of a centimeter using rulers or meter sticks.
    The students should have some practice with solving one-step equations. (This lesson is meant to help the students apply what they have learned about solving one-step equations to real-world problems.)
    The student should know how to multiply and divide whole numbers and decimals.

Guiding Questions: What are the guiding questions for this lesson?

    How do changes in speed effect distance traveled?
    How does speed affect the time it takes to travel a particular distance?
    How can you use a formula to find the rate of speed given the time and distance traveled by an object?
    How can you use graphs to compare and contrast distance versus time?


 Day #1 (60 minutes)*

Introduction:
Bell-Ringer/Warm-Up: The teacher will display the warm-up questions. The students complete the bell-ringer/warm-up questions as the teacher circulates providing assistance and checking for understanding. After the students complete the questions, the teacher will go over each question with the whole group and have the students check their answers.

Review with the students the math definition of a variable, an expression, multiplication, and division; and introduce the new
terms: rate, distance, and time. This will be a series of lessons planned for a 3-day week.  The first lesson will introduce solving rate- time-distance word problems for motion traveling in opposite directions.

Guided Practice:
I will read the "example" word problem to the students, carefully "modeling" the reading of the problem to determine what the problem is asking. I will read the problem three times; the first time, "to get a feel" for the problem; the second to set up the problem using a chart, and the third, to make sure I covered all the necessary information on the chart. Then, I will label and fill in the "known" information on the chart. After the chart has been completed, I will write and solve the equation. I will check for understanding by doing three more examples and calling on students to help create the chart, label and fill in the "known" information, and writing the equation and solving the problems. Before, I release the students to work independently and/or in small groups, I will check for understanding and review the steps to solving the problems.

Independent Practice:
The students will work independently to complete five additional problems. 

Closure:
The students will be signaled to begin the "share-out" activity to discuss in the chat on what they have learned in the lesson and the different ways they solved their rate, time, and distance problems. Students will be completing an on line game to test what they have learned. 

Homework 
Students will be given worksheets to compete and be prepared to have discussions at the start of the next class. 

Exhibits:
1. Sample Problem
2. Pre-test
3. D=rt
4. Student Observation sheet
5. Independent Practice (classwork)-4 Problems

Day #2 (60 minutes)*

Introduction:
Bell-Ringer/Warm-Up: The teacher will display the warm-up questions. The students complete the bell-ringer/warm-up questions as the teacher circulates providing assistance and checking for understanding. After the students complete the questions, the teacher will go over each question with the whole group and have the students check their answers.

This lesson follows a direct instruction format.  I will begin by asking the essential question. We will come up with equations in the form of y = mx.  Students should be able to generate similar equations.  If students are stuck, I could suggest a sample problem: bottles of OJ are selling of $0.69 each. What equation could be written to find the total, T, of n bottles.  I could be even less abstract, if necessary, and ask the total cost of a specific amount of bottles.  

I will then relate this equation to the distance formula.  Just as our equations multiplied the unit rate times a given amount, the distance formula multiples the unit rate (speed) by a specific amount of time.

Next I will go through 3 examples.  We'll find distance, rate and then time.  For each example I will substitute the given values into the equation and then solve.  Using the equation to solve the problems is an example of MP4. Each problem has a mirror problem labeled "You try!"; these are quick checks for understanding.  I want students to have a chance to immediately apply the concept to a similar problem type.


Guided Practice:

The first 3 problems are identical in structure to the examples.  The fourth problem asks students to rewrite the distance equation to solve for rate, r.  Students may need a hint.  A simple hint could be to give students a multiplication problem and have them find the related division facts.  Students could then apply this pattern to the formula to derive r = d/t.  This problem then leads into the last problem of the section.  Students who are struggling may have difficulty counting the elapsed time.  They may see that the time is 2  hours 30 minutes, but they may not realize they need to think of this as 2.5 hours.  Some may interpret 2 hours 30 minutes as 230 minutes; others may say 2.3 hours.  If this occurs I will ask students to tell me how many minutes there are in an hour.  

Independent Problem Solving

This section begins in a similar fashion to the previous section, although the rigor has increased by quite a bit.  Problem 1 and 2 involve decimal numbers.  Problem 3 requires students to determine a distance before solving.  The distance is a range of -70 to 180 for a total of 250.  I expect students to see this as 110 feet.  They may have ignored the fact that the first value is 70 feet BELOW sea level.  Asking students to draw a vertical number line will help students see the distance covered.    

Problem 5 is a paper-based version of a problem from a sample item in the SBAC assessment.  It has 3 parts and requires students to apply what they have learned in a slightly richer way.  The final problem ties in what we have learned about the graphs of proportional relationships and also how to determine proportional relationships in a table.  Students must then order the speeds from greatest to least.  Finding the unit rates of the objects will be the most efficient method here.

Exit Ticket
Before we begin, I will ask students to summarize how to use the distance formula to solve for rate, time, and distance.  Answers should hit the following points: 1) substitute the known values into the equation; 2) solve the equation.  

Once again, the first 3 questions of the exit ticket are similar to what students have already seen several times during the lesson.  

The final question is a slight variation on the problems students have already seen.  Students must determine a start time given a rate of travel and specific end time.

Therefore, if a student is able to answer the first 3 questions, I know they understood the lesson.  Students who answer all 4 show mastery beyond the basics of the lesson. 


Day #3 (60 minutes)*

Introduction:
Bell-Ringer/Warm-Up: The teacher will display the warm-up questions. The students complete the bell-ringer/warm-up questions as the teacher circulates providing assistance and checking for understanding. After the students complete the questions, the teacher will go over each question with the whole group and have the students check their answers.

Guided Practice:
I will review with the students the warm up questions and prepare them for there assessment.  

Independent Problem Solving
Students will be given a series of four complex questions that will test their knowledge on how to find the distant rate and time of a specific situation.