Grade: Elementary
Subject: Mathematics

#2763. D=rt: Distance, Rate, Time Word Problems

Mathematics, level: Elementary
Posted Tue Dec 10 16:53:45 PST 2002 by Maria Hermila L. Ciriaco (
Solving rate-time-distance word problems
Pine Valley Middle School, San Ramon, USA
Materials Required: Overhead projector or Large Butcher paper, rate-time-distance laminated charts or small (20cmx27cm)
Activity Time: 45 min class - 5-day week algebra lesson
Concepts Taught: Algebra

Maria Hermila L. Ciriaco
Patricia Ann McNeary-Calloway
Corinne Sutherland
Gulshan Pal Kaur ESPY 5125-01, December 10, 2002

Mathematics Introductory Group Lesson Plan

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

Anticipatory Set

Instructional Objective: Students will solve distance, rate, and time
(D=rt) word problems
Language Objective: Students will "share-out" what they learned in this lesson and the steps they took to solving the word problems
Learning Strategies: Metacognitive, cognitive, and affective. Students
observe "thinking-aloud (metacognition)" strategy, define new
vocabulary terms in their math journals (cognitive), and are motivated (affective) to share their new learning in their individual math journals and with their peers in their small cooperative groups
Vocabulary: distance, rate, time, variable, expression, multiplication, and

Materials: Overhead projector and/or Large Butcher Paper, Rate X Time = Distance laminated charts, Colored markers, Calculators, Pens or pencils

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 5-day week or longer. 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 in small cooperative groups of two or four students to
complete five additional problems. After the groups have worked together to solve their problems, the students will be asked to return to their desks and write in their math journal what they have learned in this lessons and the steps they took to solve their rate, time, and distance problems.

The students will be signaled to begin the "share-out" activity to discuss what they have learned in the lesson and the different ways they solved their rate, time, and distance problems.

SDAIE Techniques
The SDAIE techniques include using the overhead projector and/or large butcher
paper when introducing the lesson; dividing the students in small cooperative
groups, using a chart to set up and solve the problems, and "share-out" strategy
to help support the Language Experience Approach (LEA) to learning.

Special Education
Supporting student learning by modeling "thinking-aloud (metacognition);" using
the overhead projector to model problem solving strategies of drawing pictures, tables or charts; repeating instruction (multiple checks for understanding); using small cooperative groups; and the calculator

1. Give the students a brief pre-test on the vocabulary terms: rate, distance, time, variable, expression, multiplication, division and a rate, time and one rate, time and distance problem where two objects are moving toward each other (perhaps the example problem in the introductory lesson).
2. During the introduction, I will monitor the class to check the students who
will require more one-on-one teacher support (these may be the students
who did poorly in the pre-test and continue to struggle with new concept
during the introduction of the lesson).
3. Monitor the students during independent practice and the closure activity.
4. Review the students' math journals.
5. Once the students have a grasp of the concept, schedule a quiz and/or test.

Classroom Management Techniques:
1. Setting Expectations and Behavior: The students will listen quietly during
the guided practice part of the lesson, raising their hands to be called on if
they have any questions. When they are working in groups, they can talk
quietly with other students when they have questions or they can wait for assistance from the teacher.

2. Monitoring: When the timer rings, the students will stop what they are doing, get back in their assigned seats and get ready to "share-out."

3. Rewards/consequences: Students are encouraged to work cooperative in small groups and do their best. The students who chose appropriate behavior are rewarded with tickets they can use at the Friday math store. Students who chose inappropriate or disruptive behavior during the lesson or chose not to participate in the activity, will be required to complete the activity during recess, lunch, or after school.

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

Technology links: