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K–12 teaching and learning · from the UNC School of Education

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Learning outcomes

Students will:

  • explore problems, probably initially using guess and check to arrive at a solution.
  • communicate their understanding of the problem, verify and interpret their results in presenting potential solutions to the class.
  • make generalizations will be made in solving similar problems and in creating one of their own.

Teacher planning

Time required for lesson

2 hours

Materials/resources

  • Picture of a rocket
  • Unifix cubes (optional)

Technology resources

Calculators (optional)

Pre-activities

Set the stage by discussing rockets, why we have them and how they work (could be done during a science lesson).

Activities

Stage 1: Exploration

  1. Students are presented with the following problem:
    A rocket used to launch a weather satellite has four stages. Each stage powers the rocket twice as many miles as the previous stage before it shuts down and falls back to the earth. The total altitude reached before the last stage falls away is 90 miles. If the last stage powers the rocket eight times as far as the first stage, how far does each stage power the rocket?
    Students draw a four-stage rocket as a visual and study the problem. (10 minutes)
  2. Students go to collaborative pairs or groups to ‘tell’ the problem in their own words and determine:
    • What are you asked to find?
    • What facts are given?
  3. Students attempt to find a solution. If individual groups are stuck, ask questions that may get them started:
    • Can you draw a picture of the rocket trajectory (path) showing where the stages would separate and fall away?
    • If the first stage lifted the rocket one mile, how far would the other stages lift the rocket?
    • How high would the satellite have been when the last stage separated?
    • Can you use Unifix cubes to simulate the rocket launch?

Stage 2: Invention

  1. Students present possible solutions to the class. The teacher asks questions as to how the method of solving the problem was determined, whether the solution is reasonable, etc. The teacher indicates whether the method was on target (did or could have arrived at a correct solution) or whether it was a good try but was not on target (would not have led to a correct solution). The class should then discuss the various solution methods and results.
  2. The teacher summarizes the methods for solving the problem that were on target, making sure that each student understands at least one way to find the solution.

Stage 3: Expansion

  1. Give students similar problems to solve by adding stages, changing the increase in distance that each stage will travel, etc.
  2. The teacher asks if anyone has found a shortcut, a quick way of solving the problem. If so, help the class to write and understand the equation. Students write a paragraph describing their method of solving the problem.
  3. Have each student create their own rocket launch problem with their solution. Use several of these for a test and the remainder to give students as a practice/homework problem periodically throughout the remainder of the year.

Assessment

  • Monitor to make sure each student has drawn a picture of the rocket.
  • Monitor the discussion of the problem and attempts to find a solution.
  • Ask each group member at least one question following their presentation to determine the individual level of understanding.
  • Correct and analyze the writing assignment.
  • Collect and grade the assignment of similar problems.
  • Use student problems on a test.
  • Use student problems on future assignments to monitor retention.

Supplemental information

Solution:
1st stage - 6 miles
2nd stage - 12 miles
3rd stage - 24 miles
4th stage - 48 miles
Possible equation —— (stage 1 miles) + 2 X (stage 1 miles) + 4 X (stage 1 miles) + 8 X (stage 1 miles) = 90 miles
M + 2M + 4M + 8M = 90
15M = 90
M = 6

Comments

This lesson plan follows the format of the Guilford County Schools Math/Science Project 2005 lesson design. It was adapted from a plan developed and submitted by Mary Porter, a 5th grade teacher at Shadybrook Elementary School in High Point, as a part of Project 2005.

  • Common Core State Standards
    • Mathematics (2010)
      • Grade 4

        • Operations & Algebraic Thinking
          • 4.OAT.3Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown...
          • 4.OAT.5Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence...

North Carolina curriculum alignment

Mathematics (2004)

Grade 5

  • Goal 5: Algebra - The learner will demonstrate an understanding of patterns, relationships, and elementary algebraic representation.
    • Objective 5.01: Describe, extend, and generalize numeric and geometric patterns using tables, graphs, words, and symbols.
    • Objective 5.02: Use algebraic expressions, patterns, and one-step equations and inequalities to solve problems.
    • Objective 5.03: Identify, describe, and analyze situations with constant or varying rates of change.