Counting the Trains

In this three lesson unit plan, Cuisenaire rods are used to build trains of different lengths and patterns are investigated. Students will use tables to create graphs, define recursive functions, and approximate exponential formulas to describe the patterns.

Standards & Objectives

Academic standards
CCSS.Math.Content.4.OA.C.5
Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself....
CCSS.Math.Content.5.OA.B.3
Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting...
GLE 0406.1.5
Use mathematical ideas and processes in different settings to formulate patterns, analyze graphs, set up and solve problems and interpret solutions.
GLE 0506.3.2
Develop and apply the concept of variable.
GLE 0506.3.3
Understand and apply the substitution property.
GLE 0606.1.5
Use mathematical ideas and processes in different settings to formulate patterns, analyze graphs, set up and solve problems and interpret solutions.
GLE 0606.3.5
Use multiple representations including symbolic algebra to model and/or solve contextual problems that involve linear relationships.
SPI 0406.3.2
Make generalizations about geometric and numeric patterns.
SPI 0406.3.3
Represent and analyze patterns using words, function tables, and graphs.
SPI 0506.3.1
Evaluate algebraic expressions involving decimals and fractions using order of operations.
SPI 0506.3.2
Use variables appropriately to represent numbers whose values are not yet known.
SPI 0506.3.3
Find the unknown in single-step equations involving fractions and mixed numbers.
TSS.Math.4.OA.C.5
Generate 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 ...
TSS.Math.5.OA.B.3
Generate two numerical patterns using two given rules.
 
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Learning objectives: 

Students will:

  • Construct and use a two-pan balance.
  • Compare mass of two objects.
  • Construct a horizontal bar graph showing the results of their measurement.
  • Determine position necessary to balance uneven objects.
  • Identify the effect on balance of moving the fulcrum.

Lesson Variations

Blooms taxonomy level: 
Understanding
Extension suggestions: 
  • Develop understanding of the relationship that the product of the length of the mass arm and the mass of one object is equal to the product of the length of the mass arm and the mass of the second object when the scale is balanced.

 

Helpful Hints

Materials:

  • Maintaining the Balance Activity Sheet 
  • Shifting the Balance Activity Sheet 
  • Crayons, tape, 2 small styrofoam cups, and a centimeter ruler for each group
  • Paper clips of like mass
  • A collection of small objects to be weighed

References

Contributors: