UNIT PREPARATION

Display the Math Practices page where all students can see it.

Prepare the Digit Cards 0–9 or collect playing cards for Lessons 3 and 4.

Collect paper towels, eyedroppers, and small containers for water for Lesson 8.

Identify a large grassy area or choose one of the alternatives described in Lesson 9.

Students will need the following tools readily available for the Daily Practice and Problems items in this unit:

LESSON SESSIONS DESCRIPTION SUPPLIES

LESSON 1

Estimate Quotients

 2–3 Students use their knowledge of division facts to mentally solve division problems with multiples of ten. They model division situations as multiplication problems and vice versa. Students then use the connection between division and multiplication to estimate answers to division problems with one- and two-digit divisors.
  • calculators

LESSON 2

Modeling Division

 2–3 Students develop conceptual models and flexible strategies for division by one- and two-digit divisors. They explore how to solve division problems using a column model, a rectangle model, and mental math strategies. These methods build on estimation strategies developed in the previous lesson. They also build a foundational understanding for the partial quotient method presented in Lesson 3.
  • connecting cubes or other counters

LESSON 3

Paper-and-Pencil Division

 2–3 A paper-and-pencil method of division called the partial quotients method is reviewed. Students continue to estimate quotients and interpret remainders.
  • scissors
  • envelopes
  • calculators

LESSON 4

Workshop: Division Strategies

 1–2 Students practice estimating quotients as they play the game Quotient Quest. They use strategies to practice dividing multidigit numbers by one- and two-digit numbers and use models to solidify their understanding.
  • scissors
  • calculators

LESSON 5

Variables and Values

 1 The story “George Washington Carver: Man of Measure” is used as the context for this lesson. Students deepen their understanding of the use of variables and the standard units of measurement in mathematics and scientific investigation.  

LESSON 6

How Close Is Close Enough

 1–2 Students estimate the area of irregular shapes by counting square centimeters. The class decides which estimates are “close enough” by finding the median estimate and deciding which estimates are within a reasonable range of the median. The notion of “closeness” is related to the magnitude of the area. Students apply these skills as they solve problems.  

LESSON 7

Mean or Median

 2–3 Students review the mean as a different kind of average. Connecting cubes are used to model the mean as students even out towers that represent the value of data. The mean and median are compared. Students review the order of operations and parentheses are discussed.
  • centimeter connecting cubes or square-inch tiles
  • calculators

LESSON 8

Spreading Out

 4–5 Students investigate the absorbency of paper towels by placing drops of water on them to explore the relationship between the area of the spots relative to the number of drops of water. Students write a ratio and use the relationship to make predictions and solve problems, communicating their problem solving strategies orally and in writing.
  • paper towels
  • eyedroppers
  • scissors
  • rulers
  • small containers for water
  • books
  • calculators

LESSON 9

Grass Act

 2 Students solve an open-response problem that asks them to estimate the number of blades of grass in a specified area. Students use sampling in order to make their estimates. First students develop a plan for solving the problem. Then students collect data and use the data to solve the problem and write about their solutions.
  • calculators
  • index cards
  • centimeter/inch rulers
  • scissors
  • metersticks/yardsticks

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Suggested Titles for Students

  • Adair, Gene. George Washington Carver: Botanist. Chelsea House Publishers, New York, 1989.
  • Carter, Andy, and Carol Saller. George Washington Carver. Carolrhoda Books, Inc., Minneapolis, MN, 2001.
  • Mitchel, Barbara. A Pocketful of Goobers. Carolrhoda Books, Inc., Minneapolis, MN, 1989.
  • Moore, Eva. The Story of George Washington Carver. Scholastic, New York, 1995.

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Resources

  • Holt, Rackham. George Washington Carver: An American Biography. Doubleday, New York, 1961.
  • Kremer, Gary R. George Washington Carver: In His Own Words. University of Missouri Press, Columbia, MO, 1987.
  • McMurry, Linda L. George Washington Carver: Scientist and Symbol. Oxford University Press, New York, 1981.
  • Nugent, Christina. “How Many Blades of Grass Are in a Football Field?” Teaching Children Mathematics, (12) 6, pp. 282–288, 2006.