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How Tall Are You, Really?

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Summary

Students will determine their height in cents (pennies) by developing a measurement standard.

Coin Type(s)

  • Cent
  • Nickel
  • Dime
  • Quarter

Coin Program(s)

  • Generic

Objectives

  • Students will extend their understanding of the process of measurement.
  • Students will estimate, make and use measurements to describe and compare.
  • Students will extend their understanding of the concept of length.
  • Students will develop procedures for determining measures to solve problems.

Major Subject Area Connections

  • Math

Grades

  • Third grade
  • Fourth grade
  • Fifth grade

Class Time

Sessions: One
Session Length: 30-45 minutes
Total Length: 0-45 minutes

Groupings

  • Whole group
  • Individual work

Terms and Concepts

  • Coins
  • Estimation
  • Measurement
  • Money
  • Multiplication

Materials

  • Math Journals for each student
  • For each group of 4 students you will need:
    • A large number of cents
    • Measuring tapes
    • Calculators
  1. Have the students estimate how many cents, stacked on top of each other, it would take to equal their own height.
  2. Have the students place cents in a stack and measure the stack until it reaches an inch in height. Then have the students compare their results as a class and determine an average number so the whole class uses the same standard.
  3. Using the class standard, have the students measure each other's height and then individually calculate that measurement's equivalent in stacked cents. Have the students record this information in their math journals.
  4. On a separate sheet of paper to be turned in, have the students answer the following questions:
    • How many cents did you determine were in a stack of one inch?
    • How many cents would there be in a stack as tall as you?
    • How many dollars does that equal?
    • Explain your answers. Describe and illustrate your strategy.

Enrichments/Extensions

  • Have students repeat this activity finding their height using nickels, dimes or quarters.
  • Have students place the coins side by side.

Use the responses to the questions to assess whether the students have met the lesson objectives.

Discipline: Math
Domain: 4.MD Measurement and Data
Grade(s): Grade 4
Cluster: Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit
Standards:

  • 4.MD.1. Know relative sizes of measurement units within one system of units including km, m, cm, kg, g, lb, oz, l, ml, hr, min and sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two column table.
    • For example, know that 1ft is 12 times as long as 1in. Express the length of a 4ft snake as 48in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...
  • 4.MD.2. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
  • 4.MD.3. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. 

Discipline: Mathematics
Domain: All Problem Solving
Cluster: Instructional programs from kindergarten through grade 12 should enable all students to
Grade(s): Grades K–12
Standards:

  • Build new mathematical knowledge through problem solving
  • Solve problems that arise in mathematics and in other contexts
  • Apply and adapt a variety of appropriate strategies to solve problems
  • Monitor and reflect on the process of mathematical problem solving

Discipline: Mathematics
Domain: 3-5 Number and Operations
Cluster: Compute fluently and make reasonable estimates.
Grade(s): Grades K–12
Standards:

In grades 3–5 all students should

  • develop fluency with basic number combinations for multiplication and division and use these combinations to mentally compute related problems, such as 30 × 50;
  • develop fluency in adding, subtracting, multiplying, and dividing whole numbers;
  • develop and use strategies to estimate the results of whole-number computations and to judge the reasonableness of such results;
  • develop and use strategies to estimate computations involving fractions and decimals in situations relevant to students' experience;
  • use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals; and
  • select appropriate methods and tools for computing with whole numbers from among mental computation, estimation, calculators, and paper and pencil according to the context and nature of the computation and use the selected method or tools.

Discipline: Mathematics
Domain: 3-5 Number and Operations
Cluster: Understand meanings of operations and how they relate to one another.
Grade(s): Grades K–12
Standards:

In grades 3–5 all students should

  • understand various meanings of multiplication and division;
  • understand the effects of multiplying and dividing whole numbers;
  • identify and use relationships between operations, such as division as the inverse of multiplication, to solve problems; and
  • understand and use properties of operations, such as the distributivity of multiplication over addition.

Discipline: Mathematics
Domain: 3-5 Number and Operations
Cluster: Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
Grade(s): Grades K–12
Standards:

In grades 3–5 all students should

  • understand the place-value structure of the base-ten number system and be able to represent and compare whole numbers and decimals;
  • recognize equivalent representations for the same number and generate them by decomposing and composing numbers;
  • develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers;
  • use models, benchmarks, and equivalent forms to judge the size of fractions;
  • recognize and generate equivalent forms of commonly used fractions, decimals, and percents;
  • explore numbers less than 0 by extending the number line and through familiar applications; and
  • describe classes of numbers according to characteristics such as the nature of their factors.

Discipline: Mathematics
Domain: 3-5 Measurement
Cluster: Apply appropriate techniques, tools, and formulas to determine measurements.
Grade(s): Grades K–12
Standards:

In grades 3–5 all students should

  • develop strategies for estimating the perimeters, areas, and volumes of irregular shapes;
  • select and apply appropriate standard units and tools to measure length, area, volume, weight, time, temperature, and the size of angles;
  • select and use benchmarks to estimate measurements;
  • develop, understand, and use formulas to find the area of rectangles and related triangles and parallelograms; and
  • develop strategies to determine the surface areas and volumes of rectangular solids.

Discipline: Mathematics
Domain: 3-5 Measurement
Cluster: Understand measurable attributes of objects and the units, systems, and processes of measurement.
Grade(s): Grades K–12
Standards:

In grades 3–5 all students should

  • understand such attributes as length, area, weight, volume, and size of angle and select the appropriate type of unit for measuring each attribute;
  • understand the need for measuring with standard units and become familiar with standard units in the customary and metric systems;
  • carry out simple unit conversions, such as from centimeters to meters, within a system of measurement;
  • understand that measurements are approximations and how differences in units affect precision; and
  • explore what happens to measurements of a two-dimensional shape such as its perimeter and area when the shape is changed in some way.