nickles


 * How Many Nickels? **
 * Grade Level: **6
 * Task: **How Many Nickels?

The PTA is thinking of holding a Fun Fair with lots of different activities. One activity would be to guess the number of nickels needed to stack from floor to ceiling in our classroom. We need to help them out by giving them the most accurate answer that we can. Don’t forget to share with the PTA exactly how you figured out the answer so they will be confident in giving the prize to the person who has the closest guess during the fair.
 * Standard: **Geometry, Spatial Sense, and Measurement


 * Context: **Students had previously done an activity using a ruler to review the conversion of improper and mixed fractions

application of important concepts and skills involved with measurement and margins <span style="font-family: "Arial","sans-serif"; font-size: 16px;">of error. <span style="font-family: "Arial","sans-serif"; font-size: 16px;">have to make a decision as to whether to measure the thickness of one nickel or a <span style="font-family: "Arial","sans-serif"; font-size: 16px;">stack of nickels.
 * <span style="font-family: "Arial,Bold","sans-serif"; font-size: 16px;">What the task accomplishes… **
 * <span style="font-family: "Arial","sans-serif"; font-size: 16px;">This task has some computation imbedded in the solution, but it also requires the
 * <span style="font-family: "Arial","sans-serif"; font-size: 16px;">The students need to be accurate in measuring the height of the ceiling but they also


 * <span style="font-family: "Arial,Bold","sans-serif"; font-size: 16px;">Time Required: **<span style="font-family: "Arial","sans-serif"; font-size: 16px;">One, 45-minute math period

<span style="font-family: "Arial","sans-serif"; font-size: 16px;">measurement. It could also relate to other fundraising activities.
 * <span style="font-family: "Arial,Bold","sans-serif"; font-size: 16px;">Interdisciplinary Links: **<span style="font-family: "Arial","sans-serif"; font-size: 16px;">This task could link with other tasks involving money and


 * <span style="font-family: "Arial,Bold","sans-serif"; font-size: 16px;">Suggested Materials: **<span style="font-family: "Arial,Bold","sans-serif"; font-size: 16px;">U <span style="font-family: "Arial","sans-serif"; font-size: 16px;">sing lots of coins for each student (or group of students) and meter sticks (that have inches also - so students have a choice and have an opportunity to verify their strategy).

<span style="font-family: "Arial","sans-serif"; font-size: 16px;">nickels, and comparing that to the height of the ceiling as a strategy for an expert or <span style="font-family: "Arial","sans-serif"; font-size: 16px;">practitioner. <span style="font-family: "Arial","sans-serif"; font-size: 16px;">embedded in this problem.
 * <span style="font-family: "Arial,Bold","sans-serif"; font-size: 16px;">Possible Solution… **
 * <span style="font-family: "Arial","sans-serif"; font-size: 16px;">It depends on the height of the ceilings in your classrooms.
 * <span style="font-family: "Arial","sans-serif"; font-size: 16px;">Consider measuring the thickness of one nickel (1/16 <span style="font-family: "Arial","sans-serif"; font-size: 10.66px;">th <span style="font-family: "Arial","sans-serif"; font-size: 16px;">of an inch) or an inch of
 * <span style="font-family: "Arial","sans-serif"; font-size: 16px;">The larger the stack of nickels the student’s use will decrease the margin of error


 * <span style="font-family: "Arial,Bold","sans-serif"; font-size: 16px;">Benchmark Descriptors: **
 * <span style="font-family: "Arial","sans-serif"; font-size: 16px;">The benchmark descriptors and rubric are designed to help analyze student thinking and understanding at each of the four performance levels.
 * <span style="font-family: "Arial","sans-serif"; font-size: 16px;">The descriptors are generalizations of what student work could look like.
 * <span style="font-family: "Arial","sans-serif"; font-size: 16px;">It is not possible to anticipate every answer a student can give, so in scoring student work the teacher must use these generalizations to come to their own conclusionsas to where a student is performing on the assessment.

<span style="font-family: "Arial","sans-serif"; font-size: 16px;">inches and mix the two systems. <span style="font-family: "Arial","sans-serif"; font-size: 16px;">math representation.
 * <span style="font-family: "Arial,Bold","sans-serif"; font-size: 16px;">Novice **
 * <span style="font-family: "Arial","sans-serif"; font-size: 16px;">A novice might measure the ceiling in centimeters and the thickness of the nickel in
 * <span style="font-family: "Arial","sans-serif"; font-size: 16px;">A novice may not be able to measure the ceiling within a reasonable range.
 * <span style="font-family: "Arial","sans-serif"; font-size: 16px;">This student will use little or no accurate math language and is not likely to attempt a

<span style="font-family: "Arial","sans-serif"; font-size: 16px;">ceiling, thereby multiplying their error to the point of not being within an acceptable <span style="font-family: "Arial","sans-serif"; font-size: 16px;">range. <span style="font-family: "Arial","sans-serif"; font-size: 16px;">correctly. <span style="font-family: "Arial","sans-serif"; font-size: 16px;">attempted.
 * <span style="font-family: "Arial,Bold","sans-serif"; font-size: 16px;">Apprentice **
 * <span style="font-family: "Arial","sans-serif"; font-size: 16px;">An apprentice may try to compare the thickness of one nickel to the height of the
 * <span style="font-family: "Arial","sans-serif"; font-size: 16px;">An apprentice might also measure accurately, but not be able to do the mathematics
 * <span style="font-family: "Arial","sans-serif"; font-size: 16px;">The apprentice will use some math language, and a math representation may be

<span style="font-family: "Arial","sans-serif"; font-size: 16px;">use math representations to communicate.
 * <span style="font-family: "Arial,Bold","sans-serif"; font-size: 16px;">Practitioner **
 * <span style="font-family: "Arial","sans-serif"; font-size: 16px;">A practitioner will measure accurately and be able to perform all calculations.
 * <span style="font-family: "Arial","sans-serif"; font-size: 16px;">A practitioner also measures a stack of nickels, thereby limiting their margin of error.
 * <span style="font-family: "Arial","sans-serif"; font-size: 16px;">The practitioner will use accurate and appropriate math language and will probably

<span style="font-family: "Arial","sans-serif"; font-size: 16px;">solving the problem using centimeters and then solving it again in inches. <span style="font-family: "Arial","sans-serif"; font-size: 16px;">math representations.
 * <span style="font-family: "Arial,Bold","sans-serif"; font-size: 16px;">Expert **
 * <span style="font-family: "Arial","sans-serif"; font-size: 16px;">An expert will do all that the practitioner did, but might also verify their solution by
 * <span style="font-family: "Arial","sans-serif"; font-size: 16px;">The expert will use precise math language and will use accurate and appropriate
 * <span style="font-family: "Arial","sans-serif"; font-size: 16px;">The expert may also make mathematically relevant connections or observations.

<span style="font-family: "Arial","sans-serif"; font-size: 16px;">Students will demonstrate an understanding of concepts, properties, and relationships <span style="font-family: "Arial","sans-serif"; font-size: 16px;">of geometry and measurement through experiences with meaningful mathematical <span style="font-family: "Arial","sans-serif"; font-size: 16px;">problems, while focusing on identifying, describing, classifying, visualizing, comparing, <span style="font-family: "Arial","sans-serif"; font-size: 16px;">estimating, and measuring various aspects of shapes and sizes.
 * <span style="font-family: "Arial,Bold","sans-serif"; font-size: 18.66px;">Geometry, Spatial Sense, and Measurement: **

<span style="font-family: "Arial","sans-serif"; font-size: 16px;">dimensional shapes and identify, build and transform shapes. The student will use <span style="font-family: "Arial","sans-serif"; font-size: 16px;">inductive and deductive arguments to solve problems. The student will use metric and <span style="font-family: "Arial","sans-serif"; font-size: 16px;">customary measurement systems and select the appropriate measurement unit for a <span style="font-family: "Arial","sans-serif"; font-size: 16px;">given situation.
 * <span style="font-family: "Arial,Bold","sans-serif"; font-size: 16px;">Benchmark : **<span style="font-family: "Arial","sans-serif"; font-size: 16px;">The student will understand the relationships between 2- and 3-


 * <span style="font-family: "Arial,Bold","sans-serif"; font-size: 16px;">Performance Standards: **

<span style="font-family: "Arial","sans-serif"; font-size: 16px;">Sixth Grade: <span style="font-family: "Arial","sans-serif"; font-size: 16px;">area. <span style="font-family: "Arial","sans-serif"; font-size: 16px;">Seventh Grade: <span style="font-family: "Arial","sans-serif"; font-size: 16px;">selecting appropriate techniques and tools.
 * **<span style="font-family: "Arial,Bold","sans-serif"; font-size: 16px;">Select and apply **<span style="font-family: "Arial","sans-serif"; font-size: 16px;">appropriate formulas to solve problems.
 * **<span style="font-family: "Arial,Bold","sans-serif"; font-size: 16px;">Measure **<span style="font-family: "Arial","sans-serif"; font-size: 16px;">objects using customary and metric units for length, volume, mass, and
 * **<span style="font-family: "Arial,Bold","sans-serif"; font-size: 16px;">Explain **<span style="font-family: "Arial","sans-serif"; font-size: 16px;">both customary and metric units of measurement.
 * **<span style="font-family: "Arial,Bold","sans-serif"; font-size: 16px;">Convert **<span style="font-family: "Arial","sans-serif"; font-size: 16px;">from one unit to another accurately within the same system.
 * **<span style="font-family: "Arial,Bold","sans-serif"; font-size: 16px;">Select and apply **<span style="font-family: "Arial","sans-serif"; font-size: 16px;">appropriate formulas to solve problems.
 * **<span style="font-family: "Arial,Bold","sans-serif"; font-size: 16px;">Use **<span style="font-family: "Arial","sans-serif"; font-size: 16px;">appropriate standard units for estimating measurements.
 * **<span style="font-family: "Arial,Bold","sans-serif"; font-size: 16px;">Find **<span style="font-family: "Arial","sans-serif"; font-size: 16px;">length, area, volume, and angle measures to appropriate levels of precision,

<span style="font-family: "Arial","sans-serif"; font-size: 16px;">Students will demonstrate number sense through experiences with meaningful <span style="font-family: "Arial","sans-serif"; font-size: 16px;">mathematical problems that focus on number meaning, number relationships, place <span style="font-family: "Arial","sans-serif"; font-size: 16px;">value concepts, relative effects of operations, and multiple representations to <span style="font-family: "Arial","sans-serif"; font-size: 16px;">communicate sound mathematical thinking.
 * <span style="font-family: "Arial,Bold","sans-serif"; font-size: 18.66px;">Strand – Number Sense and Operations: **

<span style="font-family: "Arial","sans-serif"; font-size: 16px;">and percents and develop, analyze, and explain a variety of algorithms and methods to <span style="font-family: "Arial","sans-serif"; font-size: 16px;">solve problems.
 * <span style="font-family: "Arial,Bold","sans-serif"; font-size: 16px;">Benchmark: **<span style="font-family: "Arial","sans-serif"; font-size: 16px;">The student will understand problems involving fractions, decimals,

<span style="font-family: "Arial","sans-serif"; font-size: 16px;">Sixth Grade: <span style="font-family: "Arial","sans-serif"; font-size: 16px;">variety of situations, including measurement in U.S. and metric systems. <span style="font-family: "Arial","sans-serif"; font-size: 16px;">denominators. <span style="font-family: "Arial","sans-serif"; font-size: 16px;">reasonableness of the solution.
 * <span style="font-family: "Arial,Bold","sans-serif"; font-size: 16px;">Performance Standards: **
 * **<span style="font-family: "Arial,Bold","sans-serif"; font-size: 16px;">Select **<span style="font-family: "Arial","sans-serif"; font-size: 16px;">an appropriate operation to solve situational story problems.
 * **<span style="font-family: "Arial,Bold","sans-serif"; font-size: 16px;">Select and use **<span style="font-family: "Arial","sans-serif"; font-size: 16px;">the appropriate number form (fraction, decimal, or percent) in a
 * **<span style="font-family: "Arial,Bold","sans-serif"; font-size: 16px;">Develop and test **<span style="font-family: "Arial","sans-serif"; font-size: 16px;">strategies for adding and subtracting fractions with like and unlike
 * **<span style="font-family: "Arial,Bold","sans-serif"; font-size: 16px;">Develop and test **<span style="font-family: "Arial","sans-serif"; font-size: 16px;">strategies for multiplying and dividing fractions.
 * **<span style="font-family: "Arial,Bold","sans-serif"; font-size: 16px;">Develop and test **<span style="font-family: "Arial","sans-serif"; font-size: 16px;">strategies for adding and subtracting decimals.
 * **<span style="font-family: "Arial,Bold","sans-serif"; font-size: 16px;">Develop and test **<span style="font-family: "Arial","sans-serif"; font-size: 16px;">strategies for multiplying and dividing decimals.
 * **<span style="font-family: "Arial,Bold","sans-serif"; font-size: 16px;">Estimate and solve **<span style="font-family: "Arial","sans-serif"; font-size: 16px;">problems involving fractions & decimals, and justify the
 * **<span style="font-family: "Arial,Bold","sans-serif"; font-size: 16px;">Use **<span style="font-family: "Arial","sans-serif"; font-size: 16px;">the appropriate estimation strategy for a variety of situations.
 * **<span style="font-family: "Arial,Bold","sans-serif"; font-size: 16px;">Determine **<span style="font-family: "Arial","sans-serif"; font-size: 16px;">when an exact answer is necessary or when an estimate is appropriate.