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Getting Better at Guessing

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Summary

Students will work in groups to examine a jar of coins to make both "guesstimations" and more precise estimations.

Coin Type(s)

  • Cent

Coin Program(s)

  • Generic

Objectives

  • Students will practice estimation skills.
  • Students will learn how to make better estimations.
  • Students will work in groups and discuss information about their guesses and estimates.

Major Subject Area Connections

  • Math

Grades

  • Kindergarten
  • First grade
  • Second grade

Class Time

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

Groupings

  • Whole group
  • Small groups

Terms and Concepts

  • Estimation
  • Logical Reasoning
  • Penny

Materials

  • (Plastic peanut butter) jar filled with 75 to 100 pennies
  • Math journals
  • Class chart divided into 2 columns labeled “Our Penny Guesstimates” and “Our Penny Estimates”
  • Sticky notes, a different color for each group

Preparations

  • Fill a jar with pennies, counted.
  • Make a chart with 2 columns labeled "Our Penny Guesstimates" and "Our Penny Estimates"
  1. Display a clear jar filled with pennies in the classroom a few days before the lesson starts.  Let the students make observations about the pennies in the jar but not take the pennies out of the jar.
  2. Divide students in to groups with 3 to 5 members.
  3. Have each group come up with a group guesstimate for the number of pennies in the jar. Each group can have a chance to examine the jar before making their guesstimate.
  4. Have each group write their guesstimate on a sticky note and place it on a classroom chart.
  5. Remove about half of the pennies from the jar. Have the class decide how to determine about half.

  6. Count out the half of the pennies that were removed.

  7. Allow each group to make an estimate based on this new information. Have each group put their estimate on a different colored sticky note and add it to the classroom chart. Keep the group’s guesstimate and estimate next to each other.
  8. Have the students in their groups answer the following questions. The students can write their group answers in their math journal.
    • What is the order of the guesstimates from lowest to highest?
    • What is the order of the estimates from lowest to highest?
    • What is the range for the guesstimates?
    • What is the range for the estimates?
    • Find the differences between the guesstimates and estimates for each group.
  9. Have students present their answers to the class.
  10. Pick a group to count the total amount of pennies in the jar and add the actual number to the chart.
  11. Discuss as a class different strategies for making better estimates.

Enrichments/Extensions

  • Students can make simple word problems using the data on the classroom chart and the information they found in their groups.
  • Students can do research to find out what they could purchase with the exact amount of pennies in the jar.

Assess the groups' learning based on the information in their math journals and on the group presentation they gave when they answered the above questions. Give grades to the groups.

Discipline: Math
Domain: K.CC Counting and Cardinality
Grade(s): Grade K
Cluster: Compare numbers
Standards:

  • K.CC.6. Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, eg, by using matching and counting strategies.
  • K.CC.7. Compare two numbers between 1 and 10 presented as written numerals. 

Discipline: Math
Domain: K.CC Counting and Cardinality
Grade(s): Grade K
Cluster: Know number names and the count sequence
Standards:

  • K.CC.1. Count to 100 by ones and by tens.
  • K.CC.2. Count forward beginning from a given number within the known sequence (instead of having to begin at 1).
  • K.CC.3. Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). 

Discipline: Math
Domain: K.CC Counting and Cardinality
Grade(s): Grade K
Cluster: Count to tell the number of objects
Standards:

  • K.CC.4. Understand the relationship between numbers and quantities; connect counting to cardinality.
    • When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.
    • Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.
    • Understand that each successive number name refers to a quantity that is one larger.
  • K.CC.5. Count to answer "how many?" questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. 

Discipline: Mathematics
Domain: K-2 Number and Operations
Cluster: Compute fluently and make reasonable estimates.
Grade(s): Grades K–2
Standards:

In K through grade 2 all students should

  • develop and use strategies for whole-number computations, with a focus on addition and subtraction;
  • develop fluency with basic number combinations for addition and subtraction; and
  • use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators.

Discipline: Mathematics
Domain: K-2 Number and Operations
Cluster: Understand meanings of operations and how they relate to one another.
Grade(s): Grades K–2
Standards:

In K through grade 2 all students should

  • understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations;
  • understand the effects of adding and subtracting whole numbers; and
  • understand situations that entail multiplication and division, such as equal groupings of objects and sharing equally.

Discipline: Mathematics
Domain: All Reasoning and Proof
Cluster: Instructional programs from kindergarten through grade 12 should enable all students to
Grade(s): Grades K–2
Standards:

  • Recognize reasoning and proof as fundamental aspects of mathematics
  • Make and investigate mathematical conjectures
  • Develop and evaluate mathematical arguments and proofs
  • Select and use various types of reasoning and methods of proof 

Discipline: Mathematics
Domain: K-2 Number and Operations
Cluster: Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
Grade(s): Grades K–2
Standards:

In K through grade 2 all students should

  • count with understanding and recognize "how many" in sets of objects;
  • use multiple models to develop initial understandings of place value and the base-ten number system;
  • develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections;
  • develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers;
  • connect number words and numerals to the quantities they represent, using various physical models and representations; and
  • understand and represent commonly used fractions, such as 1/4, 1/3, and 1/2.

Discipline: Mathematics
Domain: All Communication
Cluster: Instructional programs from kindergarten through grade 12 should enable all students to
Grade(s): Grades K–2
Standards:

  • organize and consolidate their mathematical thinking through communication 
  • communicate their mathematical thinking coherently and clearly to peers, teachers, and others;
  • analyze and evaluate the mathematical thinking and strategies of others; and
  • use the language of mathematics to express mathematical ideas precisely.