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Ones, Tens, Hundreds:
A Place-Value Game


Subjects

Mathematics
--Arithmetic

Grade

3-5
6-8

Brief Description

By the process of elimination, students figure out the secret 3-digit number.

Objectives

Students will use their knowledge of place value to ask questions that will help them figure out a secret 3-digit number.

Keywords

3-digit number, place value, Ones, Tens, Hundreds

Materials Needed[shopmaterials]

  • pencil and paper

Lesson Plan

This game will help reinforce students understanding of the Ones, Tens, and Hundreds positions in three-digit numbers.

Before playing, refresh students knowledge of the positions of the Ones, Tens, and Hundreds columns. You might draw a representation of the columns and their positions on the board or a sheet of chart paper:

Hundreds Tens Ones

Then provide a series of numbers and ask random questions such as

  • What number is in the Tens column in the number 526? (2)
  • In which column is the 4 in the number 324? (It is in the Ones column.)
  • In the number 479, in which column in the 4? (It is in the Hundreds column.)
  • Which number is in the Ones column in the number 611? (1)

Next, write a 3-digit number on a card or a small slip of paper. Keep the number secret from your students. Then invite them to ask yes or no questions about the digits and their positions in the number that will help them figure out what the number is. For example, if you write the secret number 467, students might ask questions such as

  • Is the number an even number? (no)
  • Is the number in the Tens column between 2 and 6? (yes)
  • Is the number in the Hundreds column less than 6? (yes)
  • Is the number in the Tens column an odd number? (no)
  • Is the number in the Ones column greater than 5? (yes)
  • Is the number in the Hundreds column greater than 4? (no)

Go around the room and give each student an opportunity to ask a yes or no question that will help them pinpoint the digits that appear in the Ones, Tens, and Hundreds columns of the secret number. After each student asks her/his question, s/he is entitled to guess the secret number based on the information at hand.

Students might keep track of the possibilities by creating a chart that looks something like this one:
 

Hundreds Tens Ones
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9


Students might draw an X through each number as their questions remove it from possibility.

So far we know that

  • The number in the Hundreds column is not greater than 4, but it is less than 6; that means it cant be 5. It must be 1, 2, 3, or 4..
  • The number in the Tens column is an even number between 2 and 6; that means the number in the Tens column must be either 2, 4, or 6.
  • The number in the Ones column is an odd number (based on the answer to the first question above) that is greater than 5; that means the number in the Ones column must be either 7 or 9.

With the knowledge above, the questioning continues

  • Is the number in the Hundreds column an even number? (yes, so we can eliminate 1 and 3 from the possibilities; it must be 2 or 4)
  • Is the number in the Hundreds column less than 3? (no, so we know it must be 4)
  • Is the number in the Tens column less than 3? (no, so we know it must be 4 or 6)
  • Is the number in the Tens column between 5 and 7? (yes, so we know it must be 6)
  • Is the number in the Ones column more than 8? (no, so we know it must 7)

By the process of elimination, we now know the secret three-digit number must be 467.

When the rules of the game and the questioning techniques are clear to your students, you might give a student the opportunity to write down the secret number and respond to classmates questions about the digits that appear in the numbers Ones, Tens, and Hundreds columns.

Assessment

Who was the first student to figure out the secret 3-digit number?

Lesson Plan Source

EducationWorld.com

Submitted By

Gary Hopkins

National Standards

MATHEMATICS: Number and Operations
GRADES Pre-K - 2
NM-NUM.PK-2.1 Understand Numbers, Ways of Representing Numbers, Relationships Among Numbers, and Number Systems
GRADES 3 - 5
NM-NUM.3-5.1 Understand Numbers, Ways of Representing Numbers, Relationships Among Numbers, and Number Systems
GRADES 6 - 8
NM-NUM.6-8.1 Understand Numbers, Ways of Representing Numbers, Relationships Among Numbers, and Number Systems
GRADES 9 - 12
NM-NUM.9-12.1 Understand Numbers, Ways of Representing Numbers, Relationships Among Numbers, and Number Systems

MATHEMATICS: Problem Solving
GRADES Pre-K - 12
NM-PROB.PK-12.1 Build New Mathematical Knowledge Through Problem Solving
NM-PROB.PK-12.2 Solve Problems That Arise in Mathematics and in Other Contexts
NM-PROB.PK-12.3 Apply and Adapt a Variety of Appropriate Strategies to Solve Problems
NM-PROB.PK-12.4 Monitor and Reflect on the Process of Mathematical Problem Solving

MATHEMATICS: Communications
GRADES Pre-K - 12
NM-COMM.PK-12.1 Organize and Consolidate Their Mathematical Thinking Through Communication
NM-COMM.PK-12.2 Communicate Their Mathematical Thinking Coherently and Clearly to Peers, Teachers, and Others
NM-COMM.PK-12.3 Analyze and Evaluate the Mathematical Thinking and Strategies of Others

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    08/21/2010


     
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