The following discussions and activities are designed to deepen students' understanding of place
value and base 10, as well as introduce them to other base values.

Objectives

Upon completion of this lesson, students will:

have a deeper understanding of place value in base 10

understand how to convert from base 10 to other base values.

be able to perform simple addition and subtraction problems in base values other than 10.

Standards Addressed:

Grade 10

Estimation and Computation

The student accurately solves problems (including real-world situations).

Numeration

The student demonstrates conceptual understanding of real numbers.

Grade 3

Numeration

The student demonstrates conceptual understanding of whole numbers up to one thousand.

Grade 4

Numeration

The student demonstrates conceptual understanding of whole numbers to ten thousands.

Grade 5

Numeration

The student demonstrates conceptual understanding of whole numbers to millions.

Grade 9

Estimation and Computation

The student accurately solves problems (including real-world situations).

Numeration

The student demonstrates conceptual understanding of real numbers.

Grade 3

Number Sense

1.0 Students understand the place value of whole numbers

Fifth Grade

Number and Operations in Base Ten

Understand the place value system.

Fourth Grade

Number and Operations in Base Ten

Generalize place value understanding for multi-digit whole numbers.

Use place value understanding and properties of operations to perform multi-digit arithmetic.

Third Grade

Number and Operations in Base Ten

Use place value understanding and properties of operations to perform multi-digit arithmetic.

Grades 3-5

Numbers and Operations

Compute fluently and make reasonable estimates

4th grade

Number and Operations

Standard 4-2: The student will demonstrate through the mathematical processes an understanding of decimal notation as an extension of the place-value system; the relationship between fractions and decimals; the multiplication of whole numbers; and accurate, efficient, and generalizable methods of dividing whole numbers, adding decimals, and subtracting decimals.

5th grade

Numbers and Operations

The student will demonstrate through the mathematical processes an understanding of the place value system; the division of whole numbers; the addition and subtraction of decimals; the relationships among whole numbers, fractions, and decimals; and accurate, efficient, and generalizable methods of adding and subtracting fractions.

3rd Grade

Numbers and Operations

The student will develop number and operation sense needed to represent numbers and number relationships verbally, symbolically, and graphically and to compute fluently and make reasonable estimates in problem solving.

4th Grade

Number and Operation

The student will develop number and operation sense needed to represent numbers and number relationships verbally, symbolically, and graphically and to compute fluently and make reasonable estimates in problem solving.

5th Grade

Number and Operation

The student will develop number and operation sense needed to represent numbers and number relationships verbally, symbolically, and graphically and to compute fluently and make reasonable estimates in problem solving.

Grade 3

Number, Operation, and Quantitative Reasoning

1. The student uses place value to communicate
about increasingly large whole numbers in verbal and written form, including money.

Grade 4

Number, Operation, and Quantitative Reasoning

1. The student uses place value to represent whole
numbers and decimals.

Grade 5

Number, Operation, and Quantitative Reasoning

1. The student uses place value to represent whole
numbers and decimals.

3rd Grade

Number and Number Sense

3.01 The student will read and write six-digit numerals and identify the place value for each digit.

4th Grade

Number and Number Sense

4.1.a The student will identify (orally and in writing) the place value for each digit in a whole number
expressed through millions

5th Grade

Number and Number Sense

5.1a The student will read, write, and identify the place values of decimals through thousandths;

Student Prerequisites

Number Sense: Student must understand:

place value and what the different places represent

Arithmetic: Student must be able to:

Add and subtract multiple digit numbers in base 10

Use a basic algorithm to add and subtract

Teacher Preparation

Access to a browser

Pencil and paper

Base ten blocks

Key Terms

algorithm

Step-by-step procedure by which an operation can be carried out

Lesson Outline

Focus and Review

Remind students what has been learned in previous lessons that will be pertinent to this lesson
and/or have them begin to think about the words and ideas of this lesson:

Ask students to recall what they know about place value and base ten blocks.

Lead a discussion about
place value to review basic terminology and understanding.

Ask students if they're familiar with the term "base ten".

Objectives

Let the students know what it is they will be doing and learning today. Say something like this:

Today, class, we will be talking more about place value and base ten and even learning about
other base values.

We are going to use the computers to change numbers from base 10 to other base values, but
please do not turn your computers on or go to this page until I ask you to. I want to show you
a little about this activity first.

Teacher Input

You may choose to lead the students in a short discussion about
base ten.

Explain to the students how to do the assignment. You should model or demonstrate it for the
students, especially if they are not familiar with how to use our computer applets.

Open your browser to
Number Base Clocks in order to demonstrate this activity to the students.

Guided Practice

Try converting other numbers from base ten to other base values:

Have students convert from base ten to the other base using pencil and paper before checking
their answers on the computer.

Lead a discussion on
converting from base ten to address any misconceptions the students might have.

You may want to give the whole class certain numbers to convert into a specific base and check
answers until they are ready to work on their own or in pairs.

Independent Practice

Allow the students to work in groups of two to complete the
Exploration Questions. Monitor the room for questions and be sure that the students are on the correct web site.

Closure

You may wish to bring the class back together to discuss which base numbers were easiest to
work with and why they think that is. Once the students have been allowed to share what they
discovered, summarize once more the main points of the lesson.

Alternate Outline

This lesson can be rearranged in several ways if there is only one available computer:

Have students complete paper worksheets of problems with fractions on a number line and use
Number Base Clocks to check some examples as a class.

Alternatively, select students who need additional practice to use the game. Teams of one
strong student and one who needs help work well with this activity.

Suggested Follow-Up

This is an excellent lesson for understanding new base values and how to add and subtract in those
base values. An excellent follow-up lesson is
Clock Arithmetic