Place Value
How and when does the value of a number change?
Lesson 1: Positional Notation and the Base-10 System
I. Describe what it is you will teach. What is the content?
Positional notation is “[t]he writing side-by-side of the basic digits to tell us how many
of each place value we have” (Essentials of Elementary Mathmatics, p.91). What this
means is that depending where a symbol is in a string of symbols dictates the value of
that number. Each position in our number system is related to the next by a constant
multiplier (10), which is the base of our number system. There are 10 ones in a ten, 10
tens in a hundred, 10 hundreds in a thousand, etc. Students will review place values and
talk about patterns they notice with respect to number of zeroes and the words we use to
name the place value. To practice working with a base-10 system, students will play a
game called Trade Up. If time allows, they will practice comparing numbers to find
which is larger by playing the Digit Game.
II. Describe why the content is important for your students to know.
Understanding these concepts about our number system is important because they help
build strong number sense. The more students know about the basics of our number
system, the more easily they will be able to manipulate, work with, and compare
numbers. Place value, positional notation, and base are incredibly important to our
numeration system. Positional notation, in particular, is necessary to communicate
amounts.
III. Describe what specifically students will know and be able to do after the experience
of this class.
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Students will know that place values never change; they are always in the same
order.
Students will know that where an individual number is in a string of numbers
dictates its value, and this is called positional notation.
Students will know that the constant multiplier in our number system is 10, which
means that as you move left along a string of numbers, the value of that number is
increased 10 times.
Students will be able to describe patterns they see in the change of a value with
respect to the number of zeroes (10, 100, 1000, 10000, etc.) and words (tens,
hundreds, thousands, ten thousands, hundred thousands, etc.)
Students will be able to compare numbers to find which is larger or smaller.
IV. Describe how you and your students will know they understand what it is you want
them to know and be able to do.
I will know students understand if they can contribute to a discussion about place values
and answer questions about the concept. Students will play the game Trade Up, and if
they understand the base-10 system, they will be able to trade ones for tens and tens for
hundreds. If time allows, they will also be playing the Digit Game, which asks students to
compare numbers to find which is larger. If students have an understanding of place
value, they will be able to compare the numbers easily. They will also have a homework
assignment that asking them to compare numbers and name numbers in specific place
values.
V. Describe how you will provide for individual student strengths and weaknesses. How
will you and your lesson consider the needs of each student?
To provide for the ELL students, I will be sure to explain the terminology in this lesson in
the clearest way possible. Positional notation is an important term but it is a little
confusing to understand. Base-10 and constant multiplier are also important terms. All
students will be encouraged to use manipulatives if they need them to help with
understanding the concepts in this lesson. The students on IEPs will have a scribe for the
question in the Math Learning Log. They will also be put into small groups where they
can get peer support. Since most students are already familiar with place value, I don’t
anticipate many problems with this lesson.
VI. Describe the activities that will help your students understand the content of your
class lesson by creating an agenda with time frames for your class. Be prepared to
explain why you think each activity will help students on the path toward understanding.
Time
Teacher activity
Student activity
Materials
10 minutes
Read Math Learning Log
question aloud; scribe for
students who need scribes.
Answering the question:
What does the 6 in 563
stand for? Explain how you
know.
Math
Learning
Logs
Practice decomposing
numbers into their place
values.
Soft math
paper
Review place values up to
1,000,000.
10 minutes
10 minutes
Accompany words with
diagrams and examples of a
number that has digits in
these places.
Talk about positional
notation. Explain how where
the number is in a sequence
dictates that numbers’ value.
10 minutes
Talk about the base-10
system. Ask students how
many ones are in a ten, how
many tens in a hundred, and
so on. Ask students what
they notice about the
number of zeroes and terms.
20 minutes
Circulate.
Answering questions. Ten
ones in a ten, ten tens in a
hundred, ten hundreds in a
thousand, ten thousands in a
ten thousand, etc.
0, 10, 100, 1000, 10000, etc.
Playing Trade Up in small
groups of 3-4 students.
How to play: Each student
takes a turn rolling a die and
takes that number of small
cubes from the base-10
blocks. Students continue
taking turns rolling the die
and taking small cubes.
When they acquire 10 small
cubes, they must trade it in
for a ten, or a long block. As
they acquire more tens, they
will eventually have to trade
it for a flat, or a hundred
block. If a student forgets to
make a trade and another
student points out the
mistake, he or she must
forfeit all of his or her cubes
and start over on his or her
next turn.
VII. List the Massachusetts Learning Standards this lesson addresses.
o 2.N.1. Name and write (in numerals) whole numbers to 1000, identify the place
values of the digits, and order the numbers.
o 2. N. 4. Compare whole numbers using terms and symbols, e.g., less than, equal to,
greater than (<, =, >).
o 2.P.1. Identify, reproduce, describe, extend, and create simple rhythmic, shape, size,
number, color, and letter repeating patterns.
VIII. Reflection:
a. In light of all areas of planning, but especially in terms of your stated purpose and
objectives, in what ways was the activity/sequence successful? How do you
know? In what ways was it not successful? How might the activity be planned
differently another time?
b. What additional questions from the teacher or children need to be addressed?
Name ________________________________ Date ________________
Practicing Place Value
Look at the number 892,436 and answer the questions below.
What number is in the tens place? _______
What number is in the ten thousands place? _______
What number is in the ones place? _______
What number is in the hundred thousands place? _______
What number is in the hundreds place? _______
What number is in the thousands place? _______
Circle the biggest number in each set. Be careful!
1.
6
-
2.
23 -
71
-
3.
81
90
- 141
4.
206 - 602 - 817
-
3 - 1
19
5.
413
- 613
-
513
6.
1,060 - 7,978 - 9,999
7.
80,000 - 100,000 - 10,000
8.
831,210 - 402,107 - 264,105