This lesson helps students understand the concepts of place value and rounding.
Invitation to Learn
The Mailbox the Idea Magazine for Teachers, The Education Center; August/September
1997. Volume 19, Number 4 (Intermediate)
Background for Teachers
Students should have knowledge of place value of a given digit
up to and including a five-digit numeral and have had a chance to
practice and understand the concept of place value. They should have
understanding of numbers and number sense. Students should be
taught specific vocabulary relating to the lesson before you begin. This
should include: numeral, digit, and place value. The first activities
taught at the 2008 Core Academy on place value will give your
students the background knowledge they will need to know before you
teach the activities listed below.
Intended Learning Outcomes
1. Develop a positive learning attitude toward mathematics
4. Communicate mathematical ideas and arguments coherently to peers,
teachers, and others using the precise language and notation of mathematics.
6. Represent mathematical ideas in a variety of ways.
Invitation to Learn
This activity is called Place Value Match-Up. Have students
draw five blanks in their journal to represent a five-digit number.
You have the Place Value Match-up Digit Cards that include 0-9. You
also have Place Value Cards that include 10,000s, 1,000s, 100s, and
10s. Shuffle the ten digit cards. Draw a card and announce the digit
to the class. Each student writes that digit in one of his five blanks.
After the digit is written it cannot be moved. Lay the card aside, and
continue drawing and announcing four more cards. (Keep these cards
together to use later). After you have drawn five cards, each student
will have written a five digit number. Mix up the five discarded cards.
Draw one place value match up digit card and one place value card.
If a students number matches both the digit card and the place value
card then he earns one point. If a student has a match he/she can draw
a circle around their number. Continue drawing four more pairs of
cards: one each of the discarded digit cards and one of the place value
cards. If all five of a students digits match, he earns a bonus of five
extra points for a total of ten points altogether.
- Each student should receive a Rounding Mountains sheet. Hand
these out after you have taught them how to round using the
- The teacher should have an overhead made of the Rounding
Mountains. Show the overhead to the students.
- The first mountain on the left shows an example of rounding to
the nearest 10. Show students the number 1,523 and have them
say the number out loud. Explain to them that since we are
rounding to the nearest 10 there is an arrow pointed to the two
which is in the 10s place.
- On the line left of the mountain shows the number 1,520 then
point to the numbers starting with 0 and continue all the way to
10 going around the mountain.
- On the line right of the mountain shows the number 1, 530.
- Explain to the students that the numbers written on the
lines are the two different numbers they would choose when
rounding 1,523 to the nearest 10. (the 10 before the number
and the 10 after the number)
- Sing the song The Bear Goes over the Mountain but instead
of saying the bear say the digit to the right on the arrow.
For example, sing: Did the three go over the mountain, did
the three go over the mountain, did the three go over the
mountain? No, we didn't get up the mountain. So we know
that this rounds to the number on the line closest to the three
which is 1,520.
- Repeat this with rounding to the nearest 100 and rounding to
the nearest 1,000.
- When rounding 1,523 to the nearest 1,000 your students may
be confused because the number five is on top of the mountain.
If you use the analogy of you holding a bowling ball and
climbing the mountain. Once you got to the top would your
momentum take you forward over the mountain or back down
the mountain? Help them to understand that it would take you
forward over the mountain, so it would round to 2,000.
- Model using your rounding mountain sheet on the overhead
before you hand out their sheet. I would model this until
your class is ready to begin working on their own rounding
- Once students have practiced and have been assessed in using
the rounding mountain sheet you can then begin introducing
them to rounding with a number line.
- Make an overhead of the Number Lines sheet.
- Ask students to compare the rounding mountains to the
number line. What is the same about the two different number
lines and what is different about them?
- Ask students the following question: Would you use the
number line to round the same way you would use the
mountain number line to round? Teach them that the rounding
mountain has been stretched out to make a straight line which
is now the number line.
- Show the overhead of the Number Lines sheet.
- The first number line on the left shows an example of rounding
to the nearest 10. Show students the number 1,523 and explain
to them that since we are rounding to the nearest 10 there is an
arrow pointed to the two which is in the 10s place.
- The number line begins with 1,520 and ends with 1,530. Show
the number 1, 525 and ask why do you think they have put that
number on the number line? (it is half way)
- Have students show where 1,523 should go on the number line
and put a dot on the line and name the dot 1,523.
- Repeat this with rounding to the nearest 100 and rounding to
the nearest 1,000 on the number line.
- Make sure you have modeled this and your students understand
how to use the number line before you hand out the number
- Give each student the Number Line sheet and have them practice
- Students have learned to round numbers using a rounded
number line and a straight number line. Now introduce them
to rounding without using a number line.
- Put a number on the board or overhead (e.g. 123) and tell
students you are going to round this number to the nearest 10.
- Put an arrow underneath the two which is in the 10s place.
Underline the number three which is the number on the right
side of the two.
- The number three is the controlling number or the Boss. It
decides if we are going to keep the two which is in the 10s
place the same or bump it up to a three.
- Write 120 to the left side of our number and write 130 to the
right side of our number.
- Remind students of the mountain number line and decide if the
controlling number would go over the mountain or would go
down the mountain.
- The controlling number would go down the mountain, so 123
would round to 120.
- Model this many times using different numbers and round to
the nearest 10, 100 or 1,000.
- When students understand this concept then pass out the white
boards and markers.
- Model with your students as they practice rounding on their
own white boards.
- Put students in groups or partners and have them practice
rounding on their white boards.
- For advanced learners you can extend the Place Value Match-up
game by including larger numbers. Students can play in groups
so that you can adapt the game for each level in your classroom.
- For learners with special needs have them work together with
a partner or group to complete their Rounding Mountain and
number line sheet.
- An extension to the rounding activity with white boards is
to make up number cards with three to five digit numbers.
Underneath each number, write round to the nearest 10 or
100 or 1,000. Have students pair up in partners and give each
partner 3-5 different cards. One partner would turn over a card
and then each student would round their number on their white
board. Then share it with their partner to see if they match. If
they match turn over another card. If they don't match then
help each other find the correct answer.
- Partner up your advanced learners and have them time each
other to see how fast they can round their numbers. You can
also have them race each other and the first one that completes
their problem correctly gets a point.
- Advanced learners can round larger numbers to the nearest
10, 100 or 1,000. They can also round larger numbers to the
nearest 10,000, 100,000 etc.
- Have students take home a Rounding Mountain and a Number
Lines sheet and share what they have learned with their parents.
- Students can show their family members how they learned
to round without using a number line. Those students who
are advanced learners can race their parents or siblings when
rounding different numbers to the nearest 10s, 100s, or 1,000s.
- Parents can help students create their own rounding game to
share with the class.
- The teacher should walk around and make sure students are
completing the Rounding Mountain sheet and the Number Lines
- Have students hand in their Rounding Mountain sheet and
Number Line sheet so you can assess their work.
- Another way to assess is by having students work together
and to assess each others Rounding Mountain and Number Lines
- When students begin rounding on their white boards the
teacher should walk around making sure that each student
understands the concept of rounding.
Klein, K., & Jones, R., (2003). How Teachers Phrase Discussion Questions. Retrieved
November 24, 2006, from Studies of Teaching 2003 Research Digest, Wake Forest
University Leah P. McCoy, Editor
Classroom discussion is one of the most important teaching
techniques used to help students learn and understand the information
they are being taught. Discussion allows the students to become
engaged with the material by formulating their own opinions, listening
to other students opinions, and applying specific information to a
Mulrvan, C. (1995). Involvement and participation in cooperative small groups in
mathematics. Elementary School Journal, Volume 95.4 p. 297.
Students do not fully understand math concepts if they cannot
relate it to something in their own experiences. The use of many different techniques help make mathematics a pleasure rather than a
chore. Students are more active learners and are more motivated when
they work in small groups.