Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 35468
Place Value - 3 Digit Numbers
Students will decompose numbers by place value and represent them using concrete and pictorial models.
Subject(s): Mathematics
Grade Level(s): 2
Intended Audience: Educators
Suggested Technology: Document Camera,
Computer for Presenter, Internet Connection, LCD
Projector
Instructional Time: 1 Hour(s)
Freely Available: Yes
Keywords: place value, tens, ones, hundreds, base-ten
Resource Collection: CPALMS Lesson Plan Development Initiative
LESSON CONTENT
Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
By the end of this lesson, the students will be able to use concrete and pictorial models to represent a 3-digit number in multiple ways.
The students will be able to explain their representations by relating to the structure of our place value system.
Prior Knowledge: What prior knowledge should students have for this lesson?
Prior to this lesson, students should be able to identify tens and ones. Students should also be able to count and compare hundreds, tens, and ones blocks.
Students should be able to compose and decompose one and two-digit numbers in multiple ways.
Guiding Questions: What are the guiding questions for this lesson?
How can you show/represent a 3-digit number without writing digits? (concrete models, pictures)
What is the value of this number? How do you know? (The value of a number is decided by the place or locations of the digits.)
Can you use the place value blocks to show me another way to represent this number? (multiple possible answers)
Do these two representations show the same amount (or have the same value)? How do you know? ( The students should acknowledge the structure of our place
value system, such as ten tens is 100, ten ones is a ten, 20 tens is the same as 200, etc.)
What happens if I break apart (decompose) this hundred into tens? (1 hundred can be decomposed into 10 tens)
What does it mean to bundle ten ones or ten tens? (When you bundle, you know you have a new unit, a group of ten. Now, you do not have to count each piece
individually but can count the bundle as ten of a given place value.)
What pattern do you see in our numbers? Why does this exist? (Multiple possible answers, an example is when I reduce the hundreds place by 1, I have to show
ten more tens because 1 hundred is the same as ten tens. The pattern exist because of the structure of our place value system.)
What is the same about all these strategies? or What does all these tell us about our place value system? (Multiple possible answers, but the teacher should
emphasize the important role of 10 in changing these place value representations.
Teaching Phase: How will the teacher present the concept or skill to students?
The teacher will give the Formative Assessment and note student performance.
The teacher will introduce the lesson of demonstrating place value to the hundreds using concrete and pictorial models through the following interactive group
page 1 of 4 activity with his or her students.
Begin by passing out one note card to each student.
Tell your students to select a digit from 0-9 and write that number on their note card.
Next, select 3 random students to stand in front of the class with his or her number note card. (The students will stand shoulder to shoulder). Think aloud and
question the students as you teach the lesson. Start by talking about the 3-digit number the students you have selected make. ie. 127 - One hundred twenty seven.
There are 3 digits, what does each digit represent? Allow the students to respond but be sure to ask the question, "How do know?" or "Why do you think that?" after
each student's response.
If needed, review the value of the place value blocks with the students. Show each block and say what it represents. This is a one-block/unit representing 1, this is
a ten-rod representing ten ones as a bundle, this is a hundred-block representing one hundred ones or a bundle of ten ten-rods to make one hundred.
Ask students to volunteer to model the number the students have made. ie 127
Show the place value chart on the board or document camera and ask students to represent the number of the chart. Attached is an example of a place value
chart. 3 Digit Hundreds Place Value Chart
Ask the students
1. What is the largest number we can make with these 3 digits? Allow think time and partner discussion (721) How do you know? (We put the largest digit in the
highest place value spot (hundreds place). The next largest digit in the next highest place value spot (tens place) and the smallest digit in the smallest place
value spot (ones).) As needed, model this with the place value blocks.
2. What is the smallest number we can make with these 3 digits? Allow think time and partner discussion (127) How do you know? ( We put the smallest digit in
the highest place value spot (hundreds place). The next largest digit in the next highest place value spot (tens place) and the largest digit in the smallest place
value spot (ones).) As needed, model this with the place value blocks.
If needed, repeat this process with another set of 3 digits. Then ask,; what is the same about our strategy of finding the largest and smallest value (number)? (We
had to think about the order of the digits or what place the digit was sitting.)
At this point, the students should sit at their desks with a bank of place value blocks. Take the last number you built (be sure it is one with a small number of
hundreds) and ask the students to see if they can recreate this quantity using only tens and ones. Allow individual think time and then allow partners to discuss the
possibilities. For example, if the last number you discussed was 127, the students could create this value by using 12 ten rods and 7 ones, 11 tens and 17 ones, 10
tens and 27 ones or 9 tens and 37 ones, etc.
Ask a student who has the correct answer to show their answer and explain their reasoning. Ask several students who have different correct answers to show their
work and explain their thinking.
Use the Guiding Questions to probe and clarify student thinking.
You can do another whole class model if students need to see another example.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
(You may do the practice with each student having their own board and blocks or you may do groups of 3. The teacher will circulate, check the student responses and
clarify student thinking by asking the Guided Questions.)
The teacher will group his or her students in sets of 3. Each student will move to the group bringing along his or her number card.
Each group will need a set of base-ten blocks, a place-value chart and a dry/erase board or a pencil and paper.
Tell the group to create the largest 3-digit number using their number cards.
They will represent the place value of this number in 3 ways:
Model using base-ten blocks
Writing on a place-value chart
Drawing a picture model using the base-ten system symbols.
After you have checked a group's response, ask the students to think of other ways they can represent this number by decomposing the hundreds or the tens.
For extra practice, students can shuffle the number cards to create a new number and repeat the activity. Students in the group can self-monitor each other for
correct responses or one student in each group will raise their hand when a new number has been represented for the teacher to come over and check for
accuracy.
At some point, in this practice, switch the task by asking the students to build the smallest number with their 3 digits.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
The teacher can provide extra practice in math stations using base-ten blocks, a place value chart picture models to represent numbers.
Most students will need more practice to fully understand and fluently perform these tasks.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Bring the students back together and ask for volunteers to share some of their work. Ask the class to check for accuracy and ask the Guiding Questions to promote a
rich discussion about this standard.
To determine student proficiency of the concept, display the number 325 to the class. Using a given sheet of paper, students will create a place value chart of
hundreds/tens/ones placing the digits of the number given in the correct place value. They will then draw a picture model using the base-ten system symbols. Finally,
the students will draw 3 other ways to represent 325 by decomposing the hundred and/or the tens. The teacher will use this to determine which student(s) need
extended learning to master the concept.
A written summative assessment is attached in the Summative Assessment phase of this lesson.
Summative Assessment
The teacher will have the students represent a given 3-digit number using base-ten blocks, a place value chart and a pictorial base-ten model. This activity will be an
exit ticket completed prior to finishing the lesson. The students will use these tools to show 3 different place value representations of this number. Using this, the
teacher will be able to determine if the student is proficient independently with the concept.
For a paper and pencil summative, please see the attached document.
3 digit Numbers Summative
3 digit Numbers Summative Answer Key
page 2 of 4 Formative Assessment
You may want to give this Formative Assessment a day prior to the lesson. Each student should have a bank of place value blocks (ones, tens, hundreds) as well as a
place to record numbers (whiteboard/marker or paper/pencil). Ask the students to form the following number with their place value blocks and write this number on
their board. Say the number, 213. Note which students have difficulty and are looking at others' work. You will need to hover near these students during the lesson to
closely monitor their work and you may need to pull these students for a small group lesson at another time.
Then ask the students if they can make this number (213) by only using the tens and ones. Record the names of any students who say it cannot be done, students
who simply do nothing, and those who produce an incorrect amount. Also, note students who do this correctly. Correct answers would be 21 tens and 3 ones, 20 tens
and 13 ones, 19 tens and 23 ones, etc. or even 213 ones. The last answer would be ridiculous to make as it is doubtful that each student has 213 ones. It is not
necessary to provide correct answers at this time as it would interfere with the flow of the lesson. You can tell the students to clear their desk and that this is a puzzle
we will solve during the lesson.
The students who answered incorrectly should be closely monitored during the lesson. The students who answered correctly should be challenged to explain their
reasoning and to find multiple representations of the numbers in the lesson.
As the students are demonstrating their understanding of place value by building and recording numbers to the hundreds, the teacher will be able to determine if the
students are able to represent a 3-digit number with concrete and pictorial models.
The following attachment can be used to record student progress in this concept.
3 DIGIT Recording Form
Feedback to Students
While completing the guided practice, the students will use base-ten blocks, place value charts and dry erase boards to represent place value through the hundreds.
During this time, the teacher will observe student interaction and conversations about their answers. Teachers can probe, clarify and guide student thinking by using
the Guiding Questions. Other specific feedback is noted in the Teaching Phase and the Guided Practice.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations:
Students who need accommodations may use base-ten blocks that have the value of the block written on the block in a standard number. For example the ten-rod will
have the number 10 written on it. The student may use a teacher-made number chart that skip counts numbers by ten's and hundred's as a reference for counting.
Extensions:
The following website contains Place Value practice.
Place Value AAA Math- Place Value
Suggested Technology: Document Camera, Computer for Presenter, Internet Connection, LCD Projector
Special Materials Needed:
Base-Ten Blocks
Place Value Chart
Note Cards
Dry Erase Boards
Drawing Paper
Further Recommendations:
For the best classroom management of this lesson, have base-ten blocks along with dry erase boards ready prior to the lesson.
Additional Information/Instructions
By Author/Submitter
This lesson is likely to support student engagement with the following Standards for Mathematical Practice:
MAFS.K12.MP.7.1 - Look for and make use of structure - students are attending to the structure of our place value system.
MAFS.K12.MP.6.1 - Attend to precision - students are asked to explain their reasoning for creating different representations.
SOURCE AND ACCESS INFORMATION
Contributed by: Jennifer Palmer
Name of Author/Source: Jennifer Palmer
District/Organization of Contributor(s): Palm Beach
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
page 3 of 4 Related Standards
Name
MAFS.2.NBT.1.1:
Description
Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706
equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
a. 100 can be thought of as a bundle of ten tens — called a “hundred.”
b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight,
or nine hundreds (and 0 tens and 0 ones).
page 4 of 4