First Grade
Curriculum Unit Plan
First Grade: Mathematics
Unit 5: Place Value, Number Stories, and Fact Families
Lesson Template
Overarching Question: How does knowledge of place value help students understand that all numbers are comprised
only of 10 different digits, and that where the digits “stand” determines the number?
Previous Unit: Organizing
This Unit:
Next Unit: Geometric
and Representing Data
Place Value, Number Stories and Fact Families
Shapes, Patterns & Attributes
Place value
concepts
is about
building number
sense by
understanding
place value
by
modeling,
reading, and
writing numbers
to support
addition &
subtraction
strategies
and
Comparing and
ordering numbers
to 120 (including
>,=, < symbols.
to know
fact families
fluently
to solve
word problems
and equations
Questions to Focus Assessment and Instruction:
1. How does the placement of numbers in a given number help students
understand their place value?
2. How does a student’s understanding of place value help them build the
largest number/smallest number from a set of numbers from0-9?
3. How does the placement of zero in a given number affect its value?
Key Concepts
place Value
digit
rods (longs)
patterns
zero
greater than
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large numbers
ones, tens, hundreds
less than
Intellectual Processes (Standards
for Mathematical Practice)
• Reason abstractly and
quantitatively when
comparing and ordering
numbers.
•
Model numbers with baseten blocks.
•
Look for and make use of
structure for place value.
small numbers
expanded notation
equal to
June 16, 2011
First Grade
Lesson Abstract:
In this lesson students will focus on a deeper understanding of place value as it relates to how numbers operate. Students
will create the largest number they can build from a set of given numbers. They will explore the meaning of expanded
notation as they build large and small numbers. Students will understand the meaning of the one, tens, and hundreds
place and will learn about the placement of zero in a given number.
Common Core Standards
Numbers and Operations in Base Ten (1.NBT)
Understand place value.
1.NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the
following as special cases:
a. 10 can be thought of as a bundle of ten ones –called a “ten.”
b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or
nine ones.
c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or
nine tens (and 0 ones).
1NBT3. Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of
the comparisons with the symbols >, =, <.
Use Place Value Understanding and Properties of Operations to Add and Subtract
1.NBT5. Given a two-digit, mentally find ten more or ten less than the number, without having to count; explain
the reasoning used.
Instructional Resources
Sequence of Lesson Activities
Lesson Titles: “Sir Cumference and All the King’s Tens”
http://www.charlesbridge.com/client/client_pdfs/downloadables/SirCumference_KingsTens.pdf (Control +click to access)
One Class Period
Materials Needed:
Copy of the picture book Sir Cumference and All the King’s Tens
Neuschwander, Cindy. Sir Cumference and All the King’s Ten., Charlesbridge.ISBN 978-1-57091-728-8.2003.
(www.charlesbridge.com)
Digits in bags for each student
Large paper bag with the title “ The World’s Digits” written on the outside of bag
Large models of digits 0-9 (at least 6 inches tall) place in large bag
“Knightly Number Neighborhood” sheets (see attached document)
Assessment sheets for place value numbers
Selecting and Setting Up a Mathematical Task:
Advanced Preparation:
What are the mathematical objectives for
•
the lesson?
•
In what ways does the task build on
student’s previous knowledge?
•
What questions will you ask to access
prior knowledge?
•
This activity helps students to understand to understand that where
the digits “stand” determines the place value.
In kindergarten, students built number sense by modeling, reading,
and writing numbers to 100. They decomposed and compared
numbers using <, =,> symbols.
Write a one digit number on the board. Ask students to name the
number. Add another digit to this in the ones place and ask them to
name this number. Then write the same two digits, reversing the
place value. What is the number’s name?
Math Notes: Teachers should notice the conceptual connection
between place value and other topics such as money, etc.
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June 16, 2011
First Grade
Launch
How would you introduce the activity to
the students?
•
•
What will be heard that indicates that the
students understood what the task is
asking them to do?
•
•
•
Let students know that the real term for these 10 special numbers is
digit and that any number can be made from them. To illustrate
this, choose students to pick a digit out of the bag and stand in front
of the classroom. The rest of the class can then call out the name of
the number that digit makes. For example, if a student chooses a 2,
standing alone at the front of the class, the rest of the students would
call out, “That’s a two!” Then a second student is chosen to select
another digit from the bag and stand next to the first student. If a 9 is
chosen, the class will call out, “29!” or “92” depending on where the
second student stands. If a zero is picked first, have student set it
aside until a second number is drawn that can be combined with the
zero to make a two-digit number.
After a three digit number has been built and read, the teacher can
say to the students, “Can you take the digits you have used and
rearrange them into an order that makes it the biggest number
possible? “Explain your thinking”. Allow several explanations.
Then students can share their arrangements, reading their solutions.
Similarly, the smallest number possible can be made with the same
selected set of digits on the Knightly Number Neighborhood card.
Students will begin to see patterns: the largest number has digits that
descend in value while the smallest number has digits that ascend in
value.
You can continue this activity until all ten digits are used. This will
make a very large number that students may need help in reading.
This activity helps students to understand that all numbers are
comprised only of 10 different digits, and that where the digits “stand”
determines the number. The hundred grid can be useful at this point
of the lesson.
Explore:
Story Connections (whole group)
• Read the book, Sir Cumference and All the King’s Ten aloud to the
class. After reading the book pass out the Knightly Number
Neighborhood number boards to each student. These can be backed
with colored construction paper and laminated for durability. Each
student should also have a baggie full of multiples of all ten digits.
These digits will be placed on the lines under the tents in the
neighborhood. Having at least four of each digit will give students
many choices as they build numbers.
• Go through each part of the story, recreating on the number board the
people at King Arthur’s birthday party. This can start by building 9,
representing the nine people who fit into the tiny tent on page 12 of
the story. The tiny tent could not hold more than nine people, Sir
Cumference then decides to arrange all the people into groups of
tens because it is easier to count. That can be represented on the
number board by one group in the tens tent and a zero in the ones
tent because no one is inside the littlest tent any longer. You can also
model this with base ten blocks.
• Lady Di requests that the party guests regroup themselves into larger
formations of 100, to make the counting even easier. This can be
represented by the digit one in the hundreds place and a zero in the
tens tent and another zero in the ones tent, as both of those tents are
empty. They are too small to hold 100 people.
• Lady Di then counts all the partygoers. These can be represented on
the number board. Nine can be placed on the line under the hundreds
tent, representing 900 folks. An 8 can be put under the tens tent,
showing 80 people. Finally, a 7 can go in the ones tent, meaning
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June 16, 2011
First Grade
What questions will be asked to focus
student’s thinking on the key ideas?
How will you extend the task to provide
additional challenge?
What questions will be asked to assess
understanding of key mathematical
ideas?
there are seven people in the tiniest ones tent. Altogether, Lady Di
counts 987 for lunch.
• Then 25 more people arrive Lady Di groups them, completing another
group of 100. This now makes ten groups of one hundred, or one
thousand. Then there is just a group of ten and two additional
farmers off to the side
• As more people arrive from Camelot, they are grouped accordingly.
Students can follow along as the story unfolds, changing the numbers
as they grow.
• Finally, participants arrive from Addingmoor. The number is not
specifically mentioned in the story so that students and teachers can
experiment with an infinite number of choices, practicing building
numbers with understanding. How many people could be in each
tent?
Building Numbers
• After reading the story, more numbers can be imagined and built on
the Knightly Number Neighborhood boards. Using language from the
story, the teacher can ask students for a digit and which tent it goes
in. That digit represents how many people are in that tent. For
example, the teachers may say, “Nick, give me a digit and which tent
it goes into.” Nick might say, “Put a 7 in the hundreds tent.” That
means there are 700 people in that tent. As other students contribute
their digits and tents (or places), finally an entire number is built. Then
students can practice reading that number.
• Depending upon the age and ability of students, the Knightly Number
Neighborhood can be as large or as small as necessary. A first grade
class might have only three tents in its neighborhood; a ones tent, a
tens tent, and a hundreds tent. A fourth grade class would have a
much larger Knightly Number Neighborhood, going up to a tent that
could hold a million partygoers.
Rearranging Built Numbers
• After a number has been built and read, the teacher can say to the
students, “Can you take the digits you have used and rearrange them
into an order that makes it the biggest number possible? Then
students can share their arrangement, reading their solutions.
Similarly, the smallest number possible can be made with the same
selected set of digits on the Knightly Number Neighborhood card.
Students will begin to see patterns; the largest number has digits that
descend in value while the smallest number has digits that ascend in
value.
• What do you notice about the numbers that are larger and smaller?
A Place for Zero!
• Playing with numbers on the Knightly Number Neighborhood board
gives students plenty of opportunities to experiment with digit
placement and value. Don’t be surprised if students want to place 9s
in all tents. This is a large, exotic number for them!
• They also love to see what happens when there are 0s in the number.
A good way to express this is to say, “It looks like that tent is empty.
There is no one inside right now.” That way, students begin to
understand zero as a placeholder. The tent or place did not go away
– it is just empty.
Expanded Notation
•
Expanded notation, or stretching out numbers into their parts, can
also be incorporated into Knightly Number Neighborhood activities.
Under each digit selected in its tent (or place), the teacher or students
can write how many people are in each tent (or value). If students
use laminated number boards, they can use an overhead pen to write
this number under the place, putting + signs between each tent. In
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June 16, 2011
First Grade
•
this way, they practice identifying the value of each digit on the board
and seeing the value of the entire number.
As students gain experience with this activity, teachers can begin to
move their language towards mathematical terms. Instead of tent, the
word place can be substituted. Instead of how many people are in a
tent, the word value can be used. In this way, students can begin to
think about the concept of place value with a concrete story and end
with an abstract understanding of place value.
Summary
•
•
What specific questions will be asked so
that students make connections
between the different strategies that are
presented?
What will be seen or heard that indicates
all students understand the mathematical
ideas you intended them to learn?
•
Many experiences with this Knightly Number Neighborhood concept
can help students have a stronger understanding of place value. This
concept can also be used for teaching decimals. Numbers on the
right side of the decimal live in ever-smaller tents!
Briefly discuss the challenges of working with numbers to understand
their value. Continue this activity for several days until student have a
command of building number and the largest number. Eventually,
students will be ready to tackle the electronic version of making the
largest number possible given a set of numbers.
Some questions to consider when wrapping up the lesson:
1) What is the largest number we created today? ( Answers will
vary)
2) What do we know about digits 0-9?
3) If we have a two digit number like 74, what do the numbers tell
us? ( 7 tens, 4 ones)
4) If we are to take the number 504 apart, how would we write this?
( 5 hundreds, + 0 tens + 4 ones)
5) How do we use the zero in numbers like 110 or 804? ( The zero
acts as a place holder and means there are no ones in the
number 110 and there are 0 tens in the number 804)
Teacher Reflection/Next Steps
• The teacher will know if students have understood the
mathematical ideas if they can :
o Create a larger number from a given set of numbers
o Take numbers apart (expanded notation) and explain
their place value
o Recognize all digits are created from the set of numbers
0-9.
o Understand that zero is used in a number as a place
holder and represents nothing.
This document is the property of MAISA.
June 16, 2011