Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Number, Operation, and Quantitative Reasoning
Activity:
Let’s Frame It!
TEKS:
(1.3) Number, operation, and quantitative reasoning. The student
recognizes and solves problems in addition and subtraction situations.
The student is expected to:
(A) model and create addition and subtraction problem situations
with concrete objects and write corresponding number
sentences; and
(B) use concrete and pictorial models to apply basic addition and
subtraction facts (up to 9 + 9 = 18 and 18 – 9 = 9).
(1.5) Patterns, relationships, and algebraic thinking. The student
recognizes patterns in numbers and operations.
The student is expected to:
(D) use patterns to develop strategies to solve basic addition and
basic subtraction problems; and
Overview:
This lesson teaches using a ten-frame as a strategy to build a mental
understanding of each number. The ten-frame is used to develop an
understanding of the relationships between numbers. For example, the
number 7 can be seen as 5 and 2 more or 3 away from 10.
Just as the dot plates help connect a pattern to a numeral, the use of tenframes can be one of the most vital tools that a student uses to begin
forming a mental picture of addition and/or subtraction of math facts.
Prerequisite: Student must have modeled the numbers and developed an
understanding of the math facts that represent 0, 1, 2, 3, 4, & 5 using the
five-frame.
Materials:
Prior To Lesson
Ten-frame Mat master
Double Ten-frame Mat master
Let’s Frame It! Flash Cards master
Let’s Frame It! Number Cards master
Calculating Patterns Handout master
Give Me Ten! Cards master
Cardstock
Transparencies
Copy paper
Lesson Materials
Ten-frame Mats for each student
Number, Operation, and Quantitative Reasoning
Let’s Frame It!
Grade 1
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Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Double Ten-frame Mats for each student
Overhead Ten-frame Mat
Overhead Double Ten-frame Mat
Counters for Ten-frame Mats
(Cubes, Counters, Beans, and/or Magnets if Using Metal Cookie
Sheets)
Let’s Frame It! Flash Cards
Give Me Ten! Cards
Dominoes
Deck of cards
Computer with Internet access
Children’s literature books (Concepts of Number Development and
Addition)
Four-function calculators
Calculating Patterns Handout
Uni-link Cubes
Pattern Blocks
Anecdotal Notes Assessment Sheet
Grouping:
Part I - whole group
Part II – small groups
Part III – whole group
Part IV – small group
Time:
Part I – two days of 30 to 45 minute sessions
Part II – five days of center activities
Part III – two days of 30 to 45 minute sessions
Part IV – four days of center activities
Lesson:
1.
Procedures
Prior to lesson
Copy on cardstock the following:
• Ten-frame Mats
• Double Ten-frame Mats
• Let’s Frame It! Flash Cards (2 sets)
• Let’s Frame It! Number Cards (3 sets)
• Give Me Ten! Cards onto cardstock
Then cut out:
• Let’s Frame It! Flash Cards
• Let’s Frame It! Number Cards
• Give Me Ten! Cards
Notes
One set of the Let’s Frame It!
Flash Cards will be for teacher
use. The second set is for
students to use in centers. Write
the corresponding number on the
back of the children’s set so the
game will be self-correcting.
For teacher use, make transparencies of:
• Ten-frame Mats
Number, Operation, and Quantitative Reasoning
Let’s Frame It!
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Mathematics TEKS Refinement 2006 – K-5
Procedures
• Double Ten-frame Mats
Tarleton State University
Notes
Duplicate Calculating Patterns Handout, at
least three per student.
2.
Part I
Call out numbers and have students show
the number using their fingers. Have
students visualize their hands with five
fingers each. They understand they must
use all the fingers on one hand before
moving to the second. To show 7, they
would need all five fingers on their left hand
and two more on their right hand. Just as on
the ten-frame, they must fill the top five
spaces before adding two more on the
second row.
Begin by explaining how a ten-frame mat is
constructed.
Each box must be filled in sequential order
moving from left to right, beginning with the
top row.
For example: The number 7 is modeled by
filling all five boxes of the top row and then
the first two boxes in the second row.
You should have your students practice
making numbers using only one ten-frame
until your students can model the numbers
quickly.
Important step in building to a
mental understanding of each
number: The students should
know how to compose and
decompose all numbers less than
ten before moving onto math fact
strategies above ten. If this step
is completed using the five- and
ten-frames, a mental picture of
referents will be developed. For
example, the number 6 can be
composed in the following ways:
0 + 6, 1 + 5, 2 + 4, 3 + 3, 4 + 2,
5 + 1, and 6 + 0. This concept
can be reinforced by having the
students make ten-frame books
that represent each number.
A quick way to use formative
assessment with the students is to
call out a number and have the
students make that particular
number using magnets on small
metal boards (cookie sheets
divided off with colored tape).
Once the students have built the
number, they can hold the board
up for the teacher to assess.
Some of your students’ number
development may require them to
start counting from the number
one each time while others will
catch on quickly to the adding on
or removing a few counters to
make the new number. If students
do counting up from the beginning
each time, work with them to
develop cardinality of set and
conservation of number.
Number, Operation, and Quantitative Reasoning
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Mathematics TEKS Refinement 2006 – K-5
Procedures
Tarleton State University
Notes
Use ten-frame flash cards to drill
the students while waiting in line
for lunch or being dismissed from
school. Hold up a card for one
second to see if students can tell
you how many dots were on the
ten-frame flash card. This will
help build a mental picture of a
representation of each number.
3.
Part II
Divide the students into groups of four.
Students will rotate through centers for five
days. The amount of time spent in each
center will depend on the amount of time
allotted for mathematics instruction.
Students rotate through two centers each
day. Instructions for 10 centers are provided
in the following procedures (4 – 13).
4.
Center I: Ten-frame Practice
Students are given a stack of number cards
labeled 1-10. Students are to select a
number card (1-10) and build that number on
a Ten-frame Mat.
Teacher works with this small
group assessing students’
understanding of the ten-frame.
Use Anecdotal Notes Assessment
Sheet to record notes concerning
students’ understanding of
concepts.
5.
Center II: Domino Center
Students select a domino. Students record
the domino and the corresponding addition
fact onto notebook paper. Students solve
the addition problem and submit their work
for assessment.
Students may have Ten-frame
Mats available to solve problems.
Center III: Let’s Frame It! Flash Cards
Students challenge each other with the flash
cards. Cards should be self-correcting so
that students are working independently in
this center.
Teacher needs to record answers
on the back of each card so that it
is self-correcting for students
6.
Number, Operation, and Quantitative Reasoning
Let’s Frame It!
Students check each other’s work.
Students submit work at the end
of their rotation in this particular
center.
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Mathematics TEKS Refinement 2006 – K-5
7.
Procedures
Center IV: Reading Center
Teacher supplies center with children’s
literature books that teach number and
addition concepts. Students read books to
each other. Examples of books include:
•
•
•
•
•
•
8.
Tarleton State University
Notes
Other books can be found on the
Children’s Literature List provided
with the MTR professional
development.
Anno’s Counting House by M. Anno
Ten Black Dots by D. Crews
Two Ways to Count to Ten by R. Dee
Up to Ten and Down Again by L.C. Ernst
Feast for 10 by K. Falwell
Domino Addition by L. Long
Center V: Computer Center
Students should work in pairs in the
computer center. A suggested list of
websites that promote number development
and addition concepts is provided in the
notes. Teacher needs to check out each of
these sites and assign the website that is
appropriate for each student based on
conceptual understanding.
Illuminations Activities:
Concentration http://illuminations.nctm.org/Activiti
es.aspx?grade=1
Illuminations Activities: Electronic
Abacus http://illuminations.nctm.org/Activiti
es.aspx?grade=1
Illuminations Activities: Five
Frame http://illuminations.nctm.org/Activiti
es.aspx?grade=1
Illuminations Activities: Ten Frame http://illuminations.nctm.org/Activiti
es.aspx?grade=1
National Library of Virtual
Manipulatives
(http://nlvm.usu.edu/en/nav/vlibrar
y.html) has many examples for
student use.
Number, Operation, and Quantitative Reasoning
Let’s Frame It!
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Mathematics TEKS Refinement 2006 – K-5
9.
10.
Tarleton State University
Procedures
Notes
Center VI: Give Me Ten! Card Game
a. Tallest student is designated as dealer.
b. He/she shuffles Give Me 10! Cards and
distributes so that every student receives
seven cards. The remaining cards are
placed in the middle of the group face
down.
c. Each student identifies all pairs that
equal to 10 within their hand and lays
them down on table (Example: 6 and 4,
7 and 3). After everyone has laid down
their “make 10” pairs, the group must
agree that all pairs are correct. Once
everyone agrees, continue game.
d. The student to the left of the dealer
begins the game by asking another
student for a card that would make a pair
equal to 10. (Example: Participant is
holding an 8 and would need to ask for a
2.)
e. If the student has the card that was
requested, it is given to the student that
made the request.
f. If the student does not have the card that
was requested, the student replies with
“Go Fish.”
g. The student who requested the card
draws a card from the deck. If the card
that was drawn completes a pair to make
10, then the student lays down the pair.
h. The next student proceeds following the
same procedures.
i. Next, students record on paper the
number sentences they were able to
build throughout the game.
After peer assessment, students
j. Students compare problems with
turn in work for teacher to
someone in small group by identifying
evaluate.
same number sentences and number
sentences that show the commutative
property. (Example: 6 and 4 and the
partner had 4 and 6)
Center VII: Card Center
Teacher removes cards above the value of 6
from the deck.
Number, Operation, and Quantitative Reasoning
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Mathematics TEKS Refinement 2006 – K-5
a.
b.
c.
d.
e.
f.
11.
Procedures
Students play in pairs.
Older student shuffles cards and deals
them between the two of them.
Students lay down one card each.
The first student to say the sum of the
two cards gets to keep the pair of cards.
Students must justify their answers.
Play continues until one player has all
the cards.
Center VIII: Calculator Center
Have students work in pairs for this activity.
Each pair of students needs a four-function
calculator.
One of the students types in an equation
(i.e., 3 + 4 = 7). The number 7 will be
displayed. The second student hits the
equals sign and continues hitting the equal
sign until he or she can determine what
number is being added each time. They
then try to predict (1) what comes next and
(2) the original equation that was entered
into the calculator.
Tarleton State University
Notes
This activity is very useful for
differentiated instruction in the
classroom and is a great use of
technology. This activity can be
adapted for any grade level or
developmental level of the student
and covers all operations of whole
numbers. The students are in
charge of the learning, and they
create their own problems. They
will probably be much harder on
themselves than teachers would
be.
Have the students record answers on
Calculating Patterns Handout each time they
do this activity.
12.
Center IX: Build It!
a. Tallest student begins by drawing a
number card. Play continues to his/her
left.
b. All students may only choose two colors
of pattern blocks to build the designated
number. The quantity of each pattern
block is determined by the student.
c. Students use pattern blocks to build a
design.
d. Students record their designs and
addition facts onto notebook paper.
e. Then students submit problems for
assessment.
Number, Operation, and Quantitative Reasoning
Let’s Frame It!
The purpose of this game is to
identify all possible 2-part
combinations to compose a
number. This game aids children
in developing part/part/whole, a
foundational concept.
An example of this game would
be: One student draws a number
card and that card is labeled 10.
Then all four students in the group
select 10 shapes of two different
colors. They each make a design
and record the addition facts that
go with their design.
Grade 1
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Mathematics TEKS Refinement 2006 – K-5
Procedures
Tarleton State University
Notes
Their four designs and the
addition facts follow:
Student A:
7 + 3 = 10
3 + 7 + 10
Student B:
5 + 5 = 10
Student C:
2 + 8 = 10
8 + 2 + 10
Student D:
6 + 4 = 10
4 + 6 = 10
Number, Operation, and Quantitative Reasoning
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Mathematics TEKS Refinement 2006 – K-5
13.
Procedures
Center X: Composing Numbers
Provide students with uni-link cubes and a
set of Let’s Frame It! Number Cards.
Tarleton State University
Notes
The purpose of this game is to
identify all possible ways to
compose a number. This game
aids children in developing part to
whole, a foundational concept.
a. The goal of this center is to have
students build all possible combinations
for the designated number.
For example, the number 4 could
b. The shortest student begins by drawing
a number card. Play continues to his/her be built in the following ways:
left.
• 2 yellow uni-link cubes and 2
c. Students build the number using the unired uni-link cubes
link cubes.
• 3 yellow uni-link cubes and 1
d. Students record addition problems.
red uni-link cube
e. Students submit problems for
• 1 yellow uni-link cube and 3
assessment.
red uni-link cubes
• 1 yellow uni-link cube, 1 red
uni-link cube, 1 blue uni-link
cube, and 1 green uni-link
cube,
• 1 yellow uni-link cube, 2 red
uni-link cubes, and 1 blue unilink cube
• 2 yellow uni-link cube, 1 red
uni-link cube, and 1 blue unilink cube
• 1 yellow uni-link cube, 1 red
uni-link cube, and 2 blue unilink cubes.
Students would record the above
problem as follows:
2+2=4
3+1=4
1+3=4
1+1+1+1=4
1+2+1=4
2+1+1=4
1+1+2=4
14.
Part III
Once the math facts less than 10 are
mastered, model the math facts larger than
10 using the Double Ten-frame Mat. For
example, 7 + 4 would be modeled by
showing seven counters on the first ten-
Number, Operation, and Quantitative Reasoning
Let’s Frame It!
Instruction on building numbers
above 10 is designed for two
days, but be flexible based on
students’ understanding. The
teacher does not want to rush
Grade 1
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Mathematics TEKS Refinement 2006 – K-5
Procedures
frame as mentioned above and four counters
in a different color in the first four boxes on
the second ten-frame.
Tarleton State University
Notes
instruction. Students need a
complete understanding of using
10 as a referent number.
Instruct the students to move the last three
counters from the second ten-frame into the
three empty boxes of the first ten-frame.
Now the answer can be read easily—the first
ten-frame is full which represents 10 and the
second ten-frame has only one counter
remaining for a total of 11.
15.
Part IV
Divide the students into groups of four.
Students will rotate through centers for four
days. The amount of time spent in each
center will depend on the amount of time
allotted for mathematics instruction. Students
rotate through two centers each day.
Instructions for the centers are provided in
the following Procedures.
16.
Center I: Double Ten-frame Practice
Students are given a set of number cards
labeled 1-18. Students draw a number card
and build that number on Double Ten-frame
Mat.
Teacher works with this small
group assessing students
understanding of the double tenframe. Use Anecdotal Notes
Assessment Sheet to record notes
concerning students’
understanding of concepts.
After a few days, a fun new way to
practice making numbers is to tell
students not to clear their board
between numbers. Observe how
quickly the students assess what
is needed to compose the new
number.
17
Center II: Domino Center
Students select two dominos. Students
record dominoes and the corresponding
addition problem onto notebook paper.
Students solve the addition problem and
Number, Operation, and Quantitative Reasoning
Let’s Frame It!
Students may have Double Tenframe Mats available to solve
problems.
Students check each other’s work.
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Mathematics TEKS Refinement 2006 – K-5
Procedures
submit work for assessment.
18.
Center III: Let’s Frame It! Flash Cards
Students challenge each other with the flash
cards. One student acts as teacher and
holds up two cards while other students
determine the answer.
19.
Center IV: Reading Center
This center is the same as the Reading
Center used in Part II. See Procedure 7 for
instructions.
20.
Center V: Computer Center
This center is the same as the Computer
Center used in Part II. See Procedure 8 for
instructions.
21.
Center VI: Card Center
This center is the same as the Card Center
used in Part II except that the teacher only
removes face cards from the deck. See
Procedure 10 for instructions.
22.
Center VII: Build it!
This center is the same as the Build It Center
used in Part II except students should use
Numbers Cards from 2 through 18. See
Procedure 12 for instructions.
23.
Center VIII: Composing Numbers
This center is the same as the Composing
Numbers Center in Part II except students
should use Number Cards from 3 through
18. See Procedure 13 for instructions.
Tarleton State University
Notes
Students submit work at the end
of their rotation in this particular
center.
Assessment:
Part I:
Part II:
Part III:
Part IV:
Anecdotal Notes Assessment Sheet
Anecdotal Notes Assessment Sheet and student work
Anecdotal Notes Assessment Sheet
Anecdotal Notes Assessment Sheet and student work
Extensions:
Students could play the game “Around the World.” Teacher would
Number, Operation, and Quantitative Reasoning
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Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
model an addition sentence on a ten-frame (either using the
overhead/document camera/metal cookie sheet and two-sided
counters). Students would record the numerical addition sentence on
dry erase boards. The first student to write the numerical addition
sentence correctly moves to the next person. The game continues
until every student has had an opportunity to record an addition
sentence. This game is a great informal assessment tool. Teachers
can quickly assess the level of understanding addition in a visual and
written form.
Resources:
Anno, M. (1982). Anno’s counting house. New York: Philomel Books.
Crews, D. (1968). Ten black dots. New York: Greenwillow Books.
Dee, R. (1988). Two ways to count to ten. New York: Henry Holt & Co.
Ernst, L. C. (1986). Up to ten and down again. New York: Lothrop, Lee
& Shepard.
Falwell, K. (1993). Feast for 10. New York: Clarion Books.
Long, L. (1996). Domino addition. Watertown, MA: Charlesbridge.
National Council of Teachers of Mathematics. (2006). Illuminations
online at http://illuminations.nctm.org
National Library of Virtual Manipulatives (2006). NLVM Online at
http://nlvm.usu.edu/en/nav/vlibrary.html
Nugent, Glenda. (1995). Hands-On Math : Manipulative Activities for
the 2-3 Classroom Cypress, CA: Creative Teaching Press, Inc.
Van de Walle, J.A. (2004). Elementary and middle school
mathematics: Teaching developmentally (5th ed.) Boston, MA:Allyn
and Bacon.
Van de Walle, J.A. (2007). Elementary and middle school
mathematics: Teaching developmentally (6th ed.) Boston, MA:Allyn
and Bacon.
Number, Operation, and Quantitative Reasoning
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Let’s Frame It Flash Cards
Number, Operation, and Quantitative Reasoning
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Number, Operation, and Quantitative Reasoning
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Number, Operation, and Quantitative Reasoning
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Let’s Frame It! Number Cards
0
0
1
1
2
2
3
3
4
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4
5
5
6
6
7
7
8
8
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9
10
10
11
11
12
12
13
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Grade 1
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Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Calculating Patterns Handout
As you are looking at patterns on the calculator, fill out the
following table:
Number of
Equation
Equation
Number, Operation, and Quantitative Reasoning
Let’s Frame It!
Answer
Difference
Between
Answers
Grade 1
Page 34
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Anecdotal Notes Assessment Sheet
Add notes describing students’ understanding of the concepts.
Name
Can student make numbers on Can student make numbers on
ten-frame?
double ten-frame?
Number, Operation, and Quantitative Reasoning
Let’s Frame It!
Grade 1
Page 35
Number, Operation, and Quantitative Reasoning
Let’s Frame It!
Mathematics TEKS Refinement 2006 – K-5
Ten-frame Mat
Grade 1
Page 36
Tarleton State University
Number, Operation, and Quantitative Reasoning
Let’s Frame It!
Mathematics TEKS Refinement 2006 – K-5
Double Ten-frame Mat
Grade 1
Page 37
Tarleton State University