Unit 10: Operations Using Data Representations
1st Grade
5E Lesson Plan Math
Grade Level: 1st
Subject Area: Mathematics
Lesson Title: Operations Using Data
Unit Number: 10
Lesson Length: 5
Representations
days
Lesson Overview
This unit bundles student expectations that address interpreting, representing, explaining,
generating, and solving addition and subtraction situations as well as applying basic fact
strategies and properties of operations to solve addition and subtraction problems using the
data from picture graphs and bar-type graphs. According to the Texas Education Agency,
mathematical process standards including application, a problem-solving model, tools and
techniques, communication, representations, relationships, and justifications should be
integrated (when applicable) with content knowledge and skills so that students are prepared
to use mathematics in everyday life, society, and the workplace.
Unit Objectives:
Students will:
 Use data represented in bar-type and picture graphs to represent, generate, and
solve problem situations involving sums and minuends up to 20 using spoken
words, objects, pictorial models, and number sentences.
 Explore and explain a variety of strategies to solve one-step problems involving
addition, subtraction, and comparison of the data.
 While demonstrating various strategies, explore and apply properties of operations.
 Use a number sentence with the unknown in any position to represent the situation.
 Solve the problem and are expected to explain that the equal sign represents a
relationship where expressions on each side of the equal sign represent the same
value(s).
 Through the use of continued experiences with addition and subtraction situations,
begin to recognize basic fact relationships, which are essential for developing
computational fluency.
 Develop a thorough understanding of analyzing data and using the problem-solving
process in addition and subtraction situations involving sums and minuends up to
20 in order to set the foundation for students’ success in mathematics as they
progress through future grade levels.
Standards addressed:
TEKS:
1.1 Mathematical process standards. The student uses mathematical processes to acquire
and demonstrate mathematical understanding. The student is expected to:
1.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
1.1B Use a problem-solving model that incorporates analyzing given information, formulating
a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.
1.1C Select tools, including real objects, manipulatives, paper and pencil, and technology as
appropriate, and techniques, including mental math, estimation, and number sense as
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Unit 10: Operations Using Data Representations
1st Grade
appropriate, to solve problems.
1.1D Communicate mathematical ideas, reasoning, and their implications using multiple
representations, including symbols, diagrams, graphs, and language as appropriate.
1.1E Create and use representations to organize, record, and communicate mathematical
ideas.
1.1F Analyze mathematical relationships to connect and communicate mathematical ideas.
1.1G Display, explain, and justify mathematical ideas and arguments using precise
mathematical language in written or oral communication.
1.3 Number and operations. The student applies mathematical process standards to develop
and use strategies for whole number addition and subtraction computations in order to solve
problems. The student is expected to:
1.3B Use objects and pictorial models to solve word problems involving joining, separating,
and comparing sets within 20 and unknowns as any one of the terms in the problem such as 2
+ 4 = [ ]; 3 + [ ] = 7; and 5 = [ ] – 3.
1.3D Apply basic fact strategies to add and subtract within 20, including making 10 and
decomposing a number leading to a 10.
1.3E Explain strategies used to solve addition and subtraction problems up to 20 using spoken
words, objects, pictorial models, and number sentences.
1.3F Generate and solve problem situations when given a number sentence involving addition
or subtraction of numbers within 20.
1.5G Apply properties of operations to add and subtract two or three numbers.
1.8 Data analysis. The student applies mathematical process standards to organize data to
make it useful for interpreting information and solving problems. The student is expected to:
1.8B Use data to create picture and bar-type graphs. •Each category is represented with
labels.
1.8C Draw conclusions and generate and answer questions using information from picture and
bar-type graphs.
ELPS:
The student is expected to:
ELPS.c.1A use prior knowledge and experiences to understand meanings in English
ELPS.c.1C use strategic learning techniques such as concept mapping, drawing, memorizing,
comparing, contrasting, and reviewing to acquire basic and grade-level vocabulary
ELPS.c.2D monitor understanding of spoken language during classroom instruction and
interactions and seek clarification as needed
ELPS.c.2E use visual, contextual, and linguistic support to enhance and confirm
understanding of increasingly complex and elaborated spoken language
ELPS.c.3C speak using a variety of grammatical structures, sentence lengths, sentence types,
and connecting words with increasing accuracy and ease as more English is acquired
ELPS.c.3D speak using grade-level content area vocabulary in context to internalize new
English words and build academic language proficiency
ELPS.c.3H narrate, describe, and explain with increasing specificity and detail as more
English is acquired
ELPS.c.5B write using newly acquired basic vocabulary and content-based grade-level
vocabulary
ELPS.c.5F write using a variety of grade-appropriate sentence lengths, patterns, and
connecting words to combine phrases, clauses, and sentences in increasingly accurate ways
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Unit 10: Operations Using Data Representations
1st Grade
as more English is acquired
ELPS.c.5G narrate, describe, and explain with increasing specificity and detail to fulfill content
area writing needs as more English is acquired.
Misconceptions:
Some students may think subtraction is commutative rather than recognizing the minuend as
the total amount and the subtrahend as the amount being subtracted (e.g., 5 – 3 is not the
same as 3 – 5, etc.).
Some students may think the equal sign means that an operation must be performed on the
numbers on one side and the result of this operation is recorded on the other side of the equal
sign rather than understanding that operations and/or individual numbers can be on either side
of the equal sign as long as they represent equal quantities.
Some students may think they can compare the length of the rows/columns of pictures in a
picture graph rather than comparing the number of pictures in each row/column, not realizing
that the size of the pictures will affect the length of the row/column.
Some students may think leaving gaps between cells or using cells of differing sizes on a bartype graph does not affect the data, not realizing that the size and spacing of the cells should
be consistent.
Some students may think data in a vertical bar-type or picture graph can be arranged from the
top to bottom, not realizing that the cells on a bar graph or pictures in a picture graph are
arranged from bottom to top.
Some students may think data in a horizontal bar-type or picture graph can be arranged from
right to left, not realizing that the cells on a bar graph or pictures in a picture graph are
arranged from left to right.
Some students may think data can only be used in one type of graph rather than realizing the
same data can be represented using either a bar-type or picture graph (e.g., if it’s not
something easy to draw or find a picture for the data, then the data might be best displayed
using a bar-type graph, rather than a picture graph, etc.).
Some students may think if the orientation of the graph changes, then the data itself changes,
not realizing that the data being represented remains the same.
Some students may not recognize the difference between an addition situation and a
subtraction situation based on the context of the problem.
Some students may confuse the –, +, and = symbols due to not fully understanding the
meaning of each symbol.
Vocabulary:
Addend – a number being added or joined together with another number(s)
Additive identity – the sum/difference is not affected when zero is added/subtracted to a
number
Associative property of addition – if three or more addends are added, they can be grouped
in any order, and the sum will remain the same
Bar-type graph – a graphical representation to organize data that uses bars divided into
individual cells to demonstrate one-to-one correspondence and to show the frequency
(number of times) that each category occurs
Categorical data – data that represents the attributes of a group of people, events, or objects
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1st Grade
Unit 10: Operations Using Data Representations
Commutative property of addition – if the order of the addends are changed, the sum will
remain the same
Compose numbers – to combine parts or smaller values to form a number
Counting (natural) numbers – the set of positive numbers that begins at one and increases
by increments of one each time {1, 2, 3, ..., n}
Data – information that is collected about people, events, or objects
Decompose numbers – to break a number into parts or smaller values
Difference – the remaining amount after the subtrahend has been subtracted from the
minuend
Equal sign – a mathematical symbol representing equivalence
Equation – a mathematical statement composed of equivalent expressions separated by an
equal sign
Expression – a mathematical phrase, with no equal sign, that may contain a number(s), an
unknown(s), and/or an operator(s)
Fact families – related number sentences using the same set of numbers
Graph – a visual representation of the relationships between data collected
Minuend – a number from which another number will be subtracted
Number sentence – a mathematical statement composed of numbers, and/or an unknown(s),
and/or an operator(s), and an equality or inequality symbol
Picture graph – a graphical representation to organize data that uses pictures or symbols
evenly spaced or placed in individual cells, where each picture or symbol represents one unit
of data, to show the frequency (number of times) that each category occurs
Strip diagram – a linear model used to illustrate number relationships
Subtrahend – a number to be subtracted from a minuend
Sum – the total when two or more addends are joined
Survey – to ask a group of people a question in order to collect information about their
opinions or answers
Term – a number and/or an unknown in an expression separated by an operation symbol(s)
Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
Related Vocabulary:
 Addition
 Addition symbol
 Category
 Category label
 Cell
 Change unknown
 Combination
 Comparative language
 Compare
 Conclusion
 Frequency
 Horizontal











Join
Minus
One-to-one
correspondence
Operation
Part-part-whole
Plus
Quantity
Represent
Result unknown
Separate
Solution











Start unknown
Strategy
Subtraction
Subtraction symbol
Symbol
Title
Total
Unit of data
Unknown
Value
Vertical
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Unit 10: Operations Using Data Representations
1st Grade
List of Materials: Day 1-handwriting paper, pencil, bulletin board paper, chart paper,
markers, Snack Pictures For Survey or Blank Favorite Snack Ballot, scissors, scotch tape
Day 2-Picture Graph and Bar Graph Template, Snack Pictures For Survey and Picture
Graph or Ballot(Blank), scissors, glue, pencil, Graph Evaluation Checklist, Standard
Graph Questionnaire
Day 3- class picture graph, Picture Graph and Bar Graph Template, Graph Evaluation
Checklist, Standard Graph Questionnaire, Examples of Small Group Questioning
Practice
Day 4 and 5- Popsicle Pictures, Picture Graph and Bar Graph Template, Standard Graph
Questionnaire, counters
INSTRUCTIONAL SEQUENCE
Phase-Engage, Explore
Day 1
Activity: Discovery Education video-Math Monsters: Data Collection
Activity: (Small groups independently) *Tell the class to determine their classmates’ 3 most
favorite snacks and how many of each snack is needed for a class party. *Table groups work
together to accomplish this task. *Give only the following directions:
-Write a plan(steps)
-Carry out plan
-Make a picture-graph
Activity: (Whole Group) *After 15 minutes, have groups present work using document
camera.
*Teacher records problems/questions groups encountered on a class chart.
*After all groups have presented, the teacher facilitates a class discussion of
problems/questions encountered, how to solve them, and record discussed solutions on class
chart/plan
Include in class plan:
-How gather data?-(gather ballots-pictures, interview 1 by 1 and tally results, vote by raising
hands and tally results, etc.), discuss pros and cons of each procedure
-How make graph?-(Drawings or clip-art pictures)
-Horizontal or vertical graph?
-Labeling(Title, key-1 picture = 1 vote, label each category(column or row), numbers on side or
bottom-optional)
Activity: (Whole Group) *Students vote for favorite snack by either drawing and cutting out a
picture from Blank Favorite Snack Ballot or cutting out a picture from Snack Pictures For
Survey. *Students tape their choices on bulletin board paper on the board or wall. *Discuss
and arrange pictures into a class graph(vertical or horizontal). *Label the class graph with a
title, labels for categories, and a key(1 picture = 1 vote) *Tally each category and write number
Activity: (Individual-Exit ticket) *Each student writes a joining question and a comparison
question to be answered from the graph.
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Unit 10: Operations Using Data Representations
1st Grade
Activity: (Teacher homework) Teacher types each question into a worksheet or provide
Standard Graph Questionnaire for tomorrow’s lesson.
What’s the teacher doing?
-monitoring and facilitating discussions
in groups
-recording class plan
-monitoring and facilitating gathering
data
-monitoring and facilitating making class
picture-graph
What are the students doing?
- Writing a plan(steps), carrying out their plan,
gathering data
-Voting for favorite snack and making class picturegraph
-Writing exit-ticket question
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Unit 10: Operations Using Data Representations
1st Grade
Phase-Explain, Elaborate
Day 2
Activity: Discovery Education Video-The Number Crew Awards
Activity: (Independent) *Students make their own copy of the class graph. *Students label
their graph with a title, labels for categories, and a key(1 picture = 1 vote) *Students tally each
category and write how many.
Activity: (Table groups) *Each member of each table group is responsible for evaluating
each member’s graph for correctness, asking for help when needed, and providing help when
needed.
Checklist: ___ Graph is titled at the top
___ Each word in the title starts with a capital and is spelled correctly
___ Each category is labeled(to the left if horizontal, at the bottom if vertical)
___ Each row or column starts by or above the label
___ Pictures are lined up
___No gaps in the graph
___There is a correct number of pictures for each category
___Tally marks and number are correctly written at the end or top of each
category
Activity: (Small Group With Teacher) *Practice drawing pictures, writing number sentences,
solving, and labeling answers for the following kinds of questions: How many __ and __?,
How many more __ than __?, How many fewer __ than __?, How many “total” or “in all”?
*Other students are completing first 2 activities and Standard Graph Questionnaire about
their picture graph.
What’s the teacher doing?
What are the student’s doing?
-Teaching “Small Group With
-Making their picture graph
Teacher” activity.
-Evaluating their table group’s graphs
-Asking their table group for help and helping their
table group when needed
-Drawing pictures, writing and answering number
sentences about their graphs, and labeling
answers
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Unit 10: Operations Using Data Representations
Phase-Explain, Elaborate
1st Grade
Day 3
Activity: (Independent) *Students make a bar graph from the class picture graph. *Students
label their graph with a title, labels for categories, and a key(1 picture = 1 vote) *Students tally
each category and write how many.
Activity: (Table groups) *Each member of each table group is responsible for evaluating
each member’s graph for correctness, asking for help when needed, and providing help when
needed.
Checklist: ___ Graph is titled at the top
___ Each word in the title starts with a capital and is spelled correctly
___ Each category is labeled(to the left if horizontal, at the bottom if vertical)
___ Each row or column starts by or above the label
___No gaps in the graph, colored neatly
___There is a correct number of colored squares for each category
___Tally marks and number are correctly written at the end(horizontal) or
top(vertical) of each category
Activity: (Small Group With Teacher) *Practice drawing pictures, writing number sentences,
solving, and labeling answers for the following kinds of questions: How many __ and __?,
How many more __ than __?, How many fewer __ than __?, How many “total” or “in all”?
*Examples of Small Group Questioning Practice
*Other students are completing first 2 activities and Standard Graph Questionnaire about
their picture graph.
*Additional group activities/rotations:
1. Picture Graph
-Gather data, make a picture graph (Picture Graph and Bar Graph Template), evaluate
their/each other’s graph (Graph Evaluation Checklist), answer questions about the graph
(Standard Graph Questionnaire).
2. Bar Graph
-Gather data, make a bar graph (Picture Graph and Bar Graph Template), evaluate
their/each other’s graph (Graph Evaluation Checklist), answer questions about the graph
(Standard Graph Questionnaire).
Graph Ideas
-3 types of coins(one handful)
-3 colors of cubes(two handfuls)
-3 sizes of pom poms(two handfuls)
-3 shapes of pattern blocks(two handfuls)
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Unit 10: Operations Using Data Representations
What’s the teacher doing?
-Teaching “Small Group With
Teacher” Activity
Phase-Elaborate, Evaluate
1st Grade
What are the students doing?
-Making their bar graph
-Evaluating their table group’s graphs
-Asking their table group for help and helping their
table group when needed
-Drawing pictures, writing and answering number
sentences about their graphs, and labeling
answers
-Making graphs and answering questions about the
graphs
Day 4 and 5
Activity: Small Group With Teacher:
*Students make up and write situations/questions to match number sentences with unknowns
in each position about different graphs.
*Students follow directions to add and/or remove cells from different graphs
*Other students are completing Standard Graph Questionnaire about different graphs.
Performance Assessment Activity: Provide counting manipulatives for students to select.
Allow students to use hand drawn pictures, printed pictures, Popsicle Pictures, or technology
to create the picture graph (Picture Graph and Bar Graph Template). Present the following
classroom situations and tasks:
Mrs. Smith’s class created a bar-type graph to represent their favorite flavors of Popsicle®.
Each cell represents one student.
1) Use the data in the graph to answer the questions. For each question:


Represent each solution using objects or a pictorial model.
Record the solution to each question using a number sentence. Orally explain how the
equal sign was used in the recorded number sentence.
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Unit 10: Operations Using Data Representations

1st Grade
Orally explain the strategy, property of operation, and/or problem solving process used
to determine the answer.
a) How many classmates prefer strawberry and grape Popsicles® combined?
b) How many more classmates prefer strawberry than orange?
c) Which two flavors have a combined total of 8 votes?
d) How many total classmates are represented in the graph?
e) In writing, create and solve a problem that could be solved using the data in the graph and
the number sentence 2 + __ = 10.
2) Mr. Rogers’ class also created a graph of their favorite Popsicle® flavors. Compared to Mrs.
Smith’s graph, Mr. Rogers’ graph showed the following:



Two fewer classmates voted for strawberry.
Four more classmates voted for orange.
One more classmate voted for grape.
a) Create a picture graph that represents the favorite Popsicle® flavors in Mr. Rogers’ class.
b) Orally explain and justify the category totals represented in the picture graph.
c) In writing, create and solve two different questions and number sentences that represent the
data in the picture graph.
What’s the teacher doing?
What are the students doing?
-Completing Performance Indicators
-Asking Questions
-Monitoring students
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Unit 10: Operations Using Data Representations
1st Grade
Favorite Snack Ballot(Blank) Day 1, Day 2
Directions: Cut and distribute to collect data. Each student draws their favorite snack.
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1st Grade
Unit 10: Operations Using Data Representations
Graph Evaluation Checklist Day 2, Day 3
Name___________________________________ Date________________________________________
Checklist: ___ Graph is titled at the top
___ Each word in the title starts with a capital and is spelled correctly
___ Each category is labeled(to the left if horizontal, at the bottom if vertical)
___ Each row or column starts by or above the label
___ Pictures are lined up
___No gaps in the graph
___There is a correct number of pictures for each category
___Tally marks and number are correctly written at the end or top of each category
-----------------------------------------------------------------------------------------------------------------------------------------Name___________________________________ Date________________________________________
Checklist: ___ Graph is titled at the top
___ Each word in the title starts with a capital and is spelled correctly
___ Each category is labeled(to the left if horizontal, at the bottom if vertical)
___ Each row or column starts by or above the label
___ Pictures are lined up
___No gaps in the graph
___There is a correct number of pictures for each category
___Tally marks and number are correctly written at the end or top of each category
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1st Grade
Unit 10: Operations Using Data Representations
----------------------------------------------------------------------------------------------------------------------------------------Name ___________________________________________
Date ____________________________
Picture Graph and Bar Graph Template p. 1 Day 2, Day 3, Day 4 and 5
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Unit 10: Operations Using Data Representations
1st Grade
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Unit 10: Operations Using Data Representations
1st Grade
Popsicle Pictures Day 4 and 5
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Unit 10: Operations Using Data Representations
1st Grade
Snack Pictures For Survey Day 1, Day 2
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1st Grade
Unit 10: Operations Using Data Representations
Name ______________________________________
Date _________________________
Standard Graph Questionnaire 1 (for use with a 3-category graph) Day 2, Day 3, Day 4 and 5
Teacher Directions: Write, draw, or glue picture into blank to modify for the graph you are using.
Directions: Draw a picture and write a number sentence when asked. Label your answer.
1. How many ____________________?
2. How many ____________________?
3. How many ____________________?
4. How many ____________________ and ____________________?
5. Picture: ____________________________________________________________________
6. Number Sentence: ____________________________________________________________
7. How many ____________________ and ____________________?
8. Picture: ____________________________________________________________________
9. Number Sentence: ____________________________________________________________
10. How many ____________________ and ____________________?
11. Picture: ____________________________________________________________________
12. Number Sentence: ____________________________________________________________
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Unit 10: Operations Using Data Representations
1st Grade
Standard Graph Questionnaire 2 (for use with a 3-category graph) Day 2, Day 3, Day 4 and 5
Teacher Directions: Write, draw, or glue picture into blank to modify for the graph you are using.
Directions: Draw a picture and write a number sentence when asked. Label your answer.
1. How many total snacks?
2. Picture: ____________________________________________________________________
3. Number Sentence: __________________________________________________________
4. How many more ____________________ than ____________________?
5. Picture: ____________________________________________________________________
6. Number Sentence: __________________________________________________________
7. How many fewer ____________________ than ____________________?
8. Picture: ____________________________________________________________________
9. Number Sentence: __________________________________________________________
10. How many more ____________________ than ____________________?
11. Picture: ____________________________________________________________________
12. Number Sentence: __________________________________________________________
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Unit 10: Operations Using Data Representations
1st Grade
Standard Graph Questionnaire 3 (for use with a 3-category graph) Day 2, Day 3, Day 4 and 5
Teacher Directions: Write, draw, or glue picture into blank to modify for the graph you are using.
Directions: Draw a picture and write a number sentence when asked. Label your answer.
1. How many fewer ____________________ than ____________________?
2. Picture: ____________________________________________________________________
3. Number Sentence: ____________________________________________________________
4. How many more ____________________ than ____________________?
5. Picture: ____________________________________________________________________
6. Number Sentence: ____________________________________________________________
7. How many fewer ____________________ than ____________________?
8. Picture: ____________________________________________________________________
9. Number Sentence: ____________________________________________________________
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1st Grade
Unit 10: Operations Using Data Representations
Examples of Small Group Questioning Practice Day 3
       


   






Most-fewest=how many more
Most-fewest is the same as how many more
7-3=4
__-3=4
7-__=4
7-3=__
__ -__ is the same as __
-=3
- is the same as 3
Most-fewest=how many fewer
Most-fewest is the same as how many fewer
7-3-4
__-3=4
7-__=4
7-3=__
__ -__ is the same as __
-=3
- is the same as 3
7+3=10
3+7=10
+=10
+ is the same as 10
+=10
+ is the same as 10
__+3=10
7+__=10
7+3=__
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Unit 10: Operations Using Data Representations
1st Grade