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Charting

Last edited - August 7, 2026

One variable charts for primary grades

Questioning is the foundation of all learning.
The first step in rejecting not knowing is to ask, why?
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Overview

Introduction

This page includes activities with pedagogical information, for introducing and developing chart literacy in the primary grade levels along with the development of number values, classification, data analysis, problem solving, and patterns & algebra.

Related graphing resources

Planning information

Background information

Background information necessary is prenumber sense necessary to represent the values of the data along with experiences with activities such as the following:

  • Lock Block Graphs - Pairs of learners take two random handfuls of multi-colored connecting cubes, sort them by color, and stack them into physical columns to directly compare which stack is taller and they transferr the data to grapgh paper.
  • Spin and Graph - Pairs of learners spin a paperclip spinner multiple times, tally the results using tally marks, and color in a blank bar template to compare the outcomes.
  • Living Graphs - Pairs of learners line up physically in rows based on categories like their birth month or how they get to school (bus vs. walking), creating a real-life bar chart in the classroom.

Intended learnings

Charting and graphing K-3 mapping

K - 3 average, chart, bar graph, concrete real object graph, data, grid, picture graph, table, tally, trial.

Charts are powerful ways to communicate information about data (objects, people, thoughts, ideas, emotions, characteristics, likes, & dislikes).

In the primary grades comparisons is the focus.

Bar charts to compare the frequency of different groups or categories of data side by side. (objects, people, thoughts, ideas, emotions, characteristics, likes, & dislikes)

Column charts, similar to bar charts, but use vertical columns to show item differences over a short period or across categories. These are a good way to introduce one variable statistics - with a one variable chart that displays data for a single variable and show its distribution - frequency (how often a value occurs) or range of values (highest to lowest) & measures of central tendencies (mean, median, mode), or trend. Examples include bar charts, histograms, and pie charts.

Group of flowers with four types

How many of each type of flower is there? Make a chart to show their population!

Four flowers Four flowers

 

Use the flowers in your chart!

Social skills - Groups

Working in groups reduces stress and stereotyping: Groups provide a lower risk free environment to participate, make mistakes, and look for solutions.

Additionally learners sometimes view math more as a male subject or other racial preferences rather than gender and racial neutral.

Both can cause them to begin to doubt their competence in math and can believe they can't do math.

Most learners, including females, tend to learn math better when taught using groups rather than the traditional competitive classroom methods of teacher demonstrating and lecturing.

Making this a truly cooperative lesson would further reduce the competition.

Activities that are a cooperative endeavor in finding solutions and justifying them rather competition against accuracy rather than time will also encourage more students.

Asking each learner group to prepare as an expert to demonstrate his or her method to his or her peers can provide motivation and focus.

Mathematical content - number value, geometry, measurement, algebra, data analysis, statistics, and probability

(What mathematics explains - enduring understanding, big ideas, generalizations)

Sets of related numbers can be visually represented in charts and graphs.

Concepts and facts - from algebra & patterns ...

  • Charts are a visual representation of a distribution of a set of data.

Outcome

  • Solve and demonstrate the solutions to problems using charts.

Specific outcomes -

  1. Decide how to collect data.
  2. Set up and label a chart.
  3. Labeling the key using the correct units.
  4. Provide a title that is a relationships.

Anticipated learner thinkings & misconceptions
(Source concepts & misconceptions)

Miconception - as concepts

  • Charts only represent numbers.

Miconception - as outcomes

  • Don't use a consistent scale that creates distorted data.
  • Misplacing data points in the wrong column.

Mathematical Processes - Problem solving, representation, proof and reasoning, communications, and connections

(How mathematics inquires - process, skill, methodology)

Together people can use a general problem solving procedure to solve problems and verify their answers with different solutions to better convince each other of their validity.

Concepts and facts -

  • Solving problmes can be assissted with a problem solving heuristic.

Outcome

  • Solve a problem using a problem solving heuristic.
  • Use different representations to communicate, by demonstrating solutions.

Specific outcomes -

  1. Problem solving heuristic includes general steps for solving mathematical problems
  2. Use graphs to represent equations and mathematic relationships of variables.
  3. Solve two equations with two unknowns using four methods: graphing, substitution, addition, and determinants.
  4. Communicate with peers of the same and opposite sex mathematical ideas.

Habits of mind - values, attitudes

(Attitudes and values that contribute to mathematical success)

Curiosity, open-minded, skepticism, persistence, .

Concepts and facts -

  • Both sexes are equally capable of learning and teaching math.
  • Diverse populations can achieve similar results.
  • Cooperation brings together diverse ideas for the benefit or all.

Outcome - cooperation and planning

  • Develop attitudes and skills for cooperation.
  • Develop planning skills.

Specific outcomes -

  1. Cooperations looks, sounds, and feels like:

Scoring guides suggestions (rubric)

Graph creations (scoring guide)

Correctly graph a set of equations on the same Cartesian coordinate system

  • Decide what data to collect to answer a question.
  • Collect necessary and sufficient data to answer their question.
  • Set up and label a chart to display their data.
  • Labeling the chart using accurate units.
  • Provide an appropriate title.

Communication of mathematical ideas.

 

Habits of mind for cooperation - listen, don't interrupt, respond to others ideas, use others ideas as example or as showing an exception

 

Pedagogical Overview & Strategies to achieve educational learnings

Based on learning cycle theory & method for instruction

Activities Sequence to provide sufficient opportunities for students to achieve the targeted outcomes.

Make sure learners have the prior knowledge identified in the background information.

  1. Activity 1 - Intro with Uma's story.
  2. Activity 2 -
  3. Activity 3 -
  4. Activity 4 -
  5. Activity 5 -
  6. Activity 6 -

Vocabulary

  • Data - information we collect for a purpose. (for reference or analysis).
  • Tally - a mark to represent a number. A way to count.
  • Chart - a representation of data.
  • Compare - to see what is the same or different or more or less.
  • Inventory - a complete list of items such as property, goods in stock, or the contents of a building, classroom, or office.

Focus question

Unit focus question:

How can we make s a visual representation that describes our ___ (classroom, home, school)?

Sub focus questions:

  1. What categories describe our classroom/ home?
  2. What counts as an item in a category?
  3. What are the elements of a chart and how are they used?

Materials

  • Sheets of different colored dots, sticky notes, tally sheet,
  • Graph paper - page with 42 squares high x 32 squares wide

Lab notes

Resources

Lesson Plans

Activity 1 - Meat or cheese sandwich

Materials

  • Uma Wimple Charts Her House. by Reif Larsen and Ben Gibson - Uma's teacher gives the class what she thinks is a dream assignment. Make a chart of their own homes. However, she isn't sure what makes a house housey? Uma figures oit is her family. Tthe love that is shared inside a house's walls.
  • Graph paper - page with 42 squares high x 32 squares wide
  • Lab note

Focus questions:

  1. What is a chart?
  2. What does it mean to chart a home?
  3. How are the charts the same and different?
  4. What kind of data or information was collected in the story?
  5. What are the different ways to organize the data?
  6. What are the different ways to represent information?
  7. What makes a house, housey?
  8. How did Uma represent her home?
  9. What are love levels?
  11. How could we make a plan to find out what is in our classroom, organize it, and make sense of what we see? (desks, chairs, bookshelves windows, cubbies, plants, books, ...) What is a chair? Something to sit on? (bean bag, stool, carpet square?
  12. How do we define each category?

Learning outcomes:

  1. Decide what might represent a classroom. How to count them, count them, and represent them on a chart.

Suggested procedures overview:

  1. Put learners in groups, focus their attention, and assess their initial understanding of the focus questions.
  2. Activity -

Exploration -

  1. Put learners in pairs.
  2. Read the book Uma Wimple Charts Her House. or explain what an inventory is and suggest they make an inventory of the classroom. Inventory - a complete list of items such as property, goods in stock, or the contents of a building, classroom, or office.
  3. Sample book questions:
    1. What kind of information is collected by the characters in the book?
    2. What different ways did they organize the data?
    3. How is the bumper car and Ferris wheel data the same?
    4. How could they figure out how many were in each line?
    5. What would you want to know about the student's height?
    6. How could you collect information about people's favorite rides?
    7. What is special about the title for each chart?
    8. How does the tile help for each chart?
    9. What is on each side?
    10. What is on the x-axis and y-axis?
    11. How are the charts different and the same?
    12. How would you decide to use a bar graph or a picture graph?

Invention -

  1. Explain and discuss with the learners.
  2. Have them explore the book with a notice and wonder page.
  3. Could something be counted in more than one category?
  4. What does independent mean?
  5. What is a double bar graph? When would you use it?
  6. What is a pictograph?
  7. What is the difference between a bar chart and line graph?
  8. What kind of data does a pie chart represent well?
  9. Make an anchor chart: What do good graphs have? title, accurate clear scale, labels, organized data, accruate comparison.
  10. Whys is starting the scale at zero important?

Discover

What are you curious about in the classroom?

What questions could we answer by collecting data?

How we get to school?
What do we do when we get home?

Explore questions and ask how to make a plan to answer some.

choose a questions.

Decide how to answer it. survey count measure tally

Collect information in pairs with tally sheets

Organize the data with a frequency chart.

Decide what type of chart woul be best to represent the ata.

Use graph paper, dots, sticky notes, real objects, to design the graph.

Are all the important elements of a chart included?

Evaluate with questions such as

How does the type of graph you chose fit the data?

How is the chart clear for others to understan?

How does the title focus on attention on the purpose of the chart?

What elements make the chart informational?

 

 

Activity 2 - Meat or cheese sandwich

Materials

Focus questions:

  1. How can I make a mathematical representation for ?

Learning outcomes:

  1. Make a t .

Suggested procedures overview:

  1. Put students in groups, focus their attention, and assess their initial understanding of the focus questions.
  2. Activity -

Exploration

  1. Put students in pairs.

Invention

  1. Recall and review

Discover


Activity 3 -

Materials:

Focus questions:

Learning outcomes:

  • T

Suggested procedures overview:

  1. Put students in groups, focus their attention, and assess their initial understanding of the focus questions.
  2. Activity -

Exploration

  1. Put learners in pairs.

Invention

  1. What

Discovery

  1. Discuss how


 

Activity 4 -

Materials

Focus questions:

  1. How does

Learning outcomes:

  1. Learners

Suggested procedures overview:

  1. Put students in groups, focus their attention, and assess their initial understanding of the focus questions.
  2. Activity -

Exploration

  1. Ask.

Invention

  1. Ask. How

Discover

Activity 5 - Tee shirt decisions

Materials:

Focus questions:

  1. How do we determine t

Learning outcomes:

Suggested procedures overview:

  1. Put students in groups, focus their attention, and assess their initial understanding of the focus questions.
  2. Activity -

Exploration

  1. Organize learners into pairs or larger groups.

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Exploration

  1. Put learners into groups.
  2. Present them with the

Invention

  1. Each group explains their chart.

Discovery

Activity 6 -

Materials

Focus questions:

  1. What are the different ways to

Learning outcomes:

Pedagogical ideas

 

The jigsaw model asks learners to understand a method of solving equations, communicate their understanding to her or his peers, and to attempt to help the other group members to understand it and plan a demonstration for the method to the other peers. This enables every class member to have an area of expertise and empowers all learners to be valuable and capable among their peers, which helps improve their self-efficacy with math and social communications with peers.

Suggested procedures overview:

  1. Put students in groups, focus their attention, and assess their initial understanding of the focus questions.
  2. Activity - Have learners use the jig-saw method to learn and prepare to be an expert to demonstrate one of the four ways to solve problems with two unknowns.
  3. Repeat the process four time.
  4. Identify problems and select solution methods and discuss reasons for selecting each method.

Possible Activity Sequence

Exploration

  1. Organize learners into groups and pairs.
  2. Put learners into four work alike groups with eq

Invention

  1. Each learner in

Discover

  1. Have lear

 

Lab Notes for activities

Lab notes 1 -

Materials

Focus questions:

  • How can I make a mathematical representation for ?

Challenge

Create a procedure to represent your classroom ___

  • What data can be used to describe our classroom?
  • What data should we collect?
  • How do we collect data?
  • Collect data.

 

Object Count Other information
1    
2    
3    
4    
5    
6    
7    
8    
9    
10    

 

Draw and label a chart for the relationship of your classroom!

  • Label the axes using the correct units.
  • Provide a title

 

Lab notes 2 -

Materials

Focus questions:

  • How can I make a mathematical representation for

Challenge

Design y

 

 

 

 

Collect data

             
1            
2            
3            
4            
5            
6            
7            
8            
9            
10            

 

Draw and label a chart for the relationship of !

  • Label the axes using the correct units.
  • Provide a title that

Lab notes 3 -

Materials

Focus questions:

  • How d

 

Challenge

 

 

 

 


Lab notes 4 -

Materials

Focus questions:

  • How

Challenge

 

 

 

Lab notes 5 - Tee shirt decisions

Materials

Focus questions:

  • How can

Challenge

 

 

 

 

 

 

 

 

 

Lab notes 6 -

Materials

 

Challenge

 

 

 

 

Substitution -

 

 

 

 

Addition -

 

 

 

 

Determinants

Support materials

 

 

 

 

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