Illuminations: Looking Back and Moving Forward

Looking Back and Moving Forward
Before moving on, it is essential for students to have a command of the mathematical content and skills identified in the “Overview:” Students collect data using objects, pictures, and symbols. They organize data by sorting and classifying in different ways. Students display data using multiple representations. Students engage in such skills as problem solving, reasoning, and proving, communicating, connecting, and representing fundamental ideas about data. For a culminating activity, students should demonstrate their ability to use the experiences of all the lessons in this sequence in a new context.

Learning Objectives
 
Students will be able to:
  • formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them
  • sort and classify objects according to their attributes and organize data about the objects
  • represent data using concrete objects, pictures, and graphs

Materials
 

Instructional Plan

Accomplish this by having students organize and display a set of objects to generate a bar graph. Give students small objects to sort, organize, and display on a bar graph.

Ask students to sort the objects and name their sorting rule, then record this information by drawing a picture or writing the rule. Next have students place the objects on the graph grid (provided at the end of this lesson) to create a concrete graph. Finally ask them to generate an abstract grid by coloring a separate graph grid to represent the sorted objects.

Students at the upper end of this grade band should include a title and labels. Some younger students may be able to copy a title and label and others might dictate them. These two samples should be reviewed to determine the level of understanding of each student.

Teacher Reflection
 

Looking Back

  1. What key ideas do the majority of the students apply consistently?
  2. Which students met all the objectives of this lesson? What extension activities are
    appropriate for those students?
  3. Which students did not meet the objectives of this lesson? What instructional
    experiences do they need?
  4. What other learning experiences would help students identify similarities? Differences?
  5. What knowledge and skills do students need to better describe graphs?
  6. Can students recognize properties of objects as ways to organize them?
  7. Can students sort objects using multiple strategies? Can they explain and defend the rules they use?
  8. Do students understand that one-to-one correspondence is required for creating a bar graph?
  9. What were the greatest challenges for the most students?
  10. Which portions of this Unit Plan were the students most motivated to complete?

This set of questions may help you determine the focus of your next instructional activities.
Documenting the level of each student’s understanding makes accurate information available for planning the appropriate subsequent instructional activities.

Moving Forward

  1. 1. How can I help students focus on important ideas to record about this and other mathematics lessons?
  2. What other data could I model for students that would have meaning for them?
  3. What other learning experiences will help students develop and answer questions about graphs?
  4. How might I connect the key ideas with lessons about data with lessons about other mathematics content?
  5. What learning experiences that we routinely use would help student develop and respond to questions? How can these be changed to better facilitate question posing?
  6. In which other mathematics experiences do we or could we use a grid?
  7. How can I help students focus on important ideas to record about this and other mathematics lessons?
  8. What new assessment tools would enable me to gather data on my students’ performance and progress toward learning targets

NCTM Standards and Expectations
 
Data Analysis & Probability Pre-K-2
  1. Represent data using concrete objects, pictures, and graphs.
  2. Sort and classify objects according to their attributes and organize data about the objects.
  3. Pose questions and gather data about themselves and their surroundings.
  4. Describe parts of the data and the set of data as a whole to determine what the data show.
  5. Discuss events related to students' experiences as likely or unlikely.
This lesson prepared by Grace M. Burton and Carol Midgett.
  
1 period   

NCTM Resources

Navigating through Algebra in preK‑2

Web Sites
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