Illuminations: Looking Back and Moving Forward

Looking Back and Moving Forward
In this final lesson of the unit, students display their knowledge of properties of objects for sorting and creating patterns. They also demonstrate an understanding of commutativity and model addition and subtraction of whole numbers using different representations.

Learning Objectives
 
Students will be able to:
  • sort, classify, and order objects by size, number, and other properties
  • recognize, describe, and extend patterns such as sequences of sounds and shapes or simple numeric patterns and translate from one representation to another
  • analyze how both repeating and growing patterns are generated
  • illustrate general principles and properties of operations, such as commutativity, using specific numbers
  • Model situations that involve the addition and subtractions of whole numbers, using objects, pictures, and symbols

Materials
 
  • Crayons
  • Paper plates

Instructional Plan

Divide the class into groups, and tell the students that they are going to act out stories about making healthy food choices. Assign one group of students to each section of the food pyramid, and ask them to draw one food from that section on their paper plate. In turn, call on one volunteer from each group to select a day's worth of healthy foods from among the student drawings. For each section, assign a volunteer to record the number sentences that the groups are modeling. [For the group assigned to the fruit section, for example, if two students drew oranges, one student drew an apple, and another drew a pear, the number sentence would be 2 + 1 + 1 = 4.]

Call out the food groups one at a time and ask the students who drew the pictures in that group to stand. Record the group and the number of students on the board [fruits, six; vegetables, eight]. Now ask a student to name any food group, note how many students are in that group, and write a missing addend statement on the board [6 + __ = 8]. Next, have the student call on the number of students to come to the front of the room that are required to represent the given addend [6].

Ask the other students, "How many more students need to join them to make the addition sentence correct?" [Two] Have the volunteer give the answer by calling the correct number of additional students to the front and completing the number sentence. [For example, if the sentence is 5 + _ = 9, five students will be called in the first group and then four more called.] Then, call on other volunteers to provide and model other number sentences with missing addends.

When you have reviewed these mathematical ideas, have the students return to their seats and draw pictures of four different problems with missing addends. You might wish to use the pictures of foods included in this unit. Keep the work samples to assess the level of each student's understanding of the mathematical objectives of this unit.

Questions for Students
 
  1. What activities were most students comfortable with?
  2. Which students met all the objectives of this unit? What extension activities are appropriate for those students?
  3. Which students did not meet the objectives of this unit? What additional instructional experiences do they need?
  4. Did all the students display an ability to work with a partner?
  5. What were the greatest challenges for the students?
  6. Which books were best received by the students?

Teacher Reflection
 
Looking Back
  1. What activities were most students comfortable with?
  2. Which students met all the objectives of this unit? What extension activities are appropriate for those students?
  3. Which students did not meet the objectives of this unit? What additional instructional experiences do they need?
  4. Did all the students display an ability to work with a partner?
  5. What were the greatest challenges for the students?
  6. Which books were best received by the students?

The concept of missing addends is difficult for students to grasp when they only work with computational problems presented on a worksheet. Students need multiple experiences using models to understand the idea of the missing parts.

Kathy Richardson's book, Developing Number Concepts, presents many ways to lead students to a sound sense of number and number relationships. Richardson suggests that hiding cubes under a container helps students begin to realize that the missing addend is related to the total number of objects.

Consider the following questions as you plan for the next set of lessons appropriate for your class. Review the assessment data collected during each lesson to identify specific needs of particular students.

Moving Foward

  1. How can I help the students connect the important ideas in this set of lessons to other ideas in mathematics?
  2. What other situations would extend the students' experiences with subtraction?
  3. When should I revisit or extend the fundamental ideas of this unit?
  4. What other books could I use in this unit?
  5. What learning experiences would help the students not yet comfortable with these concepts?

NCTM Standards and Expectations
 
Algebra Pre-K-2
  1. Analyze how both repeating and growing patterns are generated.
  2. Recognize, describe, and extend patterns such as sequences of sounds and shapes or simple numeric patterns and translate from one representation to another.
  3. Use concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations.
  4. Sort, classify, and order objects by size, number, and other properties.
  5. Illustrate general principles and properties of operations, such as commutativity, using specific numbers.
  6. Model situations that involve the addition and subtraction of whole numbers, using objects, pictures, and symbols.

References
 
  • Richardson, Kathy. Developing Number Concepts: Addition and Subtraction. N.J.: Dale Seymour Publications, 1999.
This lesson prepared by Grace M. Burton.
  
1 period   

NCTM Resources

Principles and Standards for School Mathematics

Web Sites
National Council of Teachers of Mathematics Thinkfinity Verizon Foundation
More and Better Mathematics for All Students
© 2000 National Council of Teachers of Mathematics
Use of this Web site constitutes acceptance of the Terms of Use

The National Council of Teachers of Mathematics is a public voice of mathematics education, providing vision, leadership, and professional development to support teachers in ensuring mathematics learning of the highest quality for all students. The views expressed or implied, unless otherwise noted, should not be interpreted as official positions of the Council.