Sorry! This resource requires special permission and only certain users have access to it at this time.
Lesson Content

Lesson Plan Template:
General Lesson Plan

Learning Objectives: What should students know and be able to do as a result of this lesson?
The students will show understanding of the conservation of numbers regardless of the order in which they were counted. The students will be able to tell "how many" without recounting objects and be able to explain that the amount is the same because no objects were added or taken away.

Prior Knowledge: What prior knowledge should students have for this lesson?
 Students should understand the standard counting sequence when counting by ones.
 Students should know onetoone correspondence (be able to correctly assign one number word to one object).
 Students should be able to keep track of which objects have already been counted so they are not counted more than once.

Guiding Questions: What are the guiding questions for this lesson?
This question is used when initially determining the amount in a group. The child will actually count the items with the initial question.
The question is asked again after the items are put in a different order. In this case, the child should immediately answer without recounting.
 How do you know?
 Is this correct?
 Does this work all the time?
 We know this is not correct. How can we fix this?
 Do you agree? Why or why not?
 What action is taking place?

Teaching Phase: How will the teacher present the concept or skill to students?
1. The teacher will choose 3 students to stand in a straight line facing the class. The teacher will ask, How many students? Allow students to answer without accepting or correcting any answers.
2. The teacher will ask, "How do you know?" Invite at least one student to demonstrate counting using onetoone correspondence. Students should use a number word to name each child. Ask the class, "Do you agree? Why/why not?"
3. The teacher echoes the child's counting by repeating the number word naming of each child. "Let me understand...so this is one, this is two, and this is three?"
4. The teacher says, "Let's give them a label." Teacher places a label on each child (1, 2, 3). Ask the students, "Is this correct?" Discuss with students. "Do you agree? Why/why not?" Students will probably view this as correct.
5. Now change the order of the students. Put the students in order 2, 3, 1. Read the number names as if you are counting and appear puzzled to students. "Wait...something doesn't seem right. Does this make sense?" Encourage discussion among students. Students should recognize the numbers are not in order. "Why is this not correct?" Students should verbalize that numbers follow a sequence or a pattern. Students should also express that number words are "tags" that we assign when counting objects (onetoone principle). "Do you agree? Why/why not?"
6. Ask students, "How many students are here?" Students should identify there are 3 students. Discuss counting with students and be sure to discuss that the final number word assigned represents the amount of the whole group (cardinal principle).
7. "What action is taking place?" The only action that is taking place is changing the order of the students. No students are being added and no students are being taken away.
8. "We know this is not correct. How can we fix this?" Wait to see if the students suggest changing the number labels. Leave the students in the same rearranged order that you placed them in, but change the number labels. Try changing the order of the same three students a few times and discuss how many.

Guided Practice: What activities or exercises will the students complete with teacher guidance?
 Continue with the activity in the Teaching Phase. Line up different children and different amounts of children in lines (no number labels needed for this part).
 Be sure to have each child demonstrate onetoone correspondence prior to asking questions about how many. If a child is unable to correctly use onetoone correspondence, then see accommodations and remediate the child before moving on to how many without counting again.
 Rearrange the order of the lines.
 Discuss that the order of the items doesn't change the total amount of items in the line. Repeat this step until most (or all) of the students seem confident with the concept.
 Be sure to reinforce to students that the amount of students is the same each time, nothing is added and nothing is taken away. Only the order is changing.

Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
1. Set up a bag of cubes for each of your students. The amount of cubes in each bag depends upon the abilities of each student. For example, if a student is struggling, start with 35 cubes. If a student appears to grasp the concept, give the student about 10 cubes.
2. Give each student a bag of cubes, a student practice sheet, and strips of paper cubes to cut apart.
3. You will probably need to read the practice sheet to students.
4. Circulate the room and question students about their work. Use the formative assessment checklist and rubric to guide your questioning and be sure to record observations as necessary.
Practice_Student_Sheet.docx
Practice_Student_Sheet_squares.docx

Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Verbally discuss the following questions with your students:
 Use some colored cubes, or another item, and make a line.
 Ask the students "How many?"
 Students may count to determine the amount initially.
 Ask other students "How many?" "How do you know?"
 Students should reply that nothing was added, nothing taken away. Only the order is changing.
 Why is this knowledge useful in math? (no need to count items in a group if no changes to amounts are made  more efficient)
Administer the Summative Assessment when you believe the children are ready for it.
Summative Assessment: Summative_Assessment_Rubric.docx

Summative Assessment
1. Each child will be assessed individually by the teacher.
2. Give the student a bag of colored cubes (any combination of colors is fine, but be sure there is an assortment of colors). The number of cubes can vary based on a student's counting ability. A student struggling with counting abilities could start with 3, whereas a child with advanced counting abilities could have 10 cubes to count.
3. Ask the child to count the cubes. Use the rubric to determine the child's level of understanding.
4. Ask the child, "How many?" Use the rubric to determine the child's level of understanding.
5. Ask the child to rearrange the order of the colored cubes in the line. The child should move the blocks. Then ask the child, "How many?" If the child instantly identifies the number of items without counting the items again, ask, "How do you know?" Use the rubric to determine the child's level of understanding.
6. If the child is successful and has reached level 3 on each area assessed, then continue the assessment by providing the student with a new set of items (up to 10). Repeat the assessment and use the rubric to determine the child's level of understanding.
Summative Assessment Rubric: Summative_Assessment_Rubric.docx
You can print one rubric per student or print one and record the information in your gradebook, etc.

Formative Assessment
 Be sure to read the Summative Assessment Rubric prior to the lesson so you are clear on the students' expectations.
 The teacher should record observable behaviors and information about each child's explanations during the Teaching Phase and Guided Practice. You can record the information you collect on a class list kept on a clip board, or any method of your personal preference.
 Print the Summative Assessment Rubric and keep on a clip board to refer to when analyzing your observations of your students' behaviors.
 Evaluate your students' progress and abilities, and then plan further and/or future instruction. Depending on your students' level of understanding, you may need to repeat the learning activities in the teaching phase several times over a period of time.
 Assess onetoone correspondence EACH time before moving on to cardinality questions. If there are any issues with onetoone correspondence, provide remediation in this area first.
 If students are struggling in specific areas, please see the accommodations section for remediation suggestions. The suggestions can be used for the entire class, for small groups, or for individual students.
Summative Assessment Rubric: Summative_Assessment_Rubric.docx
Formative Assessment Checklist: Formative_Assessment_Checklist.docx

Feedback to Students
 During the Teaching Phase and Guided Practice, while students are participating in the learning activities, observe how the child determines "how many" and ask the student to explain and justify.
 A child demonstrates an understanding that the number of objects is the same regardless of their order/arrangement if a student instantly identifies the total amount of items without counting again. The student should be able to explain that the total amount of items is the same because none have been added or taken away.
 If a child recounts the items, did we add any or take any away? If zero were added and zero were taken away, then there is the same number as when you counted it the first time.
Assessment
 Feedback to Students:
 During the Teaching Phase and Guided Practice, while students are participating in the learning activities, observe how the child determines "how many" and ask the student to explain and justify.
 A child demonstrates an understanding that the number of objects is the same regardless of their order/arrangement if a student instantly identifies the total amount of items without counting again. The student should be able to explain that the total amount of items is the same because none have been added or taken away.
 If a child recounts the items, did we add any or take any away? If zero were added and zero were taken away, then there is the same number as when you counted it the first time.
 Summative Assessment:
1. Each child will be assessed individually by the teacher.
2. Give the student a bag of colored cubes (any combination of colors is fine, but be sure there is an assortment of colors). The number of cubes can vary based on a student's counting ability. A student struggling with counting abilities could start with 3, whereas a child with advanced counting abilities could have 10 cubes to count.
3. Ask the child to count the cubes. Use the rubric to determine the child's level of understanding.
4. Ask the child, "How many?" Use the rubric to determine the child's level of understanding.
5. Ask the child to rearrange the order of the colored cubes in the line. The child should move the blocks. Then ask the child, "How many?" If the child instantly identifies the number of items without counting the items again, ask, "How do you know?" Use the rubric to determine the child's level of understanding.
6. If the child is successful and has reached level 3 on each area assessed, then continue the assessment by providing the student with a new set of items (up to 10). Repeat the assessment and use the rubric to determine the child's level of understanding.
Summative Assessment Rubric: Summative Assessment Rubric.docx
You can print one rubric per student or print one and record the information in your gradebook, etc.
Accommodations & Recommendations
Accommodations:
The more counting experiences a child has, the fewer errors the child makes. Counting skills improve with frequent counting practice and repetition. Unison counting activities offers auditory repetition of the number word counting pattern.
If a child has not reached security in the number word sequence and/or onetoone correspondence, determine the number at which point the child is secure in counting to. (For example, the student counts, "one, two, three, four, five, six, seven, eight, nine, eleven, ten." The child appears to be stable with the counting order to nine.)
Practice counting activities to one number beyond the child"s point of difficulty. (If the child is stable counting to nine, then practice with counting activities to ten). Continue this practice and reassess periodically. If students are struggling with cardinality, follow the same guidelines and continue to work with small numbers and build to larger numbers.
Extensions:
 Children that have mastered 10 items can focus on groups up to 20.
 Give children tasks of counting objects in the classroom. See the attachment for ideas of items to count. You can modify the questions to fit your students needs and your classroom setting.
Extension Counting.docx

Suggested Technology: Computer for Presenter, Internet Connection, Microsoft Office
Special Materials Needed:
 number "labels" for students to wear in the Teaching Phase
 students
 a bag of colored cubes for EACH child
 a practice sheet for EACH child
 square sheets for children to share
 scissors
 glue
 crayons or coloring utensils & pencils or writing utensils
Further Recommendations:
 Use colored cubes, or some other type of math manipulative for the students to count during independent practice.
 Put the objects in bags prior to the independent practice. Plastic, "zipable" bags work well, or any other method you prefer.
 Create number labels prior to the lesson. You can create a "yarn necklace" by writing or printing the numbers 1, 2, & 3 on a sheet of paper and attaching yarn for easy number labels during the Teaching Phase.
Additional Information/Instructions
By Author/Submitter
The Mathematical Practice Standards aligned to this lesson include: MAFS.K12.MP.2. Make sense of problems and persevere in solving them. Students have to figure out how to correct the counting order when counting students in line. MAFS.K12.MP.6.1 Attend to precision. Students explain how they know using words, examples, and nonexamples. MAFS.K12.MP.7.1 Look for and make use of structure. Students learn the pattern of counting and apply their knowledge within the counting sequence.
Source and Access Information
Contributed by:
Tracey Mitchell
Name of Author/Source: Tracey Mitchell
District/Organization of Contributor(s): Volusia
Is this Resource freely Available? Yes
Access Privileges: Public
* Please note that examples of resources are not intended as complete curriculum.