Feast for 10

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There  are  10  kids  sitting  at  the  lunch  table  at  school.   How  many  kids  are  boys  and  how  many  are  girls?  Show  as  many  ways  as  you  can.

Centreville Group_Lesson_study_Ppt

Goals:

Task: There are 10 kids sitting at the lunch table at school.  How many kids are boys and how many are girls? Show as many ways as you can.

Students will be able to represent their thinking using mathematical models in order to demonstrate understanding of combining two sets. In this kindergarten lesson, students will understand the concept of combining two sets and be able to represent at least one model with a sum of 10. Students are learning to communicate their learning and understanding by using models and explaining them to their peers and teachers.  Students who are able to use models to represent their thinking are more flexible in their mathematical strategies and are able to solve problems in multiple ways. As students manipulate numbers with models and in problem solving tasks they will develop a stronger sense of number relationships.

After our pre-lesson discussion, we decided our goal for the lesson would be for students to show as many combinations of 10 as they can find.

Students’ prior knowledge should include the ability to orally count a set of 10 or fewer objects with one to one correspondence and the ability to make one or more groups that represent a quantity up to ten. The problem in this lesson also requires that students have some familiarity with a group sitting around a table (e.g., cafeteria table, classroom table, dinner table, etc.). They also need to understand the vocabulary of boys and girls.

To access students’ prior knowledge we will ask questions such as:
How many do you see in this group?
How do you show (a given number)?
Count from 1 to 10 or count from a given number to 10.
If two students each have some candy, how can you find out how much candy they have all together?
When we go to the cafeteria, where do we sit?
How do we sit in the cafeteria?
Where are some places that we sit in groups?
How many boys and girls are at your table group?
What is a group?
Can you have a group of 1 or zero?

Anticipate:

Kindergarten students may use a variety of mathematics manipulatives to represent their thinking. Some manipulatives they may use are: connecting cubes, bear counters, two-sided counters, fingers, tens frame, write numerals, or draw a picture. Using any of the materials above, students may solve the problem using one of the following strategies:

  1. Count one object at a time beginning with the number one. Students using this strategy may move the objects into groups first and then count from one to ten or they may count ten objects and then move them into groups. There may or may not be organization to their groupings (e.g., groups may be 5 and 5, 6 and 4, 8 and 2, 1 and 10, in random order).
  2. Count a set and then count on to 10. For example, a student may count 4 and then count on to determine the second group of 6. Students using this strategy may or may not have an organized method of determining the beginning set.
  3. Begin with a known addition fact for 10. Students that use this strategy may only know one fact and will only have one solution method. Some students that use this strategy may begin with the known fact and then manipulate the addends to create additional facts. For example, the known fact may be 5 and 5 which could then be manipulated to be 6 and 4 or 7 and 3.
  4. Anticipate:Kindergarten students may use a variety of mathematics manipulatives to represent their thinking. Some manipulatives they may use are: connecting cubes, bear counters, two-sided counters, fingers, tens frame, write numerals, or draw a picture. Using any of the materials above, students may solve the problem using one of the following strategies:

    1. Count one object at a time beginning with the number one. Students using this strategy may move the objects into groups first and then count from one to ten or they may count ten objects and then move them into groups. There may or may not be organization to their groupings (e.g., groups may be 5 and 5, 6 and 4, 8 and 2, 1 and 10, in random order).
    2. Count a set and then count on to 10. For example, a student may count 4 and then count on to determine the second group of 6. Students using this strategy may or may not have an organized method of determining the beginning set.
    3. Begin with a known addition fact for 10. Students that use this strategy may only know one fact and will only have one solution method. Some students that use this strategy may begin with the known fact and then manipulate the addends to create additional facts. For example, the known fact may be 5 and 5 which could then be manipulated to be 6 and 4 or 7 and 3.
    4. Separate one object at a time from the group of 10 objects to show two groups. Students using this strategy will initially count a set of 10. Then the student will take one from the ten to create groups of 1 and 9. The student may or may not continue in number order creating other groups such as 2 and 8, 3 and 7, 4 and 6, etc.
    5. Count 10 and separate into two groups. Students may count ten objects and then arbitrarily divide them into two groups. Students may divide the groups in an organized way or randomly.
    6. Students may use the communitive property of addition to find solutions that use the same addends. For example, students may find the solution 3 and 7 and use the communitive property to also find the solution 7 and 3.
    7. Students may look for patterns in their solutions. One pattern they may notice is when the first addend increased by 1 the second addend decreases by 1(e.g., 1 and 9, 2 and 8, 3 and 7, 4 and 6, etc.).

    Possible misconceptions:

    1. Students may not understand that a larger quantity can be represented as two smaller quantities combined. They would show a group of ten but not divide the total into two groups (one for boys, one for girls).
    2. Students may think that they can only represent the students they have in their classroom. For example, if there are only 6 girls in the class, they may only represent a group of girls up to 6.
    3. Students may believe there is only one possible combination and will not be able to show multiple solutions.
    4. Students may miscount by skipping numbers, counting an object more than once, not counting an object, or counting on incorrectly.
    5. Students may not understand that the total must be 10 and will create groups of boys and girls that are a different sum.
    6. Students may not show all possible solutions if they do not understand that zero is a possible addend.
    7. Students may think they know an addition fact and will use the fact without checking for accuracy.
    8. Students may focus on unimportant details of the task (such as food on the table).

     

    Possible errors:

    1. Students may make errors in counting and/or representing a quantity incorrectly.
    2. Students may represent 10 students in one group without differentiating boys and girls.

     

    Students will have the option of choosing a math manipulative to use to solve the problem. Choices will include connecting cubes, bear counters, double-sided counters, tens frame, and paper/pencils. Students will begin their work individually sitting in table groups. Mid-way through the work time students will be given a chance to share their solutions with a partner at their table. Students sit at table groups randomly. Students will record their solutions on a recording sheet. At the end of the lesson, the teacher will lead a group sharing time and record students’ solutions on chart paper. Students will orally explain their solutions to the teacher and use their recording sheets as a visual support.
    Monitor: When launching the lesson, we will read aloud A Feast for 10. On pages 4-5, 8-9, 16-17, and 22-23 we will stop to count the number of boys and girls separately. We will discuss the last page of the book which depicts a family of 10 sitting around a table. We will discuss how many boys and girls are at the table. We will question and guide the students to access their prior knowledge of groups and seating arrangements. We will ask students for examples of where they see students in groups and how they sit in groups in the classroom, cafeteria, and other places. We will read the problem (There are 10 kids sitting at the lunch table at school.  How many kids are boys and how many are girls? Show as many ways as you can.) to the students and discuss what the problem is asking. We will model how to count 10 and divide the group into two parts (boys and girls). Students will join the teacher in counting students. Students will count the number of girls and the number of boys. Students will explain why the group of 10 was divided into two parts. We will then model how to use connecting cubes to represent girls and boys. Next we will show students how to record their work on the recording sheet. Students will explain how the picture and connect cubes represent the groups of students.
    Note: during the pre-lesson discussion, we decided that we would only model with the actual boys and girls and not with connecting cubes or recording on the paper.    After explaining and discussing the problem. Students will be sent to work with manipulatives of their choice. Students will be given five minutes to work with the manipulatives (connecting cubes, double sided counters, bears, tens frames, and paper/pencils). After five minutes, the teacher will reread the problem and give students the problem recording sheet (see attached) to record their solutions.We noted that it may be difficult to remember these questions. A strategy would be to create a note card or question sheet for the teacher to carry or post as she is providing instruction and meeting with students in conferences.Questions to Focus Students Thinking:
    Show me your two groups.
    How did you make your groups?
    How do you know you have 10?
    How will you show this on your recording sheet?
    How many blocks do you have?
    Why did you make these groups?We will know students are thinking about the mathematical ideas if we  hear students talking about boys and girls; counting, counting on, or skip counting; or talking with a partner. If we see students making groups or pointing as they count.Questions to Assess Understanding:Tell me about what you have on your paper.
    Why did you do what you did?
    Why did you make these groups?
    How do you know your solution is correct?
    How do you know you have 10?

    Questions to Advance Understanding:

    Can you use a different tool to solve the problem?
    How do you know if you have found all of the possible solutions?
    How many possible solutions are there?
    Why wouldn’t 5 and 6 (or other non-example) work?
    Can you make 10 in a different way?

    Questions to Encourage Sharing:

    How is your combination like/different than another student’s combination? Can you explain another student’s solution?

    Some students may have difficulty getting started with the task. To help those students we may:

    • Review the directions.
    • Review the teacher model.
    • Give students a number to begin with.
    • Ask student to show 10.
    • Encourage student to draw a picture of the cafeteria table/chairs as a template to fill in.
    • Provide a table template for students to use

    We will encourage students to stick with the task by:

    • Directing students to solve the problem in a different way
    • Directing students to find a different combination to 10
    • Challenge students to find combinations to a higher number
    • Encourage students to organize their solutions (look for a pattern)

    Students who are distracted by information outside of the mathematical concepts may be refocused by:

    • Reminding them that manipulatives are tools and not toys.
    • Direct students to use a simple drawing to represent their work.
    • Prompt them to try to find another solution or use another tool
    Selecting/ Sequencing:

    1. Count one at a time to 10 with separate groups for boys and girls.

    This strategy can lead to many errors, so it is not a very efficient way of solving the problem, but it may be the only strategy that some students have. To validate their work, it will be shared first.

    1. Count a group of 10 and divide into two groups.

    This strategy requires students to count the number given in the problem and then divide it into two groups to represent boys and girls. The groups can be of any size and students may experiment with dividing the group in different amount without reason.

    1. Count 10 and separate one at a time to make two groups.

    This strategy is similar to the first strategy because students begin with the total that is given in the problem. Students strategically move one object at a time to a second group to show the number of boys and girls. This strategy is a more organized way of representing the various combinations to 10.

    1. Count on from a given number to 10.

    This strategy is more advanced than the previous two because the student understands that 10 is the target number and they can begin from any number and count on to 10.

    1. Manipulate a known fact to show other facts. For example, a student knows 5+5=10 and then moves one from the first addend to the second addend to make the fact 4+6.

    This strategy demonstrates the student’s understanding of part-part-whole relationships.

    Note: During the pre-lesson discussion, we decided that we would choose students’ solutions to share rather than their strategies. We discussed how we would record their solutions on an anchor chart. We decided to list the solutions in random order and use the anchor chart in a follow-up lesson to have students look at patterns in the solutions. We also discussed using the anchor chart in a follow-up lesson to look for all possible solutions.

    Connections: By sharing the solutions in this order, the students will see strategies of thinking that become more advanced. Students who count 10 and separate one at a time have a more organized strategy than just counting 10 and breaking the group into two smaller groups. Students who are able to count on demonstrate a more fluent understanding of counting sequentially. These students also understand the part-part-whole relationship of numbers. Students who are able to manipulate an addition fact have a thorough understanding of part-part-whole relationships. They can physically or mentally manipulate addends but keep the same sum.Note: Since we decided not to share student strategies, the order of sharing students’ solutions is less important. We determined that solutions could be shared in any order for this lesson, but that in future lessons the same data could be sorted to look for patterns.Students that understand the mathematical ideas will represent a variety of combinations to 10. Students will explain how they counted to solve the problem.

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