Grade:  4         Number of students:  4-6       Duration of lesson:  Approx. 50 minutes

 

Goals/Objectives:

 

• Students will be able to create mathematically appropriate story problems for multiplication and division scenarios when presented with a number sentence.

• Students will be able to analyze story problems to determine/select the appropriate mathematical operation (multiplication or division).

 

PA Core Standards for Mathematics:

2.2 Algebraic Concepts

• CC.2.2.4.A.1 Represent and solve problems involving the four operations.

 

CCSS for Mathematics:

• 4.OA.2     Operations and Algebraic Thinking        

  • Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

• 4.NBT.6   Number and Operations in Base Ten

  • Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

 

Materials and preparation:

 

• Scratch paper

  • For student computations

• Pencils, sharpened with erasers

• Manipulatives:[D1] 

  • Cubes

  • Bins

  • Paper bags

• Sheet with open number sentences

• Sheet with multiplication and division story problems, prepared following review of the student activity book and course materials such as the Smith and Smith study

• Chart paper:

  • To model creating and analyzing story problems

  • To record student responses during whole group discussion

• Checklist/recording sheet to assess student progress and learning throughout the lesson

 

Classroom arrangement and management issues:

 

The lesson will be conducted with all of the students and the teacher sitting together at a small table in the library.

 

I have planned this lesson knowing that the students are struggling with its underlying concepts.  I am also aware (based on previous observations) that two of the students in the group respond to frustration by shutting down.  I took this into consideration when structuring the lesson.  I have sought to provide as many differentiated options as possible in hopes that the students will avoid unnecessary frustration.

 

Additionally, I am planning to teach the lesson on the Monday following Thanksgiving break, shortly after the students have returned from recess.  I anticipate that these factors, especially in combination, may make it harder for some students to focus.

 

Plan:

 

1.  Before (launch) (15-20 minutes)

• Briefly review multiplication/division by asking students why/when they would multiply or divide

  • I anticipate responses such as:[D2] 

    • Determining how much of something there is

    • When you need to share something equally

• Note that math extends to the world outside of school, framed with words as opposed to mathematical symbols, which is which is why story problems are so important

• Introduce lesson by modeling creating and analyzing a series of multiplication and division story problems

  • Begin by creating story problems from number sentences[D3] 

    • Ask students for suggestions of scenarios in order to engage them in thinking and reasoning

    • These problems will focus most heavily on grouping situations

  • After writing one multiplication and one division story problem as a group

    • I will present pre-written story problem for both operations and model analyzing and solving each using a variety of methods such as:

      • Drawing pictures (groups, arrays)

      • Using manipulatives (separating cubes into bags or bins)

    • I will ask students to suggest solution strategies in order to engage them in thinking and reasoning

    • The prewritten story problems will include grouping and multiplicative comparison situations

 

2.  During (work and explore) (15-20 minutes)

• Students will work independently to:

  • write two story problems, illustrating their thinking for each through a drawing or the use of manipulatives

    • Each student will be required to write[D4] 

      • One multiplication story problem

      • One division story problem

    • I will provide a sheet with open number sentences to aid this process, and streamline conversation once the group comes together for discussion at the end of the task.

 

3.  After (Debrief and wrap up) (15-20 minutes)

• Following independent work, we will come together as a group to share the story problems that each student created

  • Students will be asked to explain their thinking for the problems they authored, as well as to share solution strategies

• Following group discussion, I will provide each student with a sheet with two prepared story problems, one for multiplication and the other for division

  • Each student will:

    • determine the indicated mathematical relationships

    • write and solve a number sentence for each problem

    • draw a picture or employ manipulatives to illustrate his/her thinking

  • This sheet will serve as an exit ticket [D5] for the lesson, and allow me to assess whether having written their own story problems helped the students to be able to sort and solve story problems independently.

 

Anticipating students’ responses and my possible responses:

 

• In planning and teaching this lesson, I will keep in mind that:

  • A student may resist creating both multiplication and division problems, if s/he prefers one operation to the other

  • It is possible that students may continue to struggle when analyzing story problems

  • The students may be distracted following the long weekend

  • If a student appears to be struggling or to require a greater challenge, I will adjust the task to better meet observed student needs.  As seems appropriate, I may:[D6] 

    • Reduce/increase the number of problems a student is required to write

    • Sit with a student during a period of independent work so that s/he can vocalize his/her reasoning

 

Assessment of the goals/objectives listed above:

 

The ultimate goal of the lesson is for students to strengthen their conceptual understanding of multiplication and division.  While progress would be most evident through student analysis of prepared story problems, conceptual understanding will also be shown in the story problems each student creates.  Conceptual understanding develops gradually through solving problems.  As such, both tasks will indicate progress.

 

I will conduct formative assessment throughout the lesson by observing student work.  I will employ a checklist[D7] —adapted from the Assessment Checklist for Multiplication and Division posted on Canvas—to enable me to gage individual comprehension, conduct a formative assessment, and collect information that I can share with the classroom teacher to aid the students’ future learning.  The checklist will allow me to track conceptual understanding of multiplication and division—as indicated through representation and analysis of the various problems—for each student.

 

I will compliment well-developed problems, and express that I would like the student to share his or her work with the group.  My intention is to allow students time to think about their explanations in order to encourage group discussion.

 

Accommodations:

• If a student appears to be struggling to write his/her own story problems, I may:

  • Reduce the number of problems a student is required to write

  • Sit with a student during a period of independent work so that s/he can vocalize his/her reasoning

• If multiple students appear to struggle, I will either forego the prepared story problems completely or work with the students as a group in order to focus on the underlying concepts

• If a student appears to require a greater challenge, I will ask him/her to write additional problems.  These may include:

  • multiple steps

  • greater emphasis on multiplicative comparison