TITLE:   Multiplication:Taken from: Guiding Children’s Learning of Mathematics. Kennedy, Tipps, and Johnson

CONTENT  AREAS:    Math: Relationship between multiplication and repeated addition

GRADE  LEVEL:    2-4 Grade

MATERIALS   NEEDED:  

math boxes or counting cubes 

multiplication word problem strips (4 problems in each group)

KEY   CONCEPTS:    repeated addition

EALR'S (Make the connections clear and specific):   

Grade 4:

1.5.1 Understand patterns of objects, including number patterns, using addition, subtraction, or multiplication based on a single arithmetic operation.

Extend or create patterns of numbers, shapes, or objects using addition, subtraction, or multiplication based on a single operation between terms.

Extend and represent patterns using words, tables, numbers, and pictures.

1.5.2. Understand a pattern to develop a rule describing the pattern, which may include a single arithmetic operation.

Solve a problem that uses a pattern with a single operation.

GOALS (Remember the difference between goals and objectives):   

Students will be introduced to the use of repeated addition and its relationship to multiplication through solving word problems.

OBJECTIVES:    After a teacher demonstration of repeated addition using math manipulatives, the students will solve 4 multiplication addition problems sets and explain their reasoning.

Student groups will create their own problem to send to another student group for solving.

PROCEDURES:  (Label each step in the process:  Activating Prior Knowledge, Disequilibration, Elaboration, Crystallization)

Pre set up:

            1. Agenda on the board

                        2 min   Introduction

                        3 min   Brief discussion on what they know

                        3 min   Introduce activity (go over an example?)

                        10 min Do activity

                        15 min Share solutions

                        15 min  Student teams develop one problem for another team to solve

                         10 min Review solutions

            2. Think of examples of problems they can solve for backup

            3. Have multiplication word problems 1-4 separated and ready to hand out

            4. Make sure the manipulatives are organized

• Introduction/Preassessment

( Activating Prior Knowledge)   

Today, class we are going to learn about repeated addition. Do ya’ll remember yesterday when we found objects that were the same and organized them in groups? (You are recalling the mini lesson where the class organized sets of eyes, buttons, pennies, and days of the week into groups.

1. Groups of 2: eyes, students
2. Groups of 3: pennies, chairs,
3. Groups of 4: buttons, pennies, chair legs
4. Groups of 5: fingers, toes
5. Groups of 6: pop cans, paper clips
6. Groups of 7: days of the week, pennies,

The students represented the equal groups with drawings and objects. The groups were put into an organized arrangement. An example follows for groups of 3:

Emphasis the relationship between 2 + 2 + 2 + 2 = 8 and 2 x 4 = 8

Ask the students to describe how they can think about the eyes as a group and not an individual object. Eye come in sets of two, and you can add the sets of 2 together 4 times, in the example above. Let us look at another example. Chairs have 4 legs. Think about the legs as a set, and in each set there are 4 legs. When I have 3 chairs, how many legs do I have? (4 + 4 + 4 =12 legs.)

What are some strategies we use in class to find solutions to problems? Math manipulatives, skip counting, What are the two strategies we are working with today? (writing the problem in an addition form, and thinking about objects in groups) write these strategies on the board for the students to refer to as they try to solve their problems.

• Activity

Get students into groups with 4 students in each. The expectation is that each student will receive one problem slip and attempt to solve it by themselves, than ask for help from group members if needed. They are to use the math manipulatives to represent the objects in the problems. (This is the established group procedures and the students are aware of the procedures) 

(Disequilibration and Elaboration)

1. Each team of four students is given four different multiplication word problems. All teams have the same set of problems, which are numbered.

1.      Sadie buys gum in packages that each have 7 sticks. When she buys 4 packages, how many sticks does she have?

2.      Conrad has 5 packages of trading cards. How many cards does he have if each package holds 5 cards?

3.      Jawan has 3 packages of frozen waffles. How many waffles does he have if each package has 8 waffles in it?

4.      Abdul has 8 boxes of motor oil. Each box contains 4 cans of oil. How much oil does Abdul have?

2. Each team member uses materials of choice to determine the answer for one problem. Team members may coach others after they have solved their own problem.

3. Team members share their problems and solutions.

4. At a signal, all students who solved the same problem assemble to explain their solution verbally.

5. Have students explain their solution, including repeated addition, skip counting, and multiplication thinking. Write the addition sentence for each situation on the chalkboard.

7+7+7+7=_____

5+5+5+5+5=______

8+8+8=_____

4+4+4+4+4+4+4+4=______

(Crystallization)   

(Conclude the activity by having the teams make up a problem to send to other teams to solve. Discuss solutions to the ‘sent’ problems.)

Please get out a clean piece of paper. In your teams, you are going to create 1 problem for another group to solve. You will be turning this in so listen to the requirements. You will have a group grade.

What do you think are some guidelines for writing these problems for your classmates? (As students answer write them on the board. You as the teacher need to make sure that the following also are included)

1. Your names have to be on top so we can ask you questions if we do not understand.
2. We have to be able to read your writing. 
3. The problems have to be related to what we learned today. No trick questions.
4. You have to know the answer.

What are the concepts that you learned today? 

1. repeated addition
2. solving word problems

When you are finished with your problem and your answer, place them up here on the desk until everyone is finished. When everyone is finished, we will pass them out and try them.

You are expected to work with your team to solve the problem, using math manipulatives, and when you are sure that you have the answers, go to the group that wrote them and have it checked.

• Closure

Review the skills learned today: repeated addition, skip counting, and multiplication thinking
 

POST-ASSESSMENT:

 
Individual: Keep a record of the solutions to the multiplication word problems. Note the student and the reasoning of their solution.

Group Assessment: Collect the group generated problems and grade for names on the paper, clear writing, related skills, and known answer.