Name: Michelle Loomis

Childhood/Early Childhood Department

Lesson Plan

Date of Lesson __11/13/08__ Time _9:00am-9:40 am Length of lesson 35-40 minutes

Curriculum Area Mathematics Content Area: Multiplication

Title of Lesson: Multiplication with Arrays

Age/Grade level: 2^nd Grade

Differentiation of activity is to be provided throughout the lesson plan to ensure that children’s individual learning needs are met.

1. Learning Objectives

o Students will be able to recognize multiplication facts as being the product of two 1-digit numbers.

o Students will be able to use different strategies for figuring out multiplication facts.

o Students will be able to recognize an array as a multiplication problem.

o Students will be able to show a multiplication problem using an array.

o Students will be able to connect problems to real life situations.

2. Assessment

(a) Learning outcomes of previous lesson related to this topic:

Student will have previously worked with multiplication facts using arrays. This lesson will focus on practice of the facts and connecting the facts to real life.

(b) Focus of assessment in this lesson:

The focus of the lesson will be on students recognizing how to recognize a multiplication problem and also how to form one using an array. The students will also be able to connect multiplication problems to real life situations based on examples given.

(c) Method of assessment used in this lesson:

Students will individually be assessed by the teacher observing their work, while it is being done. The teacher will look for understanding, their method for solving the problems, and their correct answers. Volunteers will be asked to share problems but this does not mean that the students who do not volunteer will not understand the topic. Special attention to those students will be given while their problems are being answered.

Students will also be assessed formally on their worksheet they must complete. This worksheet will be collected and corrected for the student. If an individual student incorrectly completes the worksheet they will then be given an opportunity to work with the teacher for further clarity. A specific date and time will be set up.

(d) Differentiation:

The environment could be changed. The students could be taken out to look at an actual tomato garden to see the problem in a real life situation. If tomatoes cannot be found other objects in nature could be used, such as trees or flowers.

For more visual learners more manipulatives could be provided. Pictures of tomatoes could be used, and the emphasis on using pennies to represent a dime will be stressed.

Students who do not learn visually will be able to solve the problem the way they want to. This lesson provides an opportunity to solve problems many different ways. Even though the lesson is focused around visually seeing the problem, students will be able to recognize that they do not need to see the problem to figure out the answer.

3. New York State Learning Standards

· 2.PS.8 – Use manipulatives to model the action in problems.

o Key Idea – Students will be able to use objects to represent what the problem looks like.

o Performance Indicator – Students will be provided with a variety of objects to use to create arrays to represent multiplication problems.

· 2.PS.10 – Explain to others how a problem was solved, giving strategies and justifications.

o Key Idea – Explaining their solution to a problem will help others who may be confused see how an answer was established. This could also introduce a new way of answering the problem to a student.

o Performance Indicator – Students will be asked to explain their answer and how they got their answer to the problems, throughout the entire lesson.

· 2.CN.1 – Recognize the connections of patterns in their everyday experiences to mathematical ideas.

o Key Idea – Students need to understand that multiplication has a purpose and that it is used every day.

o Performance Indicator – Students will visualize this by using objects such as tomatoes and money to see an everyday activity using multiplication.

· 3.N.19 – Develop fluency and apply single digit multiplication facts.

o Key Idea – Students need to know their single digit multiplication facts. Practicing them will develop fluency.

o Performance Indicator – This lesson demonstrates what each fact really is. It provides meaning behind the problem.

· 3.N.21 – Use the area model, tables, patterns, arrays, and doubling to provide meaning for multiplication.

o Key Idea – Understanding what a multiplication problem is, is crucial to a student’s ability to use multiplication.

o Performance Indicator – Students will look at and develop arrays for given multiplication problems.

4. Materials

o Chalk board or white board for the teacher

o White boards or pieces of paper for each student

o Markers for each student

o 3 dimes for each student

o 45 pennies for each student

o 1 jar with 10 strips of paper in it each one labeled with a different number, 1 – 10

o Worksheet 1 – Multiplication facts list

o Worksheet 2 – Home Link 104

5. Lesson Process

(a) Introduction (5 min.)

This lesson was designed for a small group of students; however it could easily be modified to work for a whole class.

The lesson will begin by reviewing multiplication facts.

“When I say 2 x 2 what is the answer?”

Students will most likely respond by saying 4

Students will be asked to write a multiplication problem on their board. They then will work in pairs or groups of three if there is an odd number, to answer each other’s problems. If students cannot answer a problem they will be instructed to ask their partner to help. The students will be brought back, whole group and the teacher will say:

“Now let’s learn how to represent these objects in a model so you can see exactly how multiplication works.”

(b) Learning procedures relating to objectives (15 min.):

The following problem will be written on the board.

We have 5 rows of tomato plants.

Each row has 4 plants.

How many plants are there in all?

The students will be instructed to draw a picture that would represent this problem. They will be instructed not to answer the problem. It is likely the students will have difficulty so the array would be drawn and explained by the teacher.

“The problem says we have five rows. What are rows?”

Rows will be drawn:

“How many does it say we have in each row?”

The answer will be four. The teacher will draw four plants in each row.

If students drew models correctly to begin with the teacher will still draw and explain the model for understanding. Then students will be asked to figure out how many plants are there in total. The correct answer is 20. The teacher will wait for all students to have the answers written down. The teacher will observe each students answer so that every students work is being looked at. Once all students have answered the teacher will ask for volunteers to say their answers. The teacher will ask for thumbs up or thumbs down based on the students answer. The teacher will then ask for different answers the students came up with. If no different answers are found a different student from the one who answered will explain how they answered the problem. After, other students will be asked if they solved the problem a different way.

Possible ways to solve problem:

Counting by 4’s

Adding 4+4+4+4+4

Double 4 than double the result and add 4 to the total

Double 5 and double the result

Count each individual circle

Knowing that 5 x 4 = 20

The teacher will acknowledge that all of those approaches are correct. The teacher will then have the students take a look at the last approach, 5 x 4 = 20.

“What would happen if I just gave you the problem 5 x 4. How would you solve it? Would you draw a picture still?

Students will be able to agree and disagree, knowing that they do not have to draw a picture to get an answer but that the picture represents the answer.

Students will then be given another problem involving tomato plants. They will be asked to solve this one on their own using any strategy they would like.

There were 7 tomato plants that were planted in each of the 9 rows.

How many tomato plants were there in total?

Students will solve the problem on their white boards. As before they will be observed by the teacher and help will be given to those students who are confused. Possible suggestions will be to draw a diagram as they did in the previous problem. The same process for answering the problem from above will be used.

Students will have another problem to answer:

Melanie has 3 dimes. She wants to know how much money

she has. Can you help her?

The students will be guided by first asking how much a dime is worth. The correct answer in 10 cents. Then students will then be asked to solve to problem by first drawing a picture, and then answer the question. Students will begin drawing pictures and the teacher will observe each student to see if they are on the right track. The teacher will ask a few students to share their answer and how they solved it to their other students.

If students are confused this activity could be used:

The teacher will represent one dime as 10 pennies, showing that one dime equals ten cents. Then the students will be given a bag of pennies to see if they can model the problem. This will show the students exactly how many pennies three dimes would be.

(c) Conclusion (5-10 min.)

The lesson will end by having the students make multiplication charts on their facts, using arrays. A handout will be given. Students will be given a jar with the numbers 1-10 on pieces of paper in it. The students will be asked to draw one piece of paper and that will be the number they will use for their multiplication facts. See attachment, “Multiplication Facts List, Journal 2, p 55, for further directions.

At the end of the lesson the teacher will connect their lesson to real life situations.

“Today we learned how to represent multiplication problems. Now why is this important?”

Each student will be given the opportunity to explain their answer. The teacher will emphasize that by drawing the picture you are seeing how much the answer actually is.

If more help is needed a worksheet will be provided for the students to work on at home. See attachment, home link 104.

6. “If time”/ extensions

If time allows, students will be asked to draw another number and make another multiplication facts sheet.

7. References