step 1: inquiry approaches to teaching · web viewspatial visualization is the ability to...

Step 1: Inquiry Approaches to Teaching

Cookie Combos

Teaching Partner(s): Deanna Kicklighter and Gabriela GalvezDate of Lesson: Thursday, October 27, 2011 @ 8am.Length of Lesson: 50 minutesGrade: 5thSource of the Lesson: Problem Solving: Just For The Fun Of It - AIMS Education FoundationFlorida Sunshine State Math Standards (SSS) Addressed:

Benchmark Number

Descriptor

MA.5.A.4.1 Use the properties of equality to solve numerical and real world situations.

Concepts: Spatial visualization is the ability to mentally manipulate two-dimensional and three-dimensional figures. It can be measured with simple cognitive tests and is predictive of user performance with some kinds of user interfaces. Common tests include groups of similar polygons where the test-taker is challenged with determining as many variations as possible.

Divergent thinking is a way of thinking that moves away in diverging directions so as to involve a variety of aspects and which sometimes lead to novel ideas and solutions; associated with creativity. It is a thought process or method used to generate creative ideas by exploring many possible solutions. It is often used in conjunction with convergent thinking, which follows a particular set of logical steps to arrive at one correct solution. Divergent thinking typically occurs in a spontaneous, free-flowing manner, such that many ideas are generated in a random, unorganized fashion. Many possible solutions are explored in a short amount of time, and unexpected connections are drawn. Following divergent thinking, ideas and information are organized and structured using convergent thinking.Strategies of Divergent Thinking. University of Washington. Wade, Carole; Tavris, Carol (2008). Invitation to Psychology. Upper Saddle River, NJ: Pearson - Prentice Hall. pp. 258. Materials List and Advanced Preparation: Class set of

Handout 1: Cookie Combo Introduction Handout 2 : Student Paper with Multiple Cookie Layouts Cookies Evaluation

Performance Objectives Students will be able to:

graphically represent different groupings of a collection of objects write expressions that represent the different groupings

http://faculty.washington.edu/ezent/imdt.htm

http://en.wikipedia.org/wiki/Convergent_thinking


ENGAGEMENT Time: 5 minutesWhat the Teacher

Will DoProbing Questions Student Responses and Potential

MisconceptionsShow pictures of people, bricks, and cookies one at a time grouped together in different ways and ask how many of each there are.i.e. 6 flowers can be arranged indifferent ways:2 x 3 ( 2 groups of 3),3 x 2 (3 groups of 2),2 + (1 x 4)- one group of 2 and 1 group of 4

To introduce the activity Gabriela & I will present a picture of a bouquet of flowers.How many flowers are in this bouquet?Then Gabriela & I will show a picture of a bouquet with the same number of flowers, but grouped a different way.How many flowers are in this bouquet?Then will show a picture of the two bouquets side by side.Are these two bouquets of flowers equivalent?So then we will ask:When you change the way things are grouped, does that change the number of things in the group?

6 flowers.

6 flowers.

Yes; the two bouquets are equivalent.

No; changing the way things are grouped does not change the amount.

Show a picture of items or draw shapes on the whiteboard grouped in pairs and ask students to mathematically represent a way to find the total number of items or shapes.

i.e. ** ** ** ** ** ** can be expressed as (6 x 2) or 6 groups of 2.

How could you express these two bouquets mathematically?

PowerPoint will show how to write these mathematically and it will also show the pattern for the expression.

You could express the group of 6 flowers like this:

1. (2x3) two groups of three. or2. (3x2) three groups of two.

Have students give suggestions to other ways we can group things and show them

What are different ways to group 6 pencils?

There can be 1x6 (one group of six), 2x3 (two groups of three), or 3x2 (three groups of two) and many more.


mathematically. Could you group the pencils by color, length, etc?

Yes; there are many ways to group the pencils. Not just by the number in each group.

EXPLORATION Time: 15 - 20 minutesWhat the Teacher

Will DoProbing/Eliciting Questions Student Responses and

MisconceptionsIntroduce the lesson for the day: tell the students they are going to be grouping an arrangement of cookies to make equivalent bundles.

What does equivalent mean?

What are some examples in life where you have heard the word equivalent?

Equivalent means the same amount.

Students will give their responses.-examples: Are the two pieces of pie equivalent? Are these two amounts of money equivalent?

Show the two sample arrangement of cookies. Ask the students to count how many cookies are in each.

How many cookies are in each sample?

Are the numbers of cookies in the two samples equivalent?

Why are they equivalent?

There are 25 cookies.

Yes; the numbers of cookies are equivalent. Some cookies are just bigger than the others.

Because there are the same number of cookies in each sample.

Tell the students now they are going make equivalent sets of cookies. As they do this they must also write expressions to represent their groups mathematically, as we did in the engagement.

What is a mathematical expression?

A mathematical expression is a mathematical phrase that can contain constant numbers, variables (like x or y) and operators (like add, subtract, multiply, and divide).

Ask the students to raise their hands and give suggestions for grouping the cookies on the sample paper so that everyone understands the assignment. Do this

What is one way to group the cookies?

Are there more ways?

How?

5 groups of 5.

Yes, there are more ways.

(3x8)+(1x1)(3 groups of 8 & 1 group of 1)(2x12)+(1x1)(2 groups of 12 & 1 group of 1)


a couple of times. (6x4)+(1x1)(6 groups of 4 & 1 group of 1)

Hand out worksheet. Students will work in pairs. Directions are on PowerPoint.

Deanna will tell students that are to work with their shoulder buddy. Gabriela will ask for a volunteer to hand out the worksheets.

Go around the room and watch over students. Answer any questions.

EXPLANATION Time: 5 - 10 minutesWhat the Teacher


MisconceptionsAsk volunteers to come up and show the different ways they grouped the cookies. Have the students write the expression that corresponds to their groups.

What is one way that you grouped the cookies?

Are there more ways to group the cookies?

*Remind students that the pattern for the mathematical expression will show the NUMBER of COOKIES, not the number of students.

Students will give examples on how they grouped the cookies.

Yes; there are other ways to group the cookies.

Have students show their groupings on the Smartboard.

.ELABORATION Time: 10 minutesWhat the Teacher


MisconceptionsHave students fill in any of the different ways of grouping that are shown if they don’t have it.

Does anyone have anything that hasn’t been discussed?

Answers will vary depending on what has been discussed.

Discuss with students the importance of being able to come up with many different ways to solve problems in the real world.

Why is it important to come up with different answers to questions where there isn’t just one answer?

You can come up with different ways to use objects. For a block, you can use it as a weight to stop cars in the driveway; you can build houses and fences, etc; you can build a fire pit.


Discuss the importance of being able to group things into equivalent groups. Use real world examples such as money.

Discuss what spatial & divergent thinking are.

Can anyone think of a situation where there are a bunch of items or objects that we might need to see if they are equivalent?

Does grouping things and writing expressions help when you are working on a problem with equivalence?

What is divergent thinking?

It’s being able to see multiple ways to solve the problem.

Allow for response.-If you are making change for a ten dollar bill its important to make sure that the change you give is equivalent to a ten dollar bill.-It does, it allows me to visually see the groups and realize if they are equal or not. I also can check my groups by making sure the expression is correct.

I'm not sure

EVALUATION Time: 10 - 15 minutesWhat the Teacher


MisconceptionsDistribute the student evaluation page to each student and inform the students that they are to work on it individually.Remind the students to show their groupings on the diagrams and to write expressions that represent their groupings.

PowerPoint will explain directions.


Use this sheet to show how many different ways you found the number of cookies the arrangement. Record your answers in both pictures and numbers.

______________________ ______________________ ___________________

______________________ ______________________ ______________________

______________________ ______________________ _____________________

______________________ ______________________ ______________________


You work in the cafeteria at your school. There is a class field trip that is happening and they need you to pack their lunches. There are 31 students going on this field trip. Every student will get a sandwich, a drink and a cookie. The sandwich and drink are already packed, what you must figure out is how to divide the cookies up for each student. You have 25 large cookies (cookies) and 25 small cookies (M&Ms). A large cookie (cookie) is equivalent to 2 small cookies (2 M&Ms). Each student must get an equivalent serving of cookies. You cannot break any cookie into parts. You also do not have to use all of the cookies. Use the diagrams below to help you make combinations of cookies for all the students.

How many possible groups of cookies can you create? Find at least 3 different groupings. Make sure to write an expression to represent the number of cookies.

1)

2)


3)

Name___________________________________________Once again you are working in the cafeteria and distributing cookies. Just like before one big cookie is equivalent to two small cookies. There are 20 students in the class and each student must get an equivalent number of cookies. Write an expression, if possible, for the number of cookies that need to be distributed. If it is not possible, write NOT POSSIBLE.1.

2.


3.

4.

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