Mathematical Mischief Surrounding Translating Expressions

Submitted by: Andrea Burton from Virginia

Grade level range: 6-8

Length of time to teach lesson: 2- 75 min (1 ¼ hour) class

Mentor text to be used: Mathematical Mischief by Monica Cabarcas

Writing Traits:

Writing with a clear, central idea or theme in mind,  Using precise nouns to assist the reader’s understanding, Incorporating interesting adjectives into the writing, Using strong verbs to keep the sentences interesting, Conveying passion towards the message of the writing or topic, Using a variety of sentence beginnings, sentence language, and figurative language

Suggested Books

Objectives of this lesson (aligned to the state of Virginia’s standards):

VA SOL 5.18

b) Write an open sentence to represent a given mathematical relationship, using a variable

d) Create a problem situation based on a given open sentence, using a single variable

VA SOL 7.12 The student will represent relationships with tables, graphs, rules, and words

VA SOL 7.13: Write verbal expressions as algebraic expressions and sentences as equations and vice versa

Essential Questions for students

How can algebraic expressions and equations be written?  What are the different ways to represent the relationship between two sets of numbers?  What words or symbols indicate which operation?

Resources/Supplies: Notes, Colored paper, string, straws or metal hanger, tape, glue, Verbal Expression Vocabulary Handout, Verbal Expression Examples, Verbal Expression Matching, Verbal Expression Project, Verbal Expression Day 2 Handout, Verbal Expression Exit Card.

***A flipchart file is available here for instructions and each slide is referenced in the lesson – Verbal Expression Flipchart *****

Teaching Instructions:

DAY 1          

1)  Introduction [10 min]:    What are synonyms? What are some examples of synonyms?  (flipchart Slide 1) 

2)  [5 min]   Split class into 4 groups (option: leveled grouping). Each group will discuss/brainstorm a list of “synonyms” for: addition, subtraction, multiplication, and division.  (flipchart Slide 2)

3)  [15 min]  Teacher will guide students to fill in the notes for verbal expression vocabulary. (option: Each group could send one representative to present their list and then the class can help fill in the rest) Teacher will guide students to fill in notes for translating verbal expressions to algebraic expression (& vice versa).  (flipchart Slide 3-4)

4)  [10 min]  The class will work together on translating 5 examples of algebraic expression to verbal expressions. (flipchart Slide 5)

5)  [5 min]  Matching activity with partner/small group  (flipchart Slide 6) 

6)  Read the book, Mathematical Mischief.  The following questions are to be used with "The Shrinking Cup of Cocoa” narrative poem and can be applied to the other poems as well.  Before you read explain to the students that this is a story with creative illustrations! Show them the dedication. Ask: Why did the author have the dedication written in a heart?  At the end of each narrative poem ask: What were some creative ways the author/illustrator worked together? What do you think came first- the words or the design?

After reading “The Shrinking Cup of Cocoa”: Ask: What were some creative/different ways the author & illustrator explained this story? Why did the author/illustrator write “Still Hot” and “Ring!” the way they did? Are there other ways the author could have done this?

“Chances are...”: What was the point of writing “yellow marble” the way they did? The book is black and white, how did that help with imagery? Discuss the different creative approaches the author/illustrator used.

7)  [15 min]  You will be creatively describing the mathematical operations and identifying words/terms that correspond with the mathematical operations (project directions). As a group you will combine these creative representations of the different operations and put them together to create a hanging installation (mobile). Using the book “Mathematical Mischief” as inspiration, how can you represent and describe the mathematical operations? (Describing the operation in either the outline of the operation or by filling it in). The rest of class time will be spent brainstorming and creating an initial draft of the representation. Students will pick one operation and use descriptive language to describe the operation.  (flipchart Slide 7) 

Day 2

1)  [10 min]  For each, translate the algebraic expression to verbal expression in 2 ways.  (flipchart Slide 8)

2)  [50 min]  Students will continue working on their visual representation of their operation. As they finish their draft they can begin using colored paper to make their final copy. (Tip: Give them a limit of paper and supplies that they must work within). When their final copy is done they will construct the hanging mobile. (Tip: Tell them they must have _______ done after 15 minutes, ________ after 30, and be constructing by this time)   (flipchart Slide 9) 

Post your expectations for them while they are working (work together, use inside voices, each person gets 2 sheets of paper, etc…)

3)  [5 min]   Depending on your classroom you might have a system for clean up, but assigning jobs or writing a “to do” list for the kids as they clean up will help get the job done.  (flipchart Slide 10) 

4)  [10 min]   Pass out the exit card, or have the kids write the answer on a note card/scrap sheet, etc…    Translate the verbal expression: the sum of 6 and 3 times a number.  Translate the algebraic expression: 5 – x      (flipchart Slide 11)

Cautionary notes/misconceptions:

Show examples of finished products so the kids know what they are making!!  Limit supplies so the kids must be resourceful!

See pages 2-6 for pictures of student samples.

Additional Resources:

This is a video created by Holly Young that can be used to introduce the need for algebraic expressions and equations in the real world.

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