The Grapes of Math by Gregg Tang

Mathematics Strand:

Number and Operation

Topic:

Students will practice mental addition and will use the associative and commutative properties of addition to solve problems.

Grade level:

6-8

Lesson Created by:

Shannon Kent, Fort Riley Middle School, Fort Riley, KS

LESSON Description

Materials

• Book: The Grapes of Math, pencil, paper
  

1. Engage:

1. Read the story – as you read, ask the students if they can think of any way to add up the items in the picture, without actually counting the items
   
2. Talk about grouping certain items... How does grouping items make it quicker to count? Can you do another operation to find the total of items? (Multiplying rows)
   

2. Developing the Lesson:

1. Divide the students into partners or small groups, give each group a photocopy of one of the picture riddles from the book
   
2. Ask the students within their groups to find all of the possible ways to group their items to find the total number of items.
   
3. Have each group share their findings; ask the class if they can come up with any different grouping methods.
   
4. Pose the question: When you change groupings, did the sum remain the same or did it change?"
   
5. Lead into a discussion about the associative and commutative properties of addition. Define these properties for the students. Then ask the students to share how they have used these properties in their different grouping methods.
   

1. Closure/Discussion/Elaborate:

1. End the discussion by stressing that regardless of which numbers you group together, the answer (sum) remains the same. Ask students why they think these properties are named as such.
   
2. You can further the experience by having students explore the two properties with multiplication. Have them do several problems using the properties they have learned for addition. Ask them if the properties remain true for multiplication, does the product remain the same?
   
3. Students could further the investigation by creating their own math picture riddles, then exchanging with a peer.