### Submitted by: Molly Martin, Elk Creek Elementary

In this lesson plan, students use an interactive simulation called Area Builder to figure out the area of a rectangle with fractional side lengths. Then they multiply fractional side lengths to discover that the answer is the same.

### Students will:

1. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as it would be by multiplying the side lengths.
2. Multiply fractional side lengths to find area of rectangles.

### Materials:

• Computers or other devices with Internet access
• 1-inch graph paper
• 1-inch tiles
• Recording sheet

### Preparation:

This lesson features an interactive simulation titled Area Builder , developed by our award-winning partner PhET through the University of Colorado Boulder.  The simulation challenges students to build shapes and explore the relationship between area and perimeter through two types of challenges: “Build a Shape” and “Find the Area.” Each type of challenge includes increasing levels of difficulty.

Photocopy a class set of the recording sheet.

Watch the Area Builder video primer for an introduction to the Area Builder  simulation’s features and uses. Then watch the Area Builder Simulation Overview for a summary of the of sim controls, model simplifications, and insights into student thinking.

Preview and play with the Area Builder sim to plan how you will adapt it to your students’ needs. If students will be working in small groups, review tips on Setting Cooperative Gaming Expectations.

Depending on your classroom routines and available technology, you may want to consider these grouping options:

• 1:1 with students and devices
• Two to three students sharing one device and swapping ideas and the device back and forth
• Station model where small groups rotate through using the devices.
• Build background knowledge or reinforce topics with these BrainPOP movies: Area of Polygons,  and Geometry. BrainPOP Jr also offers a movie about Area.

### Lesson Procedure:

1. Activate Prior Knowledge. Invite students to write and draw for 3 minutes all they can about a rectangle with an area of 24. Then have students share their ideas with the whole class or in small groups. Finally, have them revise their original ideas to include any missed concepts.
2. Introduction
• Using the 1-inch graph paper and one inch tiles, have students work with a partner to build and record as many rectangle shapes as possible.  Instruct them to use different colors to represent fractional parts of each rectangle.
• Model for the class on a whiteboard how to access the Area Builder sim. Then allow students to explore independently or with a partner for five minutes, sharing with each other what they discover about the navigation, games, levels, tools, etc. Prompt them by asking “What part of the sim grabbed your attention?”
• Have students explore one problem at Levels 1, 4, and 8 and compare the differences with each other.
• Discuss the dimensions tool and how it relates to an area array.
• Distribute one recording sheet to each student and discuss expectations. Tell them they may work in pairs, but each student is required to complete a recording sheet to turn in. Set expectations by modeling a mathematical diagram and dimensions as well as complete thoughts/sentences to communicate mathematical reasoning, etc.
3. Guided Exploration
• Using the Area Builder sim and the recording sheet, students will navigate, explore and advance through the game levels (keeping score).
• Level 4 includes calculating area of irregular polygons. Scaffold for students the concept of building the area of a rectangle and subtracting the units that are cut out of the rectangle. Many students will be able to be successful with this concept without guidance.
• Levels 5 and 6 are the goals of this lesson.
Students use the prompt: Example: Your goal: Area = 10, ½ green ½ blue, Perimeter = 14

### Extension Activities:

• Students can draw their successfully built area models on sticky notes and add them to the board.
• Teacher can scaffold instruction with one inch tiles and or graph paper as they relate to the sim goals in levels 5 and 6.
• Advanced students can share their models with others.
• Advanced students can write their own goals for model building using the level 5 and 6 template.