Lesson: The Lost Lucky Ball

Display a coordinate plane with a diagonal line drawn on it connecting two points. Do a think-aloud or have a student volunteer describe how to draw two legs on the diagonal line to make a right triangle with the given line as the hypotenuse. Ask: How many units long would each leg need to be to make a right triangle? Then tell students they can use a formula to find the distance of a missing leg, or side length, when working with right triangles.

• At 0:25, ask: How long ago did the Aztec empire exist? (500 years ago) What are some major differences about the way the Aztecs lived and the way we live? (Possible answers: They did not have cars, electricity, the internet, etc.) The Aztecs built their capital city in the middle of a lake. What benefits might this have had? (Possible answers: The lake provides transportation, water for food/washing, protection, etc.)

• At 1:15, ask: What are some details of Aztec society? (They had warriors, farmers, and architects. They had bustling marketplaces where they traded and sold goods. They created a complex calendar and a writing system.)

• At 2:25, ask: What happened to the Aztec Empire? (In 1519, Hernán Cortés and his men looted the city after being welcomed by the Aztec ruler Montezuma II. The Spanish were driven out but returned later to conquer the Aztecs. The Aztecs had been weakened by diseases brought by Cortes and his men.)

Explain to students that this is a blended article known as historical fiction—it contains both historical facts and a fictional storyline. The blending of different writing styles allows the author of the article to both teach and entertain. Have students draw a T-chart with the left-hand header labeled “Facts” and the right-hand header labeled “Fiction”. Allow students to read the article in pairs and fill in their T-charts. To focus on the story during this activity, students should skip the “Your Turn” questions during the first read. Students can write information they learn about Tenochtitlan in the “Facts” section of the T-chart and any plot points of the fictional storyline in the “Fiction” section. Ask for volunteers to share what they recorded, confirming what is a fact versus what is fiction.

Have students individually read through the “Using the Pythagorean Theorem and Distance Formula” box on page 8. Tell students that the distance formula in the box gives an algebraic way to find the distance between two points on a coordinate plane. Make sure students pay attention to which point they use as Point 1 and which point they use as Point 2. Students can use this formula to solve the problems, or they can draw right triangles and use the Pythagorean theorem as described in the “Engage” section. If students struggle with answering any questions, encourage them to draw and label the right triangles described by the questions.

Distribute or digitally share grid paper or the “Coordinate Plane: 4 Quadrants” template. Have students draw fictional maps on their plane with at least 5 points of interest. These maps could be creative, fictional worlds, or they could include realistic and common places, such as coffee shops and libraries. Have students then use these maps and the distance formula to find how far apart at least five pairs of places are.