The purpose of this activity is for students to make a reasonable estimate for the volume of the big red wagon which they saw in the Warm-up. Since no units are provided, students are also invited to think about which unit of measure is most appropriate for the size of the wagon. In order to compare their estimates, it is preferable if students all choose the same unit of measure, but this is not essential and it is one of the focuses of the Activity Synthesis. In particular, there are three unit choices students could make:

• A small unit such as millimeters, centimeters, or inches which will require using large numbers
• A unit that's just right, for example feet, which will yield more manageable numbers
• A large unit, such as yards, which gives reasonable numbers to calculate, but the height will likely be a fraction or decimal

Choosing an appropriate unit of measure for an estimation and understanding how that choice affects both the calculations and the meaning of the estimate are important aspects of applying mathematics to solve real world problems (MP4).

The other focus of the Activity Synthesis is how to use different parts of the image to estimate the volume of the wagon. In particular, the size and number of the people in the wagon are the key points of reference in the image that students can use to reasonably estimate.

• Invite students to share the measurements they would need to make an accurate estimate of the wagon’s volume.
• “¿Por qué son importantes el largo, el ancho y la altura?” // “Why are the length, width, and height important?” (The volume of a rectangular prism is the product of its length, width, and height.)
• Invite students to share their volume estimates, including how they chose their units and made their estimates.
• “¿Cómo escogieron una unidad de medida para estimar el volumen?” // “How did you choose a unit of measure to estimate the volume?” (I wanted a longer unit because the wagon is big. Inches, centimeters, and millimeters are too small. Feet are good. Yards or meters might work too.)
• “¿Alguien usó milímetros o centímetros para hacer su estimación?” // “Did anyone use millimeters or centimeters for their estimate?” (No, there would be so many millimeters and centimeters, so finding the product would be challenging and estimating the length, width and height would be hard too.)
• “¿Alguien usó yardas o metros para hacer su estimación?” // “Did anyone use yards or meters for their estimate?” (I tried to but I think that the height of the wagon is less than 1 yard or meter because the yardstick comes up way above my waist.)
• “¿Cómo se puede comparar una estimación en pies cúbicos con una estimación en yardas cúbicas?” // “How can you compare an estimate in cubic feet and an estimate in cubic yards?” (I can find out how many cubic feet are in a cubic yard.)
• “En la siguiente actividad, van a mejorar su estimación. Para esto, van a mirar la imagen con más cuidado para que la estimación sea lo más precisa posible” // “In the next activity, you will refine your estimate, looking more carefully at the picture to make the estimate as accurate as possible.”

The goal of this activity is to use multiplication and estimation to improve the estimates from the previous activity for the volume of the big red wagon. Students will likely count the number of people in the wagon and use this to estimate its length. They can similarly use the people in the wagon to estimate its height. Make rulers or yardsticks available in case students wish to measure how much space they take up when they stand side by side or to measure their legs or waist to estimate how tall the wagon is.

While students have the tools available to work with fractional measurements, encourage them to make whole-number estimates so they can use what they learned earlier in the course about the relationship between the (whole number) measurements of a rectangular prism and its volume.

• Invite students to share their estimates.
• “¿Por qué obtuvimos estimaciones distintas?” // “Why is there a range of estimates?” (We can’t calculate any of the side lengths exactly. Our estimates for the length, width, and height of the wagon bed were different.)
• “¿Qué les ayudaría a hacer una mejor estimación?” // “What would help you make a better estimate?” (Seeing the wagon in person would let us see how high the wagon is and how the length and width compare. More photos might help.)
• “¿Cuáles partes de la imagen fueron las más útiles al hacer sus estimaciones?” // “What parts of the picture were most helpful in making your estimates?” (The people, because I can estimate how tall they are and see how many of them are lined up along the side of the wagon.)