Jessica mixed 3 cups of red punch with 5 cups of lemon-lime…

Jessica mixed 3 cups of red punch with 5 cups of lemon-lime soda. Hayli started by making the same mixture as Jessica but then added 2 more cups of red punch and 2 more cups of lemon-lime soda. (a) What is a common error that students make about how the two mixtures compare? Why might students make this error? (b) Discuss two different ways to determine which mixture is more red-punchy and which is more lemon-limey without using fractions. In each case, explain the logic clearly. [Hint: You might want to make ratio tables to compare]

Suppose there are two rectangular pools: one is 30 feet wide…

Suppose there are two rectangular pools: one is 30 feet wide, 40 feet long, and 3 feet deep throughout, the other is 20 feet wide, 40 feet long, and 5 feet deep throughout. Compare the sizes of the pools in two meaningful ways. State whether your comparisons are related to a 1-dimensional, 2-dimensional, or 3-dimensional aspect of the pools.

What is true about the force on ball 2 if it is allowed to f…

What is true about the force on ball 2 if it is allowed to float to the surface, as shown here? Image Description Diagram of three balls of the same size in a container of water. Balls 1 and 3 are completely submerged in the container of water at approximately the same depth. Ball 2 is floating on the surface.