The purpose of this activity is for students to apply what they have learned in this section to compare a number with the product of that number and a fraction. There are two cases in which the fraction has a value of 1. Students may identify that the value of the fraction is 1 and use what they know about multiplying a number by 1. They also may use their knowledge of how to multiply fractions, and the calculations for these products have been made simpler so that students can find the product to make the comparison. For the other problems, the numbers are sufficiently complex that the most efficient way to compare is to think about the sizes of the factors.

• Invite students to share their solution for comparing and .
• “¿Cómo saben que ?” // “How do you know that ?” (If you cut the half into 10 equal pieces, then you get 10 pieces, and there are 20 in the whole.)
• “¿Pueden usar la ecuación  para concluir que  ?” // “Can you use the equation to see that ?” (Yes, because 1 times any number is that same number.)
• Invite students to share their solution for comparing and .
• “¿Encontraron el producto para poder comparar los números?” // “Did you find the product to compare?” (No, the numbers are big, so it would have taken a long time.)
• “¿Qué hicieron para comparar los números?” // “What did you do to compare the numbers?” (I know that is less than 1, it’s . So when I multiply it by any number, I get less than that number.)

The purpose of this activity is for students to reflect on different ways to compare a product of fractions to one of the factors. Students have seen multiple strategies that always will work, including calculating the product, thinking about the product on the number line, and using the distributive property to explain how the size of a product compares to the sizes of its factors. Students must use language precisely in their explanation (MP6).

• Invite students to share explanations for how to compare the size of a product to the size of one of its factors.
• “¿Qué es retador sobre dar una explicación que funcione para todos los productos?” // “What is challenging about giving an explanation that works for all products?” (When I have specific numbers, I can find the products and compare them. I can put them on the number line or write expressions. Without specific numbers, it’s hard to write or reason about the product.)