The purpose of this activity is for students to apply what they learned about rounding in prior lessons to think about all the numbers that would round to a given number. Students should be encouraged to use whatever representations make sense to them. Although the number line is often used to represent rounding, it is also worth sharing other ways that students are representing or thinking about rounding.

• “How did you decide what numbers would round to 40?” (We looked at all the numbers that are closer to 40 than to 50 or to 30.)
• Consider asking:
  • “What does 35 round to?” (40 because it is halfway between 30 and 40)
  • “What does 45 round to?” (50 because it is halfway between 40 and 50)
• “Look at your responses for the first 2 problems. What patterns do you see in the numbers? Why is that happening?” (I see each set includes numbers that start with 1 less in the tens place than the nearest ten and a 5 in the ones place, and end with the same number in the tens place as the nearest ten and a 4 in the ones place.)
• “How did you use what you learned from the first 2 problems to think about the last problem?” (Instead of thinking about fives, we thought about fifties. We looked at all the numbers that are closer to 600 than to 500 or 700.)
• Consider asking:
  • “What does 550 round to?” (600, because it is halfway between 500 and 600.)
  • “What does 650 round to?” (700, because it is halfway between 600 and to 700.)

The purpose of this activity is for students to apply what they’ve learned about rounding to play a game in which each student generates a mystery number with three clues. The three clues describe whether the mystery number is even or odd, to which number it rounds, and two numbers that it’s between. It is possible that more than one number can fit the clues provided. In the Activity Synthesis, students reflect on which clues were most helpful for determining the mystery number.

• “As you played the game, what clues were the most helpful and why?” (Knowing how the mystery number would round to the nearest ten was really helpful because that really narrowed it down. Knowing which numbers the mystery number was between was helpful if it was something like 150 and 160, but not if it was between 100 and 200.)