This number hook is called Secret Number.
I begin this trick by asking ONE student to think of a secret number! Then I ask that person to double the secret number and then multiply the number by 5. Next, I ask for the TOTAL. Whatever the total is, I eliminate the last digit. The secret number is left.
At the conclusion of this trick, I ask my students how they thought it worked. I had TWO students know immediately that it worked because of PLACE VALUE! :) One boy said, "well, really you're multiplying by 10, so to figure out my number you have to divide by 10. You taught us that when you divide by 10 your digits move to the right, so that's how you could tell my number, you removed the ones, or the zero."
I start this lesson by reminding students that rounding is a skill that mathematicians and people use to communicate or to make other math calculations easier. It's far easier to add $3.00 + $4.00 than to add $2.78 + $3.88.
Next, I ask students what changes about numbers when rounding to smaller and smaller units? (ten thousands place, thousands place, hundreds place) This is an essential question for today's lesson. I give an example like 56,239. Students discuss with their learning partner their ideas and share their thinking.
I tell students that when we round to the largest unit, every other place will have a zero. (I noticed from previous exit tickets that some students were not replacing digits with zeros, but keeping them them same. Therefor, it is important to emphasize.) I want students to realize in this lesson that rounding large numbers to the largest unit gives a very easy or friendly number to add, subtract, multiply or divide. Rounding large numbers to smaller units does not have as many zeros but is closer to the actual value of the number.
I display this problem using the document camera.
2,837 students attend Albert Elementary school. About how many chairs are neededinthe school.
Students discuss with their learning partner how they would estimate the number of chairs needed in the school. I ask several partners to share their thinking with the whole class. Many students report that they would round to the nearest thousand in this case in order to have enough chairs for all students. Students were able to realize that if they rounded to the nearest hundred, even though the number would be closer to actual number, there would not be enough chairs.
During this partner share out, I have students utilize Math Practice Standard 3 by refining their mathematical communication skills. Students answer questions like “How did you get that?” and “Why is that true?” They explain their thinking to others and respond to others’ thinking.
A phrase that students practice saying during discussion is "I think that _____ because _______." I catch students using this phrase as they talk with their learning partner. Each time they use the phrase, students get a gold ticket that goes into a basket for an end of week reward drawing. (This is one way in the beginning of the school year I encourage math talk. By the end of the year, students naturally talk math and do not seek or need these gold tickets)
Next, students work with their learning partner on number 4, side two, of the practice page- rounding practice
You can see a student explaining his thinking in this video.
Student work with their learning partners to finish the second page the of the practice pages. As students work, I circulate the room and assist as necessary. I guide students thinking with questions and help clear up misunderstandings. If students finish the second page, they work independently on the first page..
(practice sheets are from www.engageny.org)
To end this lesson, I lead a conversation centered around the problems on the independent practice page. These questions are important for students to fully make sense of the initial essential question - What changes when rounding to smaller and smaller units? Through the questions and independent practice, students begin to make conjecture about rounding. Many students begin to understand that situations really determine which place numbers are rounded to.
Some questions included:
In Problem 3 why doesn't rounding to the nearest hundred work? Would rounding to thenearest thousand have worked better? What does this show you about rounding.
When estimating, how do you choose to which unit you will round?
Would it have been more difficult to solve Problem 5 if you rounded both numbers to thehundreds? Why or why not?
Notice, in Problem 5, that 65,000 rounded to 70,000 and that 7,460 rounded to 7,000. What is the relationship between 7,000 and 70,000. How does this relationship make iteasier to determine the number of trips?
What is an advantage of rounding to smaller units? Larger units?