I begin this lesson with a number hook or magic trick. Math magic tricks are a way I engage or "hook" my kids on math. I do not expect students to understand how the tricks work or perform the tricks. Many of the magic tricks I perform through out the year, students often do discover how or why the tricks work. They begin to understand that the tricks aren't really magic, but rather they work due to various mathematical ideas. I often call myself a Mathemagician - it's just one way I show students how math is all around them.
For this trick, I give all students a calculator. I direct students to:
Enter in the first three digits of their phone number (not the area code)
Example : (905) 567 - 1111
Next, multiply these three numbers by 80
567 x 80 = 45360
Then add 1
45360 + 1 = 45361
Now multiply by 250
45361 x 250 = 11340250
Add to this the last 4 digits of your phone number
11340250 + 1111 = 11341361
Add again the last 4 digits of your phone number.
11341361 + 1111 = 1134272
Now subtract 250
1134272 - 250 = 11342222
Finally divide number by 2
11342222 / 2
The number in the calculator should be student's phone number.
I begin this lesson with a fluency sprint. Students practice finding the midpoint between two numbers in this sprint. I chose this sprint today because this is an important skill in being able to use a vertical number line for rounding. This is also a very quick formative assessment. As students work, I circulate around the room and observe students. I can tell very quickly which students need scaffolds or more help.
This sprint is from www.engageny.org
For this lesson, students use their personal white boards.
I begin by asking students to think of reasons why or when someone would want to know how to round numbers. I ask a few students to share their thinking. As students list examples, I record their thinking. I then give a personal experience about when I use numbers to round. I tell students about buying a new car this past summer and rounding the sales price of the car to a "nice number" or a number that was easier for me to remember.
Next, I ask students how many ten thousands are in 72,744? I draw a vertical number lie on the board and then mark the lower endpoint with 7 ten thousands and ask the students what 1 more ten thousand would be? I mark the upper endpoint with 8 ten thousands. (Many of my students were confused and said that there were 70 ten thousands. I had to emphasize the place value often in order for students to overcome this confusion)
Students find the midpoint between 7 and 8 ten thousands and I then mark 75,000 on the number line. I ask students where 72,744 would be located? Students can see that 72,744 rounded to the nearest ten thousand is 70,000.
I repeat this procedure with a 6-digit number rounded to the nearest ten thousand. (e.g 457,629) I use the vertical number line with this back and forth question response approach for rounding 6 - digit numbers to the hundred thousands place until I feel that most students are understanding and responding.
Next, I give each table a number to round using a different place. Each table group rounds to a different place value. hundred thousands place, ten thousands place, thousands place, etc.
I then lead a brief discussion about rounding and being close to the exact number. I want students to begin to make sense of that the smaller the place redound to, the closer the rounded number is the original number.
Part of the discussion centers around why rounding to the largest place could be problematic in some situations since the number is further away from the original number in some cases.
Students list things like programs for concerts and football games, or buying a house as example of when rounding to the largest place value could be problematic.
To wrap up this lesson, students complete an exit ticket. I ask students to round 567,499 to the nearest hundred thousand and the nearest thousand.
As you can see in these two exit tickets, both students show a correct response in rounding 567,499 to the hundred thousands place and the thousands place.
In analyzing all the exit tickets, I can tell quite a few things about each student. For example, in the above photos, I can tel that one may be still trying to solidify his or her thinking about place names. Notice the initials above each digit to help determine the places of each digit. This helps me as a design future learning opportunities and re-teaching opportunities for students to ensure success for all learners.