For this number trick, I have each student write the numbers 1 through 31 in order in their math notebooks. Then I have each student circle three numbers in a row. For example 17, 18, and 19. Then students add the three numbers together. I tell my students to write their answer down and then I call on about 5 students to tell me their sums. Once they tell me their sum, I tell them the three consecutive numbers they picked. All I have to do is divide their answer by 3.
For example, 54 divided by 3 equals 18. The quotient I get will be the middle number. Then I add 1 to 18 (19) and subtract 1 from 18 (17) to get the other two numbers.
Note: My students did an excellent job figuring out how this number trick works. While the concept of averages or mean is not a fourth grade standard, this trick gave me an opportunity to introduce the term average and tell students that they are finding the average of the three numbers when they find their sums and divide by three. My students really enjoyed being presented with a number trick that they could quite easily figure out how to do it.
For this warm up, I give students this task - 4nbt1_assessmenttask_1.docx. Students work independently to answer the question and then glue the task paper into their math notebooks. I chose to give students this math notebook task for a couple of reasons. This is the first day back to school after a two week winter break. I wanted to engage students right away in the math for today, but I also knew that students were not unlike me, sleepy and day dreaming about all the fun that was had during the two week break. This task, since it is a review concept, allowed for all students to access it and practice proving their answer either in words, pictures, or numbers. I also wanted to use this place value warm up to remind students that even though we practiced this concept months ago, I still expect them to know it, remember it, and use it.
Click here to hear my thoughts about this students thinking.
You can also click here to hear my thoughts about the above student work.
For today's lesson, students will play a Division Jeopardy game to practice and review division concepts, vocabulary, and procedures in order to be proficient in Common Core State Standard 4.NBT.6.
Math games have always been a part of my teaching instruction. Games engage my students and can be a fun way to review concepts. Besides engaging students, games also allow opportunities to develop skills related to critical thinking and problem solving. This jeopardy review game was highly engaging for my students and they didn't want to leave until we had finished the final jeopardy round.
You can access the game by clicking here - Jeopardy
One way I encourage all students to participate is to rely on team answers. I had each student use a whiteboard to record their answer. Each member of the team must agree on the answer. This Jeopardy game allows for the use of a timer. I set the timer for 58 seconds for each question. When the buzzer goes off, students at each team (table) hold up their whiteboards. I also add a rule that all teams have the ability to earn points for each question. Each time a team chooses a category, all teams answer that question. I actually have all students answer together with their whiteboards. This Jeopardy game is not about being the first team to answer. I also do not take away points if a team answers incorrectly because I want to encourage students to answer, and learn from their mistake. The only time a team could lose points is in the final Jeopardy round with their wager and in incorrect response.
This very short video clip shows students holding up whiteboards after the buzzer went off.
One advantage of making the rule that all students had to have an answer on their boards is that this really promoted math discourse and students engaging in math talk. Sometimes when students are working with a partner, the more dominant partner can tend to take over the conversation and tell the other person what to record as an answer. I have found that when students work in a group, the dominant personality can't as easily persuade or tell the other group members what to do. It's is often in a group situation that the less dominant personalities "ban together" and feel courageous enough to disagree with the more dominant personality students. This was fun to see in my students as they worked together and talked about the problems in this game.
I did not create this Jeopardy game, therefore there are several things I would change about the questions if I had editing capabilities. For example, in the long division category, students are presented with problems like 60 / 15. While I was proud of my students that they could figure this problem out by their number sense and knowing 15 + 15 = 30 and then another two 15's would be another 30 for a total of 60, this isn't necessarily a division problem I would present to fourth graders. I really want my students to have a solid understanding of how to divide multi-digit dividends by one digit divisors as CCSS 4.NBT.6 states. This problem is a two digit divisor. Another example was a problem asking students to calculate 725 / 14. Again, this is not what students need to know and be able to do for CCSS 4.NBT.6, however, I liked the other questions enough to overlook this two problems.
For this debrief, students will write on a post it note for a footprints reflection. I ask students to respond to this prompt:
While playing the game today, what is something you may have forgotten, or not thought about in a long time, that you now know or remember.
Getting my students to continually reflect on their thinking, I can promote a reflective classroom, and ensure that students are fully engaged in the process of making meaning. One of my instructional goals is to to align my instruction so that students are producers, not just consumers, of knowledge. As a facilitator and believer in student centered classrooms, my students must use self reflection in order for me to adjust my instruction and meet their needs.