Making Conjectures about the Multiples of 5-10
Lesson 8 of 11
Objective: SWBAT determine if a number is a multiple of a given number.
Today's Number Talk
For a detailed description of the Number Talk procedure, please refer to the Number Talk Explanation. For this Number Talk, I am encouraging students to represent their thinking using an array model.
Task 1: 48/6
For the first task, many students wrote a 48 on the inside of an array, placed 6 on one side, and placed 8 on the other side. Other students decomposed the 48. I found a couple students decomposing the 48 into 40 + 8. This was a great opportunity to discuss the importance of decomposing the 48 into multiples of 6. I drew this representation on the board and Discussed How to Decompose the 48 Next, I Modeled Student Ideas on the board. Here's a Student decomposing 48 in multiple ways on her board.
Task 2: 96/6
Task 3: 960/6
During the next task, students reasoned aloud, "if 96/6 equals 16, then 960/6 will equal 160 because 960 is 10x greater than 96. This means the answer will be 10x greater too."
Task 4: 1008/6
For the final task, students figured out that 960 + 48 = 1008. Here a student modeled: 1008:6 = (960 +48):6.
Throughout every number talk, I continually model student thinking on the board to inspire other students. This also requires students to use math words to explain their thinking instead of relying on a model to represent the math. As students solved each task, I wrote the answers on the board to encourage students to use prior tasks to solve the more complex tasks: Listed Tasks.
This lesson is a continuation of yesterday's lesson, Making Conjectures about the Multiplies of 0-4.
Goal & Introduction
To begin today's lesson, I reviewed the goal: I can determine if a number is a multiple of a given number. I explained: Yesterday, we analyzed the multiples for 0-4. Today, we are going to be focusing on the multiples of 5-9.
I continued: You did an amazing job coming up with conjectures and providing evidence to support your thinking! Remember to continue providing evidence today as you make your conjectures. This is an important part of being a magnificent mathematician! I really stressed this expectation as I wanted students constructing evidence-based arguments (Math Practice 3).
I didn't want to spend a lot of time talking as I wanted to provide as much time as possible for students to investigate multiples: If you get done early, you can continue on by finding the multiple for larger numbers. Please get together with the same partner as you were with yesterday and begin working!
In order to provide students with the opportunity to color hundreds charts and analyze patterns with multiples, I created a Google Presentation using Google Drive Documents called Multiples Presentation and shared this presentation with students yesterday (using their student Google email accounts). Yesterday, students completed the slides up to 12. Today, they started by working on slide 13 with the goal of getting to slide 22.
Right to Work
At this time, I asked students to work with their partners to complete slides 13-22 (multiples of 5-9). Students continued on to the next slide, Slide 13, where they found the multiples of 5 with their partners and then wrote a conjecture about the multiples of 5 on Slide 14.
During this time, I conferenced with each partnership to check on student understanding. I would also ask clarifying questions to push student thinking and to encourage precision (Math Practice 6).
Multiples of 5
Here are two students explaining their Conjecture for the Multiples of 5. Before I could even question the student on her wording, "All multiples of five end with either five or ten," her partner quietly points out that "zero" would be a better word to use instead of "ten." This is a prime example of how important collaborative work is during math time!
Multiples of 6
Ironically, this video, Conjecture for the Multiples of 6, is of the same two students as the last video. Only this time, the roles have switched. The student being helped last time is now helping this student. I try to take advantage of any chance I get to encourage students to attend to precision (Math Practice 6).
Multiples of 7
Of course, coming up with a conjecture for 7 is one of the hardest tasks of today's lesson. Here, Conjecture for the Multiples of 7, a student struggles a bit with this, but not because of a lack of understanding! Here's Another Conjecture for the Multiples of 7 I loved observing the various ways in which students think!
Multiples of 8
Here, a student made a conjecture and disproved herself using evidence: Conjecture for the Multiples of 8. Then, she uses the doubling strategy to find more multiples of 8.
Multiples of 9
Here, a student has typed her Conjecture for the Multiples of 9. The next step for this student is to provide examples/evidence for each conjecture!
As students finished with the multiples of 9, several students went on to the Extra Challenge (Slide 23-34). Here, a student explains his strategy for finding the Multiples for 19!
Student Work Example
Here's an example of a student's work at this time: Student Work Example.