Least Common Multiple

We're working on finding the LCM of numbers now. After being introduced to these types of problems through the use of cycles, my students set about finding the LCM of numbers using the usual list-making strategy. Today we're going to extend our thinking into some algebraic reasoning with a little twist on multiples through pattern exploration. This activitiy is from Connected Math.

What do you notice?  What do you wonder?   What will the 20th step look like? When will the total number of tiles in a step equal 576 tiles? Explain how you found that answer. 

Then there is another pattern to explore:

 

Once again, what do you notice?  What do you wonder? What will the 20th step look like?  When will the total number of tiles equal 110?

 
Here's my graphic organizer and an exit ticket for Least Common Multiple.

Arrays, Number Puzzles, and Factor Trees

This week my students are tackling a task I came upon from the Georgia Performance Standards web site resources. It caught my eye because my students need a LOT of work with the mathematical practices especially collaboration, communication, persistence, and reasoning. This task fit the bill for all of those skills while they practice factors, multiples, and factorization. Students work in small groups (we're working in pairs). They have three sheets of paper to share with rectangular arrays, factor trees with missing numbers, and puzzle cards. The goal is to identify the number of each representation and match them.

There are several entry points for this task - some easier than others. Most students wanted to tackle the word puzzle cards first but then realized that the other two sheets were much easier to do first and then use as clues for matching up to the word puzzles. There is a second group of cards for those that finish quickly - although no one in my two advanced classes finished yesterday. My other three
classes will begin this activity today.

Today we will finish up this activity, make posters of the matches, and present their findings with some discussion by the students to justify their answers.

For our math notebook, we will make a number puzzle of a mystery number for others to solve.

Here is the link to the file:
https://ccgpsmathematicsk-5.wikispaces.com/file/view/4-6_Arrays_Number_Puzzles.pdf

 

 

Interactive Student Notebook - Exponents

 

After dabbling in interactive student notebooks over the last two years, I have made a more dedicated commitment to using them with students. Here is our latest entry when reviewing exponents this week. We did a review of the content and took notes on the right side of the notebook page. The next day I gave the students this to fold in half and glue onto the left side as an independent activity that also served as an assessment while I worked with small groups. The cartoon idea was a hit with the creative side of the kids and a great reminder for the power of exponential growth!