Factor (and Fashion) Fun

This week we've been investigating, How can we use models to represent multiplication?

In third grade, most students learned to model multiplication using arrays, or arrangements in equal rows and columns that form rectangles.  On Monday, students were assigned a (related) pair of numbers and used this strategy to build all of the possible arrays for their numbers with tiles.  We connected the dimensions of an array to factors in a multiplication equation.

After this, students drew their arrays on graph paper.

They made posters showing an organized a list of factors and factor pairs used to model the total number the array showed, which is the product in multiplication.

Before working on their second number, we paused for a brief discussion of things we noticed.

Since then, students have thought up more helpful strategies for making sure they've found all the factors of a number:

• 2 is a factor of all even numbers.
• Test factors less than half way in order from least to greatest (or greatest to least).
• Use skip counting to see if you can "land" on a number.  If you can, then it's a factor of the number.
• If the number has a 0 or 5 in the ones place, then you know 5 will be a factor.
• If the number has a 0 in the ones place, then you know 10 will be a factor.
• When finding factors of numbers that are more than 10 groups of a number, use a x10 fact, so you don't have to do so much counting.  For example, if you're trying to figure out if 3 is a factor of 45, start at 3x10=30, then count on by 3's:  33, 36, 39, 42, 45.
• You can also use facts you know to help you count faster.

Today we looked at our array posters and answered the following questions:

• Which numbers have only one array?
• Which numbers have a square array?
• Which numbers have the most arrays?

This lead to a discussion about prime, square, and composite numbers:

In their Interactive Math Journals, students identified examples of these numbers on a hundred chart.

Tomorrow we'll discuss how finding factors for one of our numbers helped us find factors of the other (related) number.  The explanation is related to this...

On a fun note, I knew it would be a good day when I noticed this unplanned coincidence in our "cul-de-sac".  :-)

Ms. Kirkham said she almost wore a scarf and was planning on trying out a way to wear it very similar to this!  :-)

The Fantastic Flying Books of Mr Morris Lessmore

Flocabulary - Five Things (Elements of a Short Story)

PTA Membership!

At Open House time Mrs. Remley and I spoke about our WONDERFUL PTA! They are a positive force at Alimacani. Year after year they work diligently to help support our school, classrooms and student learning. If you are interested in joining the PTA it is not too late. Your student brought home an envelope last week. Please ask if you need an extra. 

I wanted to share this new membership form sent in by one of our creative students today! It brought a smile to my face and I hope it does the same for you! 

Welcome FLOWER! You are bringing "flower power" to us all!

Seeing this outside my (Mrs. Remley's) room made my day!  Thanks for supporting our school!  

Ms. Kirkham's class is almost there!

Math Literature

One of my favorite math literature authors is Greg Tang.  Last week, I used one of his books to review/introduce an addition strategy we'll be using the next few weeks and beyond.

When integrating math literature, I always read aloud the text twice.  The first reading is for students to get familiar with and enjoy the text.  This particular book uses famous works of art to pose challenges for the reader.   

Such vivid colors, pure and bright--

to some it was a shocking sight!

For this they dubbed Henri Matisse

a "fauve" which means a wild beast

Please group the fish to make a 9.  

Six smart ways would be just fine!

During the second reading, we discuss the math in the story by making connections.  Math-to-self connections happen when mathematicians notice connections between their own life experiences and mathematics.  For example, last week I needed change for a twenty dollar bill.  I could have made $20 with two tens, four fives, twenty ones, one ten/one five/five ones, etc. 

Math-to-math connections happen when students discover links between their present and past study of mathematics concepts and procedures.  During our discussion, the word equivalent came to mind.  Most students were familiar with equivalent fractions from third grade, when different numbers were used to represent the same amount.  So, we connected this concept to what we were reading.  We were trying to compose (build/put together) numbers using equivalent (equal, but differently expressed) combinations of smaller numbers.

We made another math-to-math connection when students realized that addition and multiplication are operations we use to compose numbers, resulting in greater numbers than those we started with.

A few times, we were really close to having all the possible expressions of a number.  A student suggested taking an existing expression and breaking apart the greatest number into something equivalent, keeping the rest of the expression the same if possible.  This lead us to talk about decomposing (breaking apart) numbers, which students connected to subtraction and division, where we start with a number and break it into smaller parts than what we started with.

This year, students will also make math-to-world connections, which focus on current events and links to mathematics.  My goal is for students to see that math is not an isolated subject...it is everywhere, every day!

TGIF

Thank you to all of you who attended Open House last night!  We'll be e-mailing our presentation and other helpful documents.

Pre-kindergarten through fifth grade students gathered in the courtyard for our monthly Flag Raising Ceremony this morning.  Every Friday is School Spirit Day; students are encouraged to wear our school's colors (navy and gold) or any AES t-shirt.  Today is also Jaguar Spirit Day.  We hope the Jags win their first regular season game on Sunday!

Science Workshop

Scientists follow scientific process in investigating testable questions.  This week, we've been inquiring: What is a scientific question?

Scientific questions are testable.

Given this criteria, today we sorted questions as testable and not testable.

As scientists, we worked in teams.  Fourth grade scientists discussed why they thought questions were testable or not testable.  For some questions, team members agreed.  Sometimes team members disagreed.  How was it helpful to work with other scientists today?