Associative (Grouping) Property of Multiplication

We've been collecting cans of soup for our school's SOUPer Bowl, benefiting a local food pantry.

A generous student brought these this morning:

Perfect timing for today's lesson on the Associative (Grouping) Property of Multiplication!

Sometimes, as in this situation, we need to multiply more than two numbers:

Each box has 2 rows of 5 cans.  There are 2 boxes of soup cans.  How many cans of soup is this?

We could think about it this way:

5 cans in each row x 2 rows x 2 boxes: 5 x 2 x 2

The Associative (Grouping) Property of Multiplication says that the grouping of factors can be changed, and the product will stay the same.

First, we tried grouping (5 x 2) x 2.
(Remember that parenthesis used in math mean "please pay attention to me"; do this part first.)
5 x 2 is 10, and 10 x 2 is 20 cans.

Then we tried 5 x (2 x 2).
2 x 2 is 4, and 4 x 5 is 20 cans.

So, no matter which factors you multiply first, you will always get the same product.


(By the way, you can still send in cans of soup until February 1.  :-) )

Combination Problems

Whenever I feel like I have nothing to wear (yet a closet full of clothes!), I like to dig through my closet and wear old pieces in new ways.  Yesterday, I posed this real-life dilemma to our students:

In my closet, I have three kinds of tops: tank tops, t-shirts, and sweaters.  For bottoms, I have shorts, skirts, slacks, and jeans.  How many different outfits can I make using one top and one bottom?

Some students, like Morgan, chose to approach this problem using pictures:

 We agreed this was a good start, but then realized we were missing combinations because we were just guessing and checking.  Some students, like Shawn, tried making combinations in order, for example, finding all the possible combinations with a tank top before moving on to combinations for a t-shirt:

Dylan showed us how to make an organized list to show all the possibilities.

Here's another variation of an organized list Ben shared:

And one from Devin:

When Luis showed us his picture and organized list, he also explained that he used repeated addition to find the number of combinations:

Since repeated addition is multiplication, we saw a connection.

Now we can multiply to solve combination problems!

Whoa We're Half-Way There...

(Singing the rest of the song? :-) )

Can you believe it is already day 90 of third grade?

This is my absolute favorite time of the school year with our students.  (The gorgeous weather we have had this week has made it even better!)  If you haven't started noticing already, expect your student to grow by leaps and bounds in responsibility, independence, maturity, and understanding of concepts and skills over the next few months.  Like we said at Open House, be ready to see a different (even more amazing) kid than the one who walked into our doors in August.

So, where are we going from here?

In Math Workshop, we will be challenged with reviewing skills from the beginning of the year (in the context of more word and multi-step problems this time around) and moving forward into new concepts (division, fractions, two-dimensional geometry) and skills (measuring length to the nearest half and quarter inch/centimeter, time to the nearest half or quarter hour, elapsed time).  To provide necessary review and reinforcement, expect more math homework to be assigned over the next several weeks.  Concerning basic fact timed tests, we will start multiplication fact family fluency and possibly review some of our addition and subtraction fact families to maintain fluency.

I hope you will be able to join us for Math Night on January 31 from 6:30-7:30.  We'll be sharing resources and strategies for helping students with fractions.

Curriculum Connections to Current Event

If you follow local news, you might be aware that two tagged great white sharks, Mary Lee and Genie, have been hanging out offshore of Jacksonville Beach this week.  (My husband surfs, so this has been quite a hot topic among our family this week!)  We have been checking out where they've been when their devices were pinged, and I wanted to share this with our students because of the connections to social studies (we've been looking at a physical map of Massachusetts this week and the sharks were tagged in Cape Cod) and to science (we'll be studying vertebrate animals later this year).  We can even make a math-to-world connection using a comparison problem:

If Mary Lee weighs 3,456 pounds and Genie weighs 2,292 pounds, then how much heavier is Mary Lee than Genie?

Area & Perimeter

We learned a catchy song to introduce measuring area and perimeter and connected these skills to our array strategy for multiplication since finding the product of an array is the same thing as measuring the rectangle's area.  Sometimes you can even use multiplication to help find the perimeter!  We will continue to practice these skills in Calendar Math this month.