Since today is 11-12-13, I decided to read the story Anno's Mysterious Multiplying Jar and draw students attention to the patterns happening in this story.
Anno’s Mysterious Multiplying Jar, byMasaichiro and Mitsumasa Anno, is an engaging story about counting and so much more. It starts with the idea that there is a jar that contains one island, which has two countries, each of which has three mountains. This idea continues up to ten. Each page has only a little text with many pictures to illustrate the concepts. For example, on the page describing the three mountains, there are three mountains inside separate borders to help illustrate the concepts. The story introduces the idea of factorials.
Knowing and using factorials is definitely not a fourth grade skill, but my students enjoyed this story. It is a great example of how math is all around us. I also told my students that it wasn't until I wrote today's date on the board that I decided to read them this story. It is important for them to realize that math truly is everywhere, and that outside of school math doesn't happen in 4 week unit chunks. It was a great way for me to model the important reading skill of making connections between a text and the world.
After reading the warm up book, I write on the board 5 x 48. I ask students to solve this problem. (Most students will solve this on a whiteboard using the standard algorithm or expanded notation)
After I see most students are done, I tell students that sometimes in multiplication you can make it easier for yourself and can do mental multiplication by using the doubling and halving rule. Since at this point in this unit, most students are proficient with a multi-digit multiplication strategy, I wanted to also point out that mathematicians look for patterns in numbers and structure, which is why the multiplication standard algorithm works. I remind students about CCSS Math Practice Standards 7 and 8 and that mathematicians look for and often seek out shortcuts. I tell students that sometimes in double digit multiplication there are shortcuts that allow for multi-digit multiplication to become mental math. I then very quickly tell them that I can calculate 54 x 20 within 6 seconds in my head. I tell them that while I LOVE magic, I'm not really magic by doing this, but that I've figured out a strategy and pattern that allows me to do this. Then I dramatically tell them it's because I know about doubling and halving.
Then I show or model to students how doubling the factor 5, to 10, and then halving the factor 48 to 24, I can create a new problem of 10 x 24 which is easy to do mentally. We do several more examples together from the doubling and halving pdf in the resource section, which can also be accessed here - multiplication-strategy-doubling-and-halving.pdf
Students practice this new strategy on their whiteboards. I list examples in which it doesn't work and lead a discussion about why the doubling halving strategy doesn't work. For example, students were able to identify that 6 x 27 doesn't work because it doesn't create a problem much easier to compute mentally. Students were also able to identify that a problem like 5 x 33 doesn't work either because 33 is an odd number and can't be halved equally into a whole number.
In this video, a students practices the doubling and halving strategy.
Students spend the rest of the time playing a multiplication card game. You can find it in the resources section as here - mult card game.docx. The game students play is an adaptation from this packet.
As students play this game, which is the last day of this multiplication unit, I am able to use a clipboard and observe students as they play and make anecdotal notes. This is an important opportunity for me to make notes about students who are struggling with the concept of multi-digit multiplication. Moving forward, I need to make sure I continue to provide support to these students in this skill. Beginning next week, several students I've identified will begin to receive extra math support before school for a half an hour with a certified educator in my building who is currently serving as a paraprofessional. These students will spend time working through a multiplication packet in a small group. So, in addition to an extra half an hour four days a week in which I can work with identified students, they will now also be able to work a half an hour before school on identified skills. The packet students will work through is in the resource section of this lesson. (Students will NOT complete the entire packet, but will begin with the multiplication lessons)
(I've also included an entire packets of games in which I use often in my reteaching time in the resources section)
I use an exit ticket in this lesson and have students complete this sentence:
The multiplication strategy I'm using most is ___________________. This is how I use it for 26 x 45.
The strategy that is the most difficult for me is ____________________.
If students don't have a strategy that is not difficult for them, I do not require students to fill out the last part of the exit ticket.
This is an important exit ticket as this is the last lesson in this multiplication unit. Students will begin a division unit in the next lesson. It will be imperative that students are solid in their understanding of multiplication strategies as we begin work in the division unit. The CCSS require students to apply their understanding of models for division, place value, properties of operations,and the relationship of division to multiplication as they develop, discuss, and use efficient and generalizable procedures to find quotients involving multi-digit dividends.
Note: After looking at the exit tickets, about 60% of my students are using an expanded notation method to multiply multi-digit multiplication while 40% prefer the area model. I do have a few students that are not yet proficient with any method and will be have opportunities to continue to work towards master of this skill.