In Mathematics this week we have been doing some work with the partial quotient division algorithm. The first time that I learned about this algorithm was just a few years ago, and I imagine many parents have probably never heard about it. In the blog today I will spend a little time discussing it and presenting some resources to better acquaint ourselves with it.
Part of the Everyday Mathematics curriculum’s focus is to promote sense-making in computation. While it is possible to make sense and analyze each step of the standard long division algorithm, many students encounter difficulty with those steps since they do not show visible evidence of place value. In class we discussed reasons why the partial quotient algorithm could be important to learn and the reasons we came up with included: it provides an alternative method for people to use if the standard algorithm is not working for them, it can work well with mental math because it focuses on breaking down larger numbers into sets of smaller friendly numbers and multiples, and there are multiple methods to solve a problem which allow people to capitalize on their own strengths with multiplication knowledge.
The first link I’ll provide goes directly to the University of Chicago website and a video slideshow you can watch that walks through the entire process. This is a great primer for understanding the basics of the algorithm.
Second, I’ll provide you with a link to download powerpoint slideshow by Rina Iati from the South Western School District in Hanover, Pennylvania. I think it is pretty well done and has a few more examples and practice problems.
If you still have questions about the partial quotients algorithm, feel free to drop me an email or send a note and I can take some time to walk you through it or provide you with some written materials. While I don’t think I would use it for all my long division, I can see definite advantages to using it for mental calculations and for certain sets of numbers that I immediately recognize as multiples.
One other note. Tomorrow, the class will be presenting a song at our monthly school assembly. We have been doing some singing and practicing in the classroom, and if any parents have a free Friday morning, it might be fun to come check it out.
Also, tomorrow is crazy hair day. Here is a little copy of the flyer. Please note that all styling is expected to be done before school. Please leave the hair products at home. Thanks.
- Mathematics: Study link pg. 81 (please show all work)
- Vocabulary: Finish packet and study for quiz
- Reading: Read for 25 minutes and fill out summary section in reading log.
- Social Studies: Look for resources on explorer for project
Is there another way?
Happy Wednesday to everyone.
Today I spent the first part of the morning at Emerson Elementary to observe and collaborate a bit with some 5th grade teachers there. I got some wonderful new ideas that I’ll be working on putting into action and communicating to the 5th grade team here. We had a substitute come in up until recess, and I got a glowing report back from him. Thanks to all the students who did their part to help out with the routines we have in place.
In Mathematics today we applied some of the ideas and concepts we have been talking about over the past couple days to a new division algorithm. The algorithm is called the partial quotients division algorithm and can be a pretty powerful tool for making estimations, doing mental calculations, and for just doing long division. I’m sure that many adults remember horror stories from learning long division. If you know that your child has difficulty with Long Division or is prone to making little mistakes in their calculations, make sure that they spend some time getting comfortable with the partial quotients algorithm. Here is a link to a website that goes through all the algorithms in Everyday Math, and here is a direct link to a quick explanation and example of the partial quotient algorithm. Also, here is one more site I found that has examples of different algorithms and short videos showing someone doing a problem. I hope those help. I know this algorithm will be new to many parents, but it will be well worth your time to spend a few minutes to acquaint yourself with it so that you can better understand what your children are doing, talk to them about mathematics strategies, and help them when they need it.
- Language Arts: Vocabulary Story – Write a story with the six vocabulary words of the week ( classify, straighten, beautify, lengthen, visualize, and analyze)
- Mathematics: Page 77 Division – Use the partial quotients algorithm to solve the division problems. Show your work on the back of the page.
- Social Studies: (some students) Finish Social Studies Page: Columbus Wasn’t the First.
Today in Math we learned a new algorithm for doing multiplication. The word sounds like lettuce, but it is actually lattice. The algorithm is a little like a lattice in a garden in that it involves straight diagonal lines, but it is quite different in that it is used to multiply numbers and not support vines. The algorithm involves lining up the factors around boxes, multiplying each digit, and then adding up totals along a diagonal axis for each place value. For an example, follow this link. Written publication of the lattice algorithm actually dates all the way back to the 13th century (1202) when Leonardo Fibonacci wrote Liber Abaci and explained the lattice algorithm for multiplication that he had learned based on Arabic numerals. Tomorrow we will be delving more into why and how the lattice algorithm works and how place value factors into it.
In Language Arts, Ms. Isreal came in to do an activity using short segments of a newspaper article and connecting lines of text with strong sensory details. Students used their imagination and clues in the given text to produce their own connecting sentences and fill in the gaps of the story.
For homework tonight, student’s will work on planning their final memoir to begin a rough draft on tomorrow. We have talked and written about different memoir topics from our childhood imagination to learning how to do something to food, parties and important family members. This will be their chance to pick their own memory to write about. Encourage them to think about memories that stand out to them. If they get stuck it might be a great opportunity to break out the family photo album or some home video to spur some ideas. Students will be filling out a graphic organizer of their choice. I made several choices available and also left it open for students to create their own graphic organizer to help plan. For some links to some other kinds of graphic organizers, click here or here.
One quick note about the Sally Foster fundraiser. Thanks to all the students who brought in orders. If there are any more orders out there, send them in tomorrow. It’s your last chance to get it in before they are sent out!
- Language Arts: Graphic Organizer Planning for a Memoir.
- Mathematics: Study Link Book Page 43: The Lattice Multiplication Algorithm.
- Reading: Read for 20 minutes and write in pink reading log.
- MAKE SURE TO BRING BACK SIGNED HOMEWORK AND READING LOGS TOMORROW
Today we used the students’ homework and words they clarified during their home reading to get some more practice with context clues. (Flummoxed, which is another word for being confused or befuddled, was one of the great words a student picked and we learned about through the context clues in a sentence.)
We also discussed both reading with expression and correct use of quotation marks. We had some student volunteers read passages of dialogue from their independent reading books in the morning, and they did so with amazing expression. Reading with expression helps to identify the parts of the text that are being spoken by different people and to develop a better understanding of the emotional states of the characters. We worked with passages the students found to develop a list of rules for using quotation marks. We will use the list as another self-monitoring tool.
In math we continued to work with estimation and also learned about a different addition algorithm. Algorithms are the strategies that we use to solve problems. Today we learned about the partial sum addition algorithm, which can be a very useful algorithm for doing problems mentally. Here is a site to learn about the different algorithms taught in the Everyday Mathematics Curriculum, and here is a link to a little video that shows the partial sums addition algorithm in practice.
- Language Arts: Context Clues Worksheet. Bonus: Create your own context clues problems.
- Mathematics: Study Link Book Page 29
- Reading: Read for 20 minutes and write in your pink reading log.