Everyday Math: Partial Sums Algorithm

Today we reviewed the Everyday Math algorithm for addition called the Partial-Sums Method. Most fifth graders have mastered an algorithm of their choice for addition. If the are proficient in using that algorithm then they should use it. They are, however, expected to know the partial-sums algorithm for addition. The method helps them develop their understanding of place value and addition. In the partial-sums method, addition is performed from left to right, column by column. The sum for each column is recorded on a seperate line. The partial sums are added at either each step or at the end.

Here is a video that explains how to do this method: Addition Partial-Sums. The Everyday Math company has put the algorithims used in its program online. The animated directions take you through a problem step-by-step so students can refresh their memories or parents can learn the new algorithims. These are great refreshers, models, and argument breakers!

Here is the link to take you to the algorithms. Just click on the button for "Algorithims in Everyday Math", then click on grade 5, select an operation, an algorithim, and then an animation.

Using a Multiplication Chart to Find Equivalent Fractions

This is a post I made on my teaching blog last year. I am putting it here, because I am beginning to show the class this simple and easy way to find equivalent fractions. It is a good way to check and work with fractions as student learn to understand this tricky topic.  Not many people know or use this easy way to work with fractions. This is how I wrote it for teachers.

This is one of my favorite math tricks that can really help your students as they try to understand how to work with equivalent fractions. I learned it at a workshop a couple years ago and have yet to meet a teacher who previously used or was aware of how simple this chart is to help students.


Many simple equivalent fractions (most of the ones used in upper elementary years) are easy to find on a regular multiplication chart. I feel it is very helpful to point this out to your students. Many students struggle as they try to learn the many steps that it takes to find equivalent fractions. When you look left to right on the chart you are viewing the multiples of a number. When you view two different rows of multiplies you are viewing equivalent fractions.

For example using the 1's and 2's. Look at the two rows as if they were fractions.

1/2 = 2/4 = 3/6 = 4/8 and so on. You can split rows apart. Look at the rows for 1's and 3's. 1/3 = 2/6 = 3/9 = 4/12 and so on. To show how the chart works with my class I use an overhead projector and circle the numbers to make them easy to locate. To find 1/5 = ? / 30 I circle the 1 and the 5 underneath it on the ones column on the chart. Then I move my finger from the 5 until I get to the number 30 and circle that. I can block out or just cross out other numbers to make it clearer. Then I follow the 1 across and the 30 up until they meet at the number 6. and circle that. If you do it correctly the circles will form a square or rectangle.

Of course, as the students understand how to work the chart, teach them the other ways of finding equivalent fractions. It makes it much easier for them, however, to "see" the equivalent fractions for a number and the students even start memorizing the most common equivalent fractions.

Now for the most important part. When students take a test they usually cannot use a printed multiplication chart. So what! Train them on how to make a multiplication chart from their facts and have them practice often. Then at test time, they can reproduce the chart onto their test before starting the work. It should take less than 5 minutes. Not only can they use the chart for checking fraction, but they can use it as they do multiplication and division problems too! No it is not cheating. It is about being smart, observant, and prepared!

Do play around with the chart on your own. I didn't believe it would work that simply until I practiced with it and used it with my class. There are some other tips and techniques that you can quickly figure out on your own that even make using the chart easier.

Partial-Quotients Division Algorithm

We are learning (or relearning) the Partial-Quotients Division Algorithm in math. This may be as new to parents as it was to some students. If you want to see how it is used you can view online examples at the Everyday Math website. If you go to this webpage you can find examples and animations of how to use this algorithm. If you want to see animations and explanations first click on the button for the Handbook Animations. Then scroll down to the bottom of the page under division and you can click on a few examples that you can view.

Everyday Math Algorithims Online

The Everyday Math company has put the algorithims used in its program online. The annimated directions take you through a problem step-by-step so students can refresh their memories or parents can learn the new algorithims. We are working on mutiplication using the lattice and partial products algorithims. You will also find examples of the traditional multiplication algorithims and the algorithims used in the other operations. These are great refreshers, models, and argument breakers!

Here is the link to take you to the algorithms. Just click on the button for "Algorithims in Everyday Math", then click on grade 5, select an operation, an algorithim, and then an animation. I can't link directly but it takes just seconds to get to the examples.

Everyday Math Test: Chapter 1

The Chapter 1 Everyday Math tests are being sent home today. The grading looks like a mess and could be hard to figure out so I will explain it here. There are two parts to the test: Part A of the test is used for grading purposes. It is intended to recognize student achievement towards grade 5 goals. Problems #1-5 had to do with factoring numbers and #6-7 had to do with writing whole numbers and identifying the value of digits. The class has had multiple exposures to the content of the problems. Part B is a formative part of the test, meant to inform future instruction. The class had been introduced to these concepts; however the questions are not used for grading purposes. Questions had to do with writing the prime factorization of a number, using exponents to write prime factorization, renaming numbers in exponential and standard notations, and to identify divisibility.

There were seven questions in part A. Each question then was worth about 14 points and I gave partial credit for many answers that were incomplete or partially correct. However I did give credit for correctly getting a question correct on Part B of the test. No one lost points for incorrect answers on this part but if they got one question correct. I then averaged their test as having 8 questions (each question now worth about 12 points. If they got two problems correct, I averaged the test as having 9 questions (so each question being worth about 11 points), and so forth. If someone would have aced all of part B (no one did) then each question on the test would have been worth 8 points each. If someone had a 100% on part A (two students did!) then they still had a 100% on the test even if they did not get all of part B correct. I hope I am clear on how points were scored because I have placed a lot of marks on the tests as I graded them. I wanted you to know what all the marks meant. At the top of each test I placed a mark like “out of /12” and this signifies how many questions were included when figuring out the percent score for the test.

Here are some reminders about tests that you can emphasize at home:

The test reflects how well you prepare throughout the unit by participating in class, completing homework thoughtfully, asking questions when you don’t understand, and paying attention during lessons. It is also important to use test strategies when taking a test and not to race throuugh a test just to finish. Make sure you complete all parts of the test and answer all questions. I also reviewed similar questions to each question on each part of the test the day prior to giving the test. Test review time is not the time to “tune out” during class. About 1/3 of the class received a B+ or better on this test. Congratulations to these students.