I realized how helpful it is to have students work with one divisor that they are familiar with rather than constantly changing them up. Also working with dividends that are closely related, for example 76 then 77 is impactful.
As Miranda Kaytor stated, I found really helpful to keep the divisor the same. Working with a sequence of dividends to find patterns is really great. I find the short division method very interesting as it highlights the place value of the numbers. I would introduce it after teaching long division
I had a couple “Aha” moments as I realized how many assumptions I had made when doing division. I have always been fairly efficient at applying algorithms, but had not made the connections that became apparent when working through the unraveled questions. It is interesting to me that as I make connections between concepts; it becomes easier to see other connections.
I also found that working with one divisor allowed connections to be made. The importance of place value was apparent when working through the activities.
As Miranda posted, it was very helpful to think about providing examples that used one divisor that students were familiar with and to vary the dividend by 1. It was helpful to think about how these examples could draw student attention to the pattern of the remainder.
Use contrast, juxtaposition, structured variation, etc are powerful ways to highlight critical discernments.
What was highlighted in my mind was the powerful nature of providing students with prompts that are close in relationship to each other, with variances that expose the whole understanding.
As the teacher, you need to be flexible to allow students to demonstrate which strategy works best for them (i.e., some students want to go through all the steps, some prefer the abbreviated method). It is important to ensure that students who are using an abbreviated method are doing so with full understanding and not just a desire for “shortcuts”.
Showing different variations which result in the same answer can be very engaging for students!
Using a clear contrast is very powerful for student understanding, and to see the relationships between numbers.
By juxtaposing a sequence of lessons with small alterations builds on this “Spot-the-Difference” approach that becomes an expected way to engage. It also allows a student to discover the process in their own by reverse engineering , for example, the +1000, -100 to stand for +900.
I saw the value in keeping the divisor the same for repeated examples to allow students to focus on other discernments. I also really like the shortened version of how to show the process, which really focuses on understanding of place value in the algorithm.
I thought it was really interesting to see that ‘short’ version of dividing! I will definitely be showing that to my students. Also, it was helpful to know that using the same divisor allows for those deeper connections.
It is very useful in the teaching and learning process, and more examples generated in different ways makes learners active with interest for the lesson
After going through the various engagements, I now advocate teaching long division in a manner that students/pupils can tackle every long division without fear or panic using several/individual steps. Interesting engagements so far and very glad it has impacted on my life as a mathematics teacher.
I realized that when you’re dividing with a divisor being 10, you can just delete the zero from the dividend and just think about how many tens are there in the dividend which will then be the quotient.
I learnt so much about contrast and variations and how learners can be engaged to discern differences.
My questions however, is that does these concepts work with all mathematical concepts in elementary school?
I have become more abreast with the various terminologies associated with division including dividend, divisor, etc and the various ways that learners could be assisted to work out long divisions from varied approaches.
With this i can now help my learners to do long division with ease using multiple approach.
I have learnt that solving example with two different method helps the child to understand it better.
Focusing on critical discernment help in grasping the lesson more easier. Giving appropriate examples also is a good way of helping kids understand lessons better
I realized how important it is for the timely transposition of example questions or problems to fully understand the number sense behind questions.
I remembered how often I get antsy when teaching and want to jump ahead, or point out the next critical discernment, and the next, without giving students enough time to engage with each one by juxtaposing examples where one variable changes enough.
Infact I have gotten two good steps in teaching my students long division with ease using the long and short form in dividing
I realised contrast helps learners to gain better conceptual understanding.
Looking at the example with cards (like a deck) that broke down the groups into base ten blocks (visual)was a great idea…I use the base ten blocks but having cards simplifies the visual and can be easily added and taken away as a group (without the physical distraction of the actual manipulative)…students (and teachers) sometimes get muddled with large groups of actual manipulatives…the card visual offers another aid (for demonstration anyway;))
I also have used the short division, even in younger grades…some students seem to prefer less steps.