# Q & A

Hello there,

Let’s use this page to exchange ideas, ask questions, or give suggestions on how to teach mathematics effectively. You can use the “Comments” button below to post your question or idea.

Questions may not be answered completely from the exchanges. I will not even attempt to give you a conclusive answer. The purpose of this is for us to learn from each others experience

This site is such a wonderful resource, I love the truth to the blogs and about how this isnt about making math “easy”! Keep it up 🙂

I saw you article on “Lesson Study Research Lesson: Teaching subtraction of integers”. I am understand the chip idea, but when it comes to solving this question I am at a loss. If you explain the idea that “minus and minus equals a positive” then it makes sense. But am sure you mean the students to figure that out for themselves.

e.g. -2 -(-3) = 1

in chip form: I dont have enough chips to take away

Also with this example too…

e.g. -3 – 2 = -5

in chip form: – – – / – –

In UK, we are taught the rules, and just shown to apply it, no understanding of why they work. You just accept it. Now you can derive the rules yourself, through problem solving and finding patterns in answers, yet it is still doesnot show why it is so. In the end, students must be lead to “believe” it is true.

Overall a very goood idea to explain integer arthimetic.

keep up the good work

indeed you can’t take away 3 negative chips from two negative chips so what you do is to add a positive and a negative chip to the two negative chips; basically you added 0 so the value of -2 is not changed. you can do the same to the second problem.

this is a good site. i learn many things.it’s interesting. keep on!

thanks.

hello ma’am, I am presently planning to start my thesis but i don’t have any idea of where to start. I wanna use UbD as my tool in enhancing the problem solving abilities of my pupils in gr v but i am not so familiar with it (UbD). can u please give me tips to where i should start my desired study? thanks & more power po.

UbD and problem solving are very broad areas. you may want to narrow down your topic.

hi ma’am, could you please send me your best practices in mathematics…

thanks in advance!

I’m afraid there are no hard and fast rules. You may want to read the following posts. That should give you some ideas.

# Teaching thru problem solving

# Exercises, Problem Solving, and Mathematical Investigations

# The heart of mathematics

# Features of good problem solving tasks

# Mathematical Habits of Mind

Hello.Is there anyone here who could teach me or possibly show me an example of an algebra lesson using UBD?

Hi. Technically, there is no such thing as a UbD lesson. It is not also a way of teaching but a way of planning the lesson. It prescribes a format for thinking how you should be planning your lesson in three stages. Click this link for the stages.

Hi Ma’am! I woulld just like to ask about a CHED memo called MORPHE. I was told that it was about college professors having an MS degree in order to be considered for a probationary status. Can you kindly explain the details of that memo. Thank you.

I’m sorry I have not heard of that CHED memo.

I find it really hard to come up with a UBD unit plan in geometry!!grrr!

Why do you think DepEd is not providing a sample?

i find it hard to think of the essential understanding in every topic..i need help

Hi. I am planning a lesson that hits on this standard: Select and use appropriate operations — addition, subtraction, multiplication, division, and positive integer exponents — to solve problems with rational numbers, including negative rationals. I have some good review exercises, assessment exercises and class discussions planned, but as for my lesson on the rationale of WHY you use a certian operation to solve a certian word problem involving positive and negative rational numbers (think tax or tip or commmission problems), I am struggling. Any guidance you might be willing to give on what to include in my teaching portion of my lesson? I want to make sure I’m connecting bigger dots for students, and i’m struggling with what those bigger concepts should be.

I always like to start with a problem that can be solved in different ways. In your case it would be best if you can find a problem solving task that can be solved by the different operations (e.g there are many ways of solving and representing the solution to a problem involving a 30% commission]. After the presentation of solutions I always ask students to choose the solution they like most and why. The big dots I am targeting (1) is for them to be able to develop a sense of what is considered efficient solutions in mathematics; (2) that a problem can be solved in different ways; and (3) a math concept can be represented in different ways. Let me know if I make sense and thanks for asking the question.

Hi. This response was helful, yes. After looking into solving word problems further last night, I think I am going to tackle this lesson with first a review of how to use operations on rational numbers, then take it a step further to show how you can use rational numbers to represent precentages and find “parts” of numbers and then jump into some larger word problems and review the process of deciphering the right information and the ultimate question out of a word problem and a few indicators of what operations to use. I feel a bit more confident this morning thankfully.

Hiya. I have found it tricky teaching kids to add and subtract fractions when the denominators are different. I lay lots of foundations on finding equivalent fractions, emphasising the concept that they are the same size but the jump from this to using them in the calculations of adding and subtracting fractions seems like a step too large for many kids to handle.

Any tips?

It is indeed a big jump. Have you tried teaching multiplication and division first before doing addition and subtraction? The former can take off right after operations with decimals and conversion from decimals to fraction and back. The pupils can develop their own strategy for multiplying and dividing of fraction using their knowledge on decimals. This way, they will have more experience and develop more confidence in working with fractions first before they get to do addition/subtraction of dissimilar fractions which, while easier to make sense of than multiplication and division, is harder to make an algorithm to. It is just an idea. Maybe I should do a research of that or you can. Keep us updated of the results.