Tag: signed numbers

Posted in Elementary School Math, High school mathematics, Number Sense

Teaching positive and negative numbers

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A popular approach for teaching numbers is to use it to describe a property of an object or a set of object. For example, numbers are used to describe the amount or quantity of fruits in a basket.

In introducing integers, teachers and textbooks presents integers as a set of numbers that can be used to describe both the quantity and quality of an object or idea. Contexts involving opposites are very popular situations to show the uses and importance of positive and negative numbers and the meaning of its symbols. For example, a teacher can tell the class that +5 represents going 5 floors up and -5 represents going five floors down from an initial position.

Mathematics is a language and a way of thinking and should therefore be experienced by students as such. As a language, math is presented as having its own set of symbols and “grammar” much like our spoken and written languages that we use to describe a thing, an experience or an idea.But apart from being a language, mathematics is also a way of thinking. The only way for students to learn how to think is for them to engage them in it!  Here’s my proposed activity for teaching positive and negative numbers that engages students in higher-level thinking as well.

Sort the following situations according to some categories

  1. 3o below zero
  2. 52 m below sea level
  3. $1000 net gain
  4. $5000 withdrawal from ATM machine
  5. $1000 deposit in savings account
  6. 3 kg weight loss
  7. 2 kg weight gain
  8. 80 m above sea level
  9. 37o above zero
  10. $2000 net loss

The task may seem like an ordinary sorting task but notice that the categories are not given. Students have to make their own way of grouping the situations. They can only do this after analyzing each situation, noting commonalities and differences.

Possible solutions:

1.  Distance vs money (some students may consider the reading the thermometer under distance since its about the “length” of mercury from the “base”)

2. Based on type of quantities: amount of money, temperature, mass, length

3. Based on contrasting sense: weight gain vs weight loss, above zero vs below zero, etc.

The last solution is what you want. With very little help you can guide students to come-up with the solution below.

Of course, one may wonder why make the students go through all these. Why not just tell them? Why not give the categories? Well,  mathematics is not in the curriculum because we want students to just learn mathematics. More importantly, we want our students to think critically and creatively hence we need to give them learning experiences that develops good thinking habits. Mathematics is a very good context for learning these.

Here are my other posts about integers:

Posted in Elementary School Math

What is an integer?

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Here are some ideas pupils need to learn about integers:

•A number represents a quantity. An integer is a type of number. An integer represents a quantity.

•Integers are useful in representing quantities and includes opposite sense. For example, going up 5 floors and going down 5 floors can be represented by +5 and -5 respectively. The sign ‘+’ represents up and ‘-’ represents  down. The ‘5’ represents the number of floors.

•The integer +5 is read as “positive five” and NOT “plus five”. The integer -5 is read as “negative five” and NOT “minus 5”.

•The words positive and negative are descriptions of the whole number 5 while the words plus and minus describe operation to be done with the numbers. That’s why it doesn’t make sense to read the integer -5 as “minus 5”. From what number are you subtracting it?

•The number 0 is an integer which is neither positive nor negative.

•Integers can be represented in a number line. An integer and its opposite are of the same distance from 0. For example, -4 is 4 units to the left of zero so its opposite must be 4 units to the right of 0. This integer is +4.

integers

Problem: The distance between two integers in the number line is 4 units. If one of the integer is 3 units from zero, what could be these two integers?

•The distance of an integer from zero is called the absolute value of the integer. So the absolute value of -4 is 4 and the absolute value of +4 is also 4.In symbol, /+4/ = 4 and /-4/ = 4.

Of course, merely explaining to students these ideas and giving them lots of exercises will not work. It will never work for many of them. Teachers have to design tasks or activities pupils can work on so that students can construct their own understanding of these ideas. Teachers can help scaffold their learning through problem solving tasks and through the questions and feedback they will provide the students.

Next post on this topic will be about absolute value and operations with integers.