Integer, Part 1 - Understanding Integers and Expressions

Summary

This lesson introduces integers and the concept of integer chips, providing a visual method for understanding how integers work. It covers how positive and negative integers interact, particularly through the idea of zero pairs, where positive and negative integers cancel each other out. Using real-life examples like stickers for good and bad behaviors, the lesson makes abstract math concepts more relatable. By the end, students learn to add and subtract integers using integer chips and zero pairs, setting the stage for more advanced mathematical operations.

Takeaways

• 😀 Integers are whole numbers that can be positive, negative, or zero. They do not include fractions or decimals.
• 😀 Negative numbers are considered integers, as long as they are whole numbers, like -25.
• 😀 To test whether a number is an integer, check if it has a fraction or decimal. If it does, it’s not an integer.
• 😀 Integers can be understood as representing positive or negative actions, like earning positive or negative stickers for behavior.
• 😀 A net of positive stickers (or chips) can earn a prize, but negative actions cancel out positive ones.
• 😀 The concept of a 'zero pair' refers to a positive and a negative number canceling each other out.
• 😀 One positive and one negative integer, like +1 and -1, together equal zero (1 + -1 = 0).
• 😀 Integer chips can be used as a visual tool to represent positive and negative numbers.
• 😀 In an example of adding +3 and -3, all chips cancel out to zero (3 + -3 = 0).
• 😀 In a real-life example, Jerry's positive and negative stickers can cancel each other out, so only his remaining positive stickers count toward his prize.
• 😀 The lesson helps prepare students for adding and subtracting integers, utilizing the zero pair concept with integer chips for visualization.

Q & A

What is an integer?

An integer is any whole number, which can be either positive, negative, or zero. It does not include fractions or decimals.

Is 2.5 an integer?

No, 2.5 is not an integer because it is a decimal number, not a whole number.

Is -25 an integer?

Yes, -25 is an integer because it is a whole number, and integers include both positive and negative whole numbers.

Is half (1/2) an integer?

No, half (1/2) is not an integer because it is a fraction, not a whole number.

Is 1000 an integer?

Yes, 1000 is an integer because it is a whole number.

What is a 'zero pair' in the context of integers?

A zero pair occurs when one positive integer and one negative integer cancel each other out, resulting in zero.

How would you represent the integer 2 using integer chips?

To represent the integer 2, you would draw two positive chips, each marked with a 'positive' symbol inside.

What does the expression 1 + (-1) represent?

The expression 1 + (-1) represents the cancellation of one positive integer and one negative integer, which equals zero.

What happens when you add 3 + (-3) using integer chips?

When you add 3 + (-3) using integer chips, all three positive chips cancel out with three negative chips, resulting in zero.

If Jerry has collected 7 positive stickers and 2 negative stickers, what is his net total of positive stickers?

Jerry's net total of positive stickers is 5. This is because 2 negative stickers cancel out 2 positive stickers, leaving 5 positive stickers.