Understanding ALL Operations with Integers

​Understanding All Operations with Integers

SWBAT reason ABSTRACTLY using integers.

We are about to go DEEP into the upside down and reason ABSTRACTLY (no numbers) about ALL OPERATIONS with INTEGERS!!

​

Remember: You can do HARD things!!

​Time to put on your thinking cap!

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​Directions:

• READ each situation CAREFULLY

• THINK & DISCUSS with your group

• CHOOSE your answer(s)

Here we go...

Multiple Choice

The location of $$\left[p+q\right]$$  on the number line will be to the RIGHT of $$p$$  if $$q$$  is...

• positive

• negative

• zero

• either positive or negative.

Multiple Choice

The location of $$\left[p+q\right]$$  on the number line will be to the LEFT of $$p$$  if $$q$$  is...

• positive

• negative

• zero

• either positive or negative.

Multiple Choice

The value of $$\left[-p+q\right]$$   will be POSITIVE if $$q$$  is...

• positive with an absolute value greater than

    $$\left|-p\right|$$  

• negative with an absolute value greater than

    $$\left|-p\right|$$  

• positive with an absolute value less than

    $$\left|-p\right|$$  

• negative with an absolute value less than

  $$\left|-p\right|$$   

Multiple Select

Choose ALL that apply:

The value of $$\left[-p+q\right]$$   will be NEGATIVE

if $$q$$  is...

• positive with an absolute value greater than

  $$\left|-p\right|$$  

• negative with an absolute value greater than

  $$\left|-p\right|$$  

• positive with an absolute value less than

  $$\left|-p\right|$$   

• negative with an absolute value less than

    $$\left|-p\right|$$  

Multiple Choice

The value of $$\left[p-q\right]$$  will be POSITIVE if the value of $$q$$  is...

• less than

  $$p$$  

• greater than

  $$p$$  

• equal to

  $$p$$  

Multiple Choice

If  the value of $$q$$  is NEGATIVE, the value of $$\left[p-q\right]$$  will be...

• positive

   

• negative

   

• impossible to determine 

Multiple Choice

If $$q$$  is NEGATIVE and $$\left|-q\right|>\left|-p\right|$$  

the value of $$\left[-p-q\right]$$  will be...

• positive

• negative

• zero

• impossible to determine.

Multiple Choice

The value of   $$p\left(q\right)$$ will be POSITIVE if $$q$$  is...

• positive

• negative

• zero

• either, it will always be positive.

Multiple Choice

The value of   $$p\left(q\right)$$ will be NEGATIVE if $$q$$  is...

• positive

• negative

• zero

• neither, it cannot be negative.

Multiple Choice

The value of   $$-p\left(q\right)$$ will be POSITIVE if $$q$$  is...

• positive

• negative

• zero

• neither, it cannot be positive.

Multiple Choice

The value of   $$-p\left(q\right)$$ will be NEGATIVE if $$q$$  is...

• positive

• negative

• zero

• neither, it cannot be negative.

Multiple Select

Which of the following will have a POSITIVE value?

Choose ALL that apply.

• $$\frac{-p}{q}$$  

• $$-\frac{p}{q}$$  

• $$\frac{-p}{-q}$$  

• $$\frac{p}{-q}$$  

• $$\frac{p}{q}$$  

Multiple Select

Which of the following will have a NEGATIVE value?

Choose ALL that apply.

• $$\frac{-p}{q}$$  

• $$-\frac{p}{q}$$  

• $$\frac{-p}{-q}$$  

• $$\frac{p}{-q}$$  

Poll

How are you feeling about reasoning abstractly with integer operations?

• Confused!

• Starting to Get It!

• Confident!