OPENING EXERCISES - STARTER
For your starter today, do the opening exercises for lesson 5, #’s 1 – 5.
BE SURE TO FOLLOW DIRECTIONS – IF THEY ASK FOR AN EXPRESSION,
WRITE IT. NUMBER 2 ASKS FOR A REWRITE OF THE EXPRESSION.
OPENING EXERCISES
1. In the morning, Harrison checked the temperature outside to find
that it was –12ºF. Later in the afternoon, the temperature rose 12ºF.
Write an expression representing the temperature change. What
was the afternoon temperature?
OPENING EXERCISES
2. Rewrite subtraction as adding the inverse for the following problems and find the
sum.
a.
2–2
a.
–4 – (–4)
a.
The difference of 5 and 5.
a.
g–g
OPENING EXERCISES
3. What pattern do you notice in Opening Exercises 1 & 2?
4. Add or subtract.
a. 16 + 0
a. 0 – 7
a. –4 + 0
a.
0+d
a. What pattern do you notice in parts (a) through (d)?
OPENING EXERCISES
5. Your younger sibling runs up to you and excitedly exclaims, “I’m thinking of a
number. If I add it to the number 2 ten times, that is, 2 + my number + my
number + my number . . . And so on, then the answer is 2. What is my number?”
You almost immediately answer, “zero,” but are you sure? Can you find a different
number (Other than zero) that has the same property? If not, can you justify that
your answer is the only correct answer?
EXAMPLE 1
WRITE THE SUM AND THEN WRITE AN EQUIVALENT
EXPRESSION BY COLLECTING LIKE TERMS AND
REMOVING PARENTHESES. JUSTIFY YOUR STEPS.
a.
2x and –2x + 3
a.
2x – 7 and the opposite of 2x
c. The opposite of (5x – 1) and 5x
EXERCISE 1
•
With a partner, take turns alternating roles as writer and speaker.
•
The speaker verbalizes how to rewrite the sum and properties that justify each step
•
The writer writes what is being spoken without any input.
•
Discuss in pairs the resulting equivalent expressions.
•
We’ll do letter a together.
Write the sum and then write an equivalent expression by collecting like terms and
removing parentheses whenever possible.
a.
–4 and 4b + 4
EXAMPLE 2
Do the next 5 problems on your own. (The ones with •)
•
•
•
•
•
What are these pairs of numbers called?
• Reciprocals
What is another name for reciprocal?
• The multiplicative inverse.
What happens to the sign of the expression when converting it to its multiplicative inverse?
• There is no change to the sign. The expression and its multiplicative inverse have the
same sign.
What can we conclude from the pattern in the answers?
• The product of a number and its multiplicative inverse is equal to 1.
Why is the number 1 special with multiplication?
• One is the only number that when multiplied with another the result is that number
again.
Multiplicative Identity Property of One
Any other special numbers?
EXAMPLE 2
Write the product and then write the expression in standard form by removing
parentheses and combining like terms. Justify each step.
a. The multiplicative inverse of 1/5 and (2x – 1/5)
a. The multiplicative inverse of 2 and (2x + 4)
a. The multiplicative inverse of ( 1 / 3x + 5) and 1/3
EXERCISE 2 – DONE IN PAIRS AS WITH
EXERCISE 1
Write the product and then write the expression in standard form by removing
parentheses and combining like terms. Justify each step.
a. The reciprocal of 3 and –6y – 3x
SUMMARY
• What are the other terms for opposites and reciprocals?
• What are the general rules of their sums and products?
• What does the additive identity property of zero state?
• What does the multiplicative identity property of one state?
PROBLEM SET - HOMEWORK EXAMPLES
2. Write the sum and the rewrite the expression in standard form by removing parentheses and
collecting like terms.
a. 6 and p - 6
PROBLEM SET - HOMEWORK EXAMPLES
3. Write the product and then rewrite the
expression in standard form by removing
parentheses and collecting like terms.
a. 7h – 1 and the multiplicative inverse of 7
4. Write the expressions in standard form.
a. ¼ (4x + 8)
DO YOUR EXIT TICKET!
Homework is problem set for lesson 5.
Moby Max too!!