The document outlines a timed math exercise featuring 15 problems across addition, subtraction, multiplication, and division, along with their answers. It discusses key concepts in integers, the real number system, and the number line, emphasizing the effects of adding positive and negative numbers. Additionally, it includes instructional strategies for peer review and problem-solving collaboration.

1. Activator-August 13/14
• You will have 3 minutes to solve 15 basic
addition, subtraction, multiplication, and
division problems. Get your pencils ready.
• 45 + 321= ? 52 + 78= ? 1,007 + 462= ?
936 – 278= ? 17-3 =? 791 – 588= ?
12 x 21 = ? 27 x 5= ? 13 x 13= ?
14 x 32= ? 9 x 80= ? 90 ÷ 2= ?
441 ÷ 7= ? 345 ÷ 15= ? 209 ÷ -11= ?

2. August 13/14 Answers
• 45 + 321= 366 52 + 78= 130 1,007 + 462= 1,469
936 – 278= 658 17-3 = 14 791 – 588= 203
12 x 21 = 252 27 x 5= 135 13 x 13= 169
14 x 32= 448 9 x 80= 720 90 ÷ 2= 45
441 ÷ 7= 63 345 ÷ 15= 23 209 ÷ -11= -19
• Were you still accurate even though your goal was
speed? Who noticed what made the last problem
different?

3. Integers & How to Add Them
August 13 & 14

4. The Real Number System
Rational Numbers
Repeating &
Terminating
Decimals
Integers
-5,-4,-3,-2,-
1,0,1,2,3,4,5
Whole Numbers
0,1,2,3,4,5…
Counting
Numbers
1, 2, 3, 4, 5…
Irrational Numbers
Non-terminating Decimals

5. The Number Line
-4 -3 -2 -1 0 1 2 3 4
Negative
numbers are
to the left of
zero.
Positive
numbers are
to the right of
zero.
Zero is
neither
positive nor
negative.

6. The Number Line-Adding Positive #s
-4 -3 -2 -1 0 1 2 3 4
•When we add a positive number, we are moving right on the number line.
oEx: -2 + 4=
2

7. The Number Line- Adding Negative #s
-4 -3 -2 -1 0 1 2 3 4
•When we add a negative number, we are moving left on the number line.
oEx: 3 + -5=
-2

8. Absolute Value & Opposites
• An integer’s absolute value is its distance from
zero.
▫ Ex: │ -9│= 9
▫ Ex: │ 9│= 9
• An integer’s opposite is its counter-part on the
other side of the number line with the same
absolute value. One is positive and one is
negative.
▫ Ex: The opposite of 120 is -120.

9. Modeling Addition
• Zero pairs occur when there is the same number
of positive and negative chips. They cancel each
other out.
• Color Chips Virtual Manipulative
▫ In addition, we are removing zero pairs that are
already present.

10. More Practice
• Do you see a pattern?

11. Homework Huddle
• At your tables, pair up with 1-2 others and go
over your answers to the homework. If you have
a disagreement, try to figure out who has the
correct answer. If you cannot agree, ask me. We
will go over a few problems together that we
identify as tough.