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Lesson Plan: Zero Pairs & Combining Integers
Date: September 25, 2015
Note: Friday is the only full day of math for our
classroom. My mentor teacher and I teach
science Monday through Thursday. On
Friday, we either “fill in the gaps” for our campus math teacher or we “front load”.
Goal: Front load students for math teacher by introducing the concept of zero pairs and combining/adding integers so students will have been exposed to beginning concepts. Represent integer operations with concrete models and connect the actions with the models to standardized algorithms. (6.3C) Add integers fluently. (6.3D)
Objective:
- Through jumping number line, students will define and demonstrate use of zero pairs.
- By participating in human integer signs activity, students will solve math problems by combining/adding two integers, whether positive or negative.
- By playing Integers Tic-Tac-Toe with shoulder partner, students will employ and explain strategies learned on how to combine integers.
Supplies Needed: Blue painter’s tape for number line; negative
and positive signs on cardstock; extra Mad Minutes; zero pair definition sign; Integers
Tic-Tac-Toe laminated game boards with expo markers at each table group;
Exit Tickets
Mad Minute Warm-up: Problems
#4 and 5 on Thursday’s sheet. Review
answers and take up Tuesday through Friday’s work. 3 sheets in all; 4 days’ worth of work. "Write absent for any days you were absent on
top of front page."
Opening/Focus:
"I have a story to tell you. This
morning, I spilled coffee all over the kitchen floor. That was one bad thing that happened to
me. Also this morning, my oldest son,
Sam, gave me a hug, which was one good thing that happened to me. So, I consider myself back to where I started—1 bad thing
and 1 good thing happened to me. Sam
giving me a hug, my one good thing, cancelled out me spilling coffee all over
the floor, my one bad thing."
"What happens if I had 5 bad things that happened to me and 3 good
things? What do I have more of, bad or
good things? Right, bad things. By how
much? Yes, 2. Let’s think of our bad as negative. This time, I have 2 negative things happen
and 3 positive things happen. Which do I
have more of, negative or positive? Yes,
positive; by how much? 1 positive."
"This week you have learned what an integer is and how to locate it,
along with decimals and fractions, on a number line. Who can tell me what an integer is? How do we define it? A: the set of counting/natural numbers, their opposites and zero. Or all our whole numbers and their opposites/negatives. Today, we are going to
learn how to add integers, or what I call “combining” integers."
Explanation and
Modeling:
"So, let’s start by jumping our number line and learning what a zero pair
is. Say zero pair for me. (Call name of student), I need your help
jumping my number line. Start at
zero. Please jump positive 4. Now move
negative 4. Where did you end up? Zero.
Thanks. You may sit down. (Call another
student), your turn to jump. Start at
zero. Please jump negative 5. Now move positive 5. Where did you end up? Zero. Hummmmm. (Call another student), your turn. Please jump positive 7. Now jump negative 7. Where did you end up? Zero."
"What do you see happening here?
[Clarify that as they move the same number positive and negative, they
always end up at zero.] Each of these
sets of integers that I had my helpers jump-- +4 and -4, -5 and +5, +7 and -7,
are called zero pairs. They literally
cancel each other out and end up with no value. (Show definition on board.) A zero pair is a pair of numbers whose sum
is zero, for instance, +1 and -1, my 1 positive and my 1 negative. When you combine the numbers in a zero pair,
they cancel each other out and you’re back to zero. Face your face partner in front of you and
say, 'a zero pair is a pair of numbers whose sum is zero.' Face your shoulder partner and say, '+1 and
-1 are a zero pair (pause) because, when added together, they equal zero.' Understanding zero pairs will help you
combine integers, which we are going to do right now."
Guided Practice:
"There are negative and positive sign cards in your table bucket. Please get one now. I need 6 of my positives right here. I need 4 of my negatives here. We need to make as many zero pairs as we
can. I need my negatives and positives
in my group standing to go find their opposites."
[Show how to connect 1 positive signed student with 1 negative signed
student.] "We just made a zero pair by combining 1 negative with 1
positive. They now are zero so you can
go have a seat. Let’s see if we can make
another zero pair . . . [continue until all zero pairs are made]. So we made all the zero pairs we can
make. Right? What’s left.
2 positives. So my answer to
combining positive 6 and negative 4 is positive 2."
[Continue with zero pair human sign activity] "Let’s try another one. 5 negatives, 8 positives = 3 positives; 3 positives,
9 negatives = 6 negatives; Let’s try this one . . . 4 negatives, 8
negatives. Can I get rid of any zero
pairs? Why not? [they are all the same sign, there are no positives,
can’t make any zero pairs]. So, all the
negatives are safe. They’re happy. They
get to all hang out together. So how
many do I have? 12 negatives or my
answer, -12." Continue with more examples
until concept is clear.
"Now, let’s do some on the board."
Show combining terms using + and - signs, one sign above the other all under algorithm, and circle each zero pair so they make a zero and then put line through each to cancel out. Write -5 + 3
. "Our two integers are -5 and +3. Which do I have more of? Negatives or positives? Negatives, by how many? 2. So our answer to -5+3 is -2. What about 6 + (-2). What are our 2 terms/integers? +6 and -2.
Which do I have more of? Negatives or positives? Positives by how much? 4. So
our answer to 6 + (-2) is 4. What about
4 + 10? All positive. They all get to hang out together. Answer is +14. -8 + -12?
All negatives so we just combine our integers and make sure we put the –
sign with our answer. -20."
Independent Practice: Integers Tic-Tac-Toe with shoulder partner
With your shoulder partner, you are going to play Integers
Tic-Tac-Toe. Look at the orange boards
in your table bucket. (I will read
directions.) “How to Play”. For today,
Player 1 will be our As and Player 2 will be our Bs. There are dry erase markers, 1 per pair, in
your table bucket. Go ahead and start.
It’s time to stop with Integers Tic-Tac-Toe today, even if you’re not
done yet. We will make sure to play it
another day. If I could have my As
please grab a Kleenex and wipe off your game board.
Assessment: Integer Exit Ticket
On your table cart is an Integer Exit Ticket. In a moment, you will answer the two
questions and then hand it to me on your way out of class today.
Closing: First, who can tell me
one thing you learned from today? Who
would like to answer with something different that they learned?
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