Goal: Math 7.NS.2.a Students will be able extend multiplication skills to involve integers
including the rule of multiplying by 0.
Develop:
Task: Mathematica
Subgoal: Students will create visual representation of skip counting with positive and
negative numbers.
Anticipation- struggles with number lines, use of reference points, cardinal directions,
misunderstanding rate, commutative property
Terms to know: Integers, rate, cardinal directions, number lines, commutative property
Solidify:
Task: Exploring Patterns in Multiplying Integers
Subgoal: Students will explore and discover patterns/rules for multiplying integers.
Students will produce a class poster.
Anticipation: multiplication mistakes, Sign errors,
Terms to know: Product, Factors, Rules, patterns,
(reminder: in discussion of activity, create a class/group chart for the rules/patterns of
integer multiplication. ie: + x + = +)
Practice:
Task: Integers War (cardgame)
Tools: Decks of Face cards for students, at least 2 colors
Subgoal: Students will practice multiplying integers with partner as well as comparing the
products of integers.
Anticipation: multiplication errors, color mixups (red=negative black=positive), directions,
value of face cards
Terms to know: product, factor, positive/negatives, integers, value of numbers
Mathematica
In the city of Mathematica, there is a town center which attracts visitors
to the city. From the town center, a train takes visitors to different
popular locations. Answer the following problems about travel around the
city. Make a visual representation of the town with its locations. Use a
number line to show your understanding.
The train leaves the Town Center traveling East at the speed of 2 blocks
per minute. In 4 minutes you will be at the museum.
The train leaves the Town Center going West at 2 blocks per minute. After
5 minutes you arrive at the Athletic Center. How far did you travel?
From the Athletic center, the train passes through the Town Center at the
same rate. The train travels for 7 minutes to the east to get the mall.
(Example of a number line. Don’t need to necessarily include.)
Exploring patterns in Multiplying Integers
Find as many patterns as possible using positive and negative integers in
place of n.
n*2
4*2
n * -2
8
n*3
-4 * 3
4 * -2
n * -3
-12
Create your own rules for multiplying integers
Write your own multiplication problems when:
your product is -10
your product is 36
your product is 24
Integers War (cardgame)
Launch: Introduce the Rules to Multiplication Integer War
Write on the board:
Black = positive
Red = negative
Ace = 1
Jack and Queen = 10
King = 0
Play Integers War
Two to three students are given a deck of cards. Students divide the deck
evenly amongst players. Each player flips over two cards. Each player
multiplies the two cards and announces his/her total. The player with the
greatest sum wins all cards. If there is a tie “a war”, the cards are
left and tied players complete another round to see who wins all remaining
cards. Winnings are set aside. Once all cards have been played, students
count their cards to determine the round winner. The game begins again.
Explore:
Play the game
Discuss:
1. What were some shortcuts to tell if you were a winner?
Anticipated answers:
Kings make zeros
If the cards are different colors the result is negative (unless
K)
Matching colored cards are positive (unless K)
Two red cards or two black cards are always greater than a
red/black combo.
2. How do the shortcuts relate to the rules of multiplying integers?
Homework or exit ticket.
Multiplying of Integers
Name_______________
Multiply
1) 3 * 4
_____
5) 12 * -2
_____
9) -8 * -3
_____
2) -3 * -2
_____
6) -6 * -4
_____
10) -11 * 0
_____
3) 5 * -5
_____
7) -8 * 5
_____
11) 9 * -3
_____
4) 7 * -1
_____
8)
4 * -7
_____
12) -10 * -7
_____
Additional Resources
The Party in Mathland
Have you ever been to a party like this?
Everyone is happy and having a good time. Suddenly, who should appear but the GROUCH! The grouch goes
around complaining to everyone about the food, the music, the room temperature, the other people....
What happens to the party? Everyone feels a lot less happy... the party may be doomed!!
But wait... is that another guest arriving?
What if another grouch appears? The two negative grouches pair up and gripe and moan to each other about
what a horrible party it is and how miserable they are!! But look!! They are starting to smile; they're beginning
to have a good time, themselves!!
Now that the two grouches are together the rest of the people (who were really positive all along) become happy
once again. The party is saved!!
To determine whether the outcome will be positive or negative, count the number of negatives: If there are an even number of
negatives -and you can put them in pairs- the answer will be positive, if not... it'll be negative:
Negatives in PAIRS are POSITIVE;
NOT in pairs, they're NEGATIVE.
Links:
http://www.youtube.com/watch?v=UHIZUE5iW-c
http://www.youtube.com/watch?v=YS9fqfjGIhE