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Models and Pictorials
Warm-up
Fact Families
Powerpoint
Jump, Jump
Guided Practice
Multiplication Patterns
Fact Families
(Warm Up)
Write a related subtraction problem for each.
1. -3 + (-2) = -5 -5 – (-2) = -3
2. +25 + (-32) = -7 -7 – (-32) = 25
Write a related addition problem for each.
3. +8 – (-2) = +10 8 + 2 = 10
4. -14 – (-20) = 6 -14 + 20 = 6
Write a related sentence for each.
5. n - 5 = 35
35 + 5 = n
6. n + 5 = 35
35 – 5 = n
Do your related sentences make it easier to find the
value of n? Why or why not? Answers will vary.
Jump, Jump
Since multiplication is repeated addition, we
can use the “jumps” that we used in addition
of integers to help us understand
multiplication of integers. Remember, a
positive move is to the right and a negative
move is to the left. Solve 5 x 2 = ?
-11-10 -9 -8 -7 -6 - 5 -4 -3 -2 -1 0 1 2 3 4 5 6
5 X 2 = 10
Where did the jumps start? zero
7 8 9 10 11
Jump, Jump
Solve 5 x (-2) = ?
-11-10 -9 -8 -7 -6 - 5 -4 -3 -2 -1 0 1 2 3 4 5 6
7 8 9 10 11
5 X (-2) = -10
Why are the jumps going to the left?
Because the 2 is negative, you are jumping 5
jumps of -2 in the negative direction.
Where did the jumps start? zero
Jump, Jump
In your journal, predict what will happen when
both numbers are negative. Be prepared to
share your prediction with the class. (Allow time
for sharing)
Solve -5 x (-2) = ?
-11-10 -9 -8 -7 -6 - 5 -4 -3 -2 -1 0 1 2 3 4 5 6
7 8 9 10 11
-5 X (-2) = 10
Why did the arrow reverse?
Because of the double negative -5 and -2.
Where did the jumps start? zero
Jump, Jump
With your partner, construct an algorithm for
multiplying integers.
Possible answer: When multiplying integers,
if the signs are alike the product is positive, if
the signs are unlike the product is negative.
Jump, Jump
Using our algorithm we can summarize that
positive x positive = positive
negative x negative = positive
positive x negative = negative
In your journal, write three different
scenarios that will help you remember each
of these statements. For example:
positive x positive = positive
If we do our homework (positive) and study
(positive) we will get good grades (positive).
Jump, Jump
Possible answers:
positive x negative = negative
Because people look different
(positive) and (negative) some people are
prejudice (= negative).
negative x negative = positive
Two ugly twins (negative) and (negative) still
bring a smile (= positive), just because
they are twins.
Multiplication Patterns
(Guided Practice)
After studying the relay problem, some students started
playing with number patterns to see whether what they
found in the relay race made sense. Study the
equations below. Look for patterns.
5 x 5 = 25
5 x 4 = 20
5 x 3 = 15
5 x 2 = 10
5x1=5
5x0=0
Multiplication Patterns
(Guided Practice, cont.)
1. How do the products change as the numbers
multiplied by 5 get smaller?
Each product decreases by 5.
2. Predict 5 x (-1), 5 x (-2) and 5 x (-3). Explain
your reasoning.
5 x (-1) = -5, 5 x (-2) = -10, 5 x (-3) = -15
Possible explanation: With each equation,
there is one fewer group of 5; 5 less than 0 is 5, 10 less than 0 is -10, 15 less than 0 is -15)
3. Write the next four equations in the pattern.
5 x (-4) = -20; 5 x (-5) = -25; 5 x (-6) = -30;
5 x (-7) = -35.