Student Expectation 7 th Grade 712C Use models such as concrete objects pictorial models and number lines to add subtract multiply and divide integers and connect the actions to algorithms ID: 595570
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Slide1
Multiplying Integers with Tiles
Student Expectation:
7
th
Grade:
7.1.2C
Use
models, such as concrete objects, pictorial models, and number lines, to add, subtract, multiply, and divide integers and connect the actions to algorithms. Slide2
MULTIPLICATION
Red and yellow tiles can be used to model multiplication.
Remember that multiplication can be described as repeated addition.
So 2 x 3 = ?
The University of Texas at Dallas
2 groups of 3 tiles = 6 tilesSlide3
MULTIPLICATION
2 x
-
3 means 2 groups of -3
The University of Texas at Dallas
2
x
-
3
=
-
6Slide4
MULTIPLICATION
Since 2 x 3 = 6 and 3 x 2 = 6, does it make sense that
-
3 x 2 = -6 ?
-3 x 2 = -6 is true. +2 x -3 =
-6 and -3 x +2 = -
6 belong to a fact family:
The University of Texas at Dallas
+
2 x
-
3 = -
6-3 x
+
2 =
-
6
-
6
÷
+
2 =
-
3
-
6
÷
-
3 =
+
2Slide5
MULTIPLICATION
Use your tiles to model each multiplication problem.
+
2 x +4 = ?
The University of Texas at Dallas
ANSWER
2 groups of
+
4
+
2 x
+
4 =
+
8Slide6
MULTIPLICATION
+
3 x
-3 = ?
The University of Texas at Dallas
ANSWER
3 groups of
-
3
+
3 x
-
3 =
-
9Slide7
MULTIPLICATION
-
2 x
+4 = ?
The University of Texas at Dallas
ANSWER
4 groups of
-
2
-
2 x
+
4 =
-
8
Use the fact family for
-
2 x
+
4 = ?
We can’t show
-
2 groups of
+
4
+
4 x
-
2 = ?
we can show 4 groups of
-
2Slide8
MULTIPLICATION
+
1,
-1 are opposites
the products are opposite
Since +2 and -2 are opposites of each other,
+2 x -
3 and -2 x -3 have opposite products.
The University of Texas at Dallas
+
1 x
+
3 =
+
3
-
1 x
+
3 =
-
3Slide9
MULTIPLICATION
To model
-
2 x -3 use 2 groups of the opposite of -3
The University of Texas at Dallas
-
2 x
-
3 =
+
6Slide10
MULTIPLICATION
Use tiles to illustrate
-
3 x -4 =?
The University of Texas at Dallas
ANSWER
3 groups of
+
4 (the opposite of
-
4)
-
3 x
-
4 =
+
12