Subtracting Integers with Tiles

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Presentation transcript:

Subtracting Integers with Tiles Student Expectation 7th 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.

SUBTRACTING INTEGERS +3 +3 We often think of subtraction as a “take away” operation. Which diagram could be used to compute +3 - +5 = ? +3 +3 The University of Texas at Dallas

SUBTRACTING INTEGERS This diagram also represents +3, and we can take away +5. When we take 5 yellow tiles away, we have 2 red tiles left. We can’t take away 5 yellow tiles from this diagram. There is not enough tiles to take away!! The University of Texas at Dallas

SUBTRACTING INTEGERS -2 - -4 = ? Use your red and yellow tiles to model each subtraction problem. -2 - -4 = ? ANSWER The University of Texas at Dallas

-2 - -4 = +2 SUBTRACTING INTEGERS Now you can take away 4 red tiles. 2 yellow tiles are left, so the answer is… This representation of -2 doesn’t have enough tiles to take away -4. Now if you add 2 more reds tiles and 2 more yellow tiles (adding zero) you would have a total of 4 red tiles and the tiles still represent -2. -2 - -4 = +2 The University of Texas at Dallas

SUBTRACTING INTEGERS Work this problem. +3 - -5 = ? ANSWER The University of Texas at Dallas

+3 - -5 = +8 SUBTRACTING INTEGERS Add enough red and yellow pairs so you can take away 5 red tiles. Take away 5 red tiles, you have 8 yellow tiles left. +3 - -5 = +8 The University of Texas at Dallas

SUBTRACTING INTEGERS Work this problem. -3 - +2 = ? ANSWER The University of Texas at Dallas

-3 - +2 = -5 SUBTRACTING INTEGERS Add two pairs of red and yellow tiles so you can take away 2 yellow tiles. Take away 2 yellow tiles, you have 5 red tiles left. -3 - +2 = -5 The University of Texas at Dallas

SUBTRACTING INTEGERS A fact family gives 4 true equations using the same 3 numbers. For example: 7 + 8 = 15 8 + 7 = 15 15 – 7 = 8 15 – 8 = 7 All of these statements are true. The University of Texas at Dallas

SUBTRACTING INTEGERS We can also use fact family with integers. Use your red and yellow tiles to verify this fact family: -3 + +8 = +5 +8 + -3 = +5 +5 - + 8 = -3 +5 - - 3 = +8 The University of Texas at Dallas