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- This bundled package includes:- Operations with Integers-Addition w/ Spanish translation - Operations with Integers—Subtraction w/ Spanish translation- Operations with Integers—Multiplication and Division w/ Spanish translation- A Powerpoint Lesson that coordinates with the above - Operations with$21.15$25.00Save $3.85
- The bundled package includesOperations with Integers - AdditionOperations with Integers - SubtractionOperations with Integers - Multiplication and DivisionPowerpoint Lesson that coordinates with the above three lessonsThese can all be purchased separately in my store.$12.60$15.50Save $2.90
This activity sheet engages students in using algebra tiles or colored chips to discover the rules for multiplying and dividing integers.
In two previous lesson, Operations with Integers - Addition and Operations with Integers - Subtraction, students will have been introduced to zero pairs. This is a needed foundation for multiplication and division which are defined in terms of addition and/or subtraction.
All multiplication problems begin with a blank table, one with no chips on it one with a value of zero such as 3 red chips and 3 yellow chips. When two signed numbers are multiplied together the sign of the first number tells the student how many groups of chips must be shown on the table or removed from the table. The second number tells the students what chips will be in each group. So, for example, (+2)(-3) means the students will show two groups of three red chips. In this case, the answer would be six red chips or -6. If (-2)(-3) was the example the student will remove two groups of three red chips. Since the table is blank to begin with the student reasons that they will need to add six zero pairs, which is also equals zero, to the table so there are enough red chips on the table so they can removed two groups of three red chips. The answer, in this case, would be six yellow chips or +6.
After students have worked through all the exercises by showing and removing the begin to make some generalizations as to when the answer is positive and when it is negative. They study all their exercises and try to write rules based on what they saw happening with the chips.
Students develop rules for division of two integers by rewriting each division problem as a multiplication problem. So, for example, if the students are given (+5) (-2) = -10 they know they can write two division problems based on that multiplication problem. So, if (+5) (-2) = -10, then (-10) ÷ (-2) = +5 or (-10) ÷ (+5) = -2. By rewriting several of these division statements students can observe that the same rules for multiplication of integers also work for division of integers.
A Spanish translation is included.
A digital format has been included.
Comment from a buyer:
• Thank you!
• Easy manipulatives...easy to implement!
• I got this to use with a student I was working for 6th grade tutoring...nice way to show using manipulatives.