This activity sheet engages students in using algebra tiles or colored disks to discover the rules for addition of signed integers.
First, students develop the rules using the color tiles to help them visualize the operation of addition. Every problem always begins with a blank table or a zero table. When students combine the chips, they are modeling the operation of addition. When a table has more than one color chip students can always simplify their answer by removing zero pairs.
The students are given five experiments to study:
• Combining red chips with red chips
• Combining red chips with yellow chips
• Combining yellow chips with red chips
• Combining yellow chips with yellow chips
• Combining the same number of yellow chips with the same number of red chips.
After studying these results of the five experiments students begin to generalize the results. They notice that when red chips are combined with red chips the answer is always red chips. Similarly, when yellow chips are combined with yellow chips the answer is always red yellow chips. They also notice why combining red and yellow chips sometimes turns out being red chips and other times yellow chips. They notice that the color chip that had more chips controls the sign. The students notice that when you combine the same number of yellow and red chips the answer is always zero because everything simplified with zero pairs.
From these five experiments students learned that the colored chip also represented positive and negative numbers. The students rewrite the experiments to represent positive and negative numbers. For example, combining 3 red chips with 2 red chips becomes (-3) + (-2) = -5. Because the students worked with colored chips to represent the addition, student now can visualize any new problem with chips. For example, if the students are given a new problem of (+4) + (-6) students think of combining four yellow chips with six red chips. They see four zero pairs being removed from the table and leaving two red chips on the table for an answer of -2.
Extension problems have students extend the rules to decimals and fractions. The emphasis is on determining the sign of the answer based upon what numbers they are given.
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• Love practicing with manipulatives