Multiply Integers With Counter Groups

Start with Multiply Integers With Counter Groups to show why signs work, then use Sort Integer Products by Sign for the pattern. Assign Multiply Two Digit Integers as practice and the rate and time sheet to connect the signs to real situations.

Draw groups of counters on a mat and cross out groups on a mat of zero pairs to find products like 3 x (-2). A zero pair is one positive and one negative counter, which together have a value of 0, so a mat of zero pairs has a value of 0. The directions on the page read: On an empty mat, draw the groups. On a mat of zero pairs, cross out the groups named. Write the value left on the mat as the product. An answer key is included.

Yes, both. We made it for 7th grade integers, and it works the same at home or at school. At home, a student can work through it alone and then go over it with you, which shows quickly what is solid and what needs another look. In class it works as independent practice, homework or a warm-up, and you can print one copy or a full set.

Two integers with the same sign have a positive product, and two with different signs have a negative product. With more factors, count the negative ones. Sort Integer Products by Sign has students do this without multiplying.

Taking away groups of a negative amount adds value. On a mat of zero pairs, crossing out 2 groups of (-4) leaves a value of 8. Multiply Integers With Counter Groups shows this with counters.

Divide the product by the known factor, and check the sign. Since (-9) times what equals -63, the missing factor is 7. Missing Factors in Integer Products practices this.

Rate times time can be a negative product, such as a level falling 3 centimeters each day for 8 days. Repeated Change Problems That Multiply Integers asks students to explain what the sign means.