In this lesson, students work to recognize patterns that will be useful in the associated Algebra 1 lesson when they factor quadratic expressions that contain a negative constant term. First, students find pairs of integers with a given product and sum to recognize patterns in the signs of the integers. Next, students expand binomial factors into standard form to recognize patterns of how changing the operation within factors affects the terms in standard form. Students look for and make use of structure (MP7) when they notice how slight differences in factors result in differences in the equivalent standard form. They also construct viable arguments and critique the reasoning of others (MP3) when they compare their work with a partner to expand factors.
- Identify patterns in finding pairs of integers with a given sum and product.
- Let’s explore operations with integers