In Algebra 1, students build on the skills from grade 7 involving applying the distributive property when signed numbers are involved and combining like terms. The purpose of this lesson is to revisit, refresh, and practice that grade 7 work in preparation for the work to be done in the associated Algebra 1 lesson. For example, in Algebra 1, students build on the skills from grade 7 involving applying the distributive property when signed numbers are involved and combining like terms. The purpose of this lesson is to revisit, refresh, and practice that grade 7 work in preparation. For example, in Algebra 1, students are expected to expand expressions like . In grade 7, they encountered expressions like . Throughout this lesson, students multiply expressions involving positive and negative numbers, creating equivalent expressions of a different form. As students work with equivalent expressions they reason abstractly and quantitatively (MP2). They construct viable arguments and critique the reasoning of others when explaining the reasoning used to solve problems (MP3).
Calculate the sums, differences, products, and quotients of both negative and positive numbers.
Use diagrams to expand and factor variable expressions involving negative coefficients.
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
Use the structure of an expression to identify ways to rewrite it. For example, see as , thus recognizing it as a difference of squares that can be factored as .