Arithmetic to Algebra

Students will generate and interpret equivalent numeric and algebraic expressions.

Apply properties of operations emphasizing when the commutative property applies(MGSE7.EE.1)

Use area models to represent the distributive property and develop understandings of addition and multiplication (all positive rational numbers should be included in the models)(MGSE3.MD.7)

Model numerical expressions (arrays) leading to the modeling of algebraic expressions(MGSE7.EE.1,2; MGSE9-12.A.SSE.1,3)

Add, subtract, and multiply algebraic expressions(MGSE6.EE.3, MGSE6.EE.4, MC7.EE.1, MGSE9-12.A.SSE.3)

Generate equivalent expressions using properties of operations and understand various representations within context. For example, distinguish multiplicative comparison from additive comparison. Students should be able to explain the difference between 3 more and 3 times(MGSE4.0A.2; MGSE6.EE.3, MGSE7.EE.1,2;MGSE9-12.A.SSE.3)

Evaluate formulas at specific values for variables. For example, use formulas such as A = l x w and find the area given the values for the length and width(MGSE6.EE.2)

Students will interpret and use the properties of exponents.

Substitute numeric values into formulas containing exponents, interpreting units consistently(MGSE6.EE.2, MGSE9-12.N.Q.1, MGSE9-12.A.SSE.1, MGSE9-12.N.RN.2)

Use properties of integer exponents to find equivalent numerical expressions. For example, 32 x 3 -5 = 3 -3 = 1 33 = 1 27(MGSE8.EE.1)

Evaluate square roots of perfect squares and cube roots of perfect cubes (MGSE8.EE.2)

Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x 3 = p, where p is a positive rational number(MGSE8.EE.2)

Use the Pythagorean Theorem to solve triangles based on real world contexts (Limit to finding the hypotenuse given two legs)(MGSE8.G.7)