|7th/8th Grade Math Compression Curriculum Map (Quarter 1)|
|Time Frame||Utah State Core Standard||Expected Student Outcome (Objective)||Essential Academic Vocabulary||Assessments (Formative & Summative)||Instructional Learning Activities|
|12 to 15 days||8.EE.2||I can represent solutions to equations of the form x^2 = p and x^3 = p using square and cube roots.||square, square root, cube, cube root, radical||Pre-test: #22|
ACT: Pre-Algebra;square roots and approximations
|Use the geometric representations of square area and cube volumes and their relation to the side length.|
Use the idea of inverse operations to introduce the concept of roots.
|8.NS.1||I can differentiate between rational and irrational numbers.|
I can convert a decimal expansion into a rational number.
|decimal expansion, repeating decimal, terminating decimal, rational, irrational, square root||Pre-test: #19|
|Use the Pythagorean Theorem with non-perfect squares to introduce irrational numbers.|
Use the powers of ten technique:
|8.NS.2||I can appoximate, locate on a number line, and compare size of irrational numbers.|
I can estimate expressions involving irrational numbers.
|rational, irrational, decimal expansion, square root, truncating, rounding||Pre-test: #20, 21|
Interim: #20, 21
ACT: Pre-Algebra; ordering numbers by value
|Construct the Wheel of Theodorus to create physical lengths of the square roots of the counting numbers. Transfer those lengths onto a number line.|
Find increasingly accurate estimations for square roots of numbers by guess-and-check with a calculator.
|5 days||8.NS.3||(It was proposed that this standard be added)|
I can perform operations with radicals (square roots).
I can simplify radicals (square roots).
|20 to 25 days||8.EE.7||I can solve linear equations in one variable.|
I can solve linear inequalities in one variable (new to the core).
|solve, variable, order of operations, solution, like terms, distributive property||Pre-test: 1, 2, 3|
Interim: 1, 2, 3
ACT: Pre-Algebra; linear equation in one variable.
|Build on the equations solved in seventh grade and move toward increased fluency and procedural skill in solving more complex linear equations.|
Examine solutions in the context of the original equation.
Consider teaching unique solutions, no solutions, and infinitly many solutions.
|5 to 10 days||8.EE.7c||(It was proposed that this standard be added)|
I can solve one-variable absolute value equations.
|7.EE.1||I can write equaivalent expressions by adding like terms.|
I can write equivalent expressions by using the distributive property.
|terms, coeffiecient, like-terms, distribute, expression, rational linear, expand, factor, equivalent, simplify||Model equaivalent expressions such as |
4x + 14 = 2(2x) + 2(7) + 2(2x + 7) and have students explain why all three are equivalent.
Use manipultives such as algebra Tiles or candy to model equivalent expressions.
|7.EE.2||I can write and solve equations for multi-step real-life prolems.||terms, coefficients, like-terms, distribute, expression, rational, linear, expand, factor, equivalent, simplify||Use multiple studetn-generated equivalent representation of the same problem to explore how the structure of an expression reveals different attributes of the context.|
|7.EE.3||I can solve one-step and two-step equations.|
I can solve one-step and two-step inequalities.
I can solve inequalities when adding like-terms and using the distributive property are necessary.
I can write and solve inequalities for nulti-step real-life problems.
|estimate, rational number, reasonableness, solution||Chose real-life problems to highlight the advantages of using different numerical representations (fractions, decimals, percent) or models (bar, equation, drawing).|
Assign student partneers to solve problems, present solutions, and compare solution strategies.
|7.EE.4||I can solve equations when I have to add like terms.|
I can solve equations when I have to use the distributive property.
|algebraic, inequality, equation, inverse operations, solution set, at most, at least, less than, greater than, <, >||Solve simple problems arithmetically and compare the process to that of finding solutions algebraicaly.|
Partner problems: One student solves, the other writes reasons why steps work.
Find and analyze mistakes in student work samples.
Have students solve problems based on a verbal or written description.
Use arithmetic and algebraic approaches to problems to examine the structure of the mathematics.