7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. 7.EE.4.a Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? 7.EE.4.b Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. Number Common Core Standard for Introduction 8.EE.7 Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Unit Essential Questions: What is a mathematical expression and how is it useful? What do you know about the solution to an equation? An inequality? Unit Enduring Understandings Students will understand that… Write algebraic expressions and equations given real-world situations. Use inverse operations to solve multi-step equations. Unit Objectives Students will know… How to write and solve inequalities from real- world contexts. How to translate word phrases into algebraic expressions and equations. Expressions are simplified by various means. Equations can be solved using the properties of equality and inverse operations. Unit Objectives Students will be able to… Evaluate expressions using the order of operations. Evaluate simple algebraic expressions. Describe the relationships and extend terms in arithmetic and geometric sequences. Find squares of numbers and square roots of perfect squares. Estimate square roots. Solve one, two, and multi-step equations with rational coefficients. Solve one, two, and multi-step inequalities.
composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Number Common Core Standard for Introduction 8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. Unit Essential Questions How is geometry used in the How is finding the volume of a composite figure different than finding the surface area of a composite figure? How is it similar? How are scales used to reproduce scale drawings? Unit Enduring Understandings Students will understand that… Solve real-life and mathematical problems involving angle measure, area, perimeter, surface area, and volume. Realize that scale drawings have corresponding quantities that vary proportionally. Unit Objectives Students will know… The formulas used to find area, surface area, and volume of figures and circumference of circles. How to find unknown measures and the sum of angles in polygons. Fundamental angle relationships. Changes in dimensions affect area and volume. Proportional relationships by using scale drawings. Unit Objectives Students will be able to… Find the volume of rectangular and triangular prisms. Find the volume of cylinders, cones, and pyramids. Find the surface area of prisms, cylinders, and pyramids. Find the volume and surface area of composite figures. Classify and identify angles and find missing measures. Classify and identify triangles and find missing measures. Classify quadrilaterals and find missing angle measures. Solve problems involving scale drawings of geometric figures.