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Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.

Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

Give informal arguments for the formula of the volume of a cylinder, pyramid, and cone using Cavalieri’s principle.

Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.

Apply the formulas for the volume of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

Derive the formula A = ½ ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

Explain equivalence of fractions through reasoning with visual fraction models. Compare fractions by reasoning about their size.

Recognize and generate simple equivalent fractions with denominators of 2, 3, 4, 6, and 8, Explain why the fractions are equivalent, e.g., by using a visual fraction model.

Explain why two or more fractions are equivalent by using visual fraction models. Focus attention on how the number and size of the parts differ even though the fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Solve quadratic equations in one variable.

Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from this form.

Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

Solve quadratic equations in one variable.

Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.