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2.MD.3Estimate lengths using units of inches, feet, centimeters, and meters. 2.MD.2Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. 2.MD.1Measure the length of software free an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. HSA.CED.2Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
7.G.6Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. 5.G.2Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape. Recognize that equal shares of identical wholes need not have the same shape.
When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. 3.MD.1Tell and write time to the nearest minute and measure time intervals in minutes. 2.MD.7Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. 2.MD.9Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. 2.MD.4Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.
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8.EE.3Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 108 and the population of the world as 7 × 109, and determine that the world population is more than 20 times larger. 8.EE.5Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. HSA.CED.3Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non- viable options in a modeling context.
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Specify a sequence of transformations that will carry a given figure onto another. HSG.CO.4Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. HSG.CO.1Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. HSS.CP.9(+) Use permutations and combinations to compute probabilities of compound events and solve problems. HSS.CP.6Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.
4.MD.3Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. 4.MD.4Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.
HSF.IF.9Compare properties of two functions each represented in a different way . For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. HSS.ID.2Use statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. 8.G.7Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
1.MD.3Tell and write time in hours and half-hours using analog and digital clocks. HSF.IF.5Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
1.G.3Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Understand for these examples that decomposing into more equal shares creates smaller shares. HSG.GMD.3Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. 8.F.2Compare properties of two functions each represented in a different way . For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.