2012-2013 instructional guide map math cahsee prep · 2012-07-31 · 7mg 2.2 estimate and compute...

• Note: Instructional Guide Maps are an overview of the Alliance Instructional Guides. They assist teachers with planning instructional units and effective

strategies to teach California high priority standards throughout the year. Every standard will be assessed with 2 questions on the benchmark.

* Only Quarters 1-3 have associated benchmark exams. Instruction continues with addressed standards until the end of the year. 7/2012

2012-2013 Instructional Guide Map Math CAHSEE Prep

i

Quarter 1

Instructional Days August 6 – September 28 Benchmark Assessments October 1-5

Pupil Free / Teacher PD October 8 Re-teach Targeted Standards October 9-12

Standards Assessed on

Benchmark

7MG 1.1 Compare weights, capacities, geometric measures, times, and temperatures within and between measurement systems (e.g., miles per hour and feet per second, cubic inches to cubic centimeters). 7MG 1.2 Construct and read drawings and models made to scale. 7MG 1.3 Use measures expressed as rates (e.g., speed, density) and measures expressed as products (e.g., person-days) to solve problems; check the units of the solutions; and use dimensional analysis to check the reasonableness of the answer. 7MG 2.1 Compare weights, capacities, geometric measures, times, and temperatures within and between measurement systems (e.g., miles per hour and feet per second, cubic inches to cubic centimeters). 7MG 2.2 Estimate and compute the area of more complex or irregular two- and three- dimensional figures by breaking the figures down into more basic geometric objects. 7MG 2.3 Compute the length of the perimeter, the surface area of the faces, and the volume of a three-dimensional object built from rectangular solids. Understand that when the lengths of all dimensions are multiplied by a scale factor, the surface area is multiplied by the square of the scale factor and the volume is multiplied by the cube of the scale factor. 7MG 2.4 Relate the changes in measurement with a change of scale to the units used (e.g., square inches, cubic feet) and to conversions between units (1 square foot = 144 square inches or [1 ft2] = [144 in2], 1 cubic inch is approximately 16.38 cubic centimeters or [1 in3] = [16.38 cm3], 7MG 3.2 Understand and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine their image under translations and reflections. 7MG 3.3 Know and understand the Pythagorean theorem and its converse and use it to find the length of the missing side of a right triangle and the lengths of other line segments and, in some situations, empirically verify the Pythagorean theorem by direct measurement. 7MG 3.4 Demonstrate an understanding of conditions that indicate two geometrical figures are congruent and what congruence means about the relationships between the sides and angles of the two figures. 7MR 1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns. 7MR 1.2 Formulate and justify mathematical conjectures based on a general description of the mathematical question or problem posed. 7MR 2.1 Use estimation to verify the reasonableness of calculated results. 7MR 2.3 Estimate unknown quantities graphically and solve for them by using logical reasoning and arithmetic and algebraic techniques 7MR 2.4 Make and test conjectures by using both inductive and deductive reasoning. 7MR 3.3 Develop generalizations of the results obtained and the strategies used and apply them to new problem situations.





ii

Quarter 2

Instructional Days October 15 – December 7 Benchmark Assessments December 10-14

Pupil Free / Teacher PD January 7 Re-teach Targeted Standards January 8-11


Benchmark

6PS 2.5 Identify claims based on statistical data and, in simple cases, evaluate the validity of the claims. 6PS 3.1 Represent all possible outcomes for compound events in an organized way (e.g., tables, grids, tree diagrams) and express the theoretical probability of each outcome. 6PS 3.2 Use data to estimate the probability of future events (e.g., batting averages or number of accidents per mile driven). 6PS 3.3 Represent probabilities as ratios, proportions, decimals between 0 and 1, and percentages between 0 and 100 and verify that the probabilities computer are reasonable; know that if P is the probability of an event, 1 – P is the probability of an event not occurring. 6PS 3.5 Understand the difference between independent and dependent events 7NS 1.1 Read, write, and compare rational numbers in a scientific notation (positive and negative powers of 10) with approximate numbers using scientific notation. 7NS 1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers. 7NS 1.3 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications. 7NS 1.6 Calculate the percentage of increases and decreases of a quantity. 7NS 1.7 Solve problems that involve discounts, markups, commissions, and profit and compute simple and compound interest. 7NS 2.1 Understand negative whole-number exponents. Multiply and divide expressions involving exponents with a common base. 7NS 2.2 Add and subtract fractions by using factoring to find common denominators. 7NS 2.4 Use the inverse relationship between raising to a power and extracting the root of a perfect square integer; for an integer that is not square, determine without a calculator the two integers between which its square root lies and explain why. 7NS 2.5 Understand the meaning of absolute value of a number; interpret the absolute value as the distance of the number from zero on a number line; and determine the absolute value of real numbers. 7PS 1.1 Compute the range, mean, median, and mode of data sets. 7PS 1.2 Understand how additional data added to data sets may affect these computations of measures of central tendency.





iii

Quarter Quarter 3

Instructional Days January 14 - March 15 Benchmark Assessments March 18 – 22

Pupil Free / Teacher PD April 1 Re-teach Targeted Standards April 2 - 5


Benchmark

7AF 1.1 Use variables and appropriate operations to write an expression, an equation, an inequality, or a system of equations or inequalities that represents a verbal description (e.g., three less than a number, half as large as area A). 7AF 1.2 Use the correct order of operations to evaluate algebraic expressions such as 3(2x + 5)2. 7AF 1.5 Represent quantitative relationships graphically and interpret the meaning of a specific part of a graph in the situation represented by the graph. 7AF 2.1 Interpret positive whole-number powers as repeated multiplication and negative whole-number powers as repeated division or multiplication by the multiplicative inverse. Simplify and evaluate expressions that include exponents. 7AF 2.2 Multiply and divide monomials; extend the process of taking powers and extracting roots to monomials when the latter results in a monomial with an integer exponent. 7AF 3.1 Graph the functions of the form y = nx2 and y = nx3 and use in solving problems. 7AF 3.4 Plot the values of quantities whose ratios are always the same (e.g. cost to the number of an item, feet to inches, circumference to diameter of a circle). Fit a line to the plot and understand that the slope of the line equals the quantities. 7AF 3.3 Graph linear functions, noting that the vertical change (change in y-value) per unit of horizontal change (change in x-value) is always the same and know that the ratio (“rise over run”) is called the slope of a graph. 7AF 4.1 Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results. 7AF 4.2 Solve multistep problems involving rate, average speed, distance, and time or a direct variation. Algebra1- 2.0: Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root and raising to a fractional power. They understand and use the rules of exponents Algebra1- 3.0: Students solve equations and inequalities involving absolute values Algebra1- 4.0: Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x-5) + 4(x-2) = 12 Algebra1- 5.0: Students solve multi-step problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step. Algebra1- 6.0: Students graph a linear equation and compute the x- and y- intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4). Algebra1- 7.0: Students verify that a point lies on a line, given an equation on the line. Students are able to derive linear equations by using the point-slope formula. Algebra1- 8.0: Students understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point. Algebra1- 9.0: Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets. Algebra1- 10.0: Students add, subtract, multiply, and divide monomials and polynomials. Students solve multi-step problems, including word problems, by using these techniques. Algebra1- 15.0: Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems **Geometry Review Based on Geometry Course Quarter 2 Benchmark Results.





iv

Quarter Quarter 4*

Instructional Days April 6 – June 7 Benchmark Assessments CST Testing Window:

April 22 – May 20

Pupil Free / Teacher PD Re-teach Targeted Standards


Benchmark

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2012-2013 instructional guide map math cahsee prep · 2012-07-31 · 7mg 2.2 estimate and compute...

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