Math: Grade 7

Draft Standards From The State of California Academic Standards Commission

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State of California Academic Standards Commission

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Mathematics is a language we use every day, often without knowing it. It builds and draws on conceptual understanding and skills, and helps us make decisions and solve problems. In this draft document we have tried to connect the notion of problem solving to conceptual understanding and skill development by embedding it within the content strands at every grade. Given here are only some of the ways you will see this exemplified. Students are asked to:

• ask relevant questions about problem situations
  
  
• decide between relevant and extraneous information
  
  
• choose appropriate operations tools and approaches to problem situations
  
  
• decide whether an exact or approximate answer is called for
  
  
• apply specific techniques in new situations
  
  
• explain, check, justify, prove, and judge the reasonableness of results
  
  
• create new approaches and connect knowledge and understanding in new ways
  
  

Number Sense

1. Students apply, explain attributes, and compute with real numbers expressed in a variety of forms.

1.1 read, write, and compute with rational numbers in scientific notation (positive and negative powers of 10), approximate numbers using scientific notation and explain the process

1.2 model and express rational numbers as fractions, terminating or repeating decimals, or percents and describe the equivalence relationship among these representations

1.3 demonstrate understanding of the square root symbol, determine the two integers between which a particular square root lies and explain how you know

1.4 interpret the absolute value of a real number as its distance from zero on a number line and determine the absolute value of real numbers

2. Students use correct order of operations and number properties to add, subtract, multiply, and divide positive and negative rational numbers, extract roots and determine whole number powers of positive rational numbers.

2.1 add, subtract, multiply, and divide rational numbers, integers, fractions, and decimals, and take rational numbers to whole number powers

2.2 explain and use the inverse relationship between exponentiation/root-extraction

2.3 explain and apply properties of real numbers (associative, commutative, distributive, identity, inverse) to simplify numerical expressions

3. Students reason proportionately and use ratios and rates to solve problems.

3.1 use proportions to solve problems involving a change of scale (drawings, models, maps, recipes) or a comparison of two quantities

3.2 identify and interpret situations involving direct variation and represent these situations on a coordinate graph

3.3 solve consumer application problems involving discount, markup, commission, profit and simple compound interest

Task/Assignment

Sqrt75 is between 8 and 9 because 8^2 = 64, 9^2 = 81 and 64 < 75 < 81.

Use a calculator to find an approximation for sqrt75 correct to hundredths.

Put 60 percent, 5/8, and /2 in order from smallest to largest.

Apples are 29¢ per pound means that the cost and apples vary together (c = 29p).

Symbols and Algebra

1. Students express quantitative relationships using algebraic terminology, expressions, equations, and inequalities.

1.1 use variables and appropriate operations to write an expression, equation, inequality, or system of equations or inequalities which represent a verbal description (e.g., three less than a number, half as large as area A)

1.2 apply the order of operations to evaluate algebraic expressions for given replacement values of variables

1.3 define, describe, and use algebraic terminology correctly (equation, inequality, variable, expression, term, constant, coefficient)

1.4 discuss the different uses of variables in expressions (e.g., 2w + 21), equations (e.g., y = x - 4), formulas (e.g., C = 9d), and properties (e.g., a + b = b + a)

2. Students interpret and evaluate expressions involving integer powers and roots of monomials.

2.1 interpret whole number powers as repeated addition, negative integer powers as reciprocals, and evaluate monomials having them

2.2 simplify square roots of perfect square monomials

Measurement and Geometry

1. Students choose appropriate units of measure and use proportional reasoning to convert within and between measurement and monetary systems.

1.1 select, use, and explain a method for comparing weights, capacities, geometric measures, times, and temperatures within and between measurement systems (e.g., miles per hour and feet per second, 4.5 meters is about 1190 inches)

1.2 convert between monetary systems (e.g., US $ and francs)

1.3 use rates (e.g., speed, density) and other derived units to solve problems (e.g., number of calories burned per hour per exercises, person-hours)

1.4 analyze rounding error in calculations

2. Students know and use formulas for perimeter, circumference, area, and volume of common geometric objects and use these to derive methods for finding or approximating measures of less common objects.

2.1 estimate and find the area of polygons by subdividing them into rectangles and triangles

2.2 given the vertices as ordered pairs, plot, connect points, and determine the area and perimeter of a polygon with horizontal and vertical sides

2.3 reason proportionately to find measures and the ratios in situations involving similar figures

3. Students describe and explain relationships among one-, two-, and three-dimensional objects.

3.1 identify and construct line segments, altitudes, medians, angle bisectors, and perpendicular bisectors

3.2 use deductive reasoning and inference to classify quadrilaterals

3.3 use the Pythagorean Theorem to find or approximate the length of the missing side of a right triangle or the diagonal of a square or rectangle

3.4 determine the number of diagonals, and the measures of central, interior, and exterior angles of regular polygons

3.5 identify and sketch central and inscribed angles, arcs, radii, diameters, and chords of circles

3.6 identify, describe, and construct three-dimensional models from nets (e.g., cubes, given the top, side, and/or bottom views)

Functions

1. Students identify, describe, represent, extend, and create linear and non-linear number patterns.

1.1 identify Pythagorean triples and describe patterns found in Pascal's triangle

1.2 identify, represent, extend and create number patterns involving multiples, squares, cubes, and reciprocals

2. Students relate the equation, coordinate graph, and set of ordered pairs of a linear function.

2.1 graph a linear function in two variables on the coordinate plane given a set of ordered pairs

2.2 graph a linear function in two variables on the coordinate plane given its equation, given its slope and y-intercept, or given both its x- and its y-intercepts

Statistics, Data Analysis, and Probability

1. Students display, analyze and interpret data they have generated or taken from resources.

1.1 formulate hypotheses and collect and use data to test those hypotheses

1.2 construct and interpret frequency distributions, line plots, stem­and­leaf plots, box­and­whisker plots and scattergrams

1.3 determine measures and appropriate uses of central tendencies (mean and median), frequency (mode), and distribution (range, inter-quartile range) of a set of data

2. Students use probability to answer questions about the likelihood of an event.

2.1 construct a sample space to determine theoretical probabilities and represent it in the form of a list, chart, picture, or tree diagram

2.2 determine the probability of a given simple event and express that probability as a ratio, decimal, or percent

2.3 identify and describe the number of possible arrangements of several objects, using a tree diagram or the Fundamental Counting Principle

Credits

The Draft Standards were prepared by:

The State of California Academic Standards Commission
The Commission for the Establishment of Academic Content and Performance Standards Comments may be addressed to The Commission