Math: Grade 6

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 read, write, compute with, and understand the meaning of whole numbers, fractions, decimals, and percents.

1.1 read, write, and compute with whole numbers in scientific notation (i.e. 325,600 = 3.256 x 10^5)

1.2 write fractions as equivalent terminating or repeating decimals and explain the process used

1.3 interpret and model percent in terms of parts of 100, determine the percent which is equivalent to decimals (expressed as tenths or hundredths) and simple fractions (e.g., 1/2 is 50%, 3/5 is 60%, 1/20 = 5%)

1.4 interpret and perform division of fractions (e.g., 5/8 ÷15/16 = 5/8 x 16/15 or 2/3)

1.5 describe and compare two quantities using ratios, use appropriate notations (a/b, a to b, a:b), and give ratios in lowest terms

1.6 model and solve proportions for a missing value (e.g., determine the value of N if 4/7 = N/21.)

2. Students identify, represent, add, subtract, multiply, and divide positive and negative rational numbers.

2.1 identify, compare, and order rational numbers and represent them on a number line

2.2 model multiplication and division with negative numbers and with a negative and a positive number and perform such computations with accuracy

Task/Assignment

Demonstrate understanding that multiplying by a power of ten is a matter of moving the decimal point (e.g., 1,268.5 x 1000 = 1,268,500 and 1,268.5 x 1/100 = 12.685).

Explain why two numbers written in scientific notation may not be added or subtracted in that form if they have different orders of magnitude.

Explain why 3.4 x 10^5 + 1.2 x 10^2 [does not equal]4.6 x 10^7.

-2 x 4 = -8 makes sense since it fits a pattern,;

similarly -2 x -4 = 8 makes sense because it also fits a pattern .

Symbols and Algebra

1. Students write verbal expressions/sentences as algebraic expressions/equations, graph them and interpret the results in all three representations.

1.1 write and solve two-step linear equations and inequalities in one variable using strategies involving inverse operations, integers, fractions, and decimals

1.2 identify and graph ordered pairs in the four quadrants of the coordinate plane

2. Students calculate, interpret, and solve problems involving rates.

2.1 demonstrate understanding that rate is a measure of one quantity per unit value of another quantity

2.2 solve simple problems involving rate of speed, unit cost, or unit weight

Tasks/Assignments

If May reads 600 words in 8 minutes, how many words per minute does she read?

If a family takes 4 hours to drive 200 miles on vacation, stops for a 1 hour lunch then drives 160 miles more in 3 hours, what is their average rate of speed for the entire day?

If first class postage charges are 32¢ for the first ounce or less and 23¢ for each additional ounce or less, what postage will be needed to mail a letter weighing 1.7 ounces?

Measurement and Geometry

1. Students use ratios and proportional reasoning to convert within measurement systems.

1.1 convert between units of length in metric and customary systems (e.g., 3 m = 300 cm, 97 in = _?_ ft _?_ in)

1.2 create and solve proportions to convert between units of time (e.g., 60min/1hr = 700min/xhrs)

1.3 select and model a volume of approximately unit 1 cc/cm^3, 1 in^3, 1 ft^3, 1 m^3, 1 yd^3, and select an appropriate unit with which to measure a given volume

2. Students identify and describe the properties of, and relationships among two- and three-dimensional figures.

2.1 identify, describe, and classify angles as vertical, adjacent, complementary, and/or supplementary

2.2 define, describe, and draw quadrilaterals and triangles given information about them (e.g., a quadrilateral having equal sides but no right angles, a right isosceles triangle)

2.3 present informal logical arguments about the properties of simple geometric figures

Task/Assignment

Explain why the area of a right triangle with legs of 3" and 4" has an area of 6 sq in by relating it to the rectangle with sides of 3" and 4".

Functions

1. Students analyze tables, graphs, and rules to determine functional relationships.

1.1 use information taken from a graph to answer questions about a problem situation or to create a "story"

1.2 translate between verbal, numeric, graphical, and symbolic representations of relationships

2. Students investigate and describe geometric and exponential patterns.

2.1 identify, and describe patterns involving geometric growth, square roots, or exponents (which lead to the idea of scientific notation)

2.2 consider geometric questions from a function perspective (e.g., the number of sides of a regular polygon and the sum of the measures of its interior angles)

Statistics, Data Analysis, and Probability

1. Students read and analyze data taken from tables or graphs and use the concept of average to answer relevant questions.

1.1 identify ordered pairs of data from a graph (bar, circle, line, or broken-line) and interpret the meaning of the data in terms of the situation depicted by the graph

1.2 describe the possible effects of missing or incorrect information

1.3 find and model the mean and the median of up to five quantities where the solution is a whole number

1.4 determine a missing quantity if the mean of a set of quantities is known

2. Students use samples and simulations to predict results involving chance and compare those with the theoretical probability of those events occurring.

2.1 carry out and interpret a simulation (by hand or using computer software) to predict the likelihood of an event

2.2 compute the probability of an event using counting principles, sample spaces, and geometric arguments and compare it with results from a simulation

Tasks/Assignments

The average height of four towers of blocks can be found by taking blocks off the highest tower and adding them to shorter towers until all are even in height.

The average height of three girls is 49", if two of the girls are 52" and 47", find the height of the third girl.

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