**California**

**Math Assessments**

**By the end of grade one, students learn to understand and use the concept of ones and tens in the place value number system. Students add andsubtract small numbers with ease. They measure with simple units and locateobjects in space. They describe data and analyze and solve simple problems**

**By the end of grade two, students understand place value and numberrelationships in addition and subtraction and they use simple concepts ofmultiplication. They measure quantities with appropriate units. They classify shapesand see relationships among them by paying attention to theirgeometric attributes.They collect and analyze data and verify the answers**

**By the end of grade three, students deepen their understanding of placevalue and their understanding of and skill with addition, subtraction, multiplication,and division of whole numbers. Students estimate, measure, and describe objectsin space. They use patterns to help solve problems. Theyrepresent numberrelationships and conduct simple probability experiments**

**By the end of grade four, students understand large numbers and addition,subtraction, multiplication, and division of whole numbers. They describe andcompare simple fractions and decimals. They understand the properties of, andthe relationships between, plane geometric figures. They collect, represent, and**

**analyze data to answer questions**

**By the end of grade five, students increase their facility with the fourbasic arithmetic operations applied to fractions, decimals, and positive and**

**negative numbers. They know and use common measuring units to determinelength and area and know and use formulas to determine the volume of simplegeometric figures. Students know the concept of angle measurement and use aprotractor and compass to solve problems. They use grids, tables, graphs, and**

**charts to record and analyze data**

**By the end of grade six, students have mastered the four arithmeticoperations with whole numbers, positive fractions, positive decimals, and positive**

**and negative integers; they accurately compute and solve problems. They applytheir knowledge to statistics and probability. Students understand the concepts**

**of mean, median, and mode of data sets and how to calculate the range. Theyanalyze data and sampling processes for possible bias and misleading conclusions**

**they use addition and multiplication of fractions routinely to calculate theprobabilities for compound events. Students conceptually understand and work**

**with ratios and proportions; they compute percentages (e.g., tax, tips, andinterest). Students know about p and the formulas for the circumference and**

**area of a circle. They use letters for numbers in formulas involving geometricshapes and in ratios to represent an unknown part of an expression. They solve**

**one-step linear equations**

**By the end of grade seven, students are adept at manipulating numbers andequations and understand the general principles at work. Students understand and**

**use factoring of numerators and denominators and properties of exponents. Theyknow the Pythagorean theorem and solve problems in which they compute the**

**length of an unknown side. Students know how to compute the surface area andvolume of basic three-dimensional objects and understand how area and volumechange with a change in scale. Students make conversions between different units**

**of measurement. They know and use different representations of fractional-numbers (fractions, decimals, and percents) and are proficient at changing from**

**one to another. They increase their facility with ratio and proportion, compute percents of increase and decrease, and compute simple and compound interest.**

**They graph linear functions and understand the idea of slope and its relation tor ratio.**