6th grade Mathematics worksheets

Grade 6

• 6.1The student uses mathematical processes to acquire and demonstrate mathematical understanding
• 6.1.Aapply mathematics to problems arising in everyday life, society, and the workplace
• 6.1.Buse a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution
• 6.1.Cselect tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems
• 6.1.Dcommunicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate
• 6.1.Ecreate and use representations to organize, record, and communicate mathematical ideas
• 6.1.Fanalyze mathematical relationships to connect and communicate mathematical ideas
• 6.1.Gdisplay, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication
• 6.2The student applies mathematical process standards to represent and use rational numbers in a variety of forms
• 6.2.Aclassify whole numbers, integers, and rational numbers using a visual representation such as a Venn diagram to describe relationships between sets of numbers
• 6.2.Bidentify a number, its opposite, and its absolute value
• 6.2.Clocate, compare, and order integers and rational numbers using a number line
• 6.2.Dorder a set of rational numbers arising from mathematical and real-world contexts
• 6.2.Eextend representations for division to include fraction notation such as a/b represents the same number as a ÷ b where b ≠ 0
• 6.3The student applies mathematical process standards to represent addition, subtraction, multiplication, and division while solving problems and justifying solutions
• 6.3.Arecognize that dividing by a rational number and multiplying by its reciprocal result in equivalent values
• 6.3.Bdetermine, with and without computation, whether a quantity is increased or decreased when multiplied by a fraction, including values greater than or less than one
• 6.3.Crepresent integer operations with concrete models and connect the actions with the models to standardized algorithms
• 6.3.Dadd, subtract, multiply, and divide integers fluently
• 6.3.Emultiply and divide positive rational numbers fluently
• 6.4The student applies mathematical process standards to develop an understanding of proportional relationships in problem situations
• 6.4.Acompare two rules verbally, numerically, graphically, and symbolically in the form of y = ax or y = x + a in order to differentiate between additive and multiplicative relationships
• 6.4.Bapply qualitative and quantitative reasoning to solve prediction and comparison of real-world problems involving ratios and rates
• 6.4.Cgive examples of ratios as multiplicative comparisons of two quantities describing the same attribute
• 6.4.Dgive examples of rates as the comparison by division of two quantities having different attributes, including rates as quotients
• 6.4.Erepresent ratios and percents with concrete models, fractions, and decimals
• 6.4.Frepresent benchmark fractions and percents such as 1%, 10%, 25%, 33 1/3%, and multiples of these values using 10 by 10 grids, strip diagrams, number lines, and numbers
• 6.4.Ggenerate equivalent forms of fractions, decimals, and percents using real-world problems, including problems that involve money
• 6.4.Hconvert units within a measurement system, including the use of proportions and unit rates
• 6.5The student applies mathematical process standards to solve problems involving proportional relationships
• 6.5.Arepresent mathematical and real-world problems involving ratios and rates using scale factors, tables, graphs, and proportions
• 6.5.Bsolve real-world problems to find the whole given a part and the percent, to find the part given the whole and the percent, and to find the percent given the part and the whole, including the use of concrete and pictorial models
• 6.5.Cuse equivalent fractions, decimals, and percents to show equal parts of the same whole
• 6.6The student applies mathematical process standards to use multiple representations to describe algebraic relationships
• 6.6.Aidentify independent and dependent quantities from tables and graphs
• 6.6.Bwrite an equation that represents the relationship between independent and dependent quantities from a table
• 6.6.Crepresent a given situation using verbal descriptions, tables, graphs, and equations in the form y = kx or y = x + b
• 6.7The student applies mathematical process standards to develop concepts of expressions and equations
• 6.7.Agenerate equivalent numerical expressions using order of operations, including whole number exponents and prime factorization
• 6.7.Bdistinguish between expressions and equations verbally, numerically, and algebraically