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The Number System 6.NS: Compute fluently with multi-digit numbers and find common factors and multiples. - Fluently divide multi-digit numbers using the standard algorithm.
- I can fluently multiply multi-digit whole numbers (not to exceed a three-digit factor by a two-digit factor). (5.NBT.5)
- I can fluently divide multi-digit whole numbers.
Place Value - Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
- I can read and write decimals to the thousandths using base-ten numerals and number names. (5.NBT.3)
- I can use place value understanding to round decimals to any place. (5.NTB.4)
Apply and extend previous understanding of numbers to the system of rational numbers. - 1. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
- I can understand that positive and negative numbers are used to describe amounts having opposite values.
- I can use positive and negative numbers to show amounts in real-world situations and explain what the number 0 means in those situations.
- 2. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
- A. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line, recognize that the opposite of the opposite of a number is the number itself (e.g., -(-3) = 3), and that 0 is its own opposite.
- B. Find and position integers and other rational numbers on a horizontal or vertical line diagram; find and position pairs of integers and other rational numbers on a coordinate plane
- I can understand that a rational number is a point on a number line.
- I can extend number line diagrams to show positive and negative numbers on the line and in the plane.
- I can recognize opposite signs of numbers as indicating places on opposite sides of 0 on the number line.
- I can place integers and other numbers on a number line diagram.
- 3. Understand ordering and absolute value of rational numbers.
- A. Interpret statements of inequality as statements about the relative positions of two numbers on a number line diagram.
- B. Write, interpret, and explain statements of order for rational numbers in real-world contexts.
- C. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.
- D. Distinguish comparisons of absolute value from statements about order.
- I can order positive and negative numbers.
- I can understand absolute value of rational numbers.
- I can write, understand, and explain what rational numbers mean in real-world situations.
- I can understand the absolute value as the number’s distance from 0 on the number line.
- I can understand absolute values as they apply to real-world situations.
- I can tell the difference between comparing absolute values and ordering positive and negative numbers.
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- 4. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as multiple of a sum of two whole numbers with no common factor.
- I can find the greatest common factor of two whole numbers less than or equal to 100.
- I can find the least common multiple of two whole numbers less than or equal to 12.
- I can use the distributive property to show the sum of two whole numbers 1-100 in different ways.
- Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
- I can add, subtract, multiply, and divide multi-digit numbers involving decimals.
Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
- 1. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions (e.g., by using visual fraction models and equations to represent the problem).
- I can multiply a fraction or a whole number by a fraction using visual fraction models and create a story context (5.NF.4).
- I can reduce and convert mixed numbers and improper fractions.
- I can divide two fractions.
- I can solve word problems involving the division of fractions by fractions.
- I can add, subtract, multiply, and divide multi-digit numbers involving decimals.
Expressions and Equations 6.EE:
Apply and extend previous understandings of arithmetic to algebraic expressions.
- 1. Write and evaluate numerical expressions involving whole-number exponents.
- I can evaluate exponents.
- I can solve expressions using Order of Operations.
- I can write and understand numerical expressions involving whole-number exponents.
- 2. Write, read, and evaluate expressions in which letters stand for numbers.
- A. Write expressions that record operations with numbers and with letters standing for numbers.
- B. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity.
- C. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).
- I can write, read, and evaluate expressions in which letters stand for numbers.
- I can write expressions using numbers and variables (with the variables standing for numbers).
- I can identify the parts of an expression using mathematical words (sum, term, product, factor, quotient, and coefficient).
- I can determine the answer to expressions when given the specific value of a variable.
- I can use my knowledge of the order of operations to evaluate expressions.
- 3. Apply the properties of operations to generate equivalent expressions.
- I can identify the different properties of multiplication and addition (commutative, associative, distributive, identity).
- I can apply the properties of operations to generate equivalent expressions. EX (a+a+a=3a), 3(a+2)=3a+6
- 4. Identify when two expressions are equivalent (i.e. when two expressions name the same number regardless of which value is substituted into them).
- I can identify when two expressions are equivalent.
Reason about and solve one-variable equations and inequalities.
- 5. Understand solving an equation or inequality as a process of answering a question: Which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
- I can understand that solving an equation or inequality is like answering a question.
- 6. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
- I can use variables to represent numbers and write expressions when solving real-world problems.
- 7. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q, and x are all nonnegative rational numbers.
- I can solve real-world and mathematical problems by writing and solving equations.
- 8. Write an inequality of the form x>c or x<c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x>c of x<c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
- I can write an inequality which has many solutions and represent these solutions on a number line (where x>c or x<c).
Represent and analyze quantitative relationships between dependent and independent variables.
- 9. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.
- I can use variables to represent two quantities in a real-world problem and write an equation to express the quantities.
- I can use graphs and tables to show the relationship between dependent and independent variables.
- 10. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
- I can place ordered pairs on a coordinate plane.
- I can understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane.
- 11. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points and with the same first coordinate or the same second coordinate.
- I can graph in all four quadrants of the coordinate plane to help me solve real-world and mathematical problems.
- I can determine the distance between points with the same first coordinate or the same second coordinate.
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