6th Grade Math Learning Targets
Middle School Learning Targets - 6th Grade Mathematics (Math 6)
Communicates clearly and explains my reasoning so others can follow how a problem is solved.
- Use appropriate mathematical language
- Use appropriate forms of mathematical representation to present information correctly
- Move between different forms of mathematical representation
- Communicate through lines of reasoning that are complete and coherent
- Present work that is usually organized using a logical structure.
Reasons mathematically to solve problems in real-life context.
- Identify the relevant elements of the authentic real-life situation
- Select adequate mathematical strategies to model the authentic real-life situation
- Apply the selected mathematical strategies to reach a valid solution to the authentic real-life situation
- Explain the degree of accuracy of the solution
- Explain whether the solution makes sense in the context of the authentic real-life situation.
Recognizes patterns and describes them as relationships or general rules.
- Select and apply mathematical problem-solving techniques to correctly identify the pattern.
- Pattern is described as a relationship or general rule
- Verify the validity of these general rules.
- Conclusions are consistent with the correct findings.
Uses ratio concepts and ratio reasoning to solve problems.
- Understand the concept of a ratio in authentic contexts, and use ratio language to describe a ratio relationship between two quantities.
- Understand the concept of a unit rate in authentic contexts and use rate language in the context of a ratio relationship.
- Use ratio and rate reasoning to solve problems in authentic contexts that use equivalent ratios, unit rates, percents, and/or measurement units.
Computes, applies and extends previous understandings of rational numbers fluently.
- Represent, interpret, and compute quotients of fractions to solve problems in authentic contexts involving division of fractions by fractions.
- Fluently divide multi-digit numbers using accurate, efficient, and flexible strategies and algorithms based on place value and properties of operations.
- Fluently add, subtract, multiply, and divide positive rational numbers using accurate, efficient, and flexible strategies and algorithms.
- Determine greatest common factors and least common multiples using a variety of strategies. Apply the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.
- Understand that positive and negative numbers are used together to describe quantities having opposite directions or values. Use positive and negative numbers to represent quantities in authentic contexts, explaining the meaning of zero in each situation.
- Represent a rational number as a point on the number line. Extend number line diagrams and coordinate axes to represent points on the line and in the coordinate plane with negative number coordinates.
- Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. Write, interpret, and explain statements of order for rational numbers and absolute value in authentic applications.
- Graph points in all four quadrants of the coordinate plane to solve problems in authentic contexts. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
Applies and reasons algebraically using expressions, one-variable equations and inequalities.
- Write and evaluate numerical expressions involving whole-number bases and exponents.
- Write, read, and evaluate expressions in which letters stand for numbers. Apply knowledge of common mathematical terms to move between the verbal and mathematical forms of an expression including expressions that arise from authentic contexts.
- Apply the properties of operations to generate equivalent expressions and to determine when two expressions are equivalent.
- Understand solving an equation or inequality as a process of answering which values from a specified set, if any, make the equation or inequality true. Use substitution to determine which number(s) in a given set make an equation or inequality true.
- Use variables to represent numbers and write expressions when solving problems in authentic contexts.
- Write and solve equations of the form x + p = q and px = q in problems that arise from authentic contexts for cases in which p, q and x are all nonnegative rational numbers.
- Write inequalities of the form x > c and x < c to represent constraints or conditions to solve problems in authentic contexts. Describe and graph on a number line solutions of inequalities of the form x > c and x < c.
- Use variables to represent and analyze two quantities to solve problems in authentic contexts. Including those that change in relationship to one another; write an equation to express one quantity in terms of the other quantity.
Solves mathematical problems involving area, surface area, and volume.
- Find the area of triangles, quadrilaterals, and other polygons by composing into rectangles or decomposing into triangles and other shapes. Apply these techniques to solve problems in authentic contexts.
- Find the volume of a right rectangular prism with fractional edge lengths by filling it with unit cubes of appropriate unit fraction edge lengths. Connect and apply to the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths to solve problems in authentic contexts.
- Draw polygons in the four quadrant coordinate plane given coordinates for the vertices and find the length of a side. Apply these techniques to solve problems in authentic contexts.
- Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures, including those from authentic contexts.
Develops understanding of statistical variability and summarizes and describes distributions.
- Formulate and recognize statistical investigative questions as those that anticipate changes in descriptive data related to the question and account for it in the answers.
- Collect and record data with technology to identify and describe the characteristics of numerical data sets using quantitative measures of center and variability.
- Analyze data representations and describe measures of center and variability of quantitative data using appropriate displays.
- Interpret quantitative measures of center to describe differences between groups from data collected to answer investigative questions.