Linear Functions

By (date), (name) will construct a function when given a data set for two linearly related quantities, table... of values, or a graph representing the linear function for (4 out of 5) problems on a teacher-created worksheet.
  • By (date), given a glossary of formulas for finding slope and a linear relationship (e.g. slope is m= (y2-y1)/(x2-x1), and the equation of line is y = mx + b with b being the initial value, a.k.a. the y-intercept), (name) will be able to accurately construct a function when given a data set for two linearly related quantities, table of values, or a graph representing the linear function for (4 out of 5) problems on a teacher-created worksheet.
  • By (date), given a graphing calculator to interpret the data and a step-by-step tutorial (e.g. Writing Equation of Line) on how to use the graphing calculator, (name) will construct a function when given a data set for two linearly-related quantities, table of values, or a graph representing the linear function for (4 out of 5) problems on a teacher-created worksheet.
  • By (date), when given a table of values for two linearly related quantities, using online graphing software (i.e. Geogebra - Introduction to linear equations, (name) will construct a linear function correctly for (4 out of 5) problems.

UDL Strategies About UDL

  • Foster collaboration and communication
    Instead of having students work independently on the task, teachers could allow the students to work in groups (e.g. jigsaw method where students are assigned roles and then teach each other the work from their role) so that students can learn from their peers and work together to find a solution. The group work activity teaches students to have ownership over their work and to be accountable for providing their group with the correct solution and problem solving steps.
  • UDL II 5.2 Use multiple tools for construction and composition
    Instead of expecting students to complete all the calculations in their mind, students who might not be comfortable with calculation skills but can conceptually understand linear functions, should be given a graphing calculator as a tool to help them create functions from a table values, coordinate points, or a graph. Students are to interpret how to create functions, and they might need a calculator with graphing components to facilitate that understanding.
  • UDL I 3.1 Activate or supply background knowledge
    Instead of students spending time agonizing over the exact formulas for the task, teachers can provide students with a formula chart to activate their knowledge. Providing a formula chart (i.e. a list of the formulas need for the task such as formula of a line y = mx + b in which m = slope and b = y-intercept) will still allow the student to construct the function and represent their understanding of linear functions on a coordinate plane. The use of formula charts is also beneficial because it teaches students to be resourceful, and that they can still complete a task even if they have difficulty memorizing all of the related formulas.

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Common Core Standards

8.F.4 Use functions to model relationships between quantities
8.F.4 Use functions to model relationships between quantities
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Standard Staircase

Recognize a Fraction

By (date), when given (2) of the same shape partitioned into different equal parts with (1) or more parts shaded, (name) will match a corresponding numeric fraction to each partitioned shape, for (3 out of 3) geometry exercises.

Recognize Equivalent Equations

By (date), after a review of the associative and commutative addition rules, when given an illustrated addition equation with (2) or more single-digit addends (e.g. 5 + 2 + 3 = 10), (name) will choose the equivalent illustrated equation from a bank of (3) options, for (3 out of 3) addition equations.

Differentiate Between Parts and Whole

By (date), given two versions of the same item, one whole and one separated into parts, and asked to identify either the whole item or the parts of the whole, (name) will select the answer, in (4 out of 5) item recognition activities.

Use Proportional Relationships to Solve Rate & Percent Problems

By (date), given proportional relationship scenarios, (name) will solve multi-step ratio and percent problems by cross multiplying the terms to find the correct value of the unknown term for (4 out of 5) problems.

Graphing Proportional Relationships

By (date), when given real-world scenarios with a table of (3 or more) ordered pairs, (name) will determine if the table represents a proportional relationship by graphing the coordinates and checking whether the points lie on a straight line through the origin for (4 out of 5) proportional identification activities.

Apply Operations to Equivalent Expressions

By (date), when given (5) problems involving writing or comparing equivalent linear expressions with rational coefficients, (name) will apply algebraic operations (e.g. collecting like terms, distributive property) to the linear expression to answer (4 out of 5) problems.

Unit Rates with Fractions

By (date), (name) will use ratios to correctly calculate unit rates, including ratios of fractions with quantities measured in like or different units for (4 out of 5) problems.

Recognize a Fraction

By (date), when given (2) of the same shape partitioned into different equal parts with (1) or more parts shaded, (name) will match a corresponding numeric fraction to each partitioned shape, for (3 out of 3) geometry exercises.

Recognize Equivalent Equations

By (date), after a review of the associative and commutative addition rules, when given an illustrated addition equation with (2) or more single-digit addends (e.g. 5 + 2 + 3 = 10), (name) will choose the equivalent illustrated equation from a bank of (3) options, for (3 out of 3) addition equations.

Differentiate Between Parts and Whole

By (date), given two versions of the same item, one whole and one separated into parts, and asked to identify either the whole item or the parts of the whole, (name) will select the answer, in (4 out of 5) item recognition activities.

Linear Functions Current Goal

By (date), (name) will construct a function when given a data set for two linearly related quantities, table of values, or a graph representing the linear function for (4 out of 5) problems on a teacher-created worksheet.

Recognize a Fraction

By (date), when given (2) of the same shape partitioned into different equal parts with (1) or more parts shaded, (name) will match a corresponding numeric fraction to each partitioned shape, for (3 out of 3) geometry exercises.

Recognize Equivalent Equations

By (date), after a review of the associative and commutative addition rules, when given an illustrated addition equation with (2) or more single-digit addends (e.g. 5 + 2 + 3 = 10), (name) will choose the equivalent illustrated equation from a bank of (3) options, for (3 out of 3) addition equations.

Differentiate Between Parts and Whole

By (date), given two versions of the same item, one whole and one separated into parts, and asked to identify either the whole item or the parts of the whole, (name) will select the answer, in (4 out of 5) item recognition activities.

Referenced Strategies

  • Math Dictionary

    A math dictionary is a type of dictionary that contains mathematical terms, definitions and visual representations. The math dictionary may ...

  • Reference Materials

    Reference materials are resources that a student can use when completing academic or social and emotional learning tasks. These materials pr...

  • Calculator

    A calculator is a mathematical tool that can perform basic to complex mathematical operations. A simple calculator usually has functions for...