11 Components
Big Ideas
Formative Assessment Lesson
End of Unit Assessments
Browse Components
Big Ideas
Formative Assessment Lesson
End of Unit Assessments
Big Idea:

### The relationship between the variables of a function can be represented visually by a graph.

1 week

Evidence of Understanding

• define variables within a situation and describe how they relate to each other
• describe quantities as values that include a sign, the number, and the unit in a situation
• convert between units within a single measurement system (Example: inches to feet)
• identify dependent and independent variables for a given situation/context
• justify which quantities in a situation are the most important
• function relationships in a given situation from other relations(Note: this is a introduction explored in depth in Unit 1, Big Idea 2)
• Example: If “grapes are \$2 a pound, and turkey is \$7 a pound,” then pounds of grapes to cost of grapes is a function, and pounds of grapes to cost of turkey is a relation
• determine appropriate domain and range values of a function for a given situation
• state restrictions of a function’s domain and range
• select appropriate units and round as indicated by the context
• describe the quantities in the domain and range using the terms whole, integer, rational, irrational, etc.

• analyze graphs to describe the relationship between quantities in a context/situation
• interpret the graph of a function by identifying key features and describing what those features represent within the context of the situation
• key features include: intervals where the function is increasing or decreasing, positive or negative, intercepts, turning points/maximums and minimums, symmetries
• analyze patterns within a function’s graph and use them to make predictions about outputs of a function in a situation (include piecewise and step functions)
• recognize how restrictions on a function’s domain or range can cause a graph to be continuous or discrete

Develop conceptual understanding:

dependent, independent, function, relation, units, domain, range, interval, continuous, discrete

Supporting terms to communicate:

convert, ordered pair, axes, x-axis, y-axis, coordinate point, increasing, decreasing, positive, negative, turning point, maximum, minimum, intercept, piecewise function, step function

Core Resource
A core resource supports multiple days of instruction.
• Studying Situations
A multiple-day resource that supports students in grappling with quantities, relationships, functions, and graphs.
Resource:
Studying Situations

The goal of these activities are to leverage students’ prior experiences to describe how the qualities and units belonging to variables in a situation impact the shape, direction, and features of graphs.

All Resources From:
• Unit 1

#### Modeling with Functions

Instructional Routine: Connecting Representations
These tasks are embedded within the instructional routine called Connecting Representations.
• Discrete versus Continuous
Students will make connections between examples of linear and exponential verbal situations and graphs using discrete and continuous properties.
Resource:
Discrete versus Continuous

Students will make connections between examples of linear and exponential verbal situations and graphs using discrete and continuous properties.

All Resources From:
• Unit 1