# Teachers: Resources for High School

The North Carolina Collaborative for Mathematics Learning (NC2ML) aims to support NC math educators in implementing the revised mathematics content standards in ways that align with what we know from research on students’ mathematical thinking, mathematics teaching, and teacher learning. To do so, we have co-designed research-based professional learning resources focused on content and pedagogy.

## Focusing on Student Thinking

This page includes a collection of tasks that align with the NC High School Math 1, 2, and/or 3 standards along with associated student work and videos of teacher discussions related to both the task itself and student work on the task. These resources may be helpful in university-based methods courses and school/district based Professional Development. Tasks include those selected from free online resources (Math Visions Project, Illustrative Mathematics, Desmos) as well as those developed by North Carolina teachers from across the state.

Floating Down the River

Key Words:
Graphing Stories, Functions, Rates, Relationships

Brief Description:
Three people are floating in tubes down a river. They hypothesize that the speed is faster when the water is shallow and slower when the water is deeper. They measure the depth, speed and distance every 10 mins. Students are asked if they agree or disagree with the hypothesis.

Student Work Sample

Teachers discussing learning goals for the Floating Down the River task

Teachers discussing where they might use the Floating Down the River task

Teachers discussing their anticipation of student thinking on the Floating Down the River task

Teachers discussing Student 1 & 2

Teachers discussing Student 3

Teachers discussing Student 4

Teachers discussing Student 5

Regina’s Logo

Key Words:
Patterns, Recursive Formula, Linear Functions, Equivalent Expressions

Brief Description:
Students will analyze a pattern and write a recursive formula and a function to describe the pattern.

Student Work Sample

Teachers discussing learning goals associate with Regina's Logo

Teachers discussing challenges they anticipate with Regina's Logo

Teachers discussing Student A

Teachers discussing Student B

Teachers discussing Student C

Teachers discussing Student D

Pay It Forward

Key Words:
Patterns, Exponential Function

Brief Description:
Students will analyze a pattern in which each person pays it forward to three people. They will write a function to describe the pattern.

Student Work Sample

Teachings discussing anticipation of student thinking for the Pay it Forward task

Teachers discussing Student 1

Teachers discussing Student 2

Teachers discussing Student 3

Teachers discussing Student 4

Teachers discussing Student 5

Teachers discussing Student 6

Squares Upon Squares

Key Words:
Patterns, Recursive Formula, Functions, Equivalent Expressions

Brief Description:
Students will analyze a pattern and write a recursive formula and a function to describe the pattern.

Student Work Samples

Lots of Linear Options

Key Words:
Systems of Linear Equations

Brief Description:
Students are to create linear systems without graphing given certain parameters (i.e. just the point of intersection).

Student Work Samples

Teachers discussing using Lots of Linear Options in their classes

Teachers discussing launching Lots of Linear Options

Teachers discussing student accessibility of Lots of Linear Options

Teachers discussing Students 1 & 2

Teachers discussing Student 3

Test Data Dilemma

Key Words:
Comparing Datasets, Graphs, Mean, Median, Mode, Variance, Argumentation

Brief Description:
Students are asked to compare graphs of class grades to determine which teacher should receive an award.  There are multiple types of graphs (i.e. histogram, boxplot etc.)

Student Work Samples

Teachers discussing the use of the Test Data Dilemma in their classroom

Teachers discussing anticipating student work on the Test Data Dilemma Task

Teachers discussing pressing and probing questions they might use with the Test Data Dilemma Task

Teachers discussing how they might connect students' thinking when using the Test Data Dilemma Task

Teachers discussing Student A

Teachers discussing Student B

Teachers discussing Students C & D

Creating Images

Key Words:
Transformation, Reflection, Rotation, Translation, Inverse, Composition

Brief Description:
Students are introduced to 4 transformations and asked a series of questions that delve into composition of transformations.

Student Work Samples

Teachers discussing how to set up the task

Teachers discussing challenges implementing the task

Teachers discussing the sample student work

Rigid Transformations

Key Words:
Transformation, Reflection, Rotation, Translation, Rigid Motion

Brief Description:
Students will show that two triangles are congruent by using transformations.

Student Work Samples

Teachers discussing the rigid transformations task

Teachers discussing questions they might pose with the rigid transformations task

Teachers discussing Student 1

Teachers discussing Student 2

Teachers discussing Student 3

Key Words:
Solving Quadratic Functions, Factoring, Quadratic Formula, Completing the Square, Vertex Form, Graphing

Brief Description: Students are asked to solve a quadratic by using different methods.

Student Work Samples

Teachers discussing the goals of this task

Teachers discussing questions that can support connections across strategies

Teachers discussing Student Work video 1

Teachers discussing Student Work video 2

Key Words:
Linear Regression, Rate of Change, Constant Rate of Change

Brief Description:
Students have data on the flow rate of a water tower leak.  They are asked questions about when the leak can be fixed and how long the tower has been leaking.

Student Work Samples

Teachers discussing the use of the water tower task in their classroom

Teachers discussing implementation of the water tower task (note: slide shown does not match their discussion)

Teachers discussing Student 1

Teachers discussing Student 2

Teachers discussing Student 3

Teachers discussing Student 4

Teachers discussing Student 5

Teachers discussing Student 6

Key Words:
Right Triangle, Altitude, Distance Formula

Brief Description:
Students are asked to find the length of the altitude of a right triangle situated in the coordinate plane.

Student Work Samples

Teachers discussing implementation of the task

Teachers discussing their anticipation of student thinking on the triangle relationships task

Teachers discussing Students 1, 2 and 3

Teachers discussing Students 4, 5, and 6

Teachers discussing the connections among students' work

Key Words:
Conditional Probability, Independent Events, Dependent Events

Brief Description:
A bag contains 3 black and 3 white balls. Winning is defined as drawing two balls of the same color.  Students are asked to determine if the game is fair.

Student Work Samples

Teachers discussing learning goals for this task

Teachers discussing their anticipation of student thinking

Teachers discussing students 1, 2 and 3

Teachers discussing student 4, 5, 6, and 7

Key Words:
Inverse, Exponential Functions, Logarithmic Functions, Domain, Range

Brief Description:
Students explore an exponential function, its inverse, and the relationship between the two within the context of how far the tortoise is from the starting line of the race.

Student Work Sample 1

Student Work Sample 2

Student Work Sample 3

Student Work Sample 4

Teachers discussing implementing this task in their classrooms

Teachers discussing student 1

Teachers discussing student 2

Teachers discussing student 3

Teachers discussing student 4

Key Words:
Modeling Exponential Growth, Inverse, Exponential Functions, Logarithmic Functions

Brief Description:
Students will use exponential growth to model cockroach population growth.  They will also need to then use that information to figure out how long it will take for the population to cover a specific area (i.e. North Carolina).

Student Work Samples

Teachers discussing implementation of the Cockroach task

Teachers discussing their anticipation of student thinking

Teachers discussing Student 1

Teachers discussing Student 2

Teachers discussing Student 3

Teachers discussing Student 4

Key Words:
Pattern, Representation, Rules, Recursive Formula, Equivalent Expressions

Brief Description:
Students need to determine how many bricks a stonemason will require to build the steps to the Philadelphia Art Museum (Rocky Steps).

Student Work Sample 1

Student Work Sample 2

Student Work Sample 3

Student Work Sample 4

Teachers discussing how to launch the Go the Distance Task

Teachers discussing how to maintain the cognitive demand of the Go the Distance Task

Teachers discussing how to adapt the task to make it accessible to all students

Teachers discussing Student 1

Teachers discussing Student 2

Teachers discussing Student 3

Teachers discussing Student 4

Key Words:
Geometric Formula, Optimization, Minimization, Pythagorean Theorem

Brief Description:
Students need to determine the minimum length of zip line wire required to satisfy the requirements for building the two zip lines from two towers to floating platform in a swamp.

Student Work Samples

Teachers discussing implementation of the zip line task

Classroom video of the zip line task being implemented

Classroom video of the zip line task being implemented 2

Teachers discussing student work samples

Teachers discussing desmos student solutions

Teachers discussing student work sample connections and classroom video

Mutually Tangent Circles

Key Words:
Circles, Tangent, Sectors, Triangles

Brief Description:
Students are asked to find the area of three mutually tangent circles including the area between the three circles.

Student Work Samples

Teachers discussing the use of Mutually Tangent Circles in their classrooms

Teachers discussing their anticipation of student work on the Mutually Tangent Circles task

Teachers discussing students 1 & 2

Teachers discussing student 3

Teachers discussing student 4

Key Words:
Rational Functions, Multiple Representations, Domain, Range, Graphing, Asymptotes

Brief Description:
A gift costs \$360 and several people split the cost of the gift. Students are asked to create a function that models each person’s individual contribution. After which, students are asked to consider the end behavior of rational functions.

Student Work Samples

Teachers discussing students 1 and 2

Teachers discussing students 1, 2, and 3

Key Words:
Sine, Cosine, Transformations, Periodic Functions, Multiple Representations

Brief Description:
Students are given data, asked how to model that data on a graph, and then asked to fit a function to the graphical representation of the data using sliders.