How Does the Distance Change As Time Increases?

Moving Straight Ahead

Investigation 1

Investigation: I can describe the patterns of change between the independent and dependent variables.

Problem 1.1

How does the distance change as time increases?

I can describe the patterns of change between the independent and dependent variables.

How can I calculate my walking rate using independent and dependentand use it in an equation?

I can use unit rate to see the relationship between two variables.

Students will use walking rate to understand the concept of pattern of change between independent and dependant variables.

Problem 1.2

What does a linear relationship look like in a table, graph and equation?

I can construct tables, graphs and equations to represent linear patterns of change.

How can I use rate to represent a linearrelationship on a table, graph, and equation?

I can identify linear relationships between two variables and construct tables, graphs, and equations.

Students will describe the patterns of change between independent and dependent variables and construct tables, graphs, and equations to represent linear patterns of change.

Problem 1.3

How can I show the same information in a table, graph, and equation?

I can understand how negative rates of change are represented in tables, graphs and equations.

I can make connections about linear relationships from the tables, graphs, and equations that I construct.

Howcan Iuse rate to find the relationship between two variables on a table, graph, and equation?

Students will model situations by constructing tables, graphs, and equations and utilize the connections between all 3 representations.

Students will be introduced to y-intercept.

Problem 1.4

How can I show a negative linear relationship in a table, graph, or equation?

I can describe the information the variables and numbers in an equation represent.

How does a negative rate of change look in a table, graph, and equation?

I can recognize negative rates in a table, graph, or equation and what the variables and numbers represent.

Students will understand negative rates of change and how they are represented in equations, tables, and graphs.

Investigation 2

Investigation 2: I can use tables and graphs to solve problems with equations in the form y = mx + b.

Problem 2.1

How do you find a solution using a table or graph?

Students will find solutions to a problem using a table or graph.

How can I use tables or graphs to find solutions to a problem?

I can use a table or graph to find solutions to a problem.

I can use my background knowledge to solve problems.

Problem 2.2

How can I use a table, graph, and equation to find a specific value?

Students will describe the connections between linear equations and patterns in the tables and graphs and use tables and graphs in order to find solutions.

How can I identify the differences in tables, graphs, and equations with two separate rates of change?

I can use tables and graphs to find solutions and make connections between: tables, graphs, equations, rate of change, and points of intersection.

I can see the connection between equations and patterns in a table and a graph

Problem 2.3

How does the y-intercept show up in a table and equation?

Students will be able to translate the information about linear relations given in a table, graph, or equation.

Students will understand how the y-intercept appears in tables and equations.

Can I use a table or equation to identify the y-intercept?

I can understand and use the y-intercept and coefficient to make connections and find solutions.

I can identify where the coefficient and the y-intercept appear in tables, graphs and equations.

Problem 2.4

How can I make a table and graph from an equation?

Students will make connections between all 3 representations in order to translate between the representations.

Students will understand where the y-intercept appears in the tables, graphs, and equations.

How can I find an ordered pair using either a table, graph, or equation?

I can us a table, graph, or equation to find the essential information to solve a problem.
I can connect solutions in tables and graphs to the solutions of equations.

Investigation 3

I can solve linear equations.

Problem 3.1

Students will apply variables in the equations to real-world situations.

How do I solve for variables using tables and graphs?

Can I solveforone variable in alinear equationby replacingthe othervariable?

I can solve linear equations with one variable using tables, graphs, and equations.

I can solve linear equations using tables, graphs and symbols.

Problem 3.2

Students will develop an understanding of equality in order to solve equations that are represented pictorially.

How can I find the value in a pouch by using the idea of equality?

How can I find the number of coins in one bag by using properties of equality?

I can use models to understand equality.

I can use the properties of equality to solve equations.

Problem 3.3

Students will use the properties of equality to solve equations and check solutions.

How can I use write and use an equation to find the value of a pouch?

How can I use the properties of equality to write and solve and equation?

Using a model I can write, solve, and check equations.

I can use substitution to check my solution to an equation.

Problem 3.4

Students will develop strategies for solving linear equations and understand that minor changes in the equation will affect the solution.

How do I use the property of equality to solve equations?

What is the algorithm for solving linear equations?

I can develop and use strategies to solve liner equations.

I can compare equations and determine how the differences will impact the solution.

Problem 3.5

Students will interpret equations in a real-life setting, find the point of intersection of two lines, and determine what the point of intersection means.

How can I find the point of intersection and what does it tell me?

What does the point of intersection mean in a problem?

What does the point of intersection mean in a problem?

I can analyze two equations and find their point of intersection.

I can find the point of intersection of two lines.

Investigation 4

I can describe how slope of a line is related to a table, graph or equation.

Problem 4.1

Students will learn about slope and use slope to sketch a graph of a line with given slope.

What is the slope of a line and how do I find it?

How can I use slope (rise/run)to sketch a graph?

I can determine the ratio of the rise to run and how it is related to the coefficient of an equation.

I can recognize the slope of a line as the ratio of rise over run.

Problem 4.2

Students will find the slope and y-intercept of a line from a table, graph, or equation and use them to write an equation in the form of y=mx+b, where ‘m’ is slope and ‘b’ is y-intercept.

How do I use the slope and y-intercept in a table, graph to write an equation in the form y=mx +b?

How can I identify the slope and y-intercept in a table, graph, and equation?

I can find the slope and y-intercept of a given graph, table, and equation and use the information to write an equation using y=mx+b.

I can find the slope of a line and use the slope to write an equation in the form y = mx + b.

Problem 4.3

Students will explore patterns among lines with same slope (parallel lines) and lines whose slopes are negative reciprocals of each other (perpendicular lines).

What is the pattern between slope and its line?

What do lines with similar slopes have in common?

I can compare patterns in equations and graphs and find similarities and differences between parallel and perpendicular lines.

I can connect the patterns in equations and graphs to explore parallel and perpendicular lines.

Problem 4.4

Students will write an equation for an applied situation when the only information given is 2 data points.

How can I write an equation from a real life situation?

How can I write an equation given two data points?

I can write equations with two variables to solve real world problems.

I can use two data points to write an equation for a real-world situation.