Rate of change and Slope

Common Core State Standards

7.RP.2   Recognize and represent proportional relationships between quantities.

7.RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Essential Question How can you find the unit rate from a line on a graph that goes through the origin?

Objective understand slope as it relates to rate of change

Objective identify slope using tables and graphs

Develop the Concept

Investigation

Rate of Change and Slope resource

Rate of Change and Slope worksheet

SOLVE PROPORTIONAL RELATIONSHIPS

Homework Review

Mid-Chapter 1 Check

Objective use proportions to solve problems

 Lesson Vocabulary

proportion

cross product


Bell Ringer

Opening: 

What is the ratio of shaded squares to total squares?

If you divide your rectangle into eighths, what is the ratio of shaded eighths to the total number of eighths?

What is another way to divide the rectangle into equal parts? What is the ratio of shaded parts to the total number of parts? 

 Reminder-

If two ratios are equivalent then they share the same unit rate.

Graph, Interpret and Compare Proportional Relationships

Do Now

Objective identify proportional relationships by graphing on the coordinate plane

Lesson Vocabulary

coordinate plane

quadrants

ordered pair

x-coordinate

y-coordinate

y-axis

origin

x-axis

Lesson Resources (click for videos)

Example 1: Display all possibilities in a proportional relationship by graphing

Week Outline Nov 17 - 21 2014

Monday: Proportional and Nonproportional Relationships

Tuesday:  Reteach/ Solving Proportional and Nonproportional Relationships

Wednesday: Solving Proportional and Nonproportional Relationships Activities

Thursday: Mid Chapter Assessment.  Prep before Assessment

Friday: Hands on activities, movement, laugher, thought, fun

 

PROPORTIONAL AND NONPROPORTIONAL RELATIONSHIPS

Building on the Essential Question

At the end of the lesson, students should be able to answer "What makes two quantities proportional?"

Objective identify proportional and nonproportional relationships

Lesson Vocabulary

proportional
nonproportional
equivalent ratios

There are several ways to determine whether or not a relationship is proportional.

• If ordered pairs of a relation show a constant ratio, it is a proportion.
• If the elements in the rows of a table for the relation have a constant ratio, it is a proportion.
• If there is a constant ratio between y- and x- coordinates of points on the graph of a relation, it is a proportion.
• If the relation can be expressed algebraically in the form y = kx, it is a proportion.

A relation that does not have these characteristics is not a proportion.

Converting Unit Rate: Group Presentations

Good Things

Do Now:

Today we will :

-Review Social Contract
-Finish our converting unit rate poster.
-Present our posters
-Make affirmation Envelopes 

Converting Unit Rate: Practice

Bell Ringer

Check your work. Answer to Bell Ringer

In class work:  Pair Check

Convert units using dimensional analys

Learning Goal: How can you show that two objects are proportional?

Lesson Objective: Convert Units of Measure between derived units to solve problems

DOL:

Vocabulary

Unit Ratio
Dimensional Analysis  Click for link.

What we will learn today?
To convert on rate to an equivalent rate by multiplying by a unit ratio or its reciprocal.

1. How can you find the number of feet in 2 yard?
2. How many feet are in 1 2/3 yards?
3. How can you find the number of inches in 1 yard?

refer to page 117 in your planner.

Copy down steps!

Practice Problems

1.       A remote control car travels at a rate of 10 feet per second.  How many inches per second.  How many inches per second is this?

2.       A swordfish can swim at a rate of 60 miles per hour. How many feet per hour is this?

3.       A gull can fly at a speed of 22 miles per hour. About how many feet per hour can the gull fly?

4.       An AMTRAK train travels at 125 miles per hour. Convert the speed miles per minute.  Round to the nearest tenth.

5.       Marvin walks is at a speed of 7 feet per second.  How many feet per hour is this?

6.       The average speed of one team in a relay race is about 10 miles per hour.  What is the speed in feet per second?

Evidence of Learning:

Lorenzo rides his bike at a rate of  yards per second. About how many miles per hour can Lorenzo ride his bike?

Charlie runs at a speed of 3 yards per second.  About how many miles per hour does charlie run?

HW : Volume 1 Chapter 1 pg 29 #'s 1-6