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**Objective: The student will be able to:**

Identify and interpret the slope of a scenario as a __________________. Analyze tables, graphs, and equations and ________________ their unit rates of change.

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Career Focus: Cost estimators figure out how much a project or product will cost. This helps business owners and managers decide whether to build a structure or manufacture a product. To figure out the cost of a job, a cost estimator relies on slope and unit rate of change to help him/her make decisions.

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**Activating Strategy The table shows Naziah’s height at ages 9 and 12.**

1. What is the change in Naziah’s height from ages 9 to 12? _____________ 2. Over what number of years did this change take place? _____________ 3. Write a rate that compares the change in Naziah’s height to the change in age. Express your answer as a ratio and explain its meaning. Age (years) 9 12 Height (in.) 53 59

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Rate of Change is a _______ that describes how one quantity changes in relation to another. A rate of change is usually expressed as _____________. Can also represent the __________in a word problem or real-world scenario Can be expressed in a table, graph, or equation

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**Find Rate of Change in a Table**

Ex. 1.) The table shows the amount of money a soccer team made washing cars for a fundraiser. Use the information to find the rate of change in dollars per car. Find the unit rate to determine the rate of change: Delta Y Delta x So, the number of dollars earned increases by ________for every ____________washed.

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**AP #1: Find the rate of change**

The table shows the number of miles a plane traveled while in flight. Use the information to find the approximate rate of change in miles per minute. DELTA Y DELTA X Change in: _______ = Change in:_______ _______ 290/30 = Every minute, the plane travels miles UNIT RATE:_________________

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**Find Rate of Change from a Graph**

The graph represents the distance traveled while driving on a highway. Use the graph to find the rate of change in miles per hour. To find the rate of change, pick any two points on the line, such as (1, 60) and (2, 120). DELTA Y DELTA X The distance increases by 60 miles in 1 hour. So, the rate of traveling on a highway is 60 miles per hour. This is also a good opportunity to have the students create a linear equation by reminding them of the y-intercept.

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**AP #2: Find the rate of change from a graph**

Use the graph to find the rate of change in miles per hour while driving in the city. Every hour, the distance increases by 30 miles. The speed is 30 miles/hour

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Unit Rate and Slope The table below shows the relationship between the number of seconds y it takes to hear the thunder after a lightning strike and the distance x you are from the lightning. Graph the data. Then find the slope of the line. Explain what the data represents. Walk students through the problem. Slide is set up to show answer step by step. So, for every 5 seconds between a lightning flash and the sound of the thunder, there is 1 mile between you and the lightning strike.

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**AP #3: Unit Rate and Slope**

Graph the data. Then find the slope of the line. Explain what the slope represents.

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Problems #3-9 With your partner, complete problem #3. Explain what the slope represents in 2-3 sentences. Create an equation that would represent this situation.

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Independent Practice Continue to complete problems #4-#9

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Patterns and Proportional Relationships

Patterns and Proportional Relationships

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