Thursday 20191114 Proportional Reasoning B A SSE A

Thursday, 20191114 Proportional Reasoning B. A. SSE. A. 2. Use algebraic structures to solve problems involving proportional reasoning in real world context. EQ 10: How do we use algebraic structures to solve proportional reasoning problems? Objective: Compare two different proportional relationships represented in different ways.

Thursday, 20191114 Essential Questions 1. EQ 10: How do we use algebraic structures No Sleeping! Agenda Bridge Math Store your phones Find your seat Bellwork: Bridge Scale Drawings Calculator Proportional reasoning problems/ Scale Factors Ø No Exit Ticket Ø Remain in seat until bell rings. Teacher Dismisses NOT the bell. Ø Ø Ø to solve proportional reasoning problems? Vocabulary: • Unit rates • Fractions • Solving Proportions • Ratios • Finding percent and calculating percent of a number • Determining constant of proportionality (slope) from tables of values, graphs, and algebraic relations • Interpreting constants of proportionality (slope) on a graph • Proportional Reasoning • Scale Factor It’s always a great day to be a Wolverine!

Bellwork: Thursday, 20191114 1. A scale model of the Statue of Liberty is 15 inches tall. If the Statue of Liberty is 305 feet tall, find the scale of the model. 2. A map has a scale of 2 inches = 50 miles. If the distance between two cities on the map is 7 inches, what is the actual distance between the cities?

Answers 1. A scale model of the Statue of Liberty is 15 inches tall. If the Statue of Liberty is 305 feet tall, find the scale of the model. 15 inches : 305 feet - SIMPLIFY – both are divisible by 5…. The scale of the model is 3 in : 61 ft. 2. A map has a scale of 2 inches = 50 miles. If the distance between two cities on the map is 7 inches, what is the actual distance between the cities? set up a proportion inches 2 inches = 7 inches miles 50 miles x CMAD (cross multiply and divide) … multiply 7 and 50, then divide by 2; x equals 175 miles. NOTE: simplifying the first ratio to 1 inch : 25 miles will also result in the same answer.

Word Wall Ø Indirect measurement - is a method of using proportions to find an unknown length or distance in similar figures. Ø Scale drawing - A drawing that shows a real object with accurate sizes reduced or enlarged by a certain amount (called the scale). Ø Scale - a reference standard in measurement, in which each number corresponds to some physical quantity Ø Dilation - is a transformation that produces an image that is the same shape as the original, but is a different size.

Word Wall Continued SCALE FACTOR

Cartoon Scale Drawings Using cartoons to draw similar figures

Objectives Use ratios to make indirect measurements. Use scale drawings to solve problems.

The Cartoon What to do with your cartoon: 1. Select a cartoon 2. Print it out with: Coach Dill’s Classes and Mrs. Austin’s Classes today!

The Grid Use a ruler to measure the length and width of your cartoon in centimeters and write it on your paper – near your cartoon

The Grid Use a ruler to measure the length and width of your cartoon in centimeters and write it on your paper – near your cartoon 10 cm Yours may not be 10 cm – this is just an example 10 cm

The Grid Now…Time to draw the grid! On the paper (not on the cartoon), Make two centimeter marks on opposite sides 2 cm 2 cm 2 cm Start on the left and go towards the right across the top and bottom Be careful measuring – your grid will turn out better the last block may be smaller than two centimeter

The Grid Now…Time to draw the grid! Connect the marks… BE careful you have one shot at this! 2 cm 2 cm 2 cm It is okay if all your squares aren’t exactly the same size – but try to get them as close as possible

Scale Drawing 1. 43. 2 cm x 50. 8 Large paper 2. 10 cm x 10 cm cartoon 3. Scale Factor of my scale drawing is 50. 8 cm/10 cm = 5. 08 Which means my drawing with the scale factor of 5. 08 is 5 times bigger than the cartoon I started out with.

The Scale Drawing Time to draw your cartoon on to a larger paper with a larger grid. What is the scale factor of your drawing?

The Scale Drawing Time to blow up your cartoon. The scale factor is 3. You are making your cartoon 3 times as large. What do you do? 2 cm 2 cm 2 cm multiply everything by 3!

The Scale Drawing You need to create a grid that is three times as large as your original. My original is 10 cm by 10 cm.

The Drawing To draw the large grid you need to multiply the length and width of the small cartoon by three.

The Scale Drawing You need to create a grid that is three times as large as your original. My original is 10 cm by 10 cm. I’m choosing scale factor of 3 cm, so my new grid is 30 cm to 30 cm Now mark off five 6 cm marks! – Left to right and top to bottom

The Drawing Now you can draw! You do not have to know how to draw to do this. The grid helps you with spatial relationships…

The Drawing Now you can draw! You do not have to know how to draw to do this. The grid helps you with spatial relationships… Draw the new picture one square at a time Notice spatial relationships here and it will look Exactly like original

Cartoon Similarity Finished Product

Get Ready for the EXIT TICKET!!!

EXIT TICKET Solve each proportion for x: