7th GradeOctober 5 – October 9

(Mon/Tues) What are we doing today?

• Unit 1 Lesson 5 – The Size of the Scale Factor

• Discuss Friday’s Quiz (briefly) & Discuss MATHia

• Trying to take over the world.

• Assignment #3 will close on Tuesday at 3pm.

Brief Quiz Discussion

• Currently, some of the quizzes have been graded but not all.

• So far, the results have been good though remember that you will have another opportunity to score higher if you want.

• I plan to discuss the quiz in more detail on Friday including sharing answers.

• If you were absent on Friday, you need to e-mail me to set up a time to take the quiz. If not completed by Thursday, you will not have an opportunity to complete the original quiz and will need to take the retake version.

• If you were present and did not submit a quiz, you will need to wait to take the retake version.

Learning Targets

• I can describe the effect on a scaled copy when I use a scale factor that is greater than 1, less than 1, or equal to 1.

• I can explain how the scale factor that takes Figure A to its copy Figure B is related to the scale factor that takes Figure B to Figure A.

• I can successfully connect to MATHia and use it to practice concepts learned in class and/or be exposed to concepts before a class discussion.

Scale Factor

• As a reminder, the scale factor is the number we multiply by to create a scaled copy. The length of each side is multiplied by the scale factor. The angles do notchange.

• For example, if a scaled copy is twice as large as the original then the lengths in the original are multiplied by 2. In this case, 2 is the scale factor.

Example (from Practice Problems)

Example (Solution)

• Part A: In Triangle S, the height is 4 and width is 2. In Triangle L, the height is 8 and width is 4. So, Triangle L is twice the size of Triangle S. The scale factor is 2.

• Part B: In this case, we are comparing them in the other order. Triangle S is half the size of Triangle L. The scale factor is ½.

• Part C: If we reverse the order, the scale factor is always the reciprocal (“flip the fraction”) of what it was previously. So, the scale factor here is 2/3.

Summary

• The scale factor is the number we multiply each length of the original by to get a scaled copy.

• If the scale factor is larger than 1, the scaled copy is larger. If the scale factor is between 0 and 1, the scaled copy is smaller. If the scale factor is exactly 1, the scaled copy is the same size.

• If we know the scale factor from Figure A to Figure B, then the scale factor in reverse from Figure B to Figure A is the reciprocal of this faction. To find this, we just “flip” the fraction. For example, 2

3→

3

2, 2 →

1

2,

1

4→ 4, etc.

Connecting to MATHia

• First, you need to login to Clever using your student ID and password (birthday).

• When connected to Clever, you can search for MATHia or go to the resources which I have shared. The app is called “Carnegie Learning MATHia”.

• Once you find the app, do notclick anything yet.

Connecting to MATHia

• After connecting to the MATHiaapp, simply select the teal (blue-green) button which says “MATHia” on it.

• Do not change the book setting or any other settings before hitting the “MATHia” button.

• If you are seeing a space background and the units named “Pre-Launch Protocol” and “Grade 7 Illustrative Unit 0” then you are in the correct location.

Connecting to MATHia

• To start MATHia, you will select the unit that you are working in. For most students, this is the “Pre-Launch Protocol”. If you finished this, then you start with “Grade 7 Illustrative Unit 0”.

• Once you select your unit, it will automatically give you content to work on and track your progress. If you get stuck, you can ask for a hint which includes examples. Always, try a couple of ideas before asking for a hint.

MATHia Overview

WHY MATHIA?

• MATHia is used to give you practice on concepts we have seen in class. If you work ahead (not required), you can start to see concepts before they are discussed in class.

• Since our class does not meet twice during the week, MATHiaallows you to practice during independent learning time or whenever you are available.

EXPECTATIONS

• Students will be expected to work at least 60 minutes per week in MATHia. I will start tracking this next week. You could work 30 min per day on the days our class does not meet.

• MATHia does not track time if you are not actively working. For example, if you are in another application or just not at your computer then MATHia stops tracking the time spent.

MATHia Grading

• MATHia will be part of a weekly participation/effort grade which I will begin checking next week.

• To earn full credit for MATHia, you must do one of the following:

(1) Complete the required 60 weekly focused minutes between Sunday and Saturday of the given week.

(2) Have completed all of the unit that we are currently working on in class and be working in MATHia on the next unit. For example, we are currently in Unit 1. If you were working on Unit 2 in MATHia, I would give you credit for the week.

Generally, we will not spend time on MATHia in class unless I am absent from class or we have some extra time one week.

Explore MATHia

• In our time remaining, I want you to explore MATHia and work on various completing part of your unit.

(Wed/Thurs) What are we doing today?

• Unit 1 Lesson 7 – Scale Drawings & Unit Lesson 8 Scale Drawings & Maps

• Reminder: You should try to at least complete the Pre-Launch Protocol in MATHia (which just takes a few minutes).

• Reminder #2: If you were absent Friday, you need to reschedule your quiz to be taken before Thursday afternoon.

• Trying to take over the world.

Learning Targets

• I can explain what a scale drawing is, and I can explain what its scale means.

• I can use scale factors to find missing information.

Activity 7.1 (What is the difference here?)

SCALED DRAWINGS NOT SCALED DRAWINGS

Scaled Drawings

Why might some maps not be scaled drawings?

MAP #1 MAP #2

Why might some maps not be scaled drawings?

• In some situations, you may not need the details of a scaled drawing. For example, transit maps often are not drawn to scale. Often, you just need information quickly and briefly when using a transit map. You need to know where the bus (or other transportation) goes and where the stops are. The example previous was from an STA map from 1980. The maps today are more detailed but not necessarily to scale.

• In other situations, you may need to know more details. In a street map, you may need to be able to know approximately how far apart things are to know how long the trip will take or know when your next turn will occur.

Activity 8.1

Activity 8.1 (Solution)

TRAIN

• To find the speed, we need a distance traveled and the time spent. We have this information as 243 miles in 4 hours.

•243 𝑚𝑖𝑙𝑒𝑠

4 ℎ𝑜𝑢𝑟𝑠= 60.75

𝑚𝑖

ℎ𝑟

• Hint: If considering what order to divide, think about “miles per hour”. In math, “per” means to divide in that order, “miles divided by hours”.

CAR

• The car is traveling 65 miles per hour.

• CONCLUSION: The car is faster.

• Hint #2: If you divided the wrong way, you would have

4

243= 0.164.

Would it make sense for a train to go 0.164 miles per hour?

Practice Problem (Lesson 8 - #2 ONLY)

Practice Problem (Solution)

PART A

• We know the scale is 1 in = 200 ft.

• For PART A, we have that a side is 1 foot long. We need to know that 1 foot is the same as 12 inches.

• Notice how I set up the inches on one side and feet on another. To get from 1 in to 12 in, we have tomultiply by 12. We do the same on the other side.

• So, the side of the park is 2400 ft.

Practice Problem (Solution)

PART B

• We know the scale is 1 in = 200 ft.

• For PART B, we know that a path is 900 ft. We can set it up similar tobefore using our new numbers.

• On the right, we have to multiple by 4.5 to get from 200 ft to 900ft. So, we do the same on the left.

• The path is 4.5 in on the map.

• Hint: If you struggled to find that it was 4.5, notice you could divide 900 by 200 to get that value.

(Fri) What are we doing today?

• Review Quiz #1

• Trying to take over the world.

• Reminder: If you have not completed the Pre-Launch Protocol on MATHia, you should make sure to do so.