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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/01%3A_Scale_Drawings/1.01%3A_New_Page/1.1.2%3A_Corresponding_Parts_and_Scale_Factors | 1.1.2: Corresponding Parts and Scale Factors
Lesson
Let's describe features of scaled copies.
Exercise \(\PageIndex{1}\): Number Talk: Multiplying by a Unit Fraction
Find each product mentally.
\(\frac{1}{4}\cdot 32\)
\((7.2)\cdot\frac{1}{9}\)
\(\frac{1}{4}\cdot (5.6)\)
Exercise \(\PageIndex{2}\): Corresponding Parts
O... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/01%3A_Scale_Drawings/1.01%3A_New_Page/1.1.3%3A_Making_Scaled_Copies | 1.1.3: Making Scaled Copies
Lesson
Let's draw scaled copies.
Exercise \(\PageIndex{1}\): More or Less?
For each problem, select the answer from the two choices.
-
The value of \(25\cdot (8.5)\) is:
- More than 205
- Less than 205
-
The value of \((9.93)\cdot (0.984)\) is:
- More than 10
- Less than 10
-
The value of \(... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/01%3A_Scale_Drawings/1.01%3A_New_Page/1.1.4%3A_Scaled_Relationships | 1.1.4: Scaled Relationships
Lesson
Let's find relationships between scaled copies.
Exercise \(\PageIndex{1}\): Three Quadrilaterals (Part 1)
Each of these polygons is a scaled copy of the others.
- Name two pairs of corresponding angles. What can you say about the sizes of these angles?
- Check your prediction by measu... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/01%3A_Scale_Drawings/1.01%3A_New_Page/1.1.5%3A_The_Size_of_the_Scale_Factor | 1.1.5: The Size of the Scale Factor
Lesson
Let's look at the effects of different scale factors.
Exercise \(\PageIndex{1}\): Number Talk: Missing Factor
Solve each equation mentally.
\(16x=176\)
\(16x=8\)
\(16x=1\)
\(\frac{1}{5}x=1\)
\(\frac{2}{5}x=1\)
Exercise \(\PageIndex{2}\): Card Sort: Scaled Copies
Your teacher w... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/01%3A_Scale_Drawings/1.01%3A_New_Page/1.1.6%3A_Scaling_and_Area | 1.1.6: Scaling and Area
Lesson
Let's build scaled shapes and investigate their areas.
Exercise \(\PageIndex{1}\): Scaling a Pattern Block
Use the applets to explore the pattern blocks. Work with your group to build the scaled copies described in each question.
-
How many blue rhombus blocks does it take to build a scal... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/01%3A_Scale_Drawings/1.02%3A_New_Page | Skip to main content
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Text Col... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/01%3A_Scale_Drawings/1.02%3A_New_Page/1.2.1%3A_Scale_Drawings | 1.2.1: Scale Drawings
Lesson
Let's explore scale drawings.
Exercise \(\PageIndex{1}\): What is a Scale Drawing?
Here are some drawings of a school bus, a quarter, and the subway lines around Boston, Massachusetts. The first three drawings are scale drawings of these objects.
The next three drawings are not scale drawin... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/01%3A_Scale_Drawings/1.02%3A_New_Page/1.2.2%3A_Scale_Drawings_and_Maps | 1.2.2: Scale Drawings and Maps
Lesson
Let's use scale drawings to solve problems.
Exercise \(\PageIndex{1}\): A Train And a Car
Two cities are 243 miles apart.
- It takes a train 4 hours to travel between the two cities at a constant speed.
- A car travels between the two cities at a constant speed of 65 miles per hour... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/01%3A_Scale_Drawings/1.02%3A_New_Page/1.2.3%3A_Creating_Scale_Drawings | 1.2.3: Creating Scale Drawings
Lesson
Let's create our own scale drawings.
Exercise \(\PageIndex{1}\): Number Talk: Which is Greater?
Without calculating, decide which quotient is larger.
\(11\div 23\) or \(7\div 13\)
\(0.63\div 2\) or \(0.55\div 3\)
\(15\div\frac{1}{3}\) or \(15\div\frac{1}{4}\)
Exercise \(\PageIndex{... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/01%3A_Scale_Drawings/1.02%3A_New_Page/1.2.4%3A_Changing_Scales_in_Scale_Drawings | 1.2.4: Changing Scales in Scale Drawings
Lesson
Let's explore different scale drawings of the same actual thing.
Exercise \(\PageIndex{1}\): Appropriate Measurements
1. If a student uses a ruler like this to measure the length of their foot, which choices would be appropriate measurements? Select all that apply. Be pre... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/01%3A_Scale_Drawings/1.02%3A_New_Page/1.2.5%3A_Scales_without_Units | 1.2.5: Scales without Units
Lesson
Let's explore a different way to express scales.
Exercise \(\PageIndex{1}\): One to One Hundred
A map of a park says its scale is 1 to 100.
- What do you think that means?
- Give an example of how this scale could tell us about measurements in the park.
Exercise \(\PageIndex{2}\): Apo... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/01%3A_Scale_Drawings/1.02%3A_New_Page/1.2.6%3A_Units_in_Scale_Drawings | 1.2.6: Units in Scale Drawings
Lesson
Let's use different scales to describe the same drawing.
Exercise \(\PageIndex{1}\): Centimeters in a Mile
There are 2.54 cm in an inch, 12 inches in a foot, and 5,280 feet in a mile. Which expression gives the number of centimeters in a mile? Explain your reasoning.
- \(\frac{2.54... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/01%3A_Scale_Drawings/1.03%3A_New_Page/1.3.1%3A_Draw_It_to_Scale | 1.3.1: Draw It to Scale
Lesson
Let's draw a floor plan.
Exercise \(\PageIndex{1}\): Which Measurements Matter?
Which measurements would you need in order to draw a scale floor plan of your classroom? List which parts of the classroom you would measure and include in the drawing. Be as specific as possible.
Exercise \(\... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/01%3A_Scale_Drawings/101%3A_New_Page/111%3A_What_are_Scaled_Copies | 1.1.1: What are Scaled Copies?
Lesson
Let's explore scaled copies.
Exercise \(\PageIndex{1}\): Printing Portraits
Here is a portrait of a student. Move the slider under each image, A–E, to see it change.
- How is each one the same as or different from the original portrait of the student?
- Some of the sliders make sca... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/02%3A_Introducing_Proportional_Relationships | 2: Introducing Proportional Relationships Last updated Save as PDF Page ID 34983 Illustrative Mathematics OpenUp Resources 2.1: Representing Proportional Relationships with Tables 2.1.1: One of These Things is Not Like the Others 2.1.2: Introducing Proportional Relationships with Tables 2.1.3: More about Constant of Pr... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/02%3A_Introducing_Proportional_Relationships/2.01%3A_New_Page/2.1.1%3A_One_of_These_Things_is_Not_Like_the_Others | 2.1.1: One of These Things is Not Like the Others
Lesson
Let's remember what equivalent ratios are.
Exercise \(\PageIndex{1}\): Remembering Double Number Lines
1. Complete the double number line diagram with the missing numbers.
2. What could each of the number lines represent? Invent a situation and label the diagram.... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/02%3A_Introducing_Proportional_Relationships/2.01%3A_New_Page/2.1.2%3A_Introducing_Proportional_Relationships_with_Tables | 2.1.2: Introducing Proportional Relationships with Tables
Lesson
Let's solve problems involving proportional relationships using tables.
Exercise \(\PageIndex{1}\): NOtice and Wonder: Paper Towels by The Case
Here is a table that shows how many rolls of paper towels a store receives when they order different numbers of... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/02%3A_Introducing_Proportional_Relationships/2.01%3A_New_Page/2.1.3%3A_More_about_Constant_of_Proportionality | 2.1.3: More about Constant of Proportionality
Lesson
Let's solve more problems involving proportional relationships using tables.
Exercise \(\PageIndex{1}\): Equal Measures
Use the numbers and units from the list to find as many equivalent measurements as you can. For example, you might write “30 minutes is \(\frac{1}{... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/02%3A_Introducing_Proportional_Relationships/2.02%3A_New_Page/2.2.1%3A_Proportional_Relationships_and_Equations | 2.2.1: Proportional Relationships and Equations
Lesson
Let's write equations describing proportional relationships.
Exercise \(\PageIndex{1}\): NUmber Talk: Division
Find each quotient mentally.
\(645\div 100\)
\(645\div 50\)
\(48.6\div 30\)
\(48.6\div x\)
Exercise \(\PageIndex{2}\): Feeding a Crowd, Revisited
1. A rec... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/02%3A_Introducing_Proportional_Relationships/2.02%3A_New_Page/2.2.2%3A_Two_Equations_for_Each_Relationship | 2.2.2: Two Equations for Each Relationship
Lesson
Let's investigate the equations that represent proportional relationships.
Exercise \(\PageIndex{1}\): Missing Figures
Here are the second and fourth figures in a pattern.
- What do you think the first and third figures in the pattern look like?
- Describe the 10th figu... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/02%3A_Introducing_Proportional_Relationships/2.02%3A_New_Page/2.2.3%3A_Using_Equations_to_Solve_Problems | 2.2.3: Using Equations to Solve Problems
Lesson
Let's use equations to solve problems involving proportional relationships.
Exercise \(\PageIndex{1}\): Number Talk: Quotients with Decimal Points
Without calculating, order the quotients of these expressions from least to greatest.
\(42.6\div 0.07\)
\(42.6\div 70\)
\(42.... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/02%3A_Introducing_Proportional_Relationships/2.03%3A_New_Page/2.3.1%3A_Comparing_Relationships_with_Tables | 2.3.1: Comparing Relationships with Tables
Lesson
Let's explore how proportional relationships are different from other relationships.
Exercise \(\PageIndex{1}\): Adjusting a Recipe
A lemonade recipe calls for the juice of 5 lemons, 2 cups of water, and 2 tablespoons of honey.
Invent four new versions of this lemonade ... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/02%3A_Introducing_Proportional_Relationships/2.03%3A_New_Page/2.3.2%3A_Comparing_Relationships_with_Equations | 2.3.2: Comparing Relationships with Equations
Lesson
Let's develop methods for deciding if a relationship is proportional.
Exercise \(\PageIndex{1}\): Notice and Wonder: Patterns with Rectangles
Do you see a pattern? What predictions can you make about future rectangles in the set if your pattern continues?
Exercise \(... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/02%3A_Introducing_Proportional_Relationships/2.03%3A_New_Page/2.3.3%3A_Solving_Problems_about_Proportional_Relationships | 2.3.3: Solving Problems about Proportional Relationships
Lesson
Let's solve problems about proportional relationships.
Exercise \(\PageIndex{1}\): What Do You Want to Know?
Consider the problem: A person is running a distance race at a constant rate. What time will they finish the race?
What information would you need ... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/02%3A_Introducing_Proportional_Relationships/2.04%3A_New_Page/2.4.1%3A_Introducing_Graphs_of_Proportional_Relationships | 2.4.1: Introducing Graphs of Proportional Relationships
Lesson
Let's see how graphs of proportional relationships differ from graphs of other relationships.
Exercise \(\PageIndex{1}\): Notice These Points
- Plot the points \((0,10), (1,8), (2,6), (3,4), (4,2)\).
- What do you notice about the graph?
Exercise \(\PageInd... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/02%3A_Introducing_Proportional_Relationships/2.04%3A_New_Page/2.4.2%3A_Interpreting_Graphs_of_Proportional_Relationships | 2.4.2: Interpreting Graphs of Proportional Relationships
Lesson
Let's read stories from the graphs of proportional relationships.
Exercise \(\PageIndex{1}\): What Could the Graph Represent?
Here is a graph that represents a proportional relationship.
- Invent a situation that could be represented by this graph.
- Label... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/02%3A_Introducing_Proportional_Relationships/2.04%3A_New_Page/2.4.3%3A_Using_Graphs_to_Compare_Relationships | 2.4.3: Using Graphs to Compare Relationships
Lesson
Let's graph more than one relationship on the same grid.
Exercise \(\PageIndex{1}\): Number Talk: Fraction Multiplication and Division
Find each product or quotient mentally.
\(\frac{2}{3}\cdot\frac{1}{2}\)
\(\frac{4}{3}\cdot\frac{1}{4}\)
\(4\div\frac{1}{5}\)
\(\frac{... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/02%3A_Introducing_Proportional_Relationships/2.04%3A_New_Page/2.4.4%3A_Two_Graphs_for_Each_Relationship | 2.4.4: Two Graphs for Each Relationship
Lesson
Let's use tables, equations, and graphs to answer questions about proportional relationships.
Exercise \(\PageIndex{1}\): True or False: Fractions and Decimals
Decice whether each equation is true or false. Be prepared to explain your reasoning.
- \(\frac{3}{2}\cdot 16=3\c... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/02%3A_Introducing_Proportional_Relationships/2.5%3A_Let's_Put_it_to_Work/2.5.1%3A_Four_Representations | 2.5.1: Four Representations
Lesson
Let's contrast relationships that are and are not proportional in four different ways.
Exercise \(\PageIndex{1}\): Which is the Bluest?
1. Which group of blocks is the bluest?
2. Order the groups of blocks from least blue to bluest.
Exercise \(\PageIndex{2}\): One Scenario, Four Repre... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/02%3A_Introducing_Proportional_Relationships/2.5%3A_Let's_Put_it_to_Work/2.5.2%3A_Using_Water_Efficiently | 2.5.2: Using Water Efficiently
Lesson
Let's investigate saving water.
Exercise \(\PageIndex{1}\): Comparing Baths and Showers
Some people say that it uses more water to take a bath than a shower. Others disagree.
- What information would you collect in order to answer the question?
- Estimate some reasonable values for... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/03%3A_Untitled_Chapter_3/3.01%3A_New_Page/3.1.1%3A_How_Well_Can_You_Measure | 3.1.1: How Well Can You Measure?
Lesson
Let's see how accurately we can measure.
Exercise \(\PageIndex{1}\): Estimating a Percentage
A student got 16 out of 21 questions correct on a quiz. Use mental estimation to answer these questions.
- Did the student answer less than or more than 80% of the questions correctly?
- ... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/03%3A_Untitled_Chapter_3/3.01%3A_New_Page/3.1.2%3A_Exploring_Circles | 3.1.2: Exploring Circles
Lesson
Let's explore circles.
Exercise \(\PageIndex{1}\): How Do You Figure?
Here are two figures.
Figure C looks more like Figure A than Figure B. Sketch what Figure C might look like. Explain your reasoning.
Exercise \(\PageIndex{2}\): Sorting Round Objects
Your teacher will give you some pic... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/03%3A_Untitled_Chapter_3/3.01%3A_New_Page/3.1.3%3A_Exploring_Circumference | 3.1.3: Exploring Circumference
Lesson
Let's explore the circumference of circles.
Exercise \(\PageIndex{1}\): Which is Greater?
Clare wonders if the height of the toilet paper tube or the distance around the tube is greater. What information would she need in order to solve the problem? How could she find this out?
Exe... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/03%3A_Untitled_Chapter_3/3.01%3A_New_Page/3.1.4%3A_Applying_Circumference | 3.1.4: Applying Circumference
Lesson
Let's use \(\pi\) to solve problems.
Exercise \(\PageIndex{1}\): What Do We Know? What Can we Estimate?
Here are some pictures of circular objects, with measurement tools shown. The measurement tool on each picture reads as follows:
- Wagon wheel: 3 feet
- Plane propeller: 24 inches... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/03%3A_Untitled_Chapter_3/3.01%3A_New_Page/3.1.5%3A_Circumference_and_Wheels | 3.1.5: Circumference and Wheels
Lesson
Let's explore how far different wheels roll.
Exercise \(\PageIndex{1}\): A Rope and a Wheel
Han says that you can wrap a 5-foot rope around a wheel with a 2-foot diameter because \(\frac{5}{2}\) is less than pi. Do you agree with Han? Explain your reasoning.
Exercise \(\PageIndex{... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/03%3A_Untitled_Chapter_3/3.02%3A_New_Page/3.2.1%3A_Estimating_Areas | 3.2.1: Estimating Areas
Lesson
Let's estimate the areas of weird shapes.
Exercise \(\PageIndex{1}\): Mental Calculations
Find a strategy to make each calculatoin mentally:
\(599+87\)
\(254-88\)
\(99\cdot 75\)
Exercise \(\PageIndex{2}\): House Floorplan
Here is a floor plan of a house. Approximate lengths of the walls a... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/03%3A_Untitled_Chapter_3/3.02%3A_New_Page/3.2.2%3A_Exploring_the_Area_of_a_Circle | 3.2.2: Exploring the Area of a Circle
Lesson
Let's investigate the areas of circles.
Exercise \(\PageIndex{1}\): Estimating Areas
Your teacher will show you some figures. Decide which figure has the largest area. Be prepared to explain your reasoning.
Exercise \(\PageIndex{2}\): Estimating Areas of Circles
Your teacher... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/03%3A_Untitled_Chapter_3/3.02%3A_New_Page/3.2.3%3A_Relating_Area_to_Circumference | 3.2.3: Relating Area to Circumference
Lesson
Let's rearrange circles to calculate their areas.
Exercise \(\PageIndex{1}\): Irrigating a Field
A circular field is set into a square with an 800 m side length. Estimate the field's area.
- About \(5,000\text{m}^{2}\)
- About \(50,000\text{m}^{2}\)
- About \(500,000\text{m}... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/03%3A_Untitled_Chapter_3/3.02%3A_New_Page/3.2.4%3A_Applying_Area_of_Circles | 3.2.4: Applying Area of Circles
Lesson
Lets's find the areas of shapes made up of circles.
Exercise \(\PageIndex{1}\): Still Irrigating the Field
The area of this field is about 500,000 m 2 . What is the field’s area to the nearest square meter? Assume that the side lengths of the square are exactly 800 m.
- \(502,400\... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/03%3A_Untitled_Chapter_3/3.03%3A_New_Page/3.3.1%3A_Distinguishing_Circumference_and_Area | 3.3.1: Distinguishing Circumference and Area
Lesson
Let's contrast circumference and area.
Exercise \(\PageIndex{1}\): Filling the Plate
About how many cheese puffs can fit on the plate in a single layer? Be prepared to explain your reasoning.
Exercise \(\PageIndex{2}\): Cart Sort: Circle Problems
Your teacher will giv... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/03%3A_Untitled_Chapter_3/3.03%3A_New_Page/3.3.2%3A_Stained-Glass_Windows | 3.3.2: Stained-Glass Windows
Lesson
Let's use circumference and area to design stained-glass windows.
Exercise \(\PageIndex{1}\): Cost of a Stained-Glass Window
The students in art class are designing a stained-glass window to hang in the school entryway. The window will be 3 feet tall and 4 feet wide. Here is their de... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4 | 4: Proportional Relationships and Percentages Last updated Save as PDF Page ID 34997 Illustrative Mathematics OpenUp Resources 4.1: Proportional Relationships with Fractions 4.1.1: Lots of Flags 4.1.2: Ratios and Rates With Fractions 4.1.3: Revisiting Proportional Relationships 4.1.4: Half as Much Again 4.1.5: Say It w... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.01%3A_New_Page/4.1.1%3A_Lots_of_Flags | 4.1.1: Lots of Flags
Lesson
Let's explore the U.S. flag.
Exercise \(\PageIndex{1}\): Scaled or Not?
1. Which of the geometric objects are scaled versions of each other?
2. Pick two of the objects that are scaled copies and find the scale factor.
Exercise \(\PageIndex{2}\): Flags are Many Sizes
One standard size for the... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.01%3A_New_Page/4.1.2%3A_Ratios_and_Rates_With_Fractions | 4.1.2: Ratios and Rates With Fractions
Lesson
Let's calculate some rates with fractions.
Exercise \(\PageIndex{1}\): Number Talk: Division
Find each quotient mentally.
\(5\div\frac{1}{3}\)
\(2\div\frac{1}{3}\)
\(\frac{1}{2}\div\frac{1}{3}\)
\(2\frac{1}{2}\div\frac{1}{3}\)
Exercise \(\PageIndex{2}\): A Train is Travelin... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.01%3A_New_Page/4.1.3%3A_Revisiting_Proportional_Relationships | 4.1.3: Revisiting Proportional Relationships
Lesson
Let's use constants of proportionality to solve more problems.
Exercise \(\PageIndex{1}\): Recipe Ratios
A recipe calls for \(\frac{1}{2}\) cup sugar and 1 cup flour. Complete the table to show how much sugar and flour to use in different numbers of batches of the rec... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.01%3A_New_Page/4.1.4%3A_Half_as_Much_Again | 4.1.4: Half as Much Again
Lesson
Let's use fractions to describe increases and decreases.
Exercise \(\PageIndex{1}\): Notice and Wonder: TApe Diagrams
What do you notice? What do you wonder?
Exercise \(\PageIndex{2}\): Walking Half as Much Again
-
Complete the table to show the total distance walked in each case.
- Jad... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.01%3A_New_Page/4.1.5%3A_Say_It_with_Decimals | 4.1.5: Say It with Decimals
Lesson
Let's use decimals to describe increases and decreases.
Exercise \(\PageIndex{1}\): Notice and Wonder: Fractions to Decimals
A calculator gives the following decimal representations for some unit fractions:
\(\begin{array}{lcl}{\frac{1}{2}=0.5}&{\qquad}&{\frac{1}{7}=0.142857143}\\{\fr... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.02%3A_New_Page/4.2.1%3A_Increasing_and_Decreasing | 4.2.1: Increasing and Decreasing
Lesson
Let's use percentages to describe increases and decreases.
Exercise \(\PageIndex{1}\): Improving Their Game
Here are the scores from 3 different sports teams from their last 2 games.
| sports team | total points in game 1 | total points in game 2 |
|---|---|---|
| football team |... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.02%3A_New_Page/4.2.2%3A_One_Hundred_Percent | 4.2.2: One Hundred Percent
Lesson
Let's solve more problems about percent increase and percent decrease.
Exercise \(\PageIndex{1}\): Notice and Wonder: Double Number Line
What do you notice? What do you wonder?
Exercise \(\PageIndex{2}\): Double Number Lines
For each problem, complete the double number line diagram to ... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.02%3A_New_Page/4.2.3%3A_Percent_Increase_and_Decrease_with_Equations | 4.2.3: Percent Increase and Decrease with Equations
Lesson
Let's use equations to represent increases and decreases.
Exercise \(\PageIndex{1}\): Number Talk: From 100 to 106
How do you get from one number to the next using multiplication or division?
From 100 to 106
From 100 to 90
From 90 to 100
From 106 to 100
Exercis... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.02%3A_New_Page/4.2.4%3A_More_and_Less_than_1_Percent | 4.2.4: More and Less than 1 Percent
Lesson
Let's explore percentages smaller than 1%.
Exercise \(\PageIndex{1}\): Number Talk: What Percentage?
Determine the percentage mentally.
10 is what percentage of 50?
5 is what percentage of 50?
1 is what percentage of 50?
17 is what percentage of 50?
Exercise \(\PageIndex{2}\):... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.03%3A_New_Page/4.3.1%3A_Tax_and_Tip | 4.3.1: Tax and Tip
Lesson
Let's learn about sales tax and tips.
Exercise \(\PageIndex{1}\): Notice and Wonder: The Price of SUnglasses
You are on vacation and want to buy a pair of sunglasses for $10 or less. You find a pair with a price tag of $10. The cashier says the total cost will be $10.45.
What do you notice? Wh... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.03%3A_New_Page/4.3.2%3A_Percentage_Contexts | 4.3.2: Percentage Contexts
Lesson
Let's learn about more situations that involve percentages.
Exercise \(\PageIndex{1}\): Leaving a Tip
Which of these expressions represent a 15% tip on a $20 meal? Which represent the total bill?
\(15\cdot 20\)
\(20+0.15\cdot 20\)
\(1.15\cdot 20\)
\(\frac{15}{100}\cdot 20\)
Exercise \(... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.03%3A_New_Page/4.3.3%3A_Finding_the_Percentage | 4.3.3: Finding the Percentage
Lesson
Let's find unknown percentages.
Exercise \(\PageIndex{1}\): Tax, Tip, and Discount
What percentage of the car price is the tax?
What percentage of the food cost is the tip?
What percentage of the shirt cost is the discount?
Exercise \(\PageIndex{2}\): What is the Percentage?
- A sal... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.03%3A_New_Page/4.3.4%3A_Measurement_Error | 4.3.4: Measurement Error
Lesson
Let's use percentages to describe how accurately we can measure.
Exercise \(\PageIndex{1}\): MEasuring to the Nearest
Your teacher will give you two rulers and three line segments labeled A, B, and C.
- Use the centimeter ruler to measure each line segment to the nearest centimeter. Reco... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.03%3A_New_Page/4.3.5%3A_Percent_Error | 4.3.5: Percent Error
Lesson
Let's use percentages to describe other situations that involve error.
Exercise \(\PageIndex{1}\): Number Talk: Estimating a Percentage of a Number
Estimate.
25% of 15.8
9% of 38
1.2% of 127
0.53% of 6
0.06% of 202
Exercise \(\PageIndex{2}\): Plants, Bicycles, and Crowds
- Instructions to ca... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.03%3A_New_Page/4.3.6%3A_Error_Intervals | 4.3.6: Error Intervals
Lesson
Let's solve more problems about percent error.
Exercise \(\PageIndex{1}\): A Lot of Iron Ore
An industrial scale is guaranteed by the manufacturer to have a percent error of no more than 1%. What is a possible reading on the scale if you put 500 kilograms of iron ore on it?
Exercise \(\Pag... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.04%3A_New_Page/4.4.1%3A_Posing_Percentage_Problems | 4.4.1: Posing Percentage Problems
Lesson
Let's explore how percentages are used in the news.
Exercise \(\PageIndex{1}\): Sorting the News
Your teacher will give you a variety of news clippings that include percentages.
- Sort the clippings into two piles: those that are about increases and those that are about decrease... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/05%3A_Untitled_Chapter_5 | 5: Rational Number Arithmetic Last updated Save as PDF Page ID 35004 Illustrative Mathematics OpenUp Resources 5.1: Interpreting Negative Numbers 5.1.1: Interpreting Negative Numbers 5.2: Adding and Subtracting Rational Numbers 5.2.1: Changing Temperatures 5.2.2: Changing Elevation 5.2.3: Money and Debts 5.2.4: Represe... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/05%3A_Untitled_Chapter_5/5.01%3A_New_Page/5.1.1%3A_Interpreting_Negative_Numbers | 5.1.1: Interpreting Negative Numbers
Lesson
Let's review what we know about signed numbers.
Exercise \(\PageIndex{1}\): Using the Thermometer
Here is a weather thermometer. Three of the numbers have been left off.
- What numbers go in the boxes?
- What temperature does the thermometer show?
Exercise \(\PageIndex{2}\): ... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/05%3A_Untitled_Chapter_5/5.02%3A_New_Page/5.2.1%3A_Changing_Temperatures | 5.2.1: Changing Temperatures
Lesson
Let's add signed numbers.
Exercise \(\PageIndex{1}\): Which One Doesn't Belong: Arrows
Which pair of arrows doesn't belong?
1.
2.
3.
4.
Exercise \(\PageIndex{2}\): Warmer and Colder
1. Complete the table and draw a number line diagram for each situation.
| start (\(^{\circ}\)C) | cha... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/05%3A_Untitled_Chapter_5/5.02%3A_New_Page/5.2.2%3A_Changing_Elevation | 5.2.2: Changing Elevation
Lesson
Let's solve problems about adding signed numbers.
Exercise \(\PageIndex{1}\): That's the Opposite
1. Draw arrows on a number line to represents these situations:
a. The temperature was -5 degrees. Then the temperature rose 5 degrees.
b. A climber was 30 feet above sea level. Then she de... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/05%3A_Untitled_Chapter_5/5.02%3A_New_Page/5.2.3%3A_Money_and_Debts | 5.2.3: Money and Debts
Lesson
Let's apply what we know about signed numbers to money.
Exercise \(\PageIndex{1}\): Concert Tickets
Priya wants to buy three tickets for a concert. She has earned $135 and each ticket costs $50. She borrows the rest of the money she needs from a bank and buys the tickets.
- How can you rep... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/05%3A_Untitled_Chapter_5/5.02%3A_New_Page/5.2.4%3A_Representing_Subtraction | 5.2.4: Representing Subtraction
Lesson
Let's subtract signed numbers.
Exercise \(\PageIndex{1}\): Equivalent Equations
Consider the equation \(2+3=5\). Here are some more equations, using the same numbers, that express the same relationship in a different way:
\(3+2=5\qquad\qquad 5-3=2\qquad\qquad 5-2=3\)
For each equa... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/05%3A_Untitled_Chapter_5/5.02%3A_New_Page/5.2.5%3A_Subtracting_Rational_Numbers | 5.2.5: Subtracting Rational Numbers
Lesson
Let's bring addition and subtraction together.
Exercise \(\PageIndex{1}\): Number Talk: Missing Addend
Solve each equation mentally. Rewrite each addition equation as a subtraction equation.
\(247+c=458\)
\(c+43.87=58.92\)
\(\frac{15}{8}+c=\frac{51}{8}\)
Exercise \(\PageIndex{... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/05%3A_Untitled_Chapter_5/5.02%3A_New_Page/5.2.6%3A_Adding_and_Subtracting_to_Solve_Problems | 5.2.6: Adding and Subtracting to Solve Problems
Lesson
Let's apply what we know about signed numbers to different situations.
Exercise \(\PageIndex{1}\): Positive or Negative?
Without computing:
- Is the solution to \(-2.7+x=-3.5\) positive or negative?
-
Select
all
the expressions that are solutions to \(-2.7+x=-3.5\)... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/05%3A_Untitled_Chapter_5/5.03%3A_New_Page/5.3.1%3A_Position_Speed_and_Direction | 5.3.1: Position, Speed, and Direction
Lesson
Let's use signed numbers to represent movement.
Exercise \(\PageIndex{1}\): Distance, Rate, Time
- An airplane moves at a constant speed of 120 miles per hour for 3 hours. How far does it go?
- A train moves at constant speed and travels 6 miles in 4 minutes. What is its spe... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/05%3A_Untitled_Chapter_5/5.03%3A_New_Page/5.3.2%3A_Multiplying_Rational_Numbers | 5.3.2: Multiplying Rational Numbers
Lesson
Let's multiply signed numbers.
Exercise \(\PageIndex{1}\): Before and After
Where was the girl:
- 5 seconds after this picture was taken? Mark her approximate location on the picture.
- 5 seconds before this picture was taken? Mark her approximate location on the picture.
Exer... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/05%3A_Untitled_Chapter_5/5.03%3A_New_Page/5.3.3%3A_Multiply | 5.3.3: Multiply!
Lesson
Let's get more practice multiplying signed numbers.
Exercise \(\PageIndex{1}\): Which One Doesn't Belong: Expressions
Which expression doesn't belong?
\(\begin{array}{lcl}{7.9x}&{\qquad}&{-7.9+x}\\{7.9\cdot (-10)}&{\qquad}&{-79}\end{array}\)
Exercise \(\PageIndex{2}\): Card Sort: Matching Expres... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/05%3A_Untitled_Chapter_5/5.03%3A_New_Page/5.3.4%3A_Dividing_Rational_Numbers | 5.3.4: Dividing Rational Numbers
Lesson
Let's divide signed numbers.
Exercise \(\PageIndex{1}\): Tell Me Your Sign
Consider the equation: \(-27x=-35\)
Without computing:
- Is the solution to this equation positive or negative?
- Are either of these two number solutions to the equation?
\(\frac{35}{27}\qquad\qquad -\fra... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/05%3A_Untitled_Chapter_5/5.03%3A_New_Page/5.3.5%3A_Negative_Rates | 5.3.5: Negative Rates
Lesson
Let's apply what we know about signed numbers.
Exercise \(\PageIndex{1}\): Graper per Minute
- If you eat 5 grapes per minute for 8 minutes, how many grapes will you eat?
- If you hear 9 new songs per day for 3 days, how many new songs will you hear?
- If you run 15 laps per practice, how m... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/05%3A_Untitled_Chapter_5/5.04%3A_New_Page/5.4.1%3A_Expressions_with_Rational_Numbers | 5.4.1: Expressions with Rational Numbers
Lesson
Let's develop our signed number sense.
Exercise \(\PageIndex{1}\): True or False: Rational Numbers
Decide if each statement is true or false. Be prepared to explain your reasoning.
- \((-38.76)(-15.6)\) is negative
- \(10,000-99,999<0\)
- \(\left(\frac{3}{4}\right)\left(-... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/05%3A_Untitled_Chapter_5/5.04%3A_New_Page/5.4.2%3A_Solving_Problems_with_Rational_Numbers | 5.4.2: Solving Problems with Rational Numbers
Lesson
Let's use all four operations with signed numbers to solve problems.
Exercise \(\PageIndex{1}\): Which One Doesn't Belong? Equations
Which equation doesn't belong?
\(\begin{array}{llll}{\frac{1}{2}x=-50}&{\qquad}&{\qquad}&{x+90=-100}\\{-60t=30}&{\qquad}&{\qquad}&{-0.... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/05%3A_Untitled_Chapter_5/5.05%3A_New_Page/5.5.1%3A_Solving_Equations_with_Rational_Numbers | 5.5.1: Solving Equations with Rational Numbers
Lesson
Let's solve equations that include negative values.
Exercise \(\PageIndex{1}\): Number Talk: Opposites and Reciprocals
The variables \(a\) through \(h\) all represent different numbers. Mentally find numbers that make each equation true.
\(\frac{3}{5}\cdot\frac{5}{3... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/05%3A_Untitled_Chapter_5/5.05%3A_New_Page/5.5.2%3A_Representing_Contexts_with_Equations | 5.5.2: Representing Contexts with Equations
Lesson
Let's write equations that represent situations.
Exercise \(\PageIndex{1}\): Don't Solve It
Is the solution positive or negative?
\((-8.7)(1.4)=a\)
\(-8.7b=1.4\)
\(-8.7+c=-1.4\)
\(-8.7-d=-1.4\)
Exercise \(\PageIndex{2}\): Warmer or Colder than Before?
For each situatio... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/05%3A_Untitled_Chapter_5/5.06%3A_New_Page/5.6.1%3A_The_Stock_Market | 5.6.1: The Stock Market
Lesson
Let's learn about the stock market.
Exercise \(\PageIndex{1}\): Revisiting Interest and Depreciation
- Lin deposited $300 in a savings account that has a 2% interest rate per year. How much is in her account after 1 year? After 2 years?
- Diego wants to sell his bicycle. It cost $150 when... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.01%3A_New_Page/6.1.1%3A_Relationships_between_Quantities | 6.1.1: Relationships between Quantities
Lesson
Let's try to solve some new kinds of problems.
Exercise \(\PageIndex{1}\): Pricing Theater Popcorn
A movie theater sells popcorn in bags of different sizes. The table shows the volume of popcorn and the price of the bag.
Complete one column of the table with prices where p... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.01%3A_New_Page/6.1.2%3A_Reasoning_about_Contexts_with_Tape_Diagrams | 6.1.2: Reasoning about Contexts with Tape Diagrams
Lesson
Let's use tape diagrams to make sense of different kinds of stories.
Exercise \(\PageIndex{1}\): Notice and Wonder: Remembering Tape Diagrams
- What do you notice? What do you wonder?
- What are some possible values for \(a\), \(b\), and \(c\) in the first diagr... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.01%3A_New_Page/6.1.3%3A_Reasoning_about_Equations_with_Tape_Diagrams | 6.1.3: Reasoning about Equations with Tape Diagrams
Lesson
Let's see how equations can describe tape diagrams.
Exercise \(\PageIndex{1}\): Find Equivalent Expressions
Select all the expressions that are equivalent to \(7(2-3n)\). Explain how you know each expression you select is equivalent.
- \(9-10n\)
- \(14-3n\)
- \... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.01%3A_New_Page/6.1.4%3A_Reasoning_about_Equations_and_Tape_Diagrams_(Part_1) | 6.1.4: Reasoning about Equations and Tape Diagrams (Part 1)
Lesson
Let's see how tape diagrams can help us answer questions about unknown amounts in stories.
Exercise \(\PageIndex{1}\): Algebra Talk: Seeing Structure
Find a solution to each equation without writing anything down.
\(x+1=5\)
\(2(x+1)=10\)
\(3(x+1)=15\)
\... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.01%3A_New_Page/6.1.5%3A_Reasoning_about_Equations_and_Tape_Diagrams_(Part_2) | 6.1.5: Reasoning about Equations and Tape Diagrams (Part 2)
Lesson
Let's use tape diagrams to help answer questions about situations where the equation has parentheses.
Exercise \(\PageIndex{1}\): Algebra Talk: Seeing Structure
Solve each equation mentally.
\(x-1=5\)
\(2(x-1)=10\)
\(3(x-1)=15\)
\(500=100(x-1)\)
Exercis... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.01%3A_New_Page/6.1.6%3A_Distinguishing_between_Two_Types_of_Situations | 6.1.6: Distinguishing between Two Types of Situations
Lesson
Let's think about equations with and without parentheses and the kinds of situations they describe.
Exercise \(\PageIndex{1}\): Which One Doesn't Belong: Seeing Structure
Which equation doesn't belong?
\(4(x+3)=9\)
\(4\cdot x+12=9\)
\(4+3x=9\)
\(9=12+4x\)
Exe... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.02%3A_New_Page/6.2.1%3A_Reasoning_about_Solving_Equations_(Part_1) | 6.2.1: Reasoning about Solving Equations (Part 1)
Lesson
Let's see how a balanced hanger is like an equation and moving its weight is like solving the equation.
Exercise \(\PageIndex{1}\): Hanger Diagrams
In the two diagrams, all the triangles weigh the same and all the squares weigh the same.
For each diagram, come up... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.02%3A_New_Page/6.2.2%3A_Reasoning_about_Solving_Equations_(Part_2) | 6.2.2: Reasoning about Solving Equations (Part 2)
Lesson
Let's use hangers to understand two different ways of solving equations with parentheses.
Exercise \(\PageIndex{1}\): Equivalent to \(2(x+3)\)
Select all the expressions equivalent to \(2(x+3)\).
- \(2\cdot (x+3)\)
- \((x+3)2\)
- \(2\cdot x+2\cdot 3\)
- \(2\cdot ... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.02%3A_New_Page/6.2.3%3A_Dealing_with_Negative_Numbers | 6.2.3: Dealing with Negative Numbers
Lesson
Let's show that doing the same to each side works for negative numbers too.
Exercise \(\PageIndex{1}\): Which One Doesn't Belong: Rational Number Arithmetic
Which equation doesn't belong?
\(\begin{array}{llll}{15=-5\cdot -3}&{\qquad}&{\qquad}&{4--2=6}\\{2+-5=-3}&{\qquad}&{\qq... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.02%3A_New_Page/6.2.4%3A_Different_Options_for_Solving_One_Equation | 6.2.4: Different Options for Solving One Equation
Lesson
Let's think about which way is easier when we solve equations with parentheses.
Exercise \(\PageIndex{1}\): Algebra Talk: Solve Each Equation
\(100(x-3)=1,000\)
\(500(x-3)=5,000\)
\(0.03(x-3)=0.3\)
\(0.72(x+2)=7.2\)
Exercise \(\PageIndex{2}\): Analyzing Solution ... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.02%3A_New_Page/6.2.5%3A_Using_Equations_to_Solve_Problems | 6.2.5: Using Equations to Solve Problems
Lesson
Let's use tape diagrams, equations, and reasoning to solve problems.
Exercise \(\PageIndex{1}\): Remember Tape Diagrams
- Write a story that could be represented by this tape diagram.
- Write an equation that could be represented by this tape diagram.
Exercise \(\PageInde... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.02%3A_New_Page/6.2.6%3A_Solving_Problems_about_Percent_Increase_or_Decrease | 6.2.6: Solving Problems about Percent Increase or Decrease
Lesson
Let's use tape diagrams, equations, and reasoning to solve problems with negatives and percents.
Exercise \(\PageIndex{1}\): 20% Off
An item costs \(x\) dollars and then a 20% discount is applied. Select all the expressions that could represent the price... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.03%3A_New_Page | Skip to main content
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Text Col... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.03%3A_New_Page/6.3.1%3A_Reintroducing_Inequalities | 6.3.1: Reintroducing Inequalities
Lesson
Let's work with inequalities.
Exercise \(\PageIndex{1}\): Greater Than One
The number line shows values of \(x\) that make the inequality \(x>1\) true.
-
Select
all
the values of \(x\) from this list that make the inequality \(x>1\) true.
- \(3\)
- \(-3\)
- \(1\)
- \(700\)
- \(1... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.03%3A_New_Page/6.3.2%3A_Finding_Solutions_to_Inequalities_in_Context | 6.3.2: Finding Solutions to Inequalities in Context
Lesson
Let's solve more complicated inequalities.
Exercise \(\PageIndex{1}\): Solutions to Equations and Solutions to Inequalities
- Solve \(-x=10\)
- Find 2 solutions to \(-x>10\)
- Solve \(2x=-20\)
- Find 2 solutions to \(2x>-20\)
Exercise \(\PageIndex{2}\): Earning... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.03%3A_New_Page/6.3.3%3A_Efficiently_Solving_Inequalities | 6.3.3: Efficiently Solving Inequalities
Lesson
Let's solve more complicated inequalities.
Exercise \(\PageIndex{1}\): Lots of Negatives
Here is an inequality: \(-x\geq -4\).
- Predict what you think the solutions on the number line will look like.
-
Select
all
the values that are solutions to \(-x\geq -4\):
- \(3\)
- \... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.03%3A_New_Page/6.3.4%3A_Interpreting_Inequalities | 6.3.4: Interpreting Inequalities
Lesson
Let's write inequalities.
Exercise \(\PageIndex{1}\): Solve Some Inequalities!
For each inequality, find the value or values of \(x\) that make it true.
- \(8x+21\leq 56\)
- \(56<7(7-x)\)
Exercise \(\PageIndex{2}\): Club Activities Matching
Choose the inequality that best matches... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.03%3A_New_Page/6.3.5%3A_Modeling_with_Inequalities | 6.3.5: Modeling with Inequalities
Lesson
Let's look at solutions to inequalities.
Exercise \(\PageIndex{1}\): Possible Values
The stage manager of the school musical is trying to figure out how many sandwiches he can order with the $83 he collected from the cast and crew. Sandwiches cost $5.99 each, so he lets \(x\) re... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.04%3A_New_Page/6.4.1%3A_Subtraction_in_Equivalent_Expressions | 6.4.1: Subtraction in Equivalent Expressions
Lesson
Let's find ways to work with subtraction in expressions.
Exercise \(\PageIndex{1}\): Number Talk: Additive Inverses
Find each sum or difference mentally.
\(-30+-10\)
\(-10+-30\)
\(-30-10\)
\(10--30\)
Exercise \(\PageIndex{2}\): A Helpful Observation
Lin and Kiran are ... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.04%3A_New_Page/6.4.2%3A_Expanding_and_Factoring | 6.4.2: Expanding and Factoring
Lesson
Let's use the distributive property to write expressions in different ways.
Exercise \(\PageIndex{1}\): Number Talk: Parentheses
Find the value of each expression mentally.
\(2+3\cdot 4\)
\((2+3)(4)\)
\(2-3\cdot 4\)
\(2-(3+4)\)
Exercise \(\PageIndex{2}\): Factoring and Expanding wi... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.04%3A_New_Page/6.4.3%3A_Combining_Like_Terms_(Part_1) | 6.4.3: Combining Like Terms (Part 1)
Lesson
Let's see how we can tell that expressions are equivalent.
Exercise \(\PageIndex{1}\): Why is it True?
Explain why each statement is true.
- \(5+2+3=5+(2+3)\)
- \(9a\) is equivalent to \(11a-2a\).
- \(7a+4-2a\) is equivalent to \(7a+-2a+4\).
- \(8a-(8a-8)\) is equivalent to \... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.04%3A_New_Page/6.4.4%3A_Combining_Like_Terms_(Part_2) | 6.4.4: Combining Like Terms (Part 2)
Lesson
Let's see how to use properties correctly to write equivalent expressions.
Exercise \(\PageIndex{1}\): True or False?
Select all the statements that are true. Be prepared to explain your reasoning.
- \(4-2(3+7)=4-2\cdot 3-2\cdot 7\)
- \(4-2(3+7)=4-2\cdot 3+-2\cdot 7\)
- \(4-2... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.04%3A_New_Page/6.4.5%3A_Combining_Like_Terms_(Part_3) | 6.4.5: Combining Like Terms (Part 3)
Lesson
Let's see how we can combine terms in an expression to write it with less terms.
Exercise \(\PageIndex{1}\): Are They Equal?
Select all expressions that are equal to \(8-12-(6+4)\).
- \(8-6-12+4\)
- \(8-12-6-4\)
- \(8-12+(6+4)\)
- \(8-12-6+4\)
- \(8-4-12-6\)
Exercise \(\PageI... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.05%3A_New_Page/6.5.1%3A_Applications_of_Expressions | 6.5.1: Applications of Expressions
Lesson
Let's use expressions to solve problems.
Exercise \(\PageIndex{1}\): Algebra Talk: Equivalent to \(0.75t-21\)
Decide whether each expression is equivalent to \(0.75t-21\). Be prepared to explain how you know.
\(\frac{3}{4}t-21\)
\(\frac{3}{4}(t-21)\)
\(0.75(t-28)\)
\(t-0.25t-21... | Metni etiketle ve Türkçe'ye çevir. | system_1 |
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