Jeffcoat and Scarborough Grade 7 Math Day 11: Ratios ... · Day 11: Ratios, Rates, Proportions...

Jeffcoat and Scarborough

Grade 7 Math

Day 11: Ratios, Rates, Proportions

Standard 6.RP.1- Interpret the concept of a ratio as the relationship between two quantities,

including part to part and part to whole.

7.RP.1- Compute unit rates, including those involving complex fractions, with like or different units.

Learning Targets I Can Statements

I can compute unit rates. I can solve real-world and mathematical problems with ratios and percentages using

proportional reasoning.

I can identify and model proportional relationships with tables, diagrams, verbal descriptions and real-world situations.

Essential Question(s) How are unit rates, rates, and ratios applicable to real-life situations? What is the connection between ratios, proportions, and unit rates? How does scale factor connect to proportional relationships?

Resources Carnegie Learning Textbook Aleks.com (Ratios, Rates, and Proportions)

Learning Activities or Experiences

1. Complete at least 3 topics of your ALEKS pathway. (if available)

2. Review Day 1 attached notes on pages 57-58.

3. Complete the Vocabulary on Ratios, Rates, and Proportions and the “Problem Set Activity.”

4. Complete the “Day 11 Today’s Thought” activity. 5. Make up Day 1 assignments

Day 11 Ratios, Rates, and Proportions

Vocabulary

Write the term or phrase below that best completes each statement.

Ratio Rate Unit Rate Proportion Scaling up Scaling down Equivalent ratios

1. _____________ means to multiply the numerator and the denominator of a ratio

by the same factor.

2. A ___________ is a ratio that compares two quantities that are measured in different

units.

3. ______________means to divide the numerator and the denominator of a ratio by the

same factor.

4. A_____________ is a comparison using division.

5. A______________ is an equation that states that two ratios are equal.

6. A_______________ is a comparison of two measurements in which the denominator

has a value of one unit.

7. ________________ are ratios that represent the same part-to-part relationship or the

same part-to-whole

Problem Set Activity

Write each statement as a ratio using colons and in fractional form.

1. There are 5 boys for every 3 girls.

2. There are 2 basketballs for every soccer ball.

3. There are 4 bananas in each fruit basket.

4. There are 50 gallons of water used after 4 showers.

5. There are 3 blueberry muffins in each variety pack of 6 muffins.

Day 11 Today’s Thought Activity

1. In a Friendship Bouquet, 2 out of every 5 roses are pink. If there are 6 pink roses, how

many total roses are in the bouquet? Explain your thought process to this problem and

then answer this problem using mathematical reasoning.

2. In an apartment building, there are 4 tenants who own cats for every 1 tenant who

owns fish. If there are five tenants who owns fish, how many tenants own cats? Explain

your answer using mathematical reasoning.


Grade 7 Math

Day 12: Ratios, Rates, and Proportions Cont.

Standard 7.RP.1- Compute unit rates, including those involving complex fractions, with like

or different units.

7.RP.2.b- Identify and model proportional relationships given multiple

representations, including tables, graphs, equations, diagrams, verbal

descriptions, and real-world situations. (b) Recognize or compute the constant of

proportionality.

7.RP.3- Solve real-world and mathematical problems involving ratios and percentages using proportional reasoning (e.g., multi-step dimensional analysis, percent increase/decrease, tax).


I can compute unit rates. I can solve real-world and mathematical problems with ratios and percentages

using proportional reasoning.

I can identify and model proportional relationships with tables, diagrams, verbal descriptions and real-world situations.

Essential Question(s) How are unit rates, rates, and ratios applicable to real-life situations? What is the connection between ratios, proportions, and unit rates? How does scale factor connect to proportional relationships?

Resources Carnegie Learning Textbook Aleks.com (Ratios, Rates, and Proportions)




3. Complete Vocabulary on “1.5 Using Proportions to Solve Problems” and the “Day 12 Problem Set” activity.

4. Complete the “Day 12 Today’s Thought” activity.

Day 12 Ratios, Rates, and Proportions Continued

Vocabulary

Looks Can Be Deceiving (Using Proportions to Solve Problems)

Describe a situation in which you would use each of the following.

1. variable

2. means and extremes method

3. solve a proportion

4. inverse operations

Day 12 Problem Set Activity

Tell which method (scaling, unit rate, or means and extremes) you would use to solve for each

variable and explain why.

1. 2/3 = 20/x

2. 16/4 = 100/x

3. 23/48 = 50/n

4. 49/7 = p/5

5. 37/15 = x/8

6. 63/38 = x/4


1. Marlene is planning a trip. She knows that her car gets 38 miles to the gallon on the

highway. If her trip is going to be 274 miles and one gallon of gas is $2.30, about how

much should she expect to pay for gas. Explain your thought process and reasoning

to find the answer.

2. It takes Roger about 8 minutes to type a 500-word document. How long will it take

him to type a 12-page essay with 275 words per page? Explain your answer.


Grade 7 Math 7

Day 13: Numerical and Algebraic Expressions

Day 13 Numerical and Algebraic Expressions

Vocabulary

Write an example for each term.

1. Variable

2. Algebraic expression

3. Evaluate an algebraic expression

Standard 7.EEI.1 Apply mathematical properties (e.g., commutative, associative, distributive) to simplify and to factor linear algebraic expressions with rational coefficients. 7.NS.3- Apply the concepts of all four operations with rational numbers to solve

real-world and mathematical problems.

7.EEI.2- Recognize that algebraic expressions may have a variety of equivalent forms and determine an appropriate form for a given real-world situation.


I can write expressions. I can apply the operations to solve real-world and mathematical problems.

I can simplify expressions using operations and their properties.

Essential Question(s) How can I use properties of operations to create equivalent expressions?

Resources Carnegie Learning Textbook Aleks.com (Expressions)




3. Complete the Vocabulary on “6.1 Evaluating Algebraic Expressions” and the Problem Set Activity on Evaluating Algebraic Expressions.



Evaluate each algebraic expression.

1. 2x

for x = 2

for x = -8

for x = 0

2. 3c + 17

for c = 5

for c = -2

for c = -15

3. 64 – 9p

for p = 4

for p = 9

for p = -3

4. –w + 8.5

for w = 12

for w = -1.5

for w = 5.3


Define a variable and write an algebraic expression for each problem. Evaluate the expression

for the given values.

1. The charge for ice skating is $3 for the skate rental and $2 per hour to skate. How much

will you pay if you skate for:

a. 2 hours?

b. 4 hours?

c. 3.5 hours?

2. A birthday party at the skating rink costs $45 to reserve a party area and

$4.50 per guest for skating and skate rental. How much will a party cost if

you invite:

a. 5 guests?

b. 9 guests?

c. 25 guests?


Grade 7 Math

Day 14: Numerical and Algebraic Expressions Cont.

Standard 7.EEI.1 Apply mathematical properties (e.g., commutative, associative, distributive) to simplify and to factor linear algebraic expressions with rational coefficients. 7.NS.3- Apply the concepts of all four operations with rational numbers to solve


7.EEI.2- Recognize that algebraic expressions may have a variety of equivalent forms and determine an appropriate form for a given real-world situation.


I can write expressions. I can apply the operations to solve real-world and mathematical problems.

I can simplify expressions using operations and their properties.






3. Complete the Vocabulary on “6.2 Simplifying Expressions Using Distributive

Properties” and the Problem Set Activity.


Day 14 Numerical and Algebraic Expressions

Simplifying Expressions Using Distributive Properties Vocabulary

Match each property to the correct example.

1. Distributive Property of Multiplication a. 5(10 − 3) = 5(10) − 5(3)

Over Addition

2.Distributive Property of Multiplication b. 4 + 8/2 = 4/2 + 8/2

Over Subtraction

3.Distributive Property of Division c. 3(6 + 2) = 3(6) + 3(2)

Over Addition

4.Distributive Property of Division d. 12 − 9/3 = 12/3 − 12/3

Over Subtraction


Draw a model for each expression and calculate or simplify.

1. 7(54) 3. -6(870)

2. 9(560) 4. 3(x – 11)

Use the Distributive Property to rewrite each expression in its equivalent form.

1. 4(𝑥 + 3)

2. −7𝑦(4 – 𝑦)

3. 6𝑥(3𝑥 + 5𝑦 – 4)

4. 9𝑎 – 3/3

Day 14 Thought of the Day Activity

Write a short essay on the Distributive Property. Please explain what it is, how it

can be used, and include several examples of how you use the Distributive

Property in your everyday life.


Grade 7 Math

Day 15: Solving Equations and Inequalities

Standard 7.EEI.3- Extend previous understanding of Order of Operations to solve multi-step real-world and mathematical problems involving rational numbers. Include fraction bars as a grouping symbol.


I can solve two-step equations I can write equations

Essential Question(s)

How can I use properties of operations to create equivalent expressions?




2. Review Day 5 attached notes on pages 380-381

3. Complete the Vocabulary on “7.2 Solving Equations” and the Problem Set Activity.


Day 15 Solving Equations

Vocabulary

Match the property with its definition.

1. Addition Property of Equality If a=b, then a + c = b + c

2. Subtraction Property of Equality If a=b, then ac = bc

3. Multiplication Property of Equality If a=b, then a/c = b/c

4. Division Property of Equality If a=b, then a - c = b – c


Solve each two-step equation. State the inverse operations, in the correct order of

operations, you used to isolate the variable. Check your solution.

1. 3w – 7 = 4

2. 25 + 8x = 65

3. 94 = y/4 – 18

4. g/9 + 47 = 64

5. 72 = 5h + 22

6. c/20 – 41 = 59

7. 138 = 7h + 5 8. 16 = 8 + p/2


Solve each riddle using equations.

What is a number that when you multiply it by 3 and subtract 12 from the product, you get

12?

What is a number that when you multiply it by 7 and add 25 to the product, you get 46?


What is a number that when you multiply it by 11 and subtract 30 from the product, you get

91?



Grade 7 Math

Day 16: Solving Equations and Inequalities Cont.

Standard 7. EEI.3- Extend previous understanding of Order of Operations to solve multi-step

real-world and mathematical problems involving rational numbers. Include

fraction bars as a grouping symbol.


I can solve two-step equations I can write equations I can solve multiple step equations


How can I use properties of operations to create equivalent expressions?

Resources Carnegie Learning Textbook Aleks.com (Equations and Inequalities)



2. Review Day 6 notes on pages 381-382

3. Complete Vocabulary on “7.3 Solving Two step equations” and the Problem Set Activity

4. Complete the “Day 16 Today’s thought” activity

Day 16: Solving Two- Step Equations

Vocabulary

Day 16: Problem Set Activity

Day 16: Today’s Thought Activity: Fill in the blank

?

?

?

?

-15


Grade 7 Math

Day 17: Solving Equations and Inequalities Cont.

Standard 7.EEI.4- Apply the concepts of linear equations and inequalities in one variable to

real-world and mathematical situations.


I can write equations

I can solve multistep equations.

I can write two step linear inequalities.


What types of relationships can be modeled by linear equations and inequalities?

How can algebraic expressions, equations and inequalities be used to model,

analyze, and solve mathematical situations?

Resources Carnegie Learning Textbook Aleks.com (Inequalities)



2. Review attached notes on pages 383-384

3. Complete Vocabulary and Problem Set Activity on “7.5 Solving and

Graphing Inequalities in One Variable”

4. Complete the DAY 17 “Today’s thought” activity. 5. Make-up Day 7 Assignments

Day 17: Solving Inequalities Vocabulary: Fill in the Blanks


Day 17 “Today’s Thought” Activity

There are 29 students in Miss Spelling’s class. As a special holiday gift, she bought each of them chocolate

letters with which they can spell their names. Unfortunately, some letters cost more than others—for

instance, the letter A, which is in high demand, is rather pricey; whereas the letter Q, which almost no one

needs, is relatively inexpensive.

The price of the chocolate letters for each student in her class is shown in the table below.

1

.

2


Grade 7 Math

Day 18: Rational Numbers

Standard 7.NS.3 Apply the concepts of all four operations with rational numbers to solve



I can state and apply the sign rules for multiplying and dividing rational numbers.

I can add, subtract, multiply and divide rational numbers

I can add and subtract rational numbers.

I can apply mathematical properties to add and subtract rational numbers.


Why do we use numbers, what are their properties and how does our number

system function?

How are rational numbers used to represent real-life situations?

Why do we need to be knowledgeable about all forms of numbers?

How do I apply the rules of mathematical operations to rational numbers?

Resources Carnegie Learning Textbook Aleks.com (Rational Numbers)



2. Review attached Day 8 notes on pages 334-335

3. Complete Vocabulary and Problem Set Activity on “4.5 Adding and Subtracting Rational Numbers

4. Complete Day 18 “Today’s thought” activity.

Day 18: Rational Numbers- Adding-Subtracting Integers

Vocabulary: Give examples of each type of number


Day 18: “Today’s Thought” Activity

Answer one of the two questions.

1. Create three-word problems that uses integers, fractions, and decimals.

2. Explain how to solve problems that involve adding and subtracting rational

numbers.


Grade 7 Math

Day 19: Rational Numbers Cont.




I can state and apply the sign rules for multiplying and dividing rational numbers.

I can add, subtract, multiply and divide rational numbers

I can add and subtract rational numbers.

I can apply mathematical properties to add and subtract rational numbers.


Why do we use numbers, what are their properties and how does our number

system function?

How are rational numbers used to represent real-life situations?

Why do we need to be knowledgeable about all forms of numbers?

How do I apply the rules of mathematical operations to rational numbers?

Resources Carnegie Learning Textbook Aleks.com (Rational Numbers)



2. Review attached notes on pages 334-335

3. Complete pages 254-266 on 5.1 and 5.2 ”Rational Numbers”

4. Complete the “Today’s thought” activity. (Talk the Talk pg. 262 and 266)

Day 19: Multiplying and Dividing Rational Numbers

Vocabulary


Complete Even Numbers Only

Day 19: “Today’s Thought Activity

How is multiplying and dividing rational numbers similar to multiplying and

dividing integers?


Grade 7 Math

Day 20: Cumulative Review Test



7.EEI.1 Apply mathematical properties (e.g., commutative, associative,

distributive) to simplify and to factor linear algebraic expressions with rational

coefficients.

7.EEI.2 Recognize that algebraic expressions may have a variety of equivalent

forms and determine an appropriate form for a given real-world situation.

7.EEI.4 Apply the concepts of linear equations and inequalities in one variable to

real-world and mathematical situations.

7.RP.2 Identify and model proportional relationships given multiple

representations, including tables, graphs, equations, diagrams, verbal

descriptions, and real-world situations.

7.RP.3 Solve real-world and mathematical problems involving ratios and

percentages using proportional reasoning (e.g., multi-step dimensional analysis,

percent increase/decrease, tax).


I can compute unit rates. I can solve multistep equations. I can write two step linear inequalities. I can add, subtract, multiply and divide rational numbers.

I can solve two-step equations I can write equations. I can write expressions. I can apply the operations to solve real-world and mathematical problems. I can simplify expressions using operations and their properties.


How are rational numbers used to represent real-life situations? How can I use properties of operations to create equivalent expressions?

Resources Carnegie Learning Textbook Aleks.com (Any Topic)



2. Complete Box Review (20 questions) Or 3. Complete Activities

https://www.math-play.com/rational-numbers-jeopardy/rational-numbers-jeopardy-

game_html5.html Rational Numbers Game https://www.iknowit.com/lessons/e-writing-algebraic-expressions.html Algebraic Expressions http://www.algebra4children.com/Games/games-2/Algebraic-expressions/hoopshoot-

algebraic_expressions.html Algebraic Expressions https://www.brainpop.com/games/lostattheforevermine/?topic_id=607ef72bd74c9c03 Graphing and Solving Inequalities

4. Make-up Day 10 Cumulative Review Test

https://www.math-play.com/rational-numbers-jeopardy/rational-numbers-jeopardy-game_html5.html

https://www.math-play.com/rational-numbers-jeopardy/rational-numbers-jeopardy-game_html5.html

https://www.iknowit.com/lessons/e-writing-algebraic-expressions.html

http://www.algebra4children.com/Games/games-2/Algebraic-expressions/hoopshoot-algebraic_expressions.html

http://www.algebra4children.com/Games/games-2/Algebraic-expressions/hoopshoot-algebraic_expressions.html

https://www.brainpop.com/games/lostattheforevermine/?topic_id=607ef72bd74c9c03

Jeffcoat and Scarborough Grade 7 Math Day 11: Ratios ... · Day 11: Ratios, Rates, Proportions...

Documents

Transcript of Jeffcoat and Scarborough Grade 7 Math Day 11: Ratios ... · Day 11: Ratios, Rates, Proportions...