monday 1/21: unit 6, lesson 12: solving problems about ...€¦ · web viewthe chemistry club is...

Coach Bridges’ Lesson Plans

1/21/19-1/25/19

Monday 1/21: Unit 6, Lesson 12: Solving Problems about Percent Increase or Decrease

Lesson Goals• Solve word problems leading to equations of the form px+q=r or p(x+q)=r

Required Materials• sticky notes• tools for creating a visual display

12.1: 20% Off (10 minutes)

Setup:Students in groups of 2. Give students 1 minute of quiet work time followed by 2 minutes of partner discussion. Conclude with whole-class discussion.

Student task statement

An item costs x dollars and then a 20% discount is applied. Select all the expressions that could represent the price of the item after the discount.

1.20100

x

2. x− 20100

x

3. (1−0.20 ) x

4.100−20100

x

5. 0.80 x

6. (100−20)x

Possible responses

2, 3, 4, 5

Anticipated misconceptions

Some students may choose expressions that represent the discount itself instead of the price of the item after the discount. Ask those students to refer back to the situation to identify which piece of the problem the expression they chose finds. If students are still unclear, it may be helpful to give students a price for x such as $10 and ask students if 20% of $10 makes sense as the new price of the item after the discount and then what piece of the problem they found.

12.2: Walking More Each Day (10 minutes)

Setup:Keep students in the same groups. Tell students to work on the first 3 questions and pause. 5 minutes of quiet work time and time to share their responses with a partner, followed by a whole-class discussion.

Student task statement1. Mai started a new exercise program. On the second day, she walked 5 minutes more

than on the first day. On the third day, she increased her walking time from day 2 by 20% and walked for 42 minutes. Mai drew a diagram to show her progress.

Explain how the diagram represents the situation.2. Noah said the equation 1.20(d+5)=42 also represents the situation. Do you agree with

Noah? Explain your reasoning.3. Find the number of minutes Mai walked on the first day. Did you use the diagram, the

equation, or another strategy? Explain or show your reasoning.4. Mai has been walking indoors because of cold temperatures. On Day 4 at noon, Mai

hears a report that the temperature is only 9 degrees Fahrenheit. She remembers the morning news reporting that the temperature had doubled since midnight and was expected to rise 15 degrees by noon. Mai is pretty sure she can draw a diagram to represent this situation but isn't sure if the equation is 9=15+2 t or 2(t+15)=9. What would you tell Mai about the diagram and the equation and how they might be useful to find the temperature, t , at midnight?

Possible responses

1. Answers vary. Sample response: The last day is day 2 plus 15 (20%) of day 2. Day 2 is 5

more than Day 1.

2. Answers vary. Sample responses: Yes, she walked 42 minutes on Day 3, which is the same as (equal to) 20% more than (1.20 times) 5 more than Day 1 (d+5). No, I wrote

the equation 65(d+5)=42 because the diagram shows that 42 is

15 more than d+5.

3. 30 minutes.4. Answers vary.


If students bring up that the diagram represents 120% or 65 , or if they refer to each equal

part as 20% or 15 , ask what whole the fraction or percent refers to. They should understand

that the whole is the amount from Day 2, d+5.

12.3: A Sale on Shoes (15 minutes)

Setup:Keep students in the same groups. Optionally, provide tools for creating a visual display. 5–6 minutes quiet work time and a partner discussion followed by a gallery walk or whole-class discussion.

Student task statement1. A store is having a sale where all shoes are discounted by 20%. Diego has a coupon for

$3 off of the regular price for one pair of shoes. The store first applies the coupon and then takes 20% off of the reduced price. If Diego pays $18.40 for a pair of shoes, what was their original price before the sale and without the coupon?

2. Before the sale, the store had 100 pairs of flip flops in stock. After selling some, they

notice that 35 of the flip flops they have left are blue. If the store has 39 pairs of blue flip

flops, how many pairs of flip flops (any color) have they sold?

3. When the store had sold 29 of the boots that were on display, they brought out another

34 pairs from the stock room. If that gave them 174 pairs of boots out, how many pairs were on display originally?

4. On the morning of the sale, the store donated 50 pairs of shoes to a homeless shelter. Then they sold 64% of their remaining inventory during the sale. If the store had 288 pairs after the donation and the sale, how many pairs of shoes did they have at the start?

Possible responses1. $26. Explanations vary. Sample response: I wrote the equation 0.8(x−3)=18.40 to

show that Diego paid 80% (0.8) of the original price x less the $3 coupon (x−3), which came to a discounted price of $18.40.

2. 35 pairs of flip flops. 35(100−x)=39, x=35.

3. 180 pairs of boots. 79x+34=174, x=180.

4. 850 pairs of shoes. 0.36 (x−50)=288, x=850.

Are you ready for more?A coffee shop offers a special: 33% extra free or 33% off the regular price. Which offer is a better deal? Explain your reasoning.

Possible Responses

Answers vary. Sample response: 33% off the price is a better deal. Suppose you buy 1 cup of coffee at price p. 33% off means you pay 0.67 p for one cup. 33% extra free means you

pay p for 1.33 cups of coffee, or p1.33 for 1 cup, which is about 0.75 p. The unit price for 1

cup of coffee is less with 33% off the price.

Lesson Synthesis (5 minutes)Ask students to reflect on the work done in this unit so far. What strategies have they learned? What kinds of problems can they solve that they weren't able to, previously? Ask them to write down or share with a partner one new thing they have learned and one thing they still have questions or confusion about.

12.4: Timing the Relay Race (Cool-down, 5 minutes)

Setup:None.


The track team is trying to reduce their time for a relay race. First they reduce their time by

2.1 minutes. Then they are able to reduce that time by 110 . If their final time is 3.96 minutes,

what was their beginning time? Show or explain your reasoning.

Possible responses

6.5 minutes.

Tuesday 1/22: Unit 6, Lesson 13: Reintroducing InequalitiesLesson Goals• Use substitution to determine whether a given number in a specified set makes an

inequality true.• Understand that that there are infinitely many values that make an inequality true.• Understand the terms “less than or equal to” and “greater than or equal to,” and the

symbols ≤ and ≥.Required Materials

13.1: Greater Than One (5 minutes)Setup:

Students in groups of 2. Give 2 minutes of quiet work time followed by a 1-minute partner discussion, then a whole-class discussion.Student task statement

The number line shows values of x that make the inequality x>1 true.

1. Select all the values of x from this list that make the inequality x>1 true.

1. 3

2. -3

3. 1

4. 700

5. 1.05

2. Name two more values of x that are solutions to the inequality.Possible responses

1. a, d, e2. Answers vary. Sample response: 4 and 10.Anticipated misconceptions

Some students may think 700 is not a solution to x>1. Tell students that since there is an arrow at the end of the dark line, it includes all values that would fall on that line, even the ones not shown.

13.2: The Roller Coaster (15 minutes)Setup:

5–10 minutes quiet and partner work time followed by whole class discussion.Student task statement

A sign next to a roller coaster at an amusement park says, “You must be at least 60 inches tall to ride.” Noah is happy to know that he is tall enough to ride.

1. Noah is x inches tall. Which of the following can be true: x>60, x=60, or x<60? Explain how you know.

2. Noah’s friend is 2 inches shorter than Noah. Can you tell if Noah’s friend is tall enough to go on the ride? Explain or show your reasoning.

3. List one possible height for Noah that means that his friend is tall enough to go on the ride, and another that means that his friend is too short for the ride.

4. On the number line below, show all the possible heights that Noah’s friend could be.

5. Noah's friend is y inches tall. Use y and any of the symbols ¿, ¿, ¿ to express this height.Possible responses

1. x>60 or x=602. No, we don’t know if Noah’s friend is tall enough to go on the ride.3. Answers vary. Sample response: Noah is 63 inches tall and his friend 61, Noah is 61 inches

tall and his friend 59.4. See lesson plan for the number line.5. y>58 or y=58Anticipated misconceptions

If students are having trouble interpreting the first three questions or articulating their responses, encourage them to make use of the number line that appears in question 4.

13.3: Is the Inequality True or False? (15 minutes)Setup:

Groups of 2. 5–10 minutes work time followed by whole class discussion.Student task statement

The table shows four inequalities and four possible values for x. Decide whether each value makes each inequality true, and complete the table with “true” or “false.” Discuss your thinking with your partner. If you disagree, work to reach an agreement.

x 0 100 -100 25x≤25100<4 x

−3 x>−7510≥35−x

Possible responses

See lesson plan for the table.


Students who try to apply what they know about solving equations to solve the inequalities algebraically may come up with incorrect solutions. For instance, 100<4 x may at first glance

look equivalent to x<25, since the “less than” sign appears. Students may incorrectly think that −3 x>−75 is equivalent to x>25. Ask these students, for example, what the solution to 100=4 x means (25 is the value of x that makes 4 x equal to 100). Then encourage these students to test values like 24 and 26 to see whether they are solutions to 100<4 x. This will be covered in greater detail in a later lesson, so this understanding does not need to be solidified at this time.

Are you ready for more?

Find an example of in inequality used in the real world and describe it using a number line.

Possible Responses

Answers vary.

Lesson Synthesis (5 minutes)Ask students to write an equality to which -5 is a solution, then trade with their partner to see if their partner agrees.

13.4: Some Values, All Values (Cool-down, 5 minutes)Setup:

None.Student task statement

Here is an inequality: −2 x>10.

1. List some values for x that would make this inequality true.2. How are the solutions to the inequality −2 x≥10 different from the solutions to −2 x>10?

Explain your reasoning.Possible responses

1. Any number less than -5 is a solution.2. -5 is a solution to −2 x≥10, but it's not a solution to −2 x>10Anticipated misconceptions

Students may divide both sides of the inequality by -2 to arrive at the incorrect solution x>−5.

Wednesday 1/23: Unit 6, Lesson 14: Finding Solutions to Inequalities in ContextLesson Goals• Encounter situations in which an expression evaluating to less than a certain amount

requires a variable in the expression be greater than a certain amount (and vice versa). (For example, if we want −2 x to be less than 10, x must be greater than -5.)

• Notice that if an inequality uses <, sometimes its solution uses < but sometimes its solution uses > (and vice versa). Use reasoning about a context or by substitution to decide which symbol the solution uses.

• Solve real-world and mathematical problems leading to inequalities of the form px+q>r or px+q<r .

Required Materials

14.1: Solutions to Equations and Solutions to Inequalities (10 minutes)Setup:

5 minutes of quiet work time followed by whole-class discussion.Student task statement1. Solve −x=10

2. Find 2 solutions to −x>10

3. Solve 2 x=−20

4. Find 2 solutions to 2 x>−20

Possible responses

1. -102. Answers vary. Possible responses: -12, -28.7, -209. (Any value that is less than -10 works.)3. -10

4. Answers vary. Possible responses: -9, 0, 8234 . (Any value that is greater than -10 works.)

14.2: Earning Money for Soccer Stuff (15 minutes)Setup:

Students in groups of 2. 10 minutes quiet work time and partner discussion followed by whole class discussion.Student task statement1. Andre has a summer job selling magazine subscriptions. He earns $25 per week plus $3 for every

subscription he sells. Andre hopes to make at least enough money this week to buy a new pair of soccer cleats.

1. Let n represent the number of magazine subscriptions Andre sells this week. Write an expression for the amount of money he makes this week.

2. The least expensive pair of cleats Andre wants costs $68. Write and solve an equation to find out how many magazine subscriptions Andre needs to sell to buy the cleats.

3. If Andre sold 16 magazine subscriptions this week, would he reach his goal? Explain your reasoning.

4. What are some other numbers of magazine subscriptions Andre could have sold and still reached his goal?

5. Write an inequality expressing that Andre wants to make at least $68.6. Write an inequality to describe the number of subscriptions Andre must sell to reach his

goal.

2. Diego has budgeted $35 from his summer job earnings to buy shorts and socks for soccer. He needs 5 pairs of socks and a pair of shorts. The socks cost different amounts in different stores. The shorts he wants cost $19.95.

1. Let x represent the price of one pair of socks. Write an expression for the total cost of the socks and shorts.

2. Write and solve an equation that says that Diego spent exactly $35 on the socks and shorts.

3. List some other possible prices for the socks that would still allow Diego to stay within his budget.

4. Write an inequality to represent the amount Diego can spend on a single pair of socks.

Possible responses

1. 3m+25

2. 3m+25=68, m=14 13

3. Yes. 16>1413 . He has made $73, which is more than enough to buy the cleats.

4. Answers vary. Sample responses: 15, 17, 100.5. 3n+25≥68

6. n≥14 13

1. 5 x+19.95.2. 5 x+19.95=35, x=3.01. In this situation, Diego paid $3.01 for each pair of socks.3. Answers will vary. Any price under $3.01 is an acceptable response.4. x≤3.01.

14.3: Granola Bars and Savings (15 minutes)Setup:

Students in groups of 2. 5-10 minutes quiet work time and partner discussion followed by whole class discussion.Student task statement

1. Kiran has $100 saved in a bank account. (The account doesn’t earn interest.) He asked Clare to help him figure out how much he could take out each month if he needs to have at least $25 in the account a year from now.

1. Clare wrote the inequality −12 x+100≥25, where x represents the amount Kiran takes out each month. What does −12 x represent?

2. Find some values of x that would work for Kiran.3. We could express all the values that would work using either x≤¿∨x ≥¿. Which one should

we use?

4. Write the answer to Kiran’s question using mathematical notation.2. A teacher wants to buy 9 boxes of granola bars for a school trip. Each box usually costs $7, but

many grocery stores are having a sale on granola bars this week. Different stores are selling boxes of granola bars at different discounts.

1. If x represents the dollar amount of the discount, then the amount the teacher will pay can be expressed as 9(7−x ). In this expression, what does the quantity 7−x represent?

2. The teacher has $36 to spend on the granola bars. The equation 9(7−x )=36 represents a situation where she spends all $36. Solve this equation.

3. What does the solution mean in this situation?4. The teacher does not have to spend all $36. Write an inequality relating 36 and

9(7−x ) representing this situation.5. The solution to this inequality must either look like x≥3∨x≤3. Which do you think

it is? Explain your reasoning.Possible responses

1. The difference in Kiran's account balance after one year.2. Answers vary. Any value less than or equal to 6.25 will work.3. x≤ __. Kiran must draw less than a certain amount each month in order to end up

with $25 in the account at the end of the year.4. x≤6.25.

1. The price of 1 box after the discount.2. x=3. 3. If the discount is $3, then the teacher will pay exactly $36 for the granola bars.4. 9(7−x )≤36 or 36≥9(7−x).5. x≥3, a discount higher than $3 per box will mean a lower price.


Jada and Diego baked a large batch of cookies.

• They selected 14 of the cookies to give to their teachers.

• Next, they threw away one burnt cookie.

• They delivered 25 of the remaining cookies to a local nursing home.

• Next, they gave 3 cookies to some neighborhood kids.

• They wrapped up 23 of the remaining cookies to save for their friends.

After all this, they had 15 cookies left. How many cookies did they bake?

Possible Responses

108 cookies. Possible strategy: Draw a diagram to represent the situation:

Next, work backwards:

15 ⋅3=45, 45+3=48

48÷3=16, 16 ⋅5=80, 80+1=81

81÷3=27, 27 ⋅ 4=108

An equation that represents the number of cookies remaining would be 13( 35( 34x−1)−3)=15.

To solve this equation, we would multiply by 3, add 3, multiply by 53 , add 1, and then multiply

by 43 . Compare these steps to the steps we took to solve with the diagram to see they are the

same (note that divide by 3, then multiply by 5 is the same as multiply by 53 ).

Lesson Synthesis (5 minutes)Draw the number line showing solutions to x>1 on the board. Ask students to name some values of x that satisfy the inequality. For each of those values of x, plot the value of −x on the number line together (perhaps in a different color). What inequality did we just graph?

14.4: Colder and colder (Cool-down, 5 minutes)Setup:

None.Student task statement

It is currently 0 degrees outside, and the temperature is dropping 4 degrees every hour. The temperature after h hours is −4h.

1. Explain what the equation −4h=−14 represents.2. What value of h makes the equation true?3. Explain what the inequality −4h≤−14 represents.4. What values of h make the inequality true?Possible responses

1. After h hours, the temperature has dropped to -14 degrees.2. h=3.5.3. After h hours, the temperature is less than or equal to -14 degrees.4. h≥3.5.

Thursday 1/24: Unit 6, Lesson 15: Efficiently Solving Inequalities

Lesson Goals• Encounter situations in which an expression evaluating to less than a certain amount

requires a variable in the expression be greater than a certain amount (and vice versa). (For example, if we want −2 x to be less than 10, x must be greater than -5.)

• Compare equations and inequalities in terms of solution strategies and number of solutions.

• Notice that if an inequality uses <, sometimes its solution uses < but sometimes its solution uses > (and vice versa). Use reasoning about a context or by substitution to decide which symbol the solution uses.

• Solve real-world and mathematical problems leading to inequalities of the form px+q>r or px+q<r .

Required Materials

15.1: Lots of Negatives (5 minutes)

Setup:3 minutes quiet work time followed by whole-class discussion.


Here is an inequality: −x≥−4 .

1. Predict what you think the solutions on the number line will look like.2. Select all the values that are solutions to −x≥−4:

1. 32. -33. 44. -45. 4.0016. -4.001

3. Graph the solutions to the inequality on the number line:

Possible responses1. Answers vary.2. a, b, c, d, f3. A filled-in circle at 4 and all points to its left are graphed. The same graph that one

would draw for x≤4 .

15.2: Inequalities with Tables (15 minutes)

Setup:5–10 minutes of quiet work time followed by a whole-class discussion. See lesson plan for additional instructions.

Student task statement1. Let's investigate the inequality x−3>−2.

x -4 -3

-2 -1 0 1 2 3 4

x−3 -7 -5 -1

1

1. Complete the table.2. For which values of x is it true that x−3=−2?3. For which values of x is it true that x−3>−2?

4. Graph the solutions to x−3>−2 on the number line:

2. Here is an inequality: 2 x<6.

1. Predict which values of x will make the inequality 2 x<6 true.2. Complete the table. Does it match your prediction?

x

-

-

-

-

0

1

2

3

4

2 x

3. Graph the solutions to 2 x<6 on the number line:

3. Here is an inequality: −2 x<6.

1. Predict which values of x will make the inequality −2 x<6 true.2. Complete the table. Does it match your prediction?

x

-

-

-

-

0

1

2

3

4

−2 x

3. Graph the solutions to −2 x<6 on the number line:

4. How are the solutions to 2 x<6 different from the solutions to −2 x<6?

Possible responses

See lesson plan for tables.


Some students may answer x>2 for the first question, since that is the place where the value of x−3 first surpasses the number -2. Remind these students that there are values between 1 and 2. Ask them whether 1.1 is a solution, for example.

Some students may graph only whole-number solutions. Ask these students to think about whether values in between whole numbers are also solutions.

15.3: Which Side are the Solutions? (15 minutes)

Setup:Groups of 2. 5–10 minutes of quiet work time, then time to share their responses and reasoning with a partner followed by whole-class discussion.

Student task statement1. Let’s investigate −4 x+5≥25.

1. Solve −4 x+5=25.2. Is −4 x+5≥25 true when x is 0? What about when x is 7? What about when x is

-7?3. Graph the solutions to −4 x+5≥25 on the number line.

2. Let's investigate 43x+3<23

3 .

1. Solve 43x+3=23

3 .

2. Is 43x+3<23

3 true when x is 0?

3. Graph the solutions to 43x+3<23

3 on the number line.

3. Solve the inequality 3(x+4)>17.4 and graph the solutions on the number line.

4. Solve the inequality −3(x−43 )≤6 and graph the solutions on the number line.

Possible responses1. For −4 x≥25:

1. -52. no, no, yes3. a closed circle at -5 and all values to the left shaded

2. For 43x+3<23

3 :

1.72 or equivalent

2. yes

3. an open circle at 72 and all values to the left shaded.

3. The solution is x>1.8. An open circle at 1.8 and all values to the right shaded.

4. The solution is x≥−23 . A closed circle at

−23 and all values to the right shaded.


Write at least three different inequalities whose solution is x>−10. Find one with x on the left side that uses a ¿.

Possible Responses

Answers vary. Possible responses: 2 x>−20, x+50>40. Responses that involve x<¿:

−5 x<50, x

−6<60.

Lesson Synthesis (5 minutes)Ask students to consider, “What if someone asked for your help with how to solve inequalities? What would you tell them? How would you describe to someone how to solve any inequality?”

15.4: Testing for Solutions (Cool-down, 5 minutes)

Setup:None.


For each inequality, decide whether the solution is represented by x<2.5 or x>2.5.

1. −4 x+5>−52. −25>−5 (x+2.5)

Possible responses1. x>2.52. x<2.5

Friday 1/25: Unit 6, Lesson 16: Interpreting Inequalities

Lesson Goals• Practice solving inequalities of the form px+q>r and px+q<r .• Write inequalities to represent problems in context.

Required Materials• tools for creating a visual display

16.1: Solve Some Inequalities! (5 minutes)

Setup:None.


For each inequality, find the value or values of x that make it true.

1. 8 x+21≤562. 56<7 (7−x)

Possible responses1. x≤42. x<−1


If students express the solution in words or by graphing on a number line, applaud their use of these representations. Encourage them to attempt to express the solution using the efficient notation, as well. Direct their attention to any anchor charts or notes that remind them of the meaning of the symbols involved.

16.2: Club Activities Matching (10 minutes)

Setup:5–10 minutes of quiet work time.


Choose the inequality that best matches each given situation. Explain your reasoning.

1. The Garden Club is planting fruit trees in their school’s garden. There is one large tree

that needs 5 pounds of fertilizer. The rest are newly planted trees that need 12 pound

fertilizer each.

1. 25 x+5≤ 12

2.12x+5≤25

3.12x+25≤5

4. 5 x+ 12≤25

2. The Chemistry Club is experimenting with different mixtures of water with a certain chemical (sodium polyacrylate) to make fake snow.

To make each mixture, the students start with some amount of water, and then add 17

of that amount of the chemical, and then 9 more grams of the chemical. The chemical is expensive, so there can’t be more than a certain number of grams of the chemical in any one mixture.

1.17x+9≤26.25

2. 9 x+ 17≤26.25

3. 26.25 x+9≤ 17

4.17x+26.25≤9

3. The Hiking Club is on a hike down a cliff. They begin at an elevation of 12 feet and descend at the rate of 3 feet per minute.

1. 37 x−3≥122. 3 x−37≥123. 12−3 x ≥−374. 12 x−37≥−3

4. The Science Club is researching boiling points. They learn that at high altitudes, water boils at lower temperatures. At sea level, water boils at 212∘F . With each increase of 500 feet in elevation, the boiling point of water is lowered by about 1∘F .

1. 212− 1500

e<195

2.1500

e−195<212

3. 195−212e< 1500

4. 212−195 e< 1500

Possible responses

b, a, c, a

16.3: Club Activities Display (20 minutes)

Setup:Students in groups of 2–3. Assign one situation to each group. Provide tools for making a visual display.


Your teacher will assign your group one of the situations from the last task. Create a visual display about your situation. In your display:

• Explain what the variable and each part of the inequality represent• Write a question that can be answered by the solution to the inequality• Show how you solved the inequality• Explain what the solution means in terms of the situation

Possible responses

See lesson plan for explanations.

1. x≤402. x≤120.75

3. x≤16 13

4. e>8500


{3,4,5,6 } is a set of four consecutive integers whose sum is 18.

1. How many sets of three consecutive integers are there whose sum is between 51 and 60? Can you be sure you’ve found them all? Explain or show your reasoning.

2. How many sets of four consecutive integers are there whose sum is between 59 and 82? Can you be sure you’ve found them all? Explain or show your reasoning.

Possible Responses

Both of these problems can be solved by intelligent guess-and-check, or other more conceptual strategies, and by using the first answer one finds to generate the others. If students use these strategies, help them to crystalize their reasoning: how do they know they have all of the sets? Also encourage students to see if they can write inequalities in addition (not instead of!) whatever strategies they use.

1. 4 sets: {16,17,18 },{17,18,19 }, {18,19,20 }, {19,20,21 }x+(x+1)+(x+2)≥51 and x+(x+1)+(x+2)≤60, 16≤ x≤19.

2. 5 sets: {14,15,16,17 }, {15,16,17,18 }, {16,17,18,19 }, {17,18,19,20 },{18,19,20,21 }.x+(x+1)+(x+2)+(x+3)≥59 and x+(x+1)+(x+2)+(x+3)≤82, 13.25≤x ≤18.5.

Lesson Synthesis (5 minutes)Think about an after school activity in which you are involved. Write an inequality that represents a situation related to that activity. Be prepared to share the inequality and an explanation of its terms with the class.

16.4: Party Decorations (Cool-down, 5 minutes)

Setup:None.


Andre is making paper cranes to decorate for a party. He plans to make one large paper crane for a centerpiece and several smaller paper cranes to put around the table. It takes Andre 10 minutes to make the centerpiece and 3 minutes to make each small crane. He will only have 30 minutes to make the paper cranes once he gets home.

1. Andre wrote the inequality 3 x+10≤30 to plan his time. Describe what x, 3 x, 10, and 30 represent in this inequality.

2. Solve Andre’s inequality and explain what the solution means.

Possible responses1. The variable x represents the number of small paper cranes Andre will make. 10 is the

number of minutes it takes to make the centerpiece. 3 x is the amount of time it takes to make x small cranes (it takes 3 minutes to make one crane). 30 is Andre’s time limit in minutes.

2. x≤6 23 . Andre can make 6 or fewer small cranes.

monday 1/21: unit 6, lesson 12: solving problems about ...€¦ · web viewthe chemistry club is...

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