Algebra 1 Topic 1 Quantities and Modeling Table

Algebra 1 Topic 1: Quantities and Modeling

Table of Contents • • Recommended Instructional Design and Planning Continuum …………. . Slide 3 Vocabulary …………………………………. Slides 4 – 24 Pre-Requisite Practice Items ………………………………. . Slides 25 – 52 Reporting Category Practice Items …………………. . Slides 53 – 95

RECOMMENDED INSTRUCTIONAL DESIGN AND PLANNING CONTINUUM Before Prior to the lesson: Outline content standard(s). Determine learning targets. Anticipate student understanding and misconceptions. Determine prerequisite skills. Plan for learning experiences that target Rigor o Conceptual Understanding o Procedural Fluency o Application Determine the task students will demonstrate to reach the desired learning targets. Plan instructional delivery methods that will maximize initial engagement and sustain it throughout the lesson. Decide how students will reflect upon, selfassess, and set goals for their future learning. During the lesson: Activate (or supply) prior knowledge and/or spiral back o Warm ups, Bell Ringers, Openers, etc. Tailor lesson experiences to the different needs and ability of the learners. Clarify vocabulary and mathematical notation. Incorporate a variety of higher order questions to encourage and increase critical thinking skills. Continuously check for student understanding and provide feedback. Provide opportunities for students to develop self-assessment and to reflect about their understanding and work. Bring closure to the lesson so that the students can articulate what they have learned. After the lesson: Analyze evidence of student learning to develop intervention, enrichment, and future instruction. Discuss results of assessments with students. Engage students in reflective processes and goal setting. Engage in self-reflection to adapt/modify teaching strategies to improve instruction.

Vocabulary

Mathematically Speaking! Choose 3 -4 vocabulary words for the day. Throughout the lesson, as students respond to your questions or are presenting a problem on the board, mark a tally when a vocabulary word is used accurately. This can be turned into a competition among groups or between periods. Examples of accuracy • translation vs slide • variable vs letter • addition property of equality vs adding on both sides

Addition Property of Equality • •

Subtraction Property of Equality • •

Multiplication Property of Equality • •

Division Property of Equality • •

Constant Term A term in a function or expression that does not contain variables.

Coefficient A number multiplied by a variable.

Like Terms with the same variables raised to the same exponents.

Equation A mathematical sentence that shows that two expressions are equivalent.

Algebraic Expression An expression that contains at least one variable. •

Numerical Expression An expression that contains only numbers and operations. •

Solution to an Equation • A value that makes the equation true.

Additive Inverse Property • •

Multiplicative Inverse Property • •

Formula A literal equation that states a rule for a relationship among quantities. •

Inequality An algebraic sentence comparing two quantities.

Addition/Subtraction Property of Inequality •

Multiplication Property of Inequality If both sides of an inequality are multiplied by the same positive quantity, the new inequality will have the same solution set. If both sides of an inequality are multiplied by the same negative quantity, the new inequality will reverse the inequality of the solution set.

Division Property of Inequality If both sides of an inequality are divided by the same positive quantity, the new inequality will have the same solution set. If both sides of an inequality are divided by the same negative quantity, the new inequality will reverse the inequality of the solution set.

Compound Inequality Two inequalities that are combined into one statement by the word and or or.

Pre-Requisite Practice Items

Pre-Requisites MAFS. 6. EE. 1. 2 Parts of Expressions

Pre-Requisites MAFS. 6. EE. 1. 2 Substitution Resolution

Pre-Requisites MAFS. 6. EE. 1. 2 Writing Expressions

Pre-Requisites MAFS. 6. EE. 1. 2 Rectangle Perimeter 1

Pre-Requisites MAFS. 7. EE. 1. 2 Explain Equivalent Expressions Andrew sells treats from his ice cream cart. The items he sells along with their prices are shown in the table. Item Frosty Mango Pop Frozen Fruit Yogurt Sundae Swirl Cup Chocolate Chip Cone Fudge Sandwich Price $1. 75 $2. 25 $2. 75 $2. 25 $1. 75 Quantity a b a c b

Pre-Requisites MAFS. 7. EE. 1. 2 Rectangle Expressions

Pre-Requisites MAFS. 7. EE. 1. 2 Ticket to Ride Malia is at an amusement park. She bought 14 tickets, and each ride requires 2 tickets.

Pre-Requisites MAFS. 7. EE. 2. 4 Algebra or Arithmetic? Stephanie bought a 3 D printer for $1249. 99 and some cartridges for $79. 95 each. She paid a total of $1809. 64. Haley and Luis calculated the number of cartridges Stephanie bought in two different ways. Luis’s Method: 1809. 64 - 1249. 99 = 559. 65 ÷ 79. 95 = 7 Stephanie bought 7 cartridges. Haley’s Method: Let x equal the number of cartridges that Stephanie bought 7 cartridges. 1. Luis used arithmetic to solve the problem. Identify in order the operations (add, subtract, multiply, or divide) he used. 2. Haley used algebra to solve the problem. Identify in order the operations she used. 3. Compare the sequence of operations used by Luis and Haley. What is the same or different? 4. In Haley’s method, what is the significance of 79. 95 x in terms of the story context? How is this represented in Luis’s method?

Pre-Requisites MAFS. 7. EE. 2. 4 Gift Card Inequality

Pre-Requisites MAFS. 7. EE. 2. 4 Recycled Inequalities A scrapyard had 200 tons of recycled steel. They sold 15 tons per day for several days. If there are fewer than 80 tons left at the scrapyard, how many days have passed? 1. Write and solve an inequality to answer the question. 2. What does the solution of your inequality mean in terms of the answer to the question?

Pre-Requisites MAFS. 7. EE. 2. 4 Solve Equations

Pre-Requisites MAFS. 7. EE. 2. 4 Squares

Pre-Requisites MAFS. 7. EE. 2. 4 Write and Solve an Equation The signup fee to join the Flexible Fitness gym is $25. The monthly fee is $30. Elijah has paid $115 so far. Write and solve an equation to determine the number of months for which Elijah has paid. Show all work.

Pre-Requisites MAFS. 7. EE. 2. 4 Write, Solve and Graph an Inequality When carbon dioxide is frozen, it is called dry ice. In order to keep the carbon dioxide frozen, the temperature has to be -109. 3° Fahrenheit or lower. Fahrenheit is 9/5 of the Celsius temperature plus 32 degrees. 1. Write an inequality to determine the Celsius temperatures at which dry ice can be kept. 2. Solve your inequality. 3. Scale the number line below and graph the solution to the inequality.

Pre-Requisites MAFS. 7. EE. 2. 4 Fishing Adventures 2 Fishing Adventures rents small fishing boats to tourists for day-long fishing trips. Each boat can only carry 1200 pounds of people and gear for safety reasons. Assume the average weight of a person is 150 pounds. Each group will require 200 lbs. of gear for the boat plus 10 lbs. of gear for each person. a. Create an inequality describing the restrictions on the number of people possible in a rented boat. Graph the solution set. b. Several groups of people wish to rent a boat. Group 1 has 4 people. Group 2 has 5 people. Group 3 has 8 people. Which of the groups, if any, can safely rent a boat? What is the maximum number of people that may rent a boat?

Pre-Requisites MAFS. 7. EE. 2. 4 Gotham City Taxis

Pre-Requisites MAFS. 7. EE. 2. 4 Sports Equipment Set Jonathan wants to save up enough money so that he can buy a new sports equipment set that includes a football, baseball, soccer ball, and basketball. This complete boxed set costs $50. Jonathan has $15 he saved from his birthday. In order to make more money, he plans to wash neighbors’ windows. He plans to charge $3 for each window he washes, and any extra money he makes beyond $50 he can use to buy the additional accessories that go with the sports box set. Write and solve an inequality that represents the number of windows Jonathan can wash in order to save at least the minimum amount he needs to buy the boxed set. Graph the solutions on the number line. What is a realistic number of windows for Jonathan to wash? How would that be reflected in the graph?

Pre-Requisites MAFS. 7. EE. 2. 4 Bookstore Account At the beginning of the month, Evan had $24 in his account at the school bookstore. Use a variable to represent the unknown quantity in each transaction below and write an equation to represent it. Then represent each transaction on a number line. What is the unknown quantity in each case? a. i. First he bought some notebooks and pens that cost $16. ii. Then he deposited some more money and his account balance was $28. iii. Then he bought a book for English class that cost $34. iv. Then he deposited exactly enough money so that he paid off his debt to the bookstore. Explain why it makes sense to use a negative number to represent Evan's account balance when he owes money.

Pre-Requisites MAFS. 7. EE. 2. 4 Drill Rig A water well drilling rig has dug to a height of – 60 feet after one full day of continuous use. a. Assuming the rig drilled at a constant rate, what was the height of the drill after 15 hours? b. If the rig has been running constantly and is currently at a height of – 143. 6 feet, for how long has the rig been running?

Pre-Requisites MAFS. 8. EE. 3. 7 Counting Solutions

Pre-Requisites MAFS. 8. EE. 3. 7 Equation Prototypes

Pre-Requisites MAFS. 8. EE. 3. 7 Linear Equations - 1

Pre-Requisites MAFS. 8. EE. 3. 7 Linear Equations - 2

Pre-Requisites MAFS. 8. EE. 3. 7 Linear Equations - 3

Pre-Requisites MAFS. 8. EE. 3. 7 The Sign of Solutions

Pre-Requisites MAFS. 8. EE. 3. 7 Coupon versus discount You have a coupon worth $18 off the purchase of a scientific calculator. At the same time the calculator is offered with a discount of 15%, but no further discounts may be applied. For what tag price on the calculator do you pay the same amount for each discount?

Pre-Requisites MAFS. 8. EE. 3. 7 Sammy's Chipmunk and Squirrel Observations For a science project, Sammy observed a chipmunk and a squirrel stashing acorns in holes. The chipmunk hid 3 acorns in each of the holes it dug. The squirrel hid 4 acorns in each of the holes it dug. They each hid the same number of acorns, although the squirrel needed 4 fewer holes. How many acorns did the chipmunk hide? Hint: Solve this problem using tables and then using equations.

Reporting Category Practice Items Topic 1

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-REI. 1. 1 A. associative property of addition B. associative property of multiplication C. distributive property D. commutative property of addition D

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-REI. 1. 1 A. distributive property B. associative property of addition C. associative property of multiplication D. commutative property of multiplication A

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-REI. 1. 1 D

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-REI. 1. 1 A

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-CED. 1. 1

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-CED. 1. 1 Ernesto and his family have just finished dinner at a restaurant in a region where the meal tax is 6% of the price of the meal. Ernesto leaves an 18% tip. With tax and tip, the total cost is $72. 39. + 0. 18�� + �� = 72. 39 a) Write the equation that models this situation. sample: 0. 06�� b) Use your equation to find the price of the meal without tax or tip.

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-CED. 1. 1

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-CED. 1. 1 John has a baseball card collection that is worth $280. 00. He has 64 baseball cards from 1988. Each of the 1988 cards is worth $2. 30. He also has a set of 30 baseball cards from 1983. Each of the 1983 cards are worth the same amount. a) Write an equation to model this situation. Be sure to define your variables. b) What is the value of each baseball card from 1983?

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-CED. 1. 1 100, 000=15, 000(5)+300��. 50, 000=3�� +10, 000(500). The price of a fighter plane is $15 million. 90, 000=20(100, 000�� )+15, 000��. The price of a ton of wheat is approximately $44. 67

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-CED. 1. 1 No, she will run for 4. 5 hours and she needs to run for at least 9 hours and 5. 5 minutes.

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-CED. 1. 1 You have a cell phone plan that allows for unlimited calling and 1000 text messages for $21. 25. Every text message over 1000 text messages will cost $0. 10 per text. Your parents will only pay up to $60 for your phone bill. a) Write an inequality to model this situation. Be sure to define your variable. b) How many text messages could you send each month?

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-CED. 1. 1 Tony makes a phone call at a pay phone. The charge is 25 cents for the first four minutes, and 10 cents for each additional minute. Tony has $2. 10 in change in his pocket. Write an inequality that can be used to find m, the maximum number of minutes that Tony can talk on the phone. Solve this inequality algebraically to find the maximum number of whole minutes he can talk on the phone.

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-CED. 1. 1

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-CED. 1. 1 C

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-CED. 1. 1 A

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-CED. 1. 1 B

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-REI. 2. 3

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-REI. 2. 3 D

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-REI. 2. 3 B

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-REI. 2. 3 A

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-REI. 2. 3 D

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-REI. 2. 3 C

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-REI. 2. 3

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-REI. 2. 3 C

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-CED. 1. 4 Which of the following operations will solve Ohm’s law, �� = �� , for �� ? A. Subtract �� from both sides. B. Divide both sides by ��. C. Subtract �� from both sides. D. Divide both sides by ��. B

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-CED. 1. 4 D

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-CED. 1. 4

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-CED. 1. 4 A

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-CED. 1. 4 C

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-CED. 1. 4

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-SSE. 1. 1 Total number of ink orders over a one-month period. Total number of gallons ordered over a one-month period. Average number of gallons per order over a one-month period.

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-SSE. 1. 1

MAFS. 912. A-SSE. 1. 1 A certain vine grows at a rate of three inches per day. A researcher starts observing it when it is 27 inches long. a) Write an algebraic expression for the length, in feet, of the vine d days after the researcher start observing it. b) Interpret both of the factors in the variable term.

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-SSE. 1. 1 A

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-SSE. 1. 1 D

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-CED. 1. 3 B

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-CED. 1. 3 A

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-CED. 1. 3 B

These items have been compiled and in some instances modified from various internet sources for the sole purpose of classroom use. MAFS. 912. A-CED. 1. 3 D