Functions with Multiple Parts

These materials, when encountered before Algebra 1, Unit 4, Lesson 12 support success in that lesson.

12.1: Notice and Wonder: Ticket Price (10 minutes)

Routines and Materials

Instructional Routines

  • Notice and Wonder

The purpose of this warm-up is to elicit the idea that boundary conditions on intervals are important, which will be useful when students write domain intervals for piecewise functions in a later activity. While students may notice and wonder many things about this table, the price of a ticket for people on the boundary between 2 intervals are the important discussion points.

Display the table for all to see. Ask students to think of at least one thing they notice and at least one thing they wonder. Give students 1 minute of quiet think time and then 1 minute to discuss the things they notice and wonder with their partner followed by a whole-class discussion.

Student Facing

What do you notice? What do you wonder?

Student Response

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Activity Synthesis

Ask students to share the things they noticed and wondered. Record and display their responses for all to see. If possible, record the relevant reasoning on or near the table. After all responses have been recorded without commentary or editing, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to respectfully disagree, ask for clarification, or point out contradicting information.

If the cost of a ticket for people whose ages are on the boundary of the age ranges does not come up during the conversation, ask students to discuss this idea.

12.2: Group Ticket Cost (15 minutes)

CCSS Standards

Building Towards

  • HSF-IF.C.7.b

In this activity, students use a step function to determine the price of tickets for groups composed of people in different age groups. In the associated Algebra 1 lesson, students examine piecewise functions and their graphs. Although this activity does not mention piecewise functions, understanding how to compute the ticket price for the group will help students think about this kind of function.

A community orchestra charges different amounts for tickets to shows based on the age of the person attending. A sign in front of the box office where tickets are sold shows the prices.

  • 2 adults aged 40 and 36, and 2 kids aged 4 and 1
  • 3 adults aged 74, 37, and 36
  • 5 adults in their 30s and 25 students aged 15 and 16
  • 1 adult aged 25 and 4 kids aged 1, 9, 13, and 16
  • A mother arrives and tells the box office clerk that her child is 35 months old. How much should the clerk charge for the child?
  • What is the domain for the rule?
  • What is the range for the rule?

The purpose of the discussion is to get students thinking about functions for which there are different rules for different domains. Select students to share their solutions. Ask students,

  • “Is there an equation for the function that connects the input and output?” (There is not a single, nice equation that works for all the ages.)
  • “Are there people for whom the price of a ticket would be confusing or unknown?” (No. The convention for ages is that if someone is turning 14 tomorrow, they will still be charged the $ 4 price since they are still currently 13. So, everyone should fit into one of the categories listed.)
  • “If we graphed the information in the table, can you visualize what that graph would look like?” (There would be horizontal lines for each range of ages to look a little like steps.)

12.3: A Light Trip (15 minutes)

In this activity students analyze graphs representing situations to select the intervals within the domain in which certain events are happening. In the associated Algebra 1 lesson students examine piecewise functions and use the function notation that includes domain restrictions. Students are supported by examining scenarios and noting what is happening on different parts of the domain.

Noah leaves his home, sometimes running, sometimes walking, sometimes stopping until he remembers that he doesn’t have his wallet, then he goes back home. A graph representing his journey is shown in the graph.

Expand image

Description: <p>Graph on coordinate grid, origin O. Horizontal axis, 0 to 400, by 40s, time, seconds. Vertical axis, 0 to 300, by 30s, distance from home, meters. Line starts at origin and passes through points, 20 comma 45, 60 comma 45, 120 comma 135, 180 comma 285, 210 comma 285, 400 comma 0.</p>

  • Describe what is happening on the domain \(210 < x < 400\) .
  • What are the domain intervals that represent the times when Noah was running?
  • What are the domain intervals that represent the times when Noah was stopped?
  • What are the domain intervals that represent the times when Noah was walking away from home?

Description: <p>Coordinate plane, time after midnight in hours, 0 to 24 by 2, light level in room by lux, 0 to 1,100 by 100. From 0 to 4, y = 0 until slight upturn just before 4. From 4 to 5 point 5, horizontal line at y = 200. Function jumps to 260 and increases rapidly toward 8 comma 1,000 and then levels out until 16 comma 1,000 where it drops rapidly toward 19 comma 170. From x = 19 to 23, y = 200.</p>

The purpose of the discussion is to recognize that using the domain is important when describing graphs of situations where different things may be happening. Select students to share their solutions. If students describe the domain for the light levels in words (like “between 9am and 4pm”), ask students how they might write that as an inequality.

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CCSS Math Answers

Eureka Math Grade 5 Module 4 Lesson 12 Answer Key

Engage ny eureka math 5th grade module 4 lesson 12 answer key, eureka math grade 5 module 4 lesson 12 problem set answer key.

Question 1. A baseball team played 32 games and lost 8. Katy was the catcher in \(\frac{5}{8}\) of the winning games and \(\frac{1}{4}\) of the losing games. a. What fraction of the games did the team win?

b. In how many games did Katy play catcher?

Question 2. In Mrs. Elliott’s garden, \(\frac{1}{8}\) of the flowers are red, \(\frac{1}{4}\) of them are purple, and \(\frac{1}{5}\) of the remaining flowers are pink. If there are 128 flowers, how many flowers are pink?

Question 3. Lillian and Darlene plan to get their homework finished within one hour. Darlene completes her math homework in \(\frac{3}{5}\) hour. Lillian completes her math homework with \(\frac{5}{6}\) hour remaining. Who completes her homework faster, and by how many minutes?

Bonus: Give the answer as a fraction of an hour.

Question 4. Create and solve a story problem about a baker and some flour whose solution is given by the expression \(\frac{1}{4}\) × (3 + 5).

Eureka Math Grade 5 Module 4 Lesson 12 Problem Set Answer Key 1

Question 6. Of the students in Mr. Smith’s fifth-grade class, \(\frac{1}{3}\) were absent on Monday. Of the students in Mrs. Jacobs’ class, \(\frac{2}{5}\) were absent on Monday. If there were 4 students absent in each class on Monday, how many students are in each class?

Eureka Math Grade 5 Module 4 Lesson 12 Exit Ticket Answer Key

In a classroom, \(\frac{1}{6}\) of the students are wearing blue shirts, and \(\frac{2}{3}\) are wearing white shirts. There are 36 students in the class. How many students are wearing a shirt other than blue or white?

Eureka Math Grade 5 Module 4 Lesson 12 Homework Answer Key

Question 1. Terrence finished a word search in \(\frac{3}{4}\) the time it took Frank. Charlotte finished the word search in \(\frac{2}{3}\) the time it took Terrence. Frank finished the word search in 32 minutes. How long did it take Charlotte to finish the word search?

Question 2. Ms. Phillips ordered 56 pizzas for a school fundraiser. Of the pizzas ordered, \(\frac{2}{7}\) of them were pepperoni, 19 were cheese, and the rest were veggie pizzas. What fraction of the pizzas was veggie?

Question 3. In an auditorium, \(\frac{1}{6}\) of the students are fifth graders, \(\frac{1}{3}\) are fourth graders, and \(\frac{1}{4}\) of the remaining students are second graders. If there are 96 students in the auditorium, how many second graders are there?

Question 4. At a track meet, Jacob and Daniel compete in the 220 m hurdles. Daniel finishes in \(\frac{3}{4}\) of a minute. Jacob finishes with \(\frac{5}{12}\) of a minute remaining. Who ran the race in the faster time?

Bonus: Express the difference in their times as a fraction of a minute.

Eureka Math 5th Grade Module 4 Lesson 12 Homework Answer Key 50

Question 6. Create and solve a story problem about two friends and their weekly allowance whose solution is given by the expression \(\frac{1}{5}\) × (12 + 8).

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