Tickets Notes
18. and 19
These problems assess students’ ability to develop an understanding of equation and variable; to organize information from problem situations using combination charts, notebook notation, and equations; to recognize similarities in solution strategies; and to informally solve problems that involve systems of equations.
Problem 18 also assesses students’ ability to recognize the advantages and disadvantages of various solution strategies and to choose the strategies appropriate for the problem situation.
Solutions and Samples
18. $37. Strategies will vary. Sample strategy:
A price of an adult’s ticket C price of a child’s ticket 2A 2C $20
1A 3C $17
So adding these equations:
3A 5C $37
19. One adult’s ticket costs $6.50; one child’s ticket costs $3.50. Strategies will vary. Sample strategies:
• Some students may use notebook notation as shown below.
• Some students may use a combination chart as shown below.
• Some students may use logical reasoning.
From picture 1, one adult and one child pay $10.
Using this information in picture 2, two children pay $7. So one child pays $7 2, or $3.50, and one adult pays $10.00 $3.50, or $6.50.
Adults Child Price
2 $34.00
— $14.00
— $3.50
— $7.00
2 1
6 4 1 2
2 — $13.00
1 — $6.50
2
3 $17.00
$20.00
2 row 2 row 3 row 1 row 4 4 row 5 2 row 1 row 6 row 7 2
0 1 2 3 4
14 17
20 23
26 0
1 2 3 4
3.50 6.50
Number of Adults Costs of Admissions
(in dollars)
Number of Children
Equations
E E Equations
Many problems compare quantities such as prices, weights, and widths.
One way to describe these problems is by using equations.
For example, study the picture of the umbrellas and cap.
If you let U represent the price of one umbrella and C represent the price of one cap, the equation is 2U 1C $80.
These problems can also be solved with combination charts if there are only two different items. When there are more than two items, you can use notebook notation to find the solution.
1. At a flower shop Joel paid $10 for three irises and four daisies.
Althea paid $9 for two irises and five daisies.
a. Write equations representing this information.
b. Write an equation to show the price of one iris and six daisies.
c. Find the cost of one iris and the cost of one daisy.
0 1 2 3 4 5
0 1 2 3 4 5
Number of Erasers Price of Combinations
Number of Pencils
Notebook Notation
TACO
ORDER SALAD DRINK TOTAL
$ 80.00
Notes
Have students give examples of problems in the section where they found the combination chart most useful and problems where they found the notebook notation most useful. Ask them to explain why they think this.
Reaching All Learners
Parent Involvement
Have parents review the section with their child to relate the Check Your Work problems to the problems in the section.
Assessment Pyramid
1c
1ab
Assesses Section E Goals
32 Comparing Quantities
Section E: Equations 32T
Hints and Comments
Overview
This page summarizes the use of equations,
combination charts, and notebook notation to solve problems that involve comparing quantities. Students read the Summary and start with the Check Your Work problems. Students use these Check Your Work problems as self-assessment. The answers to these problems are also provided in the Student Book.
About the Mathematics
Although the unit ends with an introduction to equations, students are not expected to have mastered equations yet. In later units in the
Mathematics in Context Algebra strand, students learn to use equations in more formal ways. If students seem ready, you may wish to call the letters unknowns or variables.
Planning
After students have read the Summary, you may want to discuss the mathematical concepts of this unit.
Students should perceive that notebook notation and formal equations have certain advantages over combination charts or pictures.
Solutions and Samples
Answers to Check your Work
1. a. 3I 4D $10 2I 5D $9 b. 1I 6D $8
c. An iris costs $2, and a daisy costs $1. You may have different explanations.
You may continue the pattern by removing one iris and adding one daisy, and then the total cost goes down by one dollar.
So 7D $7. One daisy costs $1.
Now, 1I 6($1) $8, so one iris costs $2.
Equations E
2. At a movie theater, tickets for three adults, two seniors, and two children cost $35. Tickets for one senior and two children cost
$12.50. Tickets for one adult, one senior, and two children cost $18.50.
a. Write three equations representing the ticket information. Use A to represent the price of an adult’s ticket, S to represent the price of a senior’s ticket, and C to represent the price of a child’s ticket.
b. Write two additional equations by combining your first three equations.
c. Explain how you can combine equations to get the equation 2A 1S $16.50.
d. Explain how you can combine equations to get the equation A $6.
e. What is the cost of each ticket?
3. In the following equations, the numbers 96 and 27 can represent lengths, weights, prices, or whatever you wish.
4L 3M 96 L M 27
a. Write a story to fit these equations.
b. Find the value of L and the value of M.
4. In the following equations, find the value of C and the value of K.
Imagining a story to fit the equations may help you solve for the values.
5C 4K 50 4C 5K 58
Refer back to Quinn's Quantities on page 19. Write an equation that represents the price of the two mixtures. Tell which is easier for you to use, the problem posed in words or represented by equations and explain why.
Reaching All Learners
Accommodation
Provide copies of Student Activity Sheet 5.
Assessment Pyramid
FFR 2e, 3b, 4
2abcd, 3a Assesses Section E Goals
33 Comparing Quantities
Notes
2Point out that if students answer the question in order using notebook notation, the questions guide them to find out the cost of each ticket.
For Further Reflection Reflective questions are meant to summarize and discuss important concepts.
Section E: Equations 33T
• Equations: