Bicycle Budget Bicycle Budget Problem Problem 6.EE - Reason about and solve one-variable equations and inequalities 5. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. 6. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. 7. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. 8. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
Bicycle Budget Problem 6.EE - Reason about and solve one- variable equations and inequalities 5. Understand solving an equation or inequality as a process.
Dec 29, 2015
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Bicycle Budget Bicycle Budget ProblemProblem
6.EE - Reason about and solve one-variable equations and inequalities
5. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
6. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
7. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.
8. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
Ana is saving to buy a bicycle that Ana is saving to buy a bicycle that costs $135. She has saved $98 and costs $135. She has saved $98 and wants to know how much more wants to know how much more money she needs to buy the bicyclemoney she needs to buy the bicycle. .
Part APart A
MP6: Attend to MP6: Attend to PrecisionPrecision
135 = x + 135 = x + 98 98
““Ana is saving to buy a bicycle that costs $135. Ana is saving to buy a bicycle that costs $135. She has saved $98 and wants to know how She has saved $98 and wants to know how much more money she needs to buy the much more money she needs to buy the bicyclebicycle..””
1. Explain how the equation below models the following situation:
What does x represent?
What symbols or mathematical notations
are important inthis problem?
How could you test your
solution to see if it answers
the problem?
Task #1:Task #1:
When substituting for x, which value(s), if any, from {0, 37, 98, 135, 233} will make the equation true?
Consider the following situation:
When x = 37
135 = x + 98 135 = x + 98
135 = 135 = 3737 + 98 + 98
135 = 135 135 = 135
When x = 135
135 = x + 98 135 = x + 98
135 = 135 = 135135 + 98 + 98
135 135 236 236
When x = 233
135 = x + 98 135 = x + 98
135 = 135 = 233233 + 98 + 98
135 135 331 331
When x = 98
135 = x + 98 135 = x + 98
135 = 135 = 9898 + 98 + 98
135 135 196 196
True
False False
False
135 = x + 98 135 = x + 98
135 = 135 = 00 + 98 + 98
135 135 98 98
False
When x = 0
Task #2:Task #2:
Explain what this means in terms of the amount of money needed and the cost of the bicycle.
Consider the following situation:
When x = 37
135 = x + 98 135 = x + 98
135 = 135 = 3737 + 98 + 98
135 = 135 135 = 135
When x = 135
135 = x + 98 135 = x + 98
135 = 135 = 135135 + 98 + 98
135 135 236 236
When x = 233
135 = x + 98 135 = x + 98
135 = 135 = 233233 + 98 + 98
135 135 331 331
When x = 98
135 = x + 98 135 = x + 98
135 = 135 = 9898 + 98 + 98
135 135 196 196
True
False False
False
135 = x + 98 135 = x + 98
135 = 135 = 00 + 98 + 98
135 135 98 98
False
When x = 0
How did you know your
solution was reasonable?
Ana considered buying the $135 bicycle, Ana considered buying the $135 bicycle, but then she decided to shop for a different but then she decided to shop for a different bicycle. She knows the other bicycle she bicycle. She knows the other bicycle she likes will cost at least $150. likes will cost at least $150.
Part BPart B
““Ana considered buying the $135 bicycle, but then she decided to shop Ana considered buying the $135 bicycle, but then she decided to shop for a different bicycle. She knows the other bicycle she likes will cost for a different bicycle. She knows the other bicycle she likes will cost
more than $150.more than $150.””
X + 98 ≥ X + 98 ≥
150 150
MP6: Attend to MP6: Attend to precisionprecision
1. Explain how the inequality below models the following situation:
What does x + 98 > 150 represent?What does x
represent?
What symbols or mathematical notations are important inthis problem?
Task #3:Task #3:
Ana earns her money by washing cars. She can potentially earn between $0 and $120 per month. Is it possible for Ana to afford her bicycle within a month? What is the least amount of money Ana needs to save to purchase the bicycle?
Consider the following situation:
-98 -98-98 -98
x ≥ 52x ≥ 52
x + 98 ≥ 150
What does this
solution represent?
Task #3:Task #3:
Ana earns her money by washing cars. She can potentially earn between $0 and $120 per month. Is it possible for Ana to afford her bicycle within a month? What is the least amount of money Ana needs to save to purchase the bicycle?
Graph the solution to the inequality:
-98 -98-98 -98 x x ≥ 5252
x + 98 ≥ 150
-250 250 -200 200-150 150-100 100-50 50 0
x ≥ 52 What does the graph of the inequality represent?
Joey had 26 sheets of papers in his Joey had 26 sheets of papers in his desk. His teacher gave him some more desk. His teacher gave him some more and now he has 100 sheets. How many and now he has 100 sheets. How many sheets of papers did his teacher give sheets of papers did his teacher give him?him?
The Paper ProblemThe Paper Problem
MP6: Attend to MP6: Attend to PrecisionPrecision
26 + n = 26 + n = 100 100
1. Explain how the equation below models the following situation:
““Joey had 26 sheets of papers in his desk. His Joey had 26 sheets of papers in his desk. His teacher gave him some more and now he has teacher gave him some more and now he has 100 sheets. How many sheets of papers did 100 sheets. How many sheets of papers did his teacher give him? his teacher give him?
What does n
represent?How could you test your solution to see if it answers the problem?
The equation 26 + n = 100 26 + n = 100 can be stated as “some number was added to 26 and the result was 100.”
Joey had 26 sheets of papers in his desk. His teacher Joey had 26 sheets of papers in his desk. His teacher gave him some more and now he has 100 sheets. How gave him some more and now he has 100 sheets. How many sheets of papers did his teacher give him? many sheets of papers did his teacher give him?
n
100
26
What does each bar represent?
What symbols or mathematical
notations are important in
this problem?
““Joey had 26 papers in his desk. His teacher Joey had 26 papers in his desk. His teacher gave him some more and now he has 100. gave him some more and now he has 100. How many papers did his teacher give him?How many papers did his teacher give him?””
26 + n = 26 + n = 100 100 -26 -26-26 -26
n = 74 n = 74
Additional PracticeAdditional Practice
1. The booklet of stamps costs 11 dollars and each stamp costs 44 cents. How many stamps are in the booklet? Explain the strategies used to determine the answer. Show that the solution is correct using substitution.
2. Meagan spent $56.58 on three pairs of jeans. If each pair of jeans costs the same amount, write an algebraic equation that represents this situation and solve to determine how much one pair of jeans cost.
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