This warm-up prompts student to reason in financial terms, preparing them because that subsequent jobs in the lesson. It additionally provides insight into students’ understanding of dollars and cents and also their ability to reason mentally.
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Find each answer mentally.A sticker expenses 25 cents. How countless dollars is that?A pen expenses 1.50 dollars. How plenty of cents is that?How numerous cents room in one dollar?How countless dollars space in one cent?
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In solution to “how numerous dollars room in one cent,” students might say there are no dollars at all in one cent. Ask castle what portion of a dollar one cent represents.
After students solved all difficulties mentally, because that each problem, questioning 1–2 students to share their thinking. Pause in between problems to offer everyone thistoricsweetsballroom.come to reflect ~ above the common answers.
In this activity, students find out the meaning of a percentage together a rate per 100 and apply this definition in the paper definition of money. Lock label various coin amounts as percentages that 100 cent or 1 dollar.
Students are likely able to name the values of every coin and their individual percentages (in the first two questions) relatively quickly. Assigning a portion to a group of coins (in the last 2 questions) to add complexity and also should it is in the focus of the task as students might use a variety of strategies. One feasible strategy is to factor in terms of ratios. For example, a student might think that if a dhistoricsweetsballroom.come is 10% the a dollar, climate 6 dhistoricsweetsballroom.comes is 60% of a dollar. This kind of ratio thinking is a robust way for managing percent problems and also should be encouraged early.
As student work, notification the strategies being offered to solve the 2 problems and also identify those with efficient approaches therefore they deserve to share later.
Remind student that formerly they have learned that a “rate every 1” tells united state the lot of one amount for 1 of an additional quantity. Explain that in this task, they will discover “rates every 100.”
Solicit a pair of ideas on what “rates every 100” can mean. Student are most likely to suggest a description along the currently of “the quantity of something for 100 of miscellaneous else.” tell students that a price per 100 is called a percentage and that castle will explore percentages in the context of money. Suggest out the half-dollar and also dollar coins in the task, as some students may not be familiar with them.
Arrange student in teams of 2. Offer students 3 minute of quiet think thistoricsweetsballroom.come to start work on the task. After that thistoricsweetsballroom.come, asking students to share your responses through a partner and complete the remaining inquiries together.
Action and Expression: develop Expression and Communication. Invite students to talk around their principles with a partner before writing castle down. Screen sentence frames to support students as soon as they explain their ideas. Because that example, “If _____ climate _____ because…” or “How do you know…?”Supports access for: Language; Organization
Write the surname of the coin that matches each expression.
25% of a dollar5% that a dollar1% the a dollar
100% the a dollar10% of a dollar50% of a dollar
The worth of 6 dhistoricsweetsballroom.comes is what percent that the value of a dollar?The value of 6 quarters is what percent of the worth of a dollar?
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Find two different sets of coins that each do 120% that a dollar, whereby no type of coin is in both sets.
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Students may notice a pattern details to this activity—that the percent worth is the very same as the for cents—and bring that assumption forward and also apply it incorrectly to cases in which 100% does not correspond come 100. This conversation is addressed in the task Synthesis.
Focus the discussion on the ways students approached the last 2 questions and on precise use the language and also notation (MP6). Because that example, in the first two difficulties students can write only a number or suitable a coin come a pre-written phrase. In the last 2 problems, however, to express a percentage with only a number and also without the % symbol should be taken into consideration an incomplete answer.
Select college student with effective strategies come share their reasoning with the class. Screen a concise version of their reasoning for every to see. Invite rather to refer support, disagreement, or questions (MP3).
If no one reasoned about percentages in terms of ratios (e.g., If a quarter is 25% the a dollar, 6 quarters are 150% the a dollar), highlight it.
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Many students might reason by noticing a pattern—that the variety of cents in an lot matches its percentage of a disagreement (e.g., 60 cent is 60%)—rather by thinking in terms of ratio or scaling. Because the pattern only holds up in the paper definition of percentages the 100 of a quantity, student will need to be motivated to look much more closely at the definition of “rate every 100.” finish the discussion by displaying the following twin number line v 100 in ~ the 100%:
Reading, Writing, Speaking: MLR3 Clarify, Critique, Correct. Before college student share their explanations because that the last question, current an incorrect answer and explanation. Because that example, “The value of 6 quarters is 50% that the value of a dollar due to the fact that the worth of 6 soldier is 150 cents, i m sorry is 50 cents higher than 100 cents. This way that the value of 6 soldier is 50% of the worth of a dollar.” Ask student to identify the error, critique the reasoning, and write a exactly explanation. Together students talk about in pairs, listen for students who identify and clarify the faint language in the statement. For example, the author probably supposed to say the 6 soldier is 50% greater than the worth of a dollar, or that 6 quarters is 150% the the value of a dollar. This will aid students understand how to use percentages to explain the size of one quantity as a percentage of one more quantity.Design Principle(s): Opthistoricsweetsballroom.comize calculation (for explanation); Maxhistoricsweetsballroom.comize meta-awareness