TASK

The table shows four people who earn the typical amount for their education level.

1. How much more does Niko earn than Miley in one week?
2. If Taylor and Miley both work for 2 weeks, how much more will Taylor earn?
3. How much money will Pinky earn in a month? About how long will Miley have to work to earn the same amount?

COMMENTARY

The purpose of this task is for students to add, subtract, multiply, and divide decimal numbers in a real-world context. The weekly income earned by each person in the task is the median weekly income for their education level, but they have been given names to make the task easier to read and also more personal.

There is a strong positive relationship between the level of education someone has and the income that they earn. Through this task, students can observe that an investment in education and training will increase what they can earn. This relationship is true for advanced degrees as well; those with terminal and professional degrees have higher median weekly incomes than those with bachelor degrees. A natural extension of this task would be to ask students to do some research to find out how much more they might make with different vocational or professional degrees. Both this task and the suggested extension can help students see that education beyond high school, whether technical training or college, pays off.

This task is part of a set collaboratively developed by Money as You Learn, an initiative inspired by recommendations of the President’s Advisory Council on Financial Capability, and Illustrative Mathematics. Integrating essential financial literacy concepts into the teaching of the Common Core State Standards can strengthen teaching of the Common Core and expose students to knowledge and skills they need to become financially capable young adults. A mapping of essential personal finance concepts and skills against the Common Core State Standards as well as additional tasks and texts will be available at www.moneyasyoulearn.org. This task and additional personal finance-related mathematics tasks are available at www.illustrativemathematics.org and are tagged “financial literacy.”

SOLUTION

1. Niko makes $650.35 per week and Miley makes $440.50 per week. We know that650 – 440 = 210

   and

   210.35 – 0.50 = 210 + 0.35 – 0.50 = 210 – 0.15 = 209.85

   So Niko makes $209.85 more per week than Miley.

2. Taylor makes $771.25 per week and makes twice that much in two weeks.
   2 × 771.25 = 2 (700 + 70 + 1 + 0.25) = 1400 + 140 + 2 + 0.50

    So Taylor makes $1542.50 in two weeks.

   Miley makes $440.50 per week and so will make $881 in two weeks. Since

   1542.50 – 881 = 742.50 – 81 = 741.50 – 80 = 701.50 – 40 = 661.50

   We know that Taylor will make $661.50 more than Miley in two weeks.

3. There are four weeks in a month. Pinky makes $1099.20 in a week so will make
   4 × 1099.20 = 4 × 1100 – 4 × 0.80 = 4400 – 3.20 = 4396.80

    So Pinky will make $4396.80 in a month. We can divide this by how much Miley makes in one week to find out how many weeks she will have to work.

   4396.8 ÷ 440.5 ≈ 4400 ÷ 440 = 10

   So Miley will have to work about 10 weeks, or two and a half months, to earn the same amount that Pinky will make in one month.

   Students can also calculate a more exact answer to this question if they need some practice dividing decimals.

TASK

For 70 years, Oseola McCarty earned a living washing and ironing other people’s clothing in Hattiesburg, Mississippi. Although she did not earn much money, she budgeted her money wisely, lived within her means, and began saving at a very young age. Before she died, she drew worldwide attention by donating $150,000 to the University of Southern Mississippi for a scholarship fund in her name. The fact that Ms. McCarty was able to save so much money and generously gave it away is an inspiration to many others. She was honored with the Presidential Citizens Medal for her generosity. How did she do it?

Let’s assume that she saved the same amount at the end of each year and invested it in a savings account earning 5% per year compounded annually. (When you contribute the same amount each year to an account it is called an annuity.) How much do you think Ms. McCarty would have to save each year in order to accumulate $150,000 over a 70-year period?

1. Before we figure it out, take a guess.
   • $100
   • $250
   • $500
   • $1,000
   • $2,000
2. Suppose Ms. McCarty saved $100 and then deposited it at the end of the year in an account that earns 5% interest, compounded annually.
   • How much will it be worth at the end of the second year? At the end of the third year? At the end of the 70th year?
   • Write an expression that represents the value of an investment of C dollars after 70 years. Assume as above that it is deposited at the end of the first year in an account that earns 5% interest, compounded annually.
3. Now suppose Ms. McCarty saved another $100 in the second year and then deposited it at the end of that year in her account. 
   • How much will it be worth at the end of the third year? At the end of the fourth year? At the end of the 70th year?
   • Write an expression that represents the value of an investment of C dollars after 69 years.
4. Suppose Ms. McCarty saved $100 each and every year for 70 years. Each time, she deposited it in her account at the end of the year.
   • How much would she have saved? What would it be worth at the end of 70 years?
   • Write an expression that represents the value of an investment of C dollars deposited each year for 70 years. Assume as above that it is always deposited at the end of the year in an account that earns 5% interest, compounded annually.
5. Had she saved $1,000 a year, how much would she have had after 70 years under the same conditions?
6. How much would she have to save each year in order to accumulate $150,000 after 70 years? How does this compare to your guess? Are your surprised by the answer?
7. The future value FV of an annuity is the total value of the annuity after a certain number of years. The formula for the future value of an annuity is shown below.

   

   Based on the work you did above, what is the meaning of C in this context? What is the meaning of r in this context? What is the meaning of t in this context?

COMMENTARY

The purpose of this instructional task is to give students an opportunity to construct and find the value of a geometric series (A-SSE.4) in a financial literacy context. The task assumes that students have already developed the formula for a geometric series themselves; having them recognize the need for this formula (and look up if necessary) allows them to engage in MP 5, Use appropriate tools strategically. The task also provides students with an opportunity to look for and express regularity in repeated reasoning (MP 8), as the solution shows. This task also asks students to interpret the variables in the future value formula in the context of the problem (A-SSE.1).

Natural extensions of this task include asking students how much they would have to save each year given different interest rates, numbers of years of saving, and savings goals. Another possible extension is for students to develop the formula for the future value shown in the last part. Alternatively, the work students have done to this point will have prepared them to understand a derivation presented by the teacher.

Students may not know what it means to compound interest, in which case they can be told that interest that is compounded annually is computed at the end of each year and added into the account, thereby increasing the amount of money in the account. For more information about financial literacy concepts that could help students understand this context better, visit, econedlink.

This task is part of a set collaboratively developed by Money as You Learn, an initiative inspired by recommendations of the President’s Advisory Council on Financial Capability, and Illustrative Mathematics. Integrating essential financial literacy concepts into the teaching of the Common Core State Standards can strengthen teaching of the Common Core and expose students to knowledge and skills they need to become financially capable young adults. A mapping of essential personal finance concepts and skills against the Common Core State Standards as well as additional tasks and texts will be available at www.moneyasyoulearn.org. This task and additional personal finance-related mathematics tasks are available at www.illustrativemathematics.org and are tagged “financial literacy.”

SOLUTIONS

1. Answer (b) is the closest to the correct answer, but there is no right or wrong answers here!
2. We note that for this and future parts in this solution, we round computations to the nearest cent.

   

   That is, the investment will be worth $105 at the end of the second year, $110.25 at the end of the third year, and $2,897.76 at the end of the 70th year.

   Replacing 100 by C, we see that an expression that represents the value of an investment of C dollars after 70 years is C · (1.05)⁶⁹, or approximately 29C.

3. 

   That is, $100 deposited at the end of the second year will be worth $105 at the end of the third year, $110.25 at the end of the fourth year, and $2,759.77 at the end of the 70th year.

   An expression that represents the value of an investment of C dollars after 69 years is C · (1.05)⁶⁸, or approximately 27.6C.

4. Ms. McCarty saved 100 · 70 or $7,000 over the 70 years. The technique developed above shows us how to find the ending value of each of these deposits:
   • The $100 invested in year 1 is worth 100 · (1.05)⁶⁹ at the end of the 70 years.
   • The $100 invested in year 2 is worth 100 · (1.05)⁶⁸ at the end of the 70 years.
   • The $100 invested in year 3 is worth 100 · (1.05)⁶⁷ at the end of the 70 years.
   • …and so on, until …
   • The $100 invested in year 69 is worth 100 · (1.05)¹ at the end of the 70 years.
   • The $100 invested in year 70 is worth 100 · (1.05)⁰ at the end of the 70 years.

     Now we just need to need to add these up: We recognize the sum

     

     as a geometric series, and so we can evaluate it as

     

     We conclude that she would have accumulated $58,852.85 all together by setting aside $100 each year for 70 years. Note that this is  times as much as the money she saved.

     An expression that represents the value of an investment of C dollars deposited each year for 70 years is

     

5. We can use the last part of the problem above to find this:

   

   Of course, we could also note that she is saving 10 times as much each year so the total she saves will be ten times as great. In either case we see that she would have saved $588,528.51 all together.

6. We can use what we have already found:

   

   So she would need to save approximately $254.87 each year to accumulate $150,000 in 70 years. Whether this is surprising depends on the student and their initial guess.

7. Based on the work above, C is the amount of money added to the annuity every year, r is the annual interest rate (expressed as a decimal), and t is the number of years the same amount of money is deposited in the annuity.

TASK

Hallie is in 6th grade and she can buy movie tickets for $8.25. Hallie’s father was in 6th grade in 1987 when movie tickets cost $3.75.

When he turned 12, Hallie’s father was given $20.00 so he could take some friends to the movies. How many movie tickets could he buy with this money?

How many movie tickets can Hallie buy for $20.00?

On Hallie’s 12th birthday, her father said,

When I turned 12, my dad gave me $20 so I could go with three of my friends to the movies and buy a large popcorn. I’m going to give you some money so you can take three of your friends to the movies and buy a large popcorn.

How much money do you think her father should give her?

Commentary

The purpose of this task is for students to solve problems involving decimals in a context involving a concept that supports financial literacy, namely inflation. Inflation is a sustained increase in the average price level. In this task, students are asked to compare the buying power of $20 in 1987 and 2012, at least with respect to movie tickets.

This task also engages students in Standard for Mathematical Practice 4, Model with mathematics. Specifically, students need to either make the assumption that the price of popcorn increased at the same rate as movie tickets, or they need to do some research into the current cost of a large popcorn in order to answer the last question. It is a variation on another task 4.OA Carnival Tickets that also addresses inflation in a way that is accessible to 4th graders.

This task is part of a set collaboratively developed by Money as You Learn, an initiative inspired by recommendations of the President’s Advisory Council on Financial Capability, and Illustrative Mathematics. Integrating essential financial literacy concepts into the teaching of the Common Core State Standards can strengthen teaching of the Common Core and expose students to knowledge and skills they need to become financially capable young adults. A mapping of essential personal finance concepts and skills against the Common Core State Standards as well as additional tasks and texts will be available at www.moneyasyoulearn.org. This task and additional personal finance-related mathematics tasks are available at www.illustrativemathematics.org and are tagged “financial literacy.”

SOLUTION

Students should be able to fluently multiply and divide decimals. The details of the algorithms for multiplying and dividing are not shown here.

1. To find out how many tickets he could buy with $20, we divide 20 by the price of a single ticket:

    
   20÷3.75=5.3

   Since it’s not possible to purchase a part of a ticket, this means that he could buy 5 tickets and will have some money left over. Since

   5×3.75=18.75

   and

   20-18.75=1.25

   her father could buy 5 movie tickets in 1987 with $20, and he would have $1.25 left over.

2. As before, to find out how many tickets she could buy with $20, we divide 20 by the price of a single ticket:

    
   20÷8.25=2.42

   As before, she can’t buy part of a ticket. Furthermore,

   2×8.25=16.50

   and

   20-16.50=3.50

   So Hallie can buy 2 movie tickets if she has $20, and she will have $3.50 left over.

3. Since 4×3.75=15, a large popcorn had to cost $5.00 or less if her father bought it with the change from buying the tickets. Hallie’s movie tickets cost 8.25÷3.75=2.2 times as much as movie tickets cost in 1987. Assuming the price of popcorn increased at the same rate, and since 2.2×5=11, she should be able to buy a large popcorn for $11.00. Four tickets cost 4×8.25=33 dollars. With these assumptions, Hallie’s father should give her at least $44.00.

SOLUTION: ALTERNATIVE APPROACH TO PART (C)

If you go online and look up the cost of a large popcorn at a movie theater, the values range around $10 to $12 (possibly more or less depending on the location). This means the total cost of four tickets and a large popcorn is somewhere near $45, give or take a few dollars. Often tax is included in the cost of the tickets, but it is not always included in the cost of concessions. Depending on the theater, the total cost may be a bit higher if tax is applied.

TASK

Inflation is the measure of the annual growth in the price of a good or service, computed as the percentage change in price from the previous year. For example, if the price of gasoline rose from $2.00 a gallon to $2.20 per gallon in one year, the inflation rate for gasoline for that year would be:

1. Suppose in the following year, the price of gasoline rose another twenty cents per gallon to $2.40. Find the inflation rate for this year. Is it higher or lower than 10 percent?
2. Returning to the case where the previous year ended at a price of $2.20 per gallon, what price at the end of the current year would give another inflation rate of 10%? Is it higher or lower than $2.40?
3. The price of a gallon of regular gasoline has roughly doubled over the last 8 years (2004-2012). If we assume a constant annual inflation rate r over this time frame, predict whether or not r is likely to be smaller or larger than 15%. Do you need to know the actual prices in order to solve this? Explain.
4. Use an exponential growth model to compute the value of r from the previous part to one decimal place. Note this value gives a good approximation to the average annual rate of inflation over these eight years, so this value has meaning even if we don’t assume a constant annual inflation rate.
5. The nation’s overall inflation is often measured as a change in the CPI (Consumer Price Index), a number which measures the prices paid by consumers for a representative basket of goods and services (housing, food, transportation, etc). Using data from this table of CPI values, compare gasoline inflation with overall inflation over the years 2004-2012.

COMMENTARY

The purpose of this task is to give students an opportunity to explore various aspects of exponential models (e.g., distinguishing between constant absolute growth and constant relative growth, solving equations using logarithms, applying compound interest formulas) in the context of a real-world problem with ties to developing financial literacy skills. In particular, students are introduced to the idea of inflation of prices of a single commodity, and are given a very brief introduction to the notion of the Consumer Price Index for measuring inflation of a body of goods.

The task has several parts, of varying levels of open-endedness: Some parts call for direct calculation, some involve reasoning about differences between linear and exponential models, and the last part requires some data gathering skills from an external source, namely from the table of CPI values. As such, the task is certainly intended for instructional purposes rather than assessment ones, and might profitably be done as either full-group or small-group projects, depending on the availability of computer resources to collect the CPI data. Note that the task does not develop the compound growth formula from scratch, so this task could be used as a financial application of that material once it has been developed.

Refer to the following links for further information on the consumer price index:

1. http://www.bls.gov/cpi/
2. ftp://ftp.bls.gov/pub/special.requests/cpi/cpiai.txt

This task is part of a set collaboratively developed by Money as You Learn, an initiative inspired by recommendations of the President’s Advisory Council on Financial Capability, and Illustrative Mathematics. Integrating essential financial literacy concepts into the teaching of the Common Core State Standards can strengthen teaching of the Common Core and expose students to knowledge and skills they need to become financially capable young adults. A mapping of essential personal finance concepts and skills against the Common Core State Standards as well as additional tasks and texts will be available at www.moneyasyoulearn.org. This task and additional personal finance-related mathematics tasks are available at www.illustrativemathematics.org and are tagged “financial literacy.”

SOLUTION: SOLUTION

1. A change of price from $2.20 to $2.40 would give an inflation rate of

   
   lower than the 10% rate we saw for the previous year. This illustrates a key difference between linear and exponential growth — repeatedly increasing a quantity by a constant amount leads to smaller percent changes of the amount each time.

2. We compute 2.2×1.1=2.42. That is, a price increase of 22 cents would have had to occur in order to see an inflation rate of 10%.

    
   The analogous comment to that in the previous part can be stated as follows — a constant annual percentage increase to leads to larger and larger annual increases in the cost of gasoline.

3. As we began to see in part (a), due to the compounding nature of exponential growth, a constant rate of inflation leads to ever-increasing price differences from one year to the next. The constant rate r would have to be less than 15%, since a 15% inflation rate for 8 consecutive years would increase the price by at least 15% of the starting price eight times, for a net gain of over 8×.15=1.2 times the starting price. That is, the initial price after eight years would have increased by 120%, giving a final price over double the initial price.

    
   Perhaps surprisingly, we did not need to know either the starting or finishing prices in order to makes this line of reasoning, only their ratio (which, in this case of doubling, was simply 2).

4. We model the price of gasoline as a function of time: If A is the function that returns the price after n years of compounding, we have the standard annual compounding formula for A:

   

   where P is the initial amount or value and r represents the annual growth rate in the price of gasoline. In the case of doubling, the ratio of the final amount to the initial amount is 2 to 1, and so the given information about gasoline prices is the statement that A(8)=2P. Substituting this in the compounding formula gives 2P=P(1+r)8, or after dividing both sides by P, that

   

   One approach to solving this for r is to take the natural logarithm of both sides of the equation and to use properties of logarithms to re-write the expression:

   

   Dividing, we find

   

   Exponentiating both sides to a base of e gives 1+r ≈ 1.0905, and so

   

5. The following table ftp://ftp.bls.gov/pub/special.requests/cpi/cpiai.txt gives annual CPI data for 1913 to 2012 (through the 3rd quarter). we record some observations before we being our calculations: Average annual increases in the CPI varied between 0.1 and 4.1 percent over the period 2004-2012. The average annual CPI for 2004 was 188.9 and for 2012 (through the first 3 quarters) was 231.32. Finally, the average annual increase in the CPI over this period can be roughly estimated by using the same solution method as we did above.

    
   We can now repeat our calculations form the gasoline example, where instead of doubling over the 8-year span we have a ratio of 231.32/188.90. Setting up

   

   and solving for r as above gives 1.025646 = 1+r, which gives an approximate average annual inflation rate of r≈2.6% over the period from 2004-2012. This is just over a quarter of the average annual rate of growth in the price of a gallon of regular gasoline (9.1%) over the same period in time, suggesting that something other than generic inflation is responsible for the tremendous rate of growth of the price of gasoline.

SOLUTION: ALTERNATE SOLUTION FOR PARTS (D)-(E)

One can avoid the use of logarithms in the solutions to parts (d)-(e) as follows: Given 2=(1+r)8, we take the eighth roots of both sides and subtract 1 to get

or again r ≈ 9.1%.

For (E), the analogous calculation gives

so r≈2.6%.

TASK

1. Seth wants to buy a new skateboard that costs $169. He has $88 in the bank. If he earns $7.25 an hour pulling weeds, how many hours will Seth have to work to earn the rest of the money needed to buy the skateboard?
2. Seth wants to buy a helmet as well. A new helmet costs $46.50. Seth thinks he can work 6 hours on Saturday to earn enough money to buy the helmet. Is he correct?
3. Seth’s third goal is to join some friends on a trip to see a skateboarding show. The cost of the trip is about $350. How many hours will Seth need to work to afford the trip?

COMMENTARY

The purpose of this task is for students to solve problems involving division of decimals in the real-world context of setting financial goals. The focus of the task is on modeling and understanding the concept of setting financial goals, so fluency with the computations will allow them to focus on other aspects of the task. This task is also good preparation for the study of ratios and proportional relationships in 6th and 7th grade and their lead-in to linear functions in 8th grade.

This task is part of a set collaboratively developed by Money as You Learn, an initiative inspired by recommendations of the President’s Advisory Council on Financial Capability, and Illustrative Mathematics. Integrating essential financial literacy concepts into the teaching of the Common Core State Standards can strengthen teaching of the Common Core and expose students to knowledge and skills they need to become financially capable young adults. A mapping of essential personal finance concepts and skills against the Common Core State Standards as well as additional tasks and texts will be available at www.moneyasyoulearn.org. This task and additional personal finance-related mathematics tasks are available at www.illustrativemathematics.org and are tagged “financial literacy.”

SOLUTION: 1

1. A. 167 – 88 = 79, so Seth needs to make $79. Since

   79÷7.25≈10.9

   Seth will have to work about 11 hours to make enough money to buy the skateboard.

2. No, Seth is not correct. 6 x 7.25 = 43.5 which is not enough to buy the helmet; he needs $3 more which will require a bit less than a half an hour more work.
3. Since 350÷7.25≈48.3 Seth will have to work about 50 hours.

TASK

Inflation is a term used to describe how prices rise over time. The rise in prices is in relation to the amount of money you have. The table below shows the rise in the price of bread over time:

For the price in each decade, determine what the increase is as a percent of the price in the previous decade. Is the percent increase steady over time?

Under President Roosevelt, the Fair Labor Standards Act introduced the nation’s first minimum wage of $0.25 an hour in 1938. The table shows the rise in minimum wage over time:

For hourly wage in each decade, determine what the increase is as a percent of the hourly wage in the previous decade. Is the percent increase steady over time?

Consumers are not affected by inflation when the amount of money they make increases proportionately with the increase in prices. Complete the last column of the table below to show what percentage of an hour’s pay a pound of bread costs:

In which year were people who earn minimum wage most affected by inflation? Explain.

COMMENTARY

The purpose of this task is for students to calculate the percent increase and relative cost in a real-world context. Inflation, one of the big ideas in economics, is the rise in price of goods and services over time. This is considered in relation to the amount of money you have.

This task is part of a set collaboratively developed by Money as You Learn, an initiative inspired by recommendations of the President’s Advisory Council on Financial Capability, and Illustrative Mathematics. Integrating essential financial literacy concepts into the teaching of the Common Core State Standards can strengthen teaching of the Common Core and expose students to knowledge and skills they need to become financially capable young adults. A mapping of essential personal finance concepts and skills against the Common Core State Standards as well as additional tasks and texts will be available at www.moneyasyoulearn.org. This task and additional personal finance-related mathematics tasks are available at www.illustrativemathematics.org and are tagged “financial literacy.”

SOLUTION: 1

The price of bread increases each decade. However, some decades see a much larger percent increase than others.  

The federal minimum wage increased each decade. However, some decades see a much larger percent increase than others.

In 2010, consumers making minimum wage spent 41% of one hour’s wage on a pound of bread, which is the largest percent over the time span shown. The relative cost of a loaf of bread was quite low through the 1970s, 80s, and 90s, but looking at the percent increase of the cost of bread in the last three decades and comparing it with the percent increase in the minimum wage, we can see that the cost of bread was rising more quickly than the federal minimum wage.

TASK

Mrs. Moore’s third grade class wants to go on a field trip to the science museum.

• The cost of the trip is $245.
• The class can earn money by running the school store for 6 weeks.
• The students can earn $15 each week if they run the store.

1. How much more money does the third grade class still need to earn to pay for their trip?
2. Write an equation to represent this situation.

COMMENTARY

The purpose of this instructional task is for students to solve a two-step word problem and represent the unknown quantity with a variable. This task also addresses the concept of scarcity. The students in the 3rd grade class are faced with a scarcity of time – only 6 weeks to earn enough money for the trip. They are also faced with a scarcity of money at the end of the 6 weeks. The teacher can discuss with students the definition of scarcity – not having enough resources to satisfy your wants and possible solutions to this scarcity situation.

This task is part of a set collaboratively developed by Money as You Learn, an initiative inspired by recommendations of the President’s Advisory Council on Financial Capability, and Illustrative Mathematics. Integrating essential financial literacy concepts into the teaching of the Common Core State Standards can strengthen teaching of the Common Core and expose students to knowledge and skills they need to become financially capable young adults. A mapping of essential personal finance concepts and skills against the Common Core State Standards as well as additional tasks and texts will be available at www.moneyasyoulearn.org. This task and additional personal finance-related mathematics tasks are available at www.illustrativemathematics.org and are tagged “financial literacy.”
 

Solution

1. We can start by finding out how much money the students can make at the store:
   

   6×15=6×10+6×5=60+30=90

   Since

   245−90=155

   the students still need $155 dollars for the field trip.

2. We can let n stand for the amount of money they still need. We know that the amount they can make at the store is 6×15 and the amount they need to raise is 245, so one equation is

   245−6×15=n

   Another possible equation is

   6×15+n=245

TASK

Every year a carnival comes to Hallie’s town. The price of tickets to ride the rides has gone up every year.

1. In 2008, Hallie’s allowance was $9.00 a month. How many carnival tickets could she buy with one month’s allowance?
2. How many carnival tickets could she buy in 2012 with $9.00?
3. In 2012, Hallie’s allowance was $14.00 per month. How much more did a carnival ticket cost in 2008 than it did in 2012? How much more allowance was she receiving per month?
4. Was Hallie able to buy more carnival tickets in 2008 or in 2012 with one month’s allowance?
5. What would Hallie’s allowance need to be in 2012 in order for her to be able to buy as many carnival tickets as she could in 2008?
6. What happens to your ability to buy things if prices increase and your allowance doesn’t increase?

COMMENTARY

The purpose of this task is for students to solve multi-step problems in a context involving a concept that supports financial literacy, namely inflation. Inflation is a sustained increase in the average price level. In this task, students can see that if the price level increases and people’s incomes do not increase, they aren’t able to purchase as many goods and services; in other words, their purchasing power decreases. If the price level rises and people’s incomes increase at a slower rate, their purchasing power increases but not as much as if their income increases at the same rate as the cost of goods and services. This task is a variation on another task 6.NS Movie Tickets that also addresses inflation.

From a mathematical perspective, students are asked to solve word problems involving operations only with whole numbers because students are not required in fourth grade to compute with decimal numbers. However, they are asked to understand decimal notation for fractions with denominators of 10 and 100 (see 4.NF.6) and so this task capitalizes on this by representing whole numbers with decimal notation and including dollar amounts that are not whole numbers in the table. Also, students in 4th grade should be comfortable with two-column tables (see e.g. 4.MD.1), so this task gives them some practice reading information in a table. Note that the numbers were chosen specifically so that there would be remainders for them to interpret (as described in 4.OA.3).

This task is part of a set collaboratively developed by Money as You Learn, an initiative inspired by recommendations of the President’s Advisory Council on Financial Capability, and Illustrative Mathematics. Integrating essential financial literacy concepts into the teaching of the Common Core State Standards can strengthen teaching of the Common Core and expose students to knowledge and skills they need to become financially capable young adults. A mapping of essential personal finance concepts and skills against the Common Core State Standards as well as additional tasks and texts will be available at www.moneyasyoulearn.org. This task and additional personal finance-related mathematics tasks are available at www.illustrativemathematics.org and are tagged “financial literacy.”

SOLUTION

1. If she has $9 and tickets cost $2 each, we divide 9 by 2 to find out how many tickets she has (this is a “How many groups?” division problem).

    
   9÷2=4, with a remainder of 1
   

2. So she could buy 4 carnival tickets with one month’s allowance in 2008 and would have $1.00 left over.
3. As before, we divide to find how many tickets she can buy. 9 ÷ 4 = 2 with a remainder of 1. So if her allowance was $9.00 in 2012, she could only buy 2 tickets with one month’s allowance.
4. Since tickets cost $4 in 2012 and they cost $2.00 in 2008, and

    
   4−2=2

   a carnival ticket cost $2.00 more in 2012 than it did in 2008. Her allowance was $9.00 and now it is $14.00, and

   14−9=5

   so her allowance increased by $5.00.

5. We will divide as we did in parts (a) and (b)

    
   14÷4=3, with a remainder of 2

   So she could buy 3 carnival tickets with one month’s allowance in 2012 and would have $2.00 left over. Even though her allowance went up, the number of tickets she could buy went down.

6. Since carnival tickets cost $4.00 in 2012 and she could buy 4 tickets in 2008, and 4 × 4 = 16, her allowance in 2012 would need to be at least $16.
7. You can buy fewer things if prices increase but your allowance doesn’t increase.

TASK

Your teacher was just awarded $1,000 to spend on materials for your classroom. She asked all 20 of her students in the class to help her decide how to spend the money. Think about which supplies will benefit the class the most.

1. Write down the different items and how many of each you would choose. Find the total for each category.
   • Supplies
   • Books and maps
   • Puzzles and games
   • Special items
2. Create a bar graph to represent how you would spend the money. Scale the vertical axis by $100. Write all of the labels.
3. What was the total cost of all your choices? Did you have any money left over? If so, how much?
4. Compare your choices with a partner. How much more or less did you choose to spend on each category than your partner? How much more or less did you choose to spend in total than your partner?

COMMENTARY

The purpose of this task is for students to “Solve problems involving the four operations” (3.OA.A) and “Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories” (3.MD.3). Additionally, students will engage in MP3, Model with mathematics. In this task students are asked to decide how to spend $1,000 on supplies and materials for their classroom; students will have to make choices and be careful not to exceed the budget. Students are asked to decide which supplies will benefit the class the most and will compare their choices with other students’ choices. Because the budget does not allow students to buy one of everything, this task provides an opportunity for teachers to discuss costs and benefits. A benefit is something that satisfies your wants. A cost is what you give up when you decide to do something.

In third grade students are asked to fluently add and subtract within 1,000 (3.NBT.3) which is why the total budget is $1,000. Students are also multiplying and dividing within 100 (3.OA.7), so they might choose, for example, to buy 20 boxes of markers at $5 each so that there is a box of markers for every student in the class. It is possible that students will choose to purchase a number of one of the items where the total is greater than $100; while students are not expected to be fluent in multiplication above 100, they should be able to use their multiplication strategies to find such products. This task provides students with a natural opportunity to use addition, subtraction, and multiplication, and they might also use division depending on how they approach the task; thus it is well aligned to 3.OA.8.

Bar graphs make it easy for students to compare their allocations. If all of the students in the class include all categories on their graphs (whether they allotted any spending to them or not), list the categories in the same order that they are listed in the data table, and use the same colors for each category on a final draft, the teacher can put all of the final graphs up for display and the class can see whether there is a general consensus for how to spend the $1000 or not.

As an extension, the teacher might consider asking students to represent their total purchases with an equation; for example, if a student chooses 15 boxes of markers, 3 boxes of crayons, and 2 beanbag chairs, she could write:

15×5+3×8+2×65=75+24+65+65=229

This task is part of a set collaboratively developed by Money as You Learn, an initiative inspired by recommendations of the President’s Advisory Council on Financial Capability, and Illustrative Mathematics. Integrating essential financial literacy concepts into the teaching of the Common Core State Standards can strengthen teaching of the Common Core and expose students to knowledge and skills they need to become financially capable young adults. A mapping of essential personal finance concepts and skills against the Common Core State Standards as well as additional tasks and texts will be available at www.moneyasyoulearn.org. This task and additional personal finance-related mathematics tasks are available at www.illustrativemathematics.org and are tagged “financial literacy.”
 

Resources

• Blackline Master for Table

SOLUTION

1. Solutions will vary. Here is one possible set of choices.

   

   • 8 boxes of markers will cost 8×5=4×2×5=4×10=40 dollars.
     4 boxes of crayons will cost 4×8=4×4×2=16×2=10×2+6×2=20+12=32 dollars.
     2 boxes of pencils will cost 2×5=10 dollars.
     1 box of printer paper costs 40 dollars.
     2 packages of lined paper cost 2×15=2×10+2×5=20+10=30 dollars.
     3 boxes of construction paper cost 3×32=3×30+3×2=90+6=96 dollars.
     The total for the supplies is 40+32+10+40+30+96=248 dollars.
   • 12 books cost 12×8=10×8+2×8=80+16=96 dollars.
     The total cost for the books and maps is 250+96+45=391 dollars.
   • The total cost for the puzzles and games is
     10×12+6×15=120+3×30=120+90=210 dollars.
   • The total for the special items is 130 dollars.
2. Here is a bar graph showing these totals:
   
3. The total from all the purchases would be 248+391+210+130=979. So these purchases would total $979 and $21 would be left over.
4. Comparisons will vary.

TASK

Amy went to the arcade. At the arcade, people can buy tokens to use for the games.

1. Amy paid $5 to get some tokens. Show two different ways she could have paid using some bills and some coins.
2. Amy finished playing games. She has 4 tokens left over. Can she use these at the grocery store to buy some food? Why or why not?
3. The arcade trades tokens for 15 cents. How much money could Amy trade for her 4 tokens? Can she use these at the grocery store to buy some food? Why or why not?

COMMENTARY

Cluster 2.MD.C indicates that students should be able to “work with time and money.” When students are studying money, it is good for them to think about what counts as money and what does not. The purpose of this task is to introduce students to the characteristics of money in a financial literacy sense as well as to solve problems involving money. Money must be:

• Stable in value – the value of money should be constant over long periods of time.
• Generally accepted – whatever is used as money must be accepted by everyone.
• Durable – it must be able to withstand the wear and tear of many people using it.
• Divisible – it must be easily divided into small parts so people can make purchases at any price.
• Portable – it must be easy to carry.

The tokens in this task cannot be used at a grocery store, so they are not generally accepted and therefore are not considered money. The bills and coins Amy uses at the arcade are divisible, as shown by having the student show how to make $5 in two different ways.

Depending on how comfortable students are with the value of different coins, they may benefit from having play money to help them count out and think about different combinations of coins and bills that make $5.

This task is part of a set collaboratively developed by Money as You Learn, an initiative inspired by recommendations of the President’s Advisory Council on Financial Capability, and Illustrative Mathematics. Integrating essential financial literacy concepts into the teaching of the Common Core State Standards can strengthen teaching of the Common Core and expose students to knowledge and skills they need to become financially capable young adults. A mapping of essential personal finance concepts and skills against the Common Core State Standards as well as additional tasks and texts will be available at www.moneyasyoulearn.org. This task and additional personal finance-related mathematics tasks are available at www.illustrativemathematics.org and are tagged “financial literacy.”

SOLUTION

1. Here is one solution:

   4 dollars and 4 quarters will work:

   25¢ +25¢ + 25¢ + 25¢ = 100¢
   100¢ = $1
   $4 + $1 = $5
   

   Here is another:

   2 dollars, 8 quarters, 5 dimes, 9 nickels, 5 pennies

   4 quarters makes one dollar, so 8 quarters makes 2 dollars.

   5 dimes is 5 tens: 10¢ +10¢ + 10¢ + 10¢ + 10¢ = 50¢

   9 nickels is 9 fives: 5¢ +5¢ +5¢ +5¢ +5¢ +5¢ +5¢ +5¢ +5¢ = 45¢

   5 pennies is 5¢

   45¢ + 5¢ = 50¢

   50¢ + 50¢ = 100¢ = $1

   $2 + $2 + $1 = $5

2. Amy cannot use the leftover tokens at the grocery store because they will not accept them.
3. If Amy has 4 leftover tokens, she could exchange them for 60¢.

   15¢ + 15¢ + 15¢ + 15¢= 60¢

   In principle, Amy could use this money to buy something at the grocery store because grocery stores accept money. Of course, $0.60 won’t buy much at the store these days.

TASK

Louis wants to give $15 to help kids who need school supplies. He also wants to buy a pair of shoes for $39.

1. How much money will he have to save for both?
2. Louis gets $5 a week for his allowance. He will save his allowance every week. How many weeks will it take him to reach this goal?
3. Louis remembers his sister’s birthday is next month. He sets a goal of saving $16 for her gift. How many weeks will he have to save his allowance to reach this goal? How many weeks will he have to save his allowance for all three?

COMMENTARY 

The purpose of this task is for students to relate addition and subtraction problems to money and to situations and goals related to saving money. This problem shows the difference between first and second grade students’ strategies for adding 2-digit numbers. In first grade, students are just beginning this work; see Saving Money 1  for an example of a solution approach that is appropriate for first grade. In second grade students should add two-digit numbers fluently (see 2.NBT.B.5); the solution below is written much more abstractly in this version of the task to reflect that transition.

Second graders learn to skip-count by 5′s, 10′s, and 100′s (see 2.NBT.2) and work with equal groups of 2′s and 5′s (see 2.OA.C) both to support their understanding of place-value and in preparation for formal work with multiplication in third grade. This task is an instructional task that brings many aspects of the mathematical work that second graders will be doing together with an opportunity to learn about financial literacy concepts.

Teachers can make the problem more personal by letting the student choose a toy he/she wants and the toy their sibling or friend may want and researching the costs. If students do this type of research, they will be engaging in MP 4, Model with mathematics. Students can also choose how much money they want to donate and for what cause. If the students in the class don’t receive allowance, the child in the task can make money by helping a neighbor (perhaps walking a dog or bringing in the mail).

This task is part of a set collaboratively developed by Money as You Learn, an initiative inspired by recommendations of the President’s Advisory Council on Financial Capability, and Illustrative Mathematics. Integrating essential financial literacy concepts into the teaching of the Common Core State Standards can strengthen teaching of the Common Core and expose students to knowledge and skills they need to become financially capable young adults. A mapping of essential personal finance concepts and skills against the Common Core State Standards as well as additional tasks and texts will be available at www.moneyasyoulearn.org. This task and additional personal finance-related mathematics tasks are available at www.illustrativemathematics.org and are tagged “financial literacy.”

SOLUTION: USING AN EMPTY NUMBER LINE

1. Louis needs to save 15+39 dollars:

   15 + 39 =
   10 + 5 + 30 + 9 =
   10 + 30 + 5 + 9 =
   40 + 10 + 4 =
   54

   So Louis needs to save $54.

2. If we count up by fives, we can see how long it will take:

   So it will take Louis 11 weeks to save enough money for both.

3. If we look at the number line above, we can see it will take Louis 4 weeks to save enough for his sister’s birthday present.

   To save enough for all three, Louis needs to save 54+16 dollars:

   54 + 16 =
   50 + 4 + 10 + 6 =
   60 + 10 =
   70

   So Louis needs to save $70 for all three things. If we continue to count by fives:

   
   we can see that it will take him 14 weeks altogether. The reason it took one less week than if we had added up the number of weeks we found above is that the extra money earned in the 4th week above and beyond what he needed for his sister’s present combined with the extra money saved in the 11th week equals one week’s allowance.

SOLUTION: RECORDING THE SAVINGS IN A TABLE

1. Louis needs to save 15+39 dollars:

   15 + 39 =
   10 + 5 + 30 + 9 =
   10 + 30 + 5 + 9 =
   40 + 10 + 4 =
   54

   So Louis needs to save $54.

2. If we count up by fives, we can see how long it will take:

   

   So it will take Louis 11 weeks to save enough money for both.

3. If we look in the table above, we can see it will take Louis 4 weeks to save enough for his sister’s birthday present.

   Louis needs to save 54+16 dollars:

   54 + 16 =

   50 + 4 + 10 + 6 =

   60 + 10 =

   70

   So Louis needs to save $70 for all three things. If we extend the table above, we can see how long it will take:

   

   The reason it took one less week than if we had added up the number of weeks is that the extra money earned in the 4th week above and beyond what he needed for his sister’s present combined with the extra money saved in the 11th week equals one week’s allowance.

TASK

Materials

• Popsicle sticks and rubber bands or base-10 blocks
• Paper and pencil for each student

Actions

The teacher should pose the following question to students:

Louis wants to give $15 to help kids who need school supplies. He also wants to buy a pair of shoes for $39. If Louis gets $1 every day for his allowance, how many days will it take him to save enough money for both? Explain how you know.

COMMENTARY

The purpose of this task is for students to relate addition and subtraction problems to money and to situations and goals related to saving money. This problem can be adjusted based on where students are in their understanding of addition involving two digit numbers. This task has students adding two 2-digit numbers that require regrouping, and is therefore the most advanced type of addition problem that first graders will encounter. As a result, this is a very challenging instructional task for first grade students and they should have access to the appropriate tools when working on it. 1.NBT.4 also indicates that students should be able to add a 1-digit number to a 2-digit number and a 2-digit number and a multiple of 10 with greater fluency than two two-digit numbers. If students are working on either of these simpler types of problems, then the item that Louis wants to buy for himself could be, for example, a trip to the movies for $8 or a toy for $20. The second solution shows how students who can mentally add 10 to a 2-digit number without counting (see 1.NBT.5) might approach the task.

Teachers can make the problem more personal by letting the student choose a toy he/she wants and the toy their sibling or friend may want and researching the costs. If students do this type of research, they will be engaging in MP 4, Model with mathematics. Students can also choose how much money they want to donate and for what cause. If the students in the class don’t receive allowance, the child in the task can make money by helping a neighbor (perhaps walking a dog or bringing in the mail).

To see a task with the same context that shows the mathematical work that second grade students will be doing around multi-digit addition, see 2.OA, NBT Saving Money 2 .

This task is part of a set collaboratively developed by Money as You Learn, an initiative inspired by recommendations of the President’s Advisory Council on Financial Capability, and Illustrative Mathematics. Integrating essential financial literacy concepts into the teaching of the Common Core State Standards can strengthen teaching of the Common Core and expose students to knowledge and skills they need to become financially capable young adults. A mapping of essential personal finance concepts and skills against the Common Core State Standards as well as additional tasks and texts will be available at www.moneyasyoulearn.org. This task and additional personal finance-related mathematics tasks are available at www.illustrativemathematics.org and are tagged “financial literacy.”

SOLUTION: USING BUNDLED OBJECTS

To find out how much money he needs to save, we will find 15 + 39. First, let’s represent 15 with 1 bundle of ten and 5 single sticks and 39 with 3 bundles of ten and 9 single sticks:

If we put the tens together and the ones together, we have 4 bundles of ten, and 5 singles and another 9 singles:

If we take 5 singles from the 9 and put them with the other 5:

we can make another bundle of ten:

(Students might also take 1 from the five and put it with the 9 to make 10.)

Now we have 5 bundles of ten and 4 singles, which represents 54. Since he gets $1 per day, it will take him 54 days to save for both.

SOLUTION: USING AN EMPTY NUMBER LINE

To find out how much money he needs to save, we will find 15 + 39.

We can start at 15, then count up by tens 3 times, then count up by ones 9 times:

It is actually more efficient to start with 39 and add 15 to it; some students will recognize this:

Since he gets $1 per day, it will take him 54 days to save for both.

TASK

Materials

• pictures of water bottle, snack, and ball (see black line master)
• tools such as snap cubes, number lines, or number grids
• paper, pencil, scissors, and glue for each students

Actions

The teacher should pose the following question to the students:

It’s field day! The sun is shining and the students are having fun playing games with their friends. Your teacher gives you $7 to spend at the school store. Here are the options of what you can buy.

1. How much money would you need to buy one of everything on the list?
2. Do you have enough money to buy one of everything? How do you know? How much more money would you need to buy one of everything?
3. What can you buy using only $7? Show your work.
4. What would you choose to buy? Why?

COMMENTARY

The purpose of this task is for students to relate addition and subtraction problems to money in a context that introduces the concept of scarcity. Scarcity occurs when you want or need more than you can have. Students may want to buy everything but will discover that it not possible with only $7 and they will have to make decisions. To help first graders solve this problem is would be helpful to have multiple pictures of each object with the price on the picture (see attached black line master). This way, students can try all the combinations in order to discover their options using only $7. Students can use cubes, number grids, and number lines along with the pictures to assist in solving this problem. Some students may choose to combine their money or buy, for example, a ball to share. Then they may have money leftover to buy more. This strategy should be encouraged as long as the students are able to justify their reasoning.

This task is part of a set collaboratively developed by Money as You Learn, an initiative inspired by recommendations of the President’s Advisory Council on Financial Capability, and Illustrative Mathematics. Integrating essential financial literacy concepts into the teaching of the Common Core State Standards can strengthen teaching of the Common Core and expose students to knowledge and skills they need to become financially capable young adults. A mapping of essential personal finance concepts and skills against the Common Core State Standards as well as additional tasks and texts will be available at www.moneyasyoulearn.org. This task and additional personal finance-related mathematics tasks are available at www.illustrativemathematics.org and are tagged “financial literacy.”

Resources

• Black line master

SOLUTION

1. You would need $11 to buy every item on the list. Here is a solution using cubes:

   

   Here is a solution using a number line:

   

   Here is a solution using a number grid:

   

   In each case, we can see that 2+4+5=11.

2. There is not enough money to buy one of everything, because $7 is less than $11.
3. It is possible to buy any one item, or a water bottle and a snack, or a water bottle and a ball:

   

4. Answers will vary here–there is no one right answer. Students just need to explain why they made the choice they made.

TASK

Susan wanted to make a birthday card for her best friend but needed some art supplies.

1. She emptied her piggy bank and found 1 quarter, 5 dimes, 3 nickels, and 8 pennies.
   How much money did Susan find in her piggy bank? Show or explain how you know.
2. Susan went to the store with her mother and saw a pack of stickers for 35¢ and a glitter pen for 60¢. Does Susan have enough money to buy both items to make her birthday card? Show or explain how you know.
3. While Susan was at the store, she saw a ring that she would like to have herself. The ring costs 45¢. Can she still buy one or both of the other items?

COMMENTARY

The purpose of this task is to address the concept of opportunity cost through a real-world context involving money. In economics, resources are limited, but our wants are unlimited. Therefore, choices must be made. Every choice involves a cost. Your opportunity cost is the value of the next best alternative you gave up, or did not choose, when making a decision. To learn more about opportunity cost, visit econedLink.org.

Prior to this task, it would be helpful for students to have a basic understanding of decision making. The teacher can hold a discussion with students regarding opportunity cost by asking them what Susan is giving up if she buys the ring. Responses might include 45¢, the glitter pen, the stickers, or even the ability to make the card the way she wanted to. At this point, a grade-appropriate definition/explanation of opportunity cost could be discussed.

Second graders are ready to think about the ideas presented by the task, but depending on their reading level, the questions might be best presented verbally by the teacher before students are asked to work independently or in groups. Note that the numbers were carefully chosen so that the addition and subtraction they do is within 100 (2.OA.1) and the steps shown in finding these sums and differences reflect strategies based on place value and properties of operations (2.NBT.5). Also, students in second grade are asked to skip-count by 5′s, 10′s, and 100′s (see 2.NBT.2) but have not yet formalized these ideas in terms of the concept of multiplication. As a result, the solution given shows a skip-counting approach; if this task were given to third graders, they would be more likely to naturally formulate the solution in terms of multiplication.

This task is part of a set collaboratively developed by Money as You Learn, an initiative inspired by recommendations of the President’s Advisory Council on Financial Capability, and Illustrative Mathematics. Integrating essential financial literacy concepts into the teaching of the Common Core State Standards can strengthen teaching of the Common Core and expose students to knowledge and skills they need to become financially capable young adults. A mapping of essential personal finance concepts and skills against the Common Core State Standards as well as additional tasks and texts will be available at www.moneyasyoulearn.org. This task and additional personal finance-related mathematics tasks are available at www.illustrativemathematics.org and are tagged “financial literacy.”

SOLUTION

1. Susan found 1 quarter which is worth 25¢. She also found 5 dimes which are worth

    
   10, 20, 30, 40, 50

   So the dimes are worth 50¢.

   She also found 3 nickels which are worth

   5, 10, 15

   So the nickels are worth 15¢.

   Her 8 pennies are worth 8¢. All together she found:

   25¢ + 50¢ + 15¢ + 8¢ =
   75¢ + 15¢ + 8¢ =
   80¢ + 10¢ + 8¢ =
   90¢ + 8¢ =
   98¢

   (Students may add the values in many different ways; the way shown above is just one of them.)

2. We can add the values of the two items to find their total cost:

   35¢ + 60¢ =
   90¢+ 5¢ =
   95¢

   Since she has 98¢, she has enough money to buy both the the pack of stickers and the glitter pen.

3. If Susan buys the ring, we know she can’t buy both of the other items because together they cost 95¢ and she only has 98¢. If we subtract the cost of the ring from the money she has, we can see what (if anything) she can still buy:

   98¢ – 45¢ =
   (90¢ – 40¢) + (8¢ – 5¢) =
   50¢ + 3¢ =
   53¢

   left.

   That is more than enough to buy the stickers, but not enough to buy the glitter pen.

TASK

You won first place at your school Science Fair! You have two choices for the prize:

Option 1: You can take $20 home with you today.

Option 2: Take $2 a day for the next 15 days.

1. Which option earns more money? How much more?
2. Which option will you choose? Explain why. 

COMMENTARY

The purpose of this task is for students to compare two options for a prize where the value of one is given $2 at a time, giving them an opportunity to “work with equal groups of objects to gain foundations for multiplication.” This context also provides students with an introduction to the concept of delayed gratification, or resisting an immediate reward and waiting for a later reward, while working with money.

This task would work well with partners so that students can discuss options and check each other’s work. Students should discover that while they can take the money now, if they wait, they will receive 10 more dollars. After the students have answered questions (a) and (b), ask the class:

Even though you would earn more with Option 2, why might some people want to choose Option 1?

Reasons students might give include things like wanting to buy a present for someone who has a birthday very soon, needing the money to buy lunch or some groceries, or simply being impatient. The task presents an opportunity for the teacher to discuss the idea of being patient and planning ahead. The teacher can change the numbers to be higher or lower as a way of differentiating instruction.

This task is part of a set collaboratively developed by Money as You Learn, an initiative inspired by recommendations of the President’s Advisory Council on Financial Capability, and Illustrative Mathematics. Integrating essential financial literacy concepts into the teaching of the Common Core State Standards can strengthen teaching of the Common Core and expose students to knowledge and skills they need to become financially capable young adults. A mapping of essential personal finance concepts and skills against the Common Core State Standards as well as additional tasks and texts will be available at www.moneyasyoulearn.org. This task and additional personal finance-related mathematics tasks are available at www.illustrativemathematics.org and are tagged “financial literacy.”

SOLUTION

1. Using a number line or number grid, count by twos 15 times. 

   

   Option 2 is worth $30. 

   Since $30-$20 = $10, Option 2 is worth 10 more dollars than Option 1. (Note that by the end of second grade, students should be able to compute this difference mentally; see 2.NBT.B.8 and 2.NBT.B.5. To see the types of strategies that students might use before reaching this milestone, see 1.NBT.C.6)

2. Students might answer either Option 1 or Option 2 to this question. Most students are likely to choose Option 2 because it is the larger amount, although some may choose Option 1 if they would rather take the money now than wait. The purpose of asking part (b) is to set up the discussion about delayed gratification described in the commentary.

SOLUTION: A SECOND APPROACH TO FINDING THE VALUE OF OPTION

2 + 2 + 2 + 2 + 2 = 10. Therefore, every 5 days I would make 10.

5 + 5 + 5 = 15 days.

$10 + $10 + $10 = $30 in 15 days. I would make $30 if I choose Option 2.

SOLUTION: A THIRD APPROACH TO FINDING THE VALUE OF OPTION 2

I know that if I make $1 a day for 15 days I would make $15. $2 a day for 15 days would be $30 because 15 + 15 = 30.

SOLUTION: A FOURTH APPROACH TO FINDING THE VALUE OF OPTION 2

Students can use fake money: they can count out fifteen $2 bills and then count by twos as they put them down.