This a culminating activity for unit rates that has students apply knowledge to purchasing groceries. Specifically how knowledge of unit rates can help save money over time.
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This a culminating activity for unit rates that has students apply knowledge to purchasing groceries. Specifically how knowledge of unit rates can help save money over time.
Students will apply knowledge of unit rates to make decisions about what size of products they should purchase.
rounding decimals, rates, unit rates (this is a culminating activity so students will need experience finding and using unit rates)
How can my knowledge of unit rates be used to help me make decisions about what to purchase?
How can I help my family save money when we go grocery shopping?
1. Start with the formative assessment.
2. Pose the following question to students: "Have you ever wanted something while you were grocery shopping with your parents but they said it was too expensive? Or have you ever tried to compare prices to figure out which is the better buy?" Give students a chance to share some experiences either with the class, a small group or a partner. "What if you could help your parents save money while shopping? Today we are going to look at how you can use your knowledge about unit rates to save your family money."
3. Have students work in partners to complete "Savvy Shopper." Since the goal of the lesson is to apply knowledge of unit rates, you may wish to allow calculators; use of this tool allows all students (including struggling students) to focus on the task. Calculators can be a motivating factor for reluctant workers. Students find this lesson engaging because they are given a choice of items and the content is relevant to their lives. As students work, they will be moving between independent practice and guided practice based on their needs.
During the activity the teacher should move between pairs, ask clarifying questions and gather informal intelligence on student mastery of concepts. The teacher should check back with students who had trouble rounding correctly during the formative assessment to ensure they are successfully rounding correctly now. The directions ask students to round to the thousandths place which may be confusing to some since money usually rounds to the hundredths. We are rounding to thousandths since some of the differences in unit price will not be evident if students round to the hundredths instead.
Examples of questions the teacher may ask as he/she moves about the room:
What does "size per item" mean? How can I calculate the total number of fluid ounces? (If students are having trouble with this conversion pose a similar problem such as there are two peanut butter cups per package and ten packages in a box. How many peanut butter cups are in a box? Students should be able to figure out they need to multiply. Relating this problem back to the problem at hand--each can is 7.5 fl oz and there are 8 in a pack, how many fluid ounces are in a whole pack?)
What does it mean to justify? (For students who are having trouble with this remind them that justifying means to provide evidence that proves you are correct. You can relate this back to having a topic sentence in language arts--you can't stop with just the topic sentence you need to provide supporting evidence).
4. Complete the closure activity.
The task will move between guided and independent practice based on student needs. Some students may be able to complete the entire "Savvy Shopper" sheet independently while others may need more assistance.
The task will move between guided and independent practice based on student needs. Some students may be able to complete the entire "Savvy Shopper" sheet independently while others may need more assistance.
Bring the class back together and discuss the results of part 2. Students should realize there is a significant difference between the most expensive and least expensive.
Discussion may include students sharing out about what they found or display their work to share under the document camera.
Discussion should include how students were able to calculate unit rates, cost per day, week and year. Discussion should also include strategies for calculating these numbers while shopping (such as having a small calculator and maybe a pencil and small notepad).
The teacher can also bring up the fact that one larger container often creates less waste than several smaller containers (this ties in with the idea of surface area also a sixth grade concept) which is better for the environment.
This activity should be done toward the end of a unit on rates. After completing this task, it would be appropriate to have students complete some sort of assessment (quiz, test, performance task, etc.).
One suggestion: have students complete a task similar to the formative assessment for the summative assessment.
Mrs. Evans wants to buy scented erasers for all 140 of her students. The store sells packs in three sizes: $2.49 for a pack of 10, $3.29 for a pack of 14 and $4.50 for a pack of 20.
Pose the following to students:
The Palmer family is picking out candy to fill a piñata for Maria's birthday. The family wants to purchase 120 candies to add to the piñata. The grocery store sells bags in three sizes: $2.99 for a bag of twelve pieces of candy, $4.59 for a bag of twenty-four pieces of candy and $7.99 for a bag of forty pieces of candy.
a. Which bag is the most economical (least expensive per piece of candy)? Explain how you found your answer.
b. How much will the family save by buying 120 pieces of candy at the most economical price instead of the most expensive price? Justify your answer.
Give students 5 to 10 minutes to solve the problem. Have students share solutions with a partner or group. Then have several students share with the class how they solved the problem.
This activity can be done the day before the lesson and the solutions collected to be reviewed by the teacher that night or it can be done the day you start the lesson. In either case, the teacher should circulate while the students work in order to get an idea of the comfort level of students and accuracy of calculations.
Some students may have difficulty connecting the task to the skill of finding a unit rate. Finding the unit rate is not the only option (since all of the candy amounts are divisible by four, students might decide to find the cost for four pieces of candy or use the least common multiple of 120; since the prompt doesn't specifically ask for the unit price, only the least expensive per candy, finding the unit price is not necessary) but will probably be the most common plan for determining the answer. For students who are stuck, the teacher might ask, "If it costs $2.99 for 12 pieces of candy, how much would it cost for one piece of candy at the same rate?"
Also, students will have to round their answers. Since money is typically written out to the hundredths place, students should round to the nearest hundredths. Struggling students may have some difficulty rounding when a decimal is involved. Write the number with out the decimal (ex. 0.249166... write as 249) and ask the student if 49 is closer to 40 or 50. Relating the rounding back to whole numbers and then showing the student how to round the decimal will help clear up any confusion.
Answers:
12 pieces of candy for $2.99 is about $0.25 per piece
24 pieces of candy for $4.59 is about $0.19 per piece
40 pieces of candy for $7.99 is about $0.20 per piece
Least expensive 24 pieces of candy for $4.59--you would need five bags which would be $22.95
Most expensive 12 pieces of candy for $2.99--you would need 10 bags which would be $29.90
$29.90 - $22.95=$6.95 saved
*The teacher may wish to bring in a pinata and candy as a way to generate interest.
During the activity, allow students to work with a partner; this will allow students to give feedback to each other as they work.
The teacher should be moving between pairs of students as they work, asking questions to help clarify thinking and guide students who are having difficulty with the activity. See Teaching Phase section for more specific information.
Differentiation of Content:
Students have a choice between two different drinks (cola and milk) and two different foods (cereal and candy coated chocolates). In each case, one of the choices has one less unit price to calculate and compare.
Differentiation of Process:
Students can complete this activity with or without the aid of a calculator. For students who have thoroughly mastered unit rates, this activity can be given as summative performance task (in which case students could choose to use this as their summative assessment and skip taking a quiz or test later). Students choosing this as a summative assessment would need to complete this activity individually.
Differentiation of Product:
Instead of writing a paragraph for #3 on part 2, give students the option of creating a visual, either with paper and pencil or electronically, that clearly shows the benefits (using specific examples from the activity).
Active Learning through Writing and Dicussion:
Students are able to complete this activity in pairs, allowing them to talk through procedures with a partner. At the end of each part, students are asked to summarize their findings.
Students can pick a different product and find the best price next time they go to the store with their parents (and then share their findings with the class). Extend the connection of surface area and packaging by having students calculate the surface area of different size boxes of cereal (then using rates of surface area to ounces to compare the different size boxes).
Four function calculators.
If you are allowing students to create visuals on the computer students would need access to computers.
Prices in the lesson are the prices from a local grocery store during the summer 2012. You may wish to check your local store in order to obtain current local prices. Seeing the actual prices next time students go to the store with their families helps solidify authenticity and practically for students.
Standard for Mathematical Practice:
MAFS.K12.MP.6.1 - Attend to precision
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