Thursday, August 1, 2013

Free Lesson Plans: Using Fractions and Percentages in the Real World

 Using Statistics, Fractions, and Percentages in the Real World Lesson Plans

This lesson plan is to help show students why they’re learning the math that you’ve taught. It gives a great way to help them understand how to practice their knowledge and how to utilize it in the real world.

Necessary Background Knowledge (but need practice on)

Functions:
Addition
Subtraction
Multiplication
Division

Statistics:
Range
Mean
Median
Mode
Line Graph

Percentages:
Convert decimals to percent
Convert fractions to percent
Convert percent into decimal
Convert percent into fraction

Fractions:
Create fractions from decimals
Create fractions given two numbers
Simplify fractions

CommonCore Standards:

CCSS.Math.Content.3.NF.A.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
CCSS.Math.Content.4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.1
CCSS.Math.Content.4.NF.C.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.2 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
CCSS.Math.Content.4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.
CCSS.Math.Content.5.NF.B.3 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?
CCSS.Math.Content.5.NF.B.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
CCSS.Math.Content.5.NF.B.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.1
CCSS.Math.Content.5.NF.B.7c Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?

CCSS.Math.Content.6.NS.B.2 Fluently divide multi-digit numbers using the standard algorithm.
CCSS.Math.Content.6.NS.B.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
CCSS.Math.Content.6.NS.C.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
CCSS.Math.Content.6.NS.C.6c Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane

CCSS.Math.Content.6.SP.B.5 Summarize numerical data sets in relation to their context, such as by:
CCSS.Math.Content.6.SP.B.5c Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.


CCSS.Math.Content.6.EE.A.2 Write, read, and evaluate expressions in which letters stand for numbers.
CCSS.Math.Content.6.EE.B.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.
CCSS.Math.Content.6.EE.B.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
CCSS.Math.Content.7.EE.A.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
CCSS.Math.Content.7.EE.A.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.

CCSS.Math.Content.7.EE.B.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
CCSS.Math.Content.7.EE.B.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
CCSS.Math.Content.7.EE.B.4a Solve word problems leading to equations of the form px + qr and p(x + q) = r, where pq, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?


Materials:

Board and your favorite way of writing on it
Restaurant menu of your students’ choosing
Knowledge of your local taxes (google it)
Field trip
Students will need paper and pencils

Goals:

Help students understand fractions, percentages, and statistics.
Help students understand why knowledge of fractions, percentages, and statistics are necessary in their everyday life.
Help students practice their knowledge of fractions, percentages, and statistics.

Built-In Interventions:

Friendly towards auditory, visual, and kinesthetic learners
Includes a good deal of practice on the same skills
Includes carrying the skills over to outside situations
Based on students’ interests
Builds off of pervious knowledge
Relates to the real world

Possible Additional Interventions:

Calculator
Bold font
More space/paper
Student help (preferred)
Teacher help

I Can Statement:

I can use my knowledge of fractions and percentages to help me in a restaurant. 

Spans 10 days- each day is scheduled for a 1 1/2 hour lesson with 3 minute breaks every 15 minutes to play The Fraction Game, exercise/stretch, and socialize. There is a field trip included. If you are unable to do the field trip, try to set up a pretend restaurant in the classroom. It is preferred to actually take the field trip though, so the students can carry their skills over. This is important for all students, but especially so for students with disabilities.

Day 1:

Beginning Board Work:

Decimals to Fractions
2.34
4.5
3.25
4.75
6.98

1. Find out what restaurant a lot of the students enjoy.
2. Discuss the food at that restaurant and how their experience was. Ask what they got last time they were there or their favorite items on the menu. Discuss what your favorite items are there. (Mine chose Steak and Shake.)
3. Find the menu online.
4. Ask the students to come up with 3 meals with anything they want in them. Write them on the board. (Students can follow along on their papers if they wish (or if you need to make sure they’re paying attention.))
5. On the board, together, add up the prices of each meal to find out what each one would cost.
6. Find the range of prices for the given meals.
7. Find the mean, median, and mode of the prices for the given meals.
8. Draw a number line to show the prices, the range, the mean, median, and the mode.


Day2:

Beginning Board Work:

Decimals to Fractions
6.5
7.3
7.6
7.75
3.25

1. Remind the students what you did yesterday with the 3 meals on the menu. Discuss the range, mean, median, and mode of the prices.
2. Discuss with the students about state taxes. (I will be using 5.5% since that’s what it is in Ohio.) Explain to the students why we have taxes and where they go to. (Include things students would agree are necessary and places it may go to that they don’t agree with too- it’s a great way to have an open economics and social studies discussion and debate since most likely you’ll have many sides!) My students also asked about income taxes at this point, so I discussed how my employers pay a tax on my pay, then I pay a tax on my pay, then when I spend my pay I pay taxes again. We discussed whether they agreed with this or not and the places it goes to. This part might take a while. That’s fine.
3. Remind the students how to turn a percent into a decimal. (I like to use 100 pennies in a dollar, so each penny is a percent- so 5.5% is 5 and ½ pennies for every dollar I spend or 55 cents for every $10.00 I spend.) Remind them to always double check that they made the correct conversion from percent to decimals is that the tax will never be more than what they spent to begin with.
4. Discuss tips with the students- how an average job is 15%, a bad job is 10%, an extremely horrifically bad job is 0% (very rare- but has happened!), a good job is 20% and a great job is 25% or more- heck, you can even give 100% tip or higher! Talk with the students how if they get a job as a waiter or waitress, this is why you must always be polite and prompt with your customers, because the better you do, the more tips you get.
5. Ask the students how much money they generally take with them when they go out to eat. Write it on the board.
At this point you’ll probably have ran out of time.

Day 3:

Beginning Board Work:

Fractions to Percent
1/20
1/3
½
2/3
4/5

1.  Remind the students about taxes and tips. Remind the students you need to turn a percent into a decimal to use it with prices.
2. With the students, calculate the tax and tip on the board for each meal.
3. Add the tax and tip to the price of each meal for the total cost.
4. Using the amount of money the students said they’d take with them to the restaurant, see if they can afford the meals and which ones.
5. Discuss with the students why they need this knowledge.
6. On the board, find the percent of money spent and percent saved for each meal.
7. On the board, find the fraction of money spent and the fraction saved for each meal.

Day 4

Beginning Board Work:

Fractions to Percent
¼
7/8
¾
5/3
9/11

1.  Have the students pick a different restaurant. Tell them their budget (it will depend on which restaurant they picked.) Mine picked McDonald's- so we discussed how tipping is not generally done for fast food (unless the person does an amazing job.) (I decided to add a little language arts into the lesson.)
A little English lesson in math. ;)

2. Let each student pick their own meal and add up the costs. While you do your own on the board.
3. Ask the students to find the range, mean, median, and mode of the prices of the food they have ordered.
4. Remind the students about taxes and tip. Assume that the waiter/waitress did an average job.
At this point you may have run out of time. Actually calculating the tip and tax will come on Day 5.

Day 5

Beginning Board Work:

Percent to Decimals
75%
50%
30%
20%
11%

1. Have the students calculate the tip and tax for their meal.
2. Add the tip and tax to the price of the meal for the total cost.
3. Find out if their meal was in the budget.
4. Have the students find the percent they spent and the percent they saved.
5. Have the students find the fraction they spent and the fraction they saved.
6. If there is extra time (hopefully!) Discuss why it’s a good idea to save some of that money- put it in the bank for later so instead of needing loans you can pay with what you have. Discuss loans, interest, and paying plans (my students were really interested in finding out how old they would be to pay off a car or a house if they bought it right now) as well as bank accounts, CD’s, stocks, bonds, and interest on them.


Day 6

Beginning Board Work:

Percent to Decimals
25%
100%
60%
15%
13%

1. Remind the students what you’ve been doing with the students so far. Review.
2. Discuss how the students will be going to a restaurant later to practice these skills. Go over table manners and politeness in general.
3. Ask if students have any difficulty or questions about any of the steps in what they’ve been doing.
4. Review and help the students work out the issues they may be having with any of the steps.

Day 7:

Beginning Board Work:

Percent to Fractions
30%
50%
60%
45%
100%

1.Give students the Dairy Queen Quiz.

Day 8:

Beginning Board Work:

Percent to Fractions
15%
75%
80%
70%
13%

1. Go over Dairy Queen Quiz as a class.

Day 9:

Field Trip!
1. Go to a restaurant with the students and bring along the Field Trip Worksheet.

Day 10:


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