Integers: How We Use Them in The Real World

    An integer can be any natural number positive or negative. As we know, we are surrounded by integers every day in the real world. Learning how to work with negative and positive integers will benefit students in everyday experiences, such as, reading a thermometer in below-zero weather, loss of football yards, along with assets and debts relating to one’s finances.

          

When introducing younger students to integers, it is essential to use visual manipulative's to represent positive and negative integers. A common manipulative used in math classrooms are colored counters. Teachers can use a black or yellow counter to signify positive, and a red for negative. Students will then be able to visualize the process of adding and subtracting integers. An example of using colored counters is shown below to represent the integer, -3.

Number-lines are another visual tool that should be used when teaching younger students, the concept of adding and subtracting integers. Number-line representations allow students to visualize how negative and positive numbers are ordered on a number-line, which will be useful when reading thermometers, and adding and subtracting negative and positive integers.

One especially useful concept is Mail-Time Representations. This represents integers in real-life situations, for example, when students are interested in determining a loss, or gain in football yards, or determining overall net worth. An example of a mail-time representation question is shown below:

Q: At mail-time, you are delivered a bill for $50. What happens to your net worth?

A: It goes down $50.

Q: At mail-time, you receive a check for $100, and are delivered a bill for $40. What happened to your net worth?

A: It goes down to $60.

These mail-time representations can include hand writing out checks and bills for the students to visualize, which will make learning this essential concept more engaging and memorable for students in the classroom.

The internet has an overwhelming number of resources that can be used to engage students while learning this concept. Technology is a great way to connect students to the concept through something their familiar with. I have found some that are particularly appropriate for the primary grades.

http://www.mathgoodies.com/games/integer_game/

This game offers students an opportunity to practice with gains and losses in football.

http://www.mathnook.com/math/skill/integergames.php

Adding, subtracting, multiplying integers. Multiple games including aliens, bike racing, digit drop, and brain racer.

http://www.math-play.com/integer-games.html

Games for reviewing positive and negative numbers.

Algorithms: 

How We Can Use Them in the Real World

          Algorithms; the word may look technical, but using algorithms in math is a simple step-by-step process. Algorithms can be used with addition, subtraction, multiplication, and division problems.

Solving a math problem using algorithms can be compared to baking a cake. Just as baking a cake requires one to follow steps, so too does an algorithm. Following each step is essential! If you skip a step when your baking a cake, your cake will not turn out. If you skip a step when solving algorithm your results may be flawed.

In this post, I am going to focus on the standard addition algorithm, which involves adding whole numbers in columns of ones, tens, hundreds, and so on, from right to left. When a column adds to a value of 10 or larger it carries over to the next column. The standard addition algorithm is the most widely used for solving mathematical equations.

Example of a Standard Addition Algorithm:

11

464                             The first step is to add the numbers in the ones                 

  78                              column. (The column furthest to the right). This      

+56                              has a total of 18. The 8 would be placed below the       

5 9 8                            one’s column, and the 1 will carry over into the tens    

                                    column.

The second step would be to add the numbers in the tens column. This column adds up to a total of 19. The 9 is placed below the tens column, and the 1 is carried over into the 100’s column.

The final step is to add the 100’s column. The total of this column adds up to be 5.

When teachers are introducing algorithms to their younger students, using manipulative's is necessary. Teachers can use a variety of items to teach algorithms such as, cubes, money, diagrams, place value mats, and counter coins. Below is an example of how teachers can use hands-on materials to teach students the concept of algorithms. Students will learn this important math concept through a visual, and tactile approach, ensuring that the learning experience is memorable and motivating. 

 

Rounding: 

How We Use It in Our Everyday Lives

  Although I wasn’t very confident with my math skills when I was in school, rounding was a math concept that I felt capable of doing. The realization that I was able to successfully grasp a math concept gave me determination in math class. Not only was this a math concept that boosted my self-esteem, but it’s also a concept I use in my everyday life.

     Rounding allows the replacement of a number with another number that holds approximately the same value. When encountering the number 1,899, this number can be rounded to 1,900. Or say you encountered a number such as this, 3486.083456879532321309. Instead of taking this number for its exact value, this number can be simply rounded to an approximate value. There is no doubt that rounding and estimation are essential for children to learn. The concept of rounding can be incorporated into creative and memorable activities for children. Some activities that provide students with a hands-on experience with rounding are as follows:

*Students will receive various index cards containing a variety of numbers. The numbers 0, 10, 20, 30, etc. can be listed on the board, or on large pieces of poster board. The students will then be asked to place their numbers under the correct answer. This lesson can be adjusted for multiple grade levels.

http://www.education.com/activity/article/six_tricks_practice_math_third/

*Students will sit in a circle for this activity. The students are given a piece of paper to tape to their shirts. There are numbers in increments of 10’s and 100’s on the student’s papers. The teacher will call out a number 1-100 and ask the student to round to the nearest 10. The student will round the number to the nearest 10, and throw a ball to the student with that corresponding number on their shirts. This activity could also be adapted for different grade levels.

http://www.learnnc.org/lp/pages/3075

*A time line will be placed on the floor using tape, or poster boards. A timeline can be used in younger grade levels to give them the opportunity to visualize the rounding rules. The teacher can ask students to point to any number on the timeline such as, 17 using a ruler. The students will then be asked to identify which number 17 is closer too, the 10 or the 20.

http://www.mathcoachscorner.com/2012/08/rounding-on-an-open-number-line/

          

Rounding and estimating can be hard for students to understand, but with the use of visuals, and hands-on experiences, this concept will become easier for students to comprehend. Teachers can also use chants, and catchy songs to introduce students to rounding. Chants are rhythmic, and therefore recalling the rounding rules will become more automatic. The approaches and strategies used in the classroom will ensure recall of these rules for later use. 

                        Problem Solving:

When We Use it in the Real World

 Problem Solving is a principle that is taught in math class, but it’s used in every subject area. Problem Solving is a skill that every person will use in the real world from, deciding on whether or not there’s enough cake for every person at the party, to strategizing in the workplace. Problem Solving is an essential life skill that students will use in, and out of the classroom.

 

                                    

When initially encountering a problem, it can seem overwhelming, but with Polya’s Problem-Solving Principle it can be broken down into four simple steps. The first step in this principle is to understand the problem. This step may seem obvious, but this step requires analyzing the problem. What is the problem asking of you as the problem solver? Do you understand all the words in the question? Do you need a peer to help explain the problem? Before moving on to step 2, the question must be fully understood.

The second step in Polya’s principle is to devise a plan. When this step is being used in a mathematical context, planning can call for developing strategies, and recognizing the correct strategy to use for the particular question. These strategies can include: guess and check, looking for patterns, making diagrams, tables, or orderly lists, eliminate possibilities, use a formula, or think of a similar problem you may have solved prior. When a strategy has been selected, it’s time to move onto step 3, which is to carry out the plan. This step may take some patience, but remember that if one strategy doesn’t work, you can discard it for another.

    The final step is to look back at your work. Once you have successfully completed your problem, looking back at the strategy used to reach the answer is the key to solving similar problems in the future.

  One problem you may encounter in which you may need to use problem solving is:

 If there are a total of 18 kids coming to your birthday party, and one cake mix serves a total of 8 people, how many boxes of cake should you ask your mom to buy?

On your class visit to the zoo, the zoo keeper asked the students they will be feeding the elephants but he’s having trouble deciding how many buckets to bring. Each elephant got one bucket. How many buckets should they bring if:

There are more than 8 elephants, less than 10, and there is an odd number of them.

Problem solving may look scary at first, but Polya’s Problem-Solving Principle breaks solving a problem into steps that simplify this process. Whether your solving a problem in the classroom, or out of it, Polya’s steps can come in handy!

The link below provides interactive problem-solving games for kids.

http://www.kidsmathgamesonline.com/problemsolving.html

Fractions: How We Use Them in the     Real World

          There were many times I sat in math class asking myself, when am I going to need this in life? Why do I need to learn this stuff? As I’ve come to learn, math is an essential skill that I use every day, for example yesterday, when I decided I wanted to make cookies for an employee party.

          The wind was fiercely blowing, and the air was brisk, it was the perfect day to stay in the house and bake some warm, chewy chocolate chip cookies. The recipe that I followed is posted below: https://www.verybestbaking.com/recipes/18476/original-nestle-toll-house-chocolate-chip-cookies/

2 1/4 cups all-purpose flour

1 teaspoon baking soda

1 teaspoon salt

1 cup (2 sticks) butter, softened

3/4 cup granulated sugar

3/4 cup packed brown sugar

1 teaspoon vanilla extract

2 large eggs

2 cups (12-oz. pkg.) NESTLÉ® TOLL HOUSE® Semi-Sweet Chocolate Morsels

1 cup chopped nuts (optional)                          

         

*The first thing I did was preheat my oven to 375 degrees

*The next step was to mix the flour, baking soda, and salt into a bowl, but I decided I wanted to double my recipe, and this is where my knowledge of fractions is required. In order to double my recipe each ingredient in the recipe will need to be doubled

*The first ingredient the recipe calls for is 2 ¼ cups of flower.

2 ¼ x 2 =

2 ¼ x 2/1=

The first fraction we focus on is the 2 ¼

The 4 is multiplied by the 2 too equal 6, and then add the numerator (1) too equal 7, the original numerator will stay the same in the end result, which would be 7/4. 

The 7/4 is then multiplied by the 2/1 straight across

7/4 x 2/1 = 14/4, we end up with an improper fraction that needs to be changed back into a mixed number, to do this we need to divide.

14 goes into 4, 3 times, the 2 is carried, and the 4 becomes the denominator. The end result looks like this, 3 2/4

*I followed these same steps to figure out how much of each ingredient I needed in order to double my cookie recipe.

*I mixed my sugars, vanilla, and butter in another bowl. The eggs were then added one by one, next the flower was mixed in. The final step is to add the chocolate chips. 

*Put your cookies in the oven, and wait to enjoy!

             

This recipe makes 5 dozen cookies before doubling it! If you plan to double this recipe, I hope you have a lot of friends to share with!

If you are having troubles doubling your recipes, watch this video! It gives an example of how to double fractions.

https://www.youtube.com/watch?v=LmkAWbHS1dk

Percentages: How We Use Them in Our Real Word

         
 Percentages are often a concept I struggle with, but for this post I want to discuss the various ways percentages are used in our everyday lives. I also want it to be shown that solving percentages can be made simple. It’s extremely important for educators to teach the concept of percentages thoroughly, but it’s just as important to teach students how they will be using percentages in the real world.

            In our real world, we encounter percentages in stores when their having a sale, there on our food and drink labels, the interest your bank accounts earn, in the work place, while reading data charts, food recipes, calculating tips when you go out to eat, reviewing test scores, etc.  

                                                                                       

A situation in which you may need to use percentages in the real world would be when you’re shopping at a store and they are having a sale. The sale states that everything is 40% off its regular price. You happen to come across a video game that you can’t pass up, but it’s $70 dollars! When you remember everything is 40% off its original price, you quickly try to calculate the price to see if you have enough cash.

Using the example above, 40% also means 40 out of 100.

First we would need to find 40% of $70 dollars.

40% = 40/100, and 40/100 x $70= $28

This means there will be a $28-dollar reduction from the original price.

You will pay a total of $42 dollars for the pair of jeans.

 A web resource I found gives clear, simple examples for solving percentages at the elementary level. This web site describes percentage examples through visuals, such as graphs and a pizza, along with the written instructions on how to solve the problem.

https://www.mathsisfun.com/percentage.html
I think it would be fun to teach students how to compute tips on a restaurant bill, and then bring them to a restaurant to do it themselves. The link below shows an example of how a lesson like this could be conducted.

http://www.classtrips.com/lpitem/96339/restaurant-trip-tips-lesson-plan

Another idea for incorporating percentages into the classroom is, setting an area of the classroom up as if it were a grocery store. The students can partner up and take turns going “shopping”. Each group can have a list of different groceries to locate in the grocery store. Once the students have discovered the item, they must figure out if they have enough “fake cash” to buy the item. All items will be marked with a specific percentage off, and students will work together to decide whether or not they can purchase the item.