Yumiko Kishikawa

Content Standards

6.1.1 Select and use appropriate strategies to estimate fraction and decimal products and quotients. (I only taught estimation of sums and differences of fractions.)

6.1.7 Use the relationship between common decimals and fractions to solve problems including problems involving measurement.

Big idea

• Mathematical reasoning
• Mixed numbers

Essential questions

• How can a situation in the world be represented in mixed numbers?
• How can mixed numbers represent a real world situation?
• How is a sum or a difference of fractions estimated?
• How is a sum or a difference of expressions that include mixed numbers found?
• How is renaming of a fraction used to find a sum or a difference of expressions that include mixed numbers?
• What is polygon?
• How is the perimeter of a polygon found?

Yumiko Kishikawa

Rationale for adding and subtracting mixed numbers and finding the perimeter of polygons

Students will start learning estimating sums and differences of fractions and mixed numbers. Then, they will investigate adding and subtracting mixed numbers using previous knowledge on fractions and mixed numbers. They will also evaluate the perimeter of polygons of which sides are expressed in fractions or mixed numbers.  

Subject

When people use sums and differences of fractions and mixed numbers, they sometimes need estimation rather than exact values. Therefore, students should be able to estimate them by learning how to round fractions. Furthermore, when people measure something, the numbers they get from the measurements are not always only whole numbers or only fractions but mixed numbers in many real-world situations. These mixed numbers are often needed to be manipulated by adding to or subtracting from each other. Students already understand simplifying fractions, the least common denominators, comparing fractions, converting mixed numbers into improper fractions or vice versa, adding and subtracting fractions and estimating sums and differences of expressions with fractions and mixed numbers. Students will investigate how a mixed number can be added to or subtracted from another mixed number using these pieces of knowledge they already have. Furthermore, they will apply the knowledge of adding and subtracting mixed numbers to evaluate the perimeter of polygons.

Student

Students should know how to estimate sums and differences of expressions with mixed numbers. They will use estimation when they want to know approximate values expressed in fractions and mixed numbers. For instance, one might want to know the total amount of drink he has would be enough to invite eight friends if ½ gallon of apple cider and 1/3 gallon of orange juice in his fridge. However, they may need more accuracy than estimation in certain situations. They already can add or subtract fractions that have different denominators by finding the least common denominator. They also know how a mixed number is renamed as an improper fraction or vice versa. They can simplify a fraction as well. With the understanding these operations of fractions, students will be able to explore how they can add or subtract mixed numbers. It would be beneficial for students to be able to handle mixed numbers by adding or subtract because they are practical numbers in real life. They will also investigate how they can find the perimeter of polygons of which sides are expressed in mixed numbers.

Society

Estimation is prevalently used in the real world. People might estimate fractions or mixed numbers to the nearest eighth of an inch or the nearest sixteenth of an inch when they measure lengths of things. It is important to understand how fractions and mixed numbers are rounded to approximate sums and differences. It is also essential that students understand addition and subtraction of mixed numbers and are able to use the skills in the real world. People may encounter situations where they need to add or subtract mixed numbers in their lives. One example is that they may want to add ingredients expressed in mixed numbers while cooking. Another example is that they may want to find the rest of the distance when biking by subtracting mixed numbers. 

Mixed numbers are added or subtracted to evaluate situations including the national budgets, business transactions, designing buildings, distributing commodities and personal shopping.  People may want to subtract one price per unit from another price per unit of the same product to decide a better buy. Doctors may want to find out how much weight their patients have gained or lost by subtracting mixed numbers in pounds. An airplane company may want to find the total distance a plane can fly, which is expressed in mixed numbers. Understanding adding and subtracting mixed numbers will benefit people and society to assess or make wise decisions in various situations.

Goals            

Students will understand the concept of estimating sums and differences of fractions

Students will understand the concept of adding and subtracting mixed numbers.

Students will understand the concept of a polygon.

Students will understand how perimeters of a polygon can be found.

Students will be able to find the perimeters of polygons.

Objectives

Students will be able to estimate sums and differences of fractions.

Students will be able to add or subtract mixed numbers converting mixed numbers into improper fractions.

Students will be able to add or subtract mixed numbers by renaming.

Students will be able to identify polygons.

Students will be able to measure the perimeter of polygons.