Unit III: Operations Using Standard Method
2018 ETAP 623 Home Page | Teaching Fractions and Number Sense
Return to: Unit II: Operations with Models Go to: Unit I: Basics of Fractions
Unit III: Operations Using Standard Method
Lesson 7: Adding and Subtracting Fractions
Lesson Notes
When students are ready to find common denominators and equivalent fractions without using manipulatives, it is important to stress that equivalent fractions can be made by multiplying by 1 or 1 whole. This is important so that students understand why fractions are equivalent instead of memorizing “what you do to the denominator you do to the numerator.” Students should make the connection that multiplying any number by 1 will get the same number back. When dividing by 1, the result is also the same number. Students should see that even know the numbers are changing, that the fractions are equivalent and still have the same value. This is why equivalent fractions are sometimes called renaming fractions.
Students will skip count to find the lowest common denominator. They should know that they common denominator is the higher of the two numbers of the denominators, or a number larger than both, since we are looking at multiples. Students will work on making equivalent fractions with that common denominator. Sometimes only one fraction needs to be changed, such as ½ + ¼ and sometimes both need to be changed to equivalent fractions, such as ⅔ + ¼ .
Objectives
- Students will add and subtract fractions using common denominators.
Task I
Watch the Adding & Subtracting Fractions video on EdPuzzle that is connected to our google Classroom Page. If you have not yet joined our class, you may use the link: Lesson VII Video I
Lesson 8: Multiplying Fractions
Lesson Notes
Multiplying fractions is very straight forward. Students need to multiply the numerator times numerator and denominator times denominators. There is no need for a common denominator. Multiplying fractions is probably one of the easiest operations with fractions. It is critical that students have their multiplication facts down in order to be fluent in multiplying fractions.
Additional Notes: The 5th grade standard for NYS has students converting fractions to decimals by trying to get the denominator to be a 10 or 100 using equivalent fractions. Again, stress that fractions are only equivalent because they are being multiplied by 1. Again, numbers multiplied or divided by one whole is itself. Stress that students are multiplying or dividing by two-halves, or 2/2, three thirds, or 3/3, etc. If students are still having trouble, give them a real world scenario. For example, if you take a candy bar and break it into 3 pieces, and you get all three pieces, how much of the candy bar did you get? Students should make the connection that they get the whole thing, or 1 whole. Ask students to pronounce fractions such as 2/10 or 34/100. When they can convert fractions to fractions with those denominators, it is much easier to convert to decimal.
Objectives
- Students will multiply fractions.
Task II
Watch the Multiplying Fractions video on EdPuzzle that is connected to our google Classroom Page. If you have not yet joined our class, you may use the link: Lesson VIII Video I
Lesson 9: Dividing Fractions
Lesson Notes
Students will learn that we can divide fractions just like we do with multiplication-numerator times numerator and denominator times denominators. In this case it is critical to have a common denominator. This is not required by can be helpful. This helps by seeing how many groups can be formed and connects to the modeling method.
Depending on the level of the student, the students can understand changing division of fractions to multiplication by “invert and multiply” or “multiply by the reciprocal.” This is done by multiplying by 1 whole as shown. Students should practice identifying the reciprocal of whole numbers and fractions, as this is helpful for the students to see that any fraction multiplied by its reciprocal is 1. This will be helpful later one when solving equations with a fractional coefficient.
Objectives
- Students will divide fractions by finding common denominators.
- Students will divide fractions by multiplying by the reciprocal.
Task III
Watch the Dividing Fractions video on EdPuzzle. You may use the link: Lesson IX Video I
Task IV: Mini-Course Fraction Assessment
Now that you have completed this Unit and Mini-Course, please take the summative assessment using Quizizz using code: 784333
Task VII
Writing Journal
Now write in your journal what you have learned from this unit. Be sure to reflect on what you learned and what questions you have. Try creating your own fraction problems and answer them using the standard method. Reflect on what you learned in this mini-course. If you have any suggestions on how to improve the course, please feel free to email me.