Fractions
To begin this unit, I needed to understand what the students already have learned about fractions. As you may have guessed, with 21 students in my class, I have 21 different levels of understanding about fractions! This is going to be a difficult unit because there are many gaps in understanding that need to be filled in order to move on and make sense of what we are learning. Please make sure to use some of the websites listed below to practice at home and talk to your child about fractions in their everyday life. As always, knowing their facts FLUENTLY is going to make a big difference!
Common Core Standards for Unit 3:
5.NF.1 - add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.
5.NF.2 - solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.
5.NF.3 - interpret a fraction as division of the numerator by the denominator. Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.
5.NF.4 - apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
5.NF.4a - interpret the product as a part of a partition into equal parts
5.NF.4b - find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
5.NF.5 - interpret multiplication as scaling (resizing) by:
5.NF.5a - comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
5.NF.5b - explaining why multiplying a given number by a fraction greater than 1 results in the product greater than the given number; explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence to the effect of multiplying by 1.
5.NF.6 - solve real world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations to represent the problem.
5.MD.2 - make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots.
Common Core Standards for Unit 3:
5.NF.1 - add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.
5.NF.2 - solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.
5.NF.3 - interpret a fraction as division of the numerator by the denominator. Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.
5.NF.4 - apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
5.NF.4a - interpret the product as a part of a partition into equal parts
5.NF.4b - find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
5.NF.5 - interpret multiplication as scaling (resizing) by:
5.NF.5a - comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
5.NF.5b - explaining why multiplying a given number by a fraction greater than 1 results in the product greater than the given number; explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence to the effect of multiplying by 1.
5.NF.6 - solve real world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations to represent the problem.
5.MD.2 - make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots.
Review of vocabulary:
numerator: the top number of a fraction; shows the number of pieces
denominator: the bottom number of a fraction; show the total number of pieces in the whole
equivalent: equal or the same
simplest form/reduced: 8/16 = 1/2
mixed number: whole number with a fraction (3 1/2)
improper fraction: numerator is greater than the denominator; shows a fraction greater than 1 whole
benchmark fractions: 1/2 1/4 3/4
greatest common factor (GCF): the biggest factor that 2 numbers have in common
16: 1, 2, 4, 8, 16 24: 1, 2, 3, 4, 6, 8, 12, 24 GCF of 16 and 24 = 8
least common multiple (LCM): the smallest multiple that 2 numbers have in common (multiples are like skip counting)
6: 6, 12, 18, 24, 30, 36 8: 8, 16, 24, 32 LCM of 6 and 8 = 24
What we're doing in class:
What does GCF and LCM have to do with fractions?
LCM helps to find a common denominator; useful when adding, subtracting, comparing, or finding equivalent fractions
GCF helps us to simplify or reduce fractions to lowest terms; if the GCF = 1, then the fraction cannot be simplified or reduced
How do I add/subtract fractions with unlike denominators and mixed numbers?
We have added and subtracted fractions with visual pictures, number lines, and using the multi-step algorithm.
1) WE MUST FIRST FIND A COMMON DENOMINATOR! The Least Common Denominator (LCD) IS the Least Common Multiple (LCM). So if we find the LCM of the denominators, then we have the LCD.
2) Then we must make equivalent fractions using our new denominator. Only then can we add/subtract fractions with unlike denominators.
3) Adding/subtracting with mixed numbers is the same - unless you have to REGROUP! When you regroup to subtract, you "borrow" 1 whole from the whole number and add that to the fraction you already have. For example: if you have 2/3 as the fraction and you borrow one from the whole number, you will add 3/3 + 2/3 to get 5/3. Then you can subtract your numerators.
This website has a video tutorial and some practice problems that you can self check:
http://www.mathvillage.info/node/34
In class, we are working in small groups on skills that we need. Please see the websites below to review skills that your child is working on in class. Thanks for your support!
Wow - we have done SO much in class in the past few weeks! Not only have we learned to add and subtract fractions with unlike denominators, but we have also learned how to multiply and divide fractions and mixed numbers. Please continue to check out the websites below as I try to continue adding others. Also, don't forget that students can go on www.khanacademy.org in order to practice skills. I am able to monitor this site and check student progress.
Websites for practice:
adding fractions: http://www.sheppardsoftware.com/mathgames/fractions/FruitShootFractionsAddition.htm
subtracting fractions: http://www.sheppardsoftware.com/mathgames/fractions/FruitShootFractionsSubtraction.htm
equivalent fractions: http://www.ixl.com/math/grade-5/equivalent-fractions
least common denominator: http://www.ixl.com/math/grade-5/least-common-denominator
ordering fractions: http://www.ixl.com/math/grade-5/put-fractions-in-order
add/subtract with like denominators: http://www.ixl.com/math/grade-5/add-and-subtract-fractions-with-like-denominators
add/subtract with like denominators word problems: http://www.ixl.com/math/grade-5/add-and-subtract-fractions-with-like-denominators-word-problems
add with unlike denominators: http://www.ixl.com/math/grade-5/add-fractions-with-unlike-denominators
subtract with unlike denominators: http://www.ixl.com/math/grade-5/subtract-fractions-with-unlike-denominators
subtract with regrouping: http://learnzillion.com/lessons/345-subtract-mixed-fractions-regrouping
numerator: the top number of a fraction; shows the number of pieces
denominator: the bottom number of a fraction; show the total number of pieces in the whole
equivalent: equal or the same
simplest form/reduced: 8/16 = 1/2
mixed number: whole number with a fraction (3 1/2)
improper fraction: numerator is greater than the denominator; shows a fraction greater than 1 whole
benchmark fractions: 1/2 1/4 3/4
greatest common factor (GCF): the biggest factor that 2 numbers have in common
16: 1, 2, 4, 8, 16 24: 1, 2, 3, 4, 6, 8, 12, 24 GCF of 16 and 24 = 8
least common multiple (LCM): the smallest multiple that 2 numbers have in common (multiples are like skip counting)
6: 6, 12, 18, 24, 30, 36 8: 8, 16, 24, 32 LCM of 6 and 8 = 24
What we're doing in class:
What does GCF and LCM have to do with fractions?
LCM helps to find a common denominator; useful when adding, subtracting, comparing, or finding equivalent fractions
GCF helps us to simplify or reduce fractions to lowest terms; if the GCF = 1, then the fraction cannot be simplified or reduced
How do I add/subtract fractions with unlike denominators and mixed numbers?
We have added and subtracted fractions with visual pictures, number lines, and using the multi-step algorithm.
1) WE MUST FIRST FIND A COMMON DENOMINATOR! The Least Common Denominator (LCD) IS the Least Common Multiple (LCM). So if we find the LCM of the denominators, then we have the LCD.
2) Then we must make equivalent fractions using our new denominator. Only then can we add/subtract fractions with unlike denominators.
3) Adding/subtracting with mixed numbers is the same - unless you have to REGROUP! When you regroup to subtract, you "borrow" 1 whole from the whole number and add that to the fraction you already have. For example: if you have 2/3 as the fraction and you borrow one from the whole number, you will add 3/3 + 2/3 to get 5/3. Then you can subtract your numerators.
This website has a video tutorial and some practice problems that you can self check:
http://www.mathvillage.info/node/34
In class, we are working in small groups on skills that we need. Please see the websites below to review skills that your child is working on in class. Thanks for your support!
Wow - we have done SO much in class in the past few weeks! Not only have we learned to add and subtract fractions with unlike denominators, but we have also learned how to multiply and divide fractions and mixed numbers. Please continue to check out the websites below as I try to continue adding others. Also, don't forget that students can go on www.khanacademy.org in order to practice skills. I am able to monitor this site and check student progress.
Websites for practice:
adding fractions: http://www.sheppardsoftware.com/mathgames/fractions/FruitShootFractionsAddition.htm
subtracting fractions: http://www.sheppardsoftware.com/mathgames/fractions/FruitShootFractionsSubtraction.htm
equivalent fractions: http://www.ixl.com/math/grade-5/equivalent-fractions
least common denominator: http://www.ixl.com/math/grade-5/least-common-denominator
ordering fractions: http://www.ixl.com/math/grade-5/put-fractions-in-order
add/subtract with like denominators: http://www.ixl.com/math/grade-5/add-and-subtract-fractions-with-like-denominators
add/subtract with like denominators word problems: http://www.ixl.com/math/grade-5/add-and-subtract-fractions-with-like-denominators-word-problems
add with unlike denominators: http://www.ixl.com/math/grade-5/add-fractions-with-unlike-denominators
subtract with unlike denominators: http://www.ixl.com/math/grade-5/subtract-fractions-with-unlike-denominators
subtract with regrouping: http://learnzillion.com/lessons/345-subtract-mixed-fractions-regrouping