Post 1: Fractions

 A topic of math that I find myself being a bit uncomfortable with is fractions. I remember dreading them in school and even having my 3rd-grade teacher yell at the class for not understanding. Given my lack of proficiency with fractions, I don't feel the most comfortable having to teach about them to students. This is something I would definitely love to change as the semester progresses. Funny enough, I just started my student-teaching placement in a 4th-grade classroom and what are they focusing on right now for math? Fractions! Right now they are learning how to simplify fractions using the Greatest Common Factor, create equivalent fractions, and see if fractions are greater than, less than, or equal to one another by cross multiplying. Soon they will learn how to add and subtract fractions with the same and different denominators. I've already started learning so much in just a short amount of time and I'm already starting to feel a bit more comfortable. I've also been given the opportunity to work in small groups with students and help them review the chapter so it's nice to see how I am able to teach and go over the material with them. This is my first student teaching placement so I hope when I do my second placement and am in a lower elementary grade that doesn't learn fractions, that I don't forget what I have learned and remembered.

Some resources I could use to help me brush up on fractions are:

https://www.math-salamanders.com/how-to-simplify-fractions.html

https://www.ducksters.com/kidsmath/fractions_reducing_simplifying.php

https://mathtechconnections.com/2021/02/15/fractions-in-fourth-how-to-teach-adding-and-subtracting/

and youtube

Some NYS standards that coincide with the 4th-grade fractions I am exposed to are:

Extend understanding of fraction equivalence and ordering:

4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

        NY-4.NF.1 Explain why a fraction 𝑎𝑎 𝑏𝑏 is equivalent to a fraction 𝑎𝑎 × 𝑛𝑛 𝑏𝑏 × 𝑛𝑛 by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

        NY-4.NF.2 Compare two fractions with different numerators and different denominators. Recognize that comparisons are valid only when the two fractions refer to the same whole. e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1 2 . Record the results of comparisons with symbols >, =, or <, and justify the conclusions. e.g., using a visual fraction model. 

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b. 

    a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. 

    b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8 ; 2 1 8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. 

    c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. 

    d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

4.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. 

    a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4). 

    b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.) 

    c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?