Loading the player ...
Download list:
FriendlyFractionpt3.mp4
This podcast is part of the series: Friendly Fractions

Creator: Tynisa Williams
School/Organization: Auburn University Montgomery
Overview:
This podcast is part of a series on operations with fractions. Designed with the middle school student in mind, it is a refresher on the basics of fractions. The lesson also covers adding and subtracting unlike fractions (unlike denominators). The podcast can be used as a lesson or as a supplement to a lesson. A suggestion would be to stop the lesson as it goes along and allow the students to work problems out themselves.
Length: 02:36
Content Areas: Math
Alabama Course of Study Alignments and/or Professional Development Standard Alignments:
MA2015 (5)  11. 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. [5NF1] Example: ^{2}/_{3} + ^{5}/_{4} = ^{8}/_{12} + ^{15}/_{12} = ^{23}/_{12}. (In general, ^{a}/_{b} + ^{c}/_{d} = ^{(ad + bc)}/_{bd}.)   MA2015 (5)  12. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally, and assess the reasonableness of answers. [5NF2] Example: Recognize an incorrect result ^{2}/_{5} + ^{1}/_{2} = ^{3}/_{7} by observing that ^{3}/_{7} < ^{1}/_{2}.   MA2015 (5)  13. Interpret a fraction as division of the numerator by the denominator (^{a}/_{b} = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. [5NF3] Examples: Interpret ^{3}/_{4} as the result of dividing 3 by 4, noting that ^{3}/_{4} multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size ^{3}/_{4}. If 9 people want to share a 50pound sack of rice equally by weight, how many pounds of rice should each person get' Between which two whole numbers does your answer lie'   MA2015 (5)  14. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. [5NF4] a. Interpret the product (^{a}/_{b}) x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷ b. [5NF4a] Example: Use a visual fraction model to show (^{2}/_{3}) x 4 = ^{8}/_{3}, and create a story context for this equation. Do the same with (^{2}/_{3}) x (^{4}/_{5}) = ^{8}/_{15}. (In general, (^{a}/_{b}) x (^{c}/_{d}) = ^{ac}/_{bd}.) b. 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. [5NF4b]   MA2015 (5)  16. Solve realworld problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. [5NF6]   MA2015 (5)  17. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (Students able to multiply fractions in general can develop strategies to divide fractions in general by reasoning about the relationship between multiplication and division. However, division of a fraction by a fraction is not a requirement at this grade.)
[5NF7] a. Interpret division of a unit fraction by a nonzero whole number, and compute such quotients. [5NF7a] Example: Create a story context for (^{1}/_{3}) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (^{1}/_{3}) ÷ 4 = ^{1}/_{12} because (^{1}/_{12}) x 4 = ^{1}/_{3}. b. Interpret division of a whole number by a unit fraction, and compute such quotients. [5NF7b] Example: Create a story context for 4 ÷ (^{1}/_{5}), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (^{1}/_{5}) = 20 because 20 x (^{1}/_{5}) = 4. c. Solve realworld problems involving division of unit fractions by nonzero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. [5NF7c] Examples: How much chocolate will each person get if 3 people share ^{1}/_{2} lb of chocolate equally' How many ^{1}/_{3} cup servings are in 2 cups of raisins'   MA2015 (6)  4. Interpret and compute quotients of fractions, and solve word problems involving division of fractions, e.g., by using visual fraction models and equations to represent the problem. [6NS1] Examples: Create a story context for (^{2}/_{3}) ÷ (^{3}/_{4}), and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (^{2}/_{3}) ÷ (^{3}/_{4}) = ^{8}/_{9} because ^{3}/_{4} of ^{8}/_{9} is ^{2}/_{3}. (In general, (^{a}/_{b}) ÷ (^{c}/_{d}) = ^{ad}/_{bc}.) How much chocolate will each person get if 3 people share ^{1}/_{2} lb of chocolate equally' How many ^{3}/_{4} cup servings are in ^{2}/_{3} of a cup of yogurt' How wide is a rectangular strip of land with length ^{3}/_{4} mi and area ^{1}/_{2} square mi'   MA2015 (6)  22. Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = Bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems. [6G2]   MA2015 (7)  4. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. [7NS1] a. Describe situations in which opposite quantities combine to make 0. [7NS1a] Example: A hydrogen atom has 0 charge because its two constituents are oppositely charged. b. Understand p + q as the number located a distance q from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing realworld contexts. [7NS1b] c. Understand subtraction of rational numbers as adding the additive inverse, p  q = p + (q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in realworld contexts. [7NS1c] d. Apply properties of operations as strategies to add and subtract rational numbers. [7NS1d]   MA2015 (7)  5. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. [7NS2] a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (1)(1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing realworld contexts. [7NS2a] b. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with nonzero divisor) is a rational number. If p and q are integers, then  (^{p}/_{q}) = ^{(p)}/_{q} = ^{p}/_{(q)}. Interpret quotients of rational numbers by describing realworld contexts. [7NS2b] c. Apply properties of operations as strategies to multiply and divide rational numbers. [7NS2c] d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. [7NS2d]   MA2015 (7)  6. Solve realworld and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.) [7NS3]   MA2015 (7)  9. Solve multistep reallife and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form, convert between forms as appropriate, and assess the reasonableness of answers using mental computation and estimation strategies. [7EE3] Examples: If a woman making $25 an hour gets a 10% raise, she will make an additional ^{1}/_{10} of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 ^{3}/_{4} inches long in the center of a door that is 27 ^{1}/_{2} inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.  
