Unit 3

Addition and Subtraction of Fractions

 

Grade 5

Math

Description:

Students use models, manipulatives, or number lines to add fractions with unlike denominators. Students find like denominators to add fractions. Students solve problems involving addition and subtraction of fractions with unlike denominators. Students also use benchmarks, comparisons and mental math to justify their thinking and to determine whether their answer is reasonable. Students learn to express the remainder of a division problem as a fraction as they solve real-life problems.

 

Standards:

 

NBT - Number and Operation in Base Ten

Use equivalent fractions as a strategy to add and subtract fractions.

5.NF.A.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.

For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (in general, a/b + c/d = (ab + bc)/bd.)

5.NF.A.2

Solve word problems involving addition and subtraction of fractions.

  1. 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.
  2. Use benchmark fractions and number sense of fractions to estimate mentally and justify the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

5.NF.B.3

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. For example, 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 what two whole numbers does your answer lie?

Enduring Understandings:

 

         Landmark/benchmark numbers should be used when making decisions about other numbers.

         Models can be used to compute fractions with like and unlike denominators.

         A fraction describes the division of a whole into equal parts, and it can be interpreted in more than one way depending on the whole to be divided.

         Multiplying a whole number by a fraction involves division as well as multiplication. The product is a fraction of the whole number.

         Rounding and compatible numbers can be used to estimate the product of fractions or mixed numbers.

         The relative size of the factors can be used to determine the relative size of the product.

 

Essential Questions:

 

         Why would I need to use landmark/benchmark numbers when making decisions about other numbers?

         How can models (line plots, etc.) be used to compute fractions with like and unlike denominators?

         What strategies can be used to determine if answers are reasonable?

         How can I tell if a fraction is greater than, less than, or equal to one whole?

         How can fractions with different denominators be added together? Subtracted?

         How are fractions related to division?

         How can I multiply fractions and whole numbers?

         How does multiplying by a fraction change the other factor?