Livingston County Schools

5th Unit 4-Number and Operations Fractions

Math

Unit Overview
Use equivalent fractions as strategy to add and subtract fractions. Add and subtract fractions with unlike denominators (including mixed numbers) and solve word problems.
Apply and extend previous understanding of multiplication and division to multiply and divide fractions. Interpret a fraction as division of the numerator by the denominator and solve word problems involving division of whole numbers. Multiply a fraction or whole number by a fraction. (5.NF.4a) Interpret the product of a fraction multiplied by a whole number or by another fraction. (5.NF.4b)Find the area of a rectangle with fractional side lengths. Interpret multiplication as scaling (resizing). Solve real world problems involving multiplication of fractions and mixed numbers. Divide unit fractions by whole numbers and whole numbers by unit fractions and solve real world problems with the same division process.

Length of unit: ___8 weeks______

KY Core Academic Standard / Learning Target / K / R / S / P / Critical Vocabulary / Texts/Resources/Activities
5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given 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 = (ad + bc)/bd) / I can generate equivalent fractions to find the like denominator. / X / Denominator
Numerator
Equivalent
Sum
Difference / Text: Math Connects
*Chapter 10 Lesson 3
*Chapter 10 Lesson 4
Study Island 4a
Coach Lesson 17
Coach Lesson 18
*Coach Lesson 19
*Coach Lesson 20
I can solve fraction addition problems with like and unlike denominators using an equivalent fraction strategy. / X
I can change improper fractions to mixed numbers and mixed numbers to improper fractions. / X
5.NF.2 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. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7<1/2. / I can solve word problems involving addition and subtraction of fractions with unlike denominators.
(e.g. by using visual fraction models or equations to represent the problem) / X / Estimate / Text: Math Connects
Chapter 9 Lesson 3
Chapter 9 Lesson 4
*Chapter 10 Lesson 3
*Chapter 10 Lesson 4
StudyIsland 4C
*Coach Lesson 19
*Coach Lesson 20
Teachers’ Domain (Using Recipes to Add Fractions and Convert Improper Fractions to Proper Fractions or Mixed Numbers)
I can evaluate the reasonableness of an answer, using fractional number sense, by comparing it to a benchmark fraction. / X / Evaluate
5.NF.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 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? / I can interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). / X / Interpret / Text: Math Connects
Chapter 8 Lesson 1
StudyIsland 4B?
Coach Lesson 23
Teachers’ Domain (Choosing the Most Orange Crystal)
I can solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.
(e.g. using visual fraction models or equations to represent the problem.) / X
I can interpret the remainder as a fractional part of the problem. / X
5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
a. Interpret the product (a/b) x q as a parts of a partition of q into b equal parts; equivalently, as a result of a sequence of operations a x q / b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) / I can multiply fractions by whole numbers. / X / Product / Text: Math Connects
n/a
StudyIsland 4B
*Coach Lesson 22
I can multiply fractions by fractions. / X
I can interpret the product of a fraction times a whole number as total number of parts of the whole.
(for example ¾ x 3 = ¾ + ¾ + ¾ = 9/4) / X
I can determine the sequence of operations that result in the total number of parts of the whole.
(for example ¾ x 3 = (3 x 3)/4 = 9/4) / X
I can interpret the product of a fraction times a fraction as the total number of parts of the whole / X
5.NF.4b Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
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. / I can find area of a rectangle with fractional side lengths using different strategies.
(e.g., tiling with unit squares of the appropriate unit fraction side lengths, multiplying side lengths) / X / Area / Text: Math Connects
n/a
*Coach Lesson 22
I can represent fraction products as rectangular areas.
I can justify multiplying fractional side lengths to find the area is the same as tiling a rectangle with unit squares of the appropriate unit fraction side lengths. / X
I can model the area of rectangles with fractional side lengths with unit squares to show the area of rectangles. / X
5.NF.5a Interpret multiplication as scaling (resizing), by:
a. 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. / I can know that scaling (resizing) involves multiplication. / X / Scaling / Text: Math Connects
Chapter 14 Lesson 2?
Chapter 14 Lesson 3?
*Coach Lesson 21
I can compare 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.
For example, a 2x3 rectangle would have an area twice the length of 3. / X
5.NF.5b Interpret multiplication as scaling (resizing), by:
b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); 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 a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. / I can know that multiplying whole numbers and fractions result in products greater than or less than one depending upon the factors. / X / Text: Math Connects
n/a
*Coach Lesson 21
I can draw the conclusion that multiplying a fraction greater than one will result in a product greater than the given number. / X
I can draw the conclusion that when you multiply a fraction by one (which can be written as various fractions, ex 2/2, 3/3, etc.) the resulting fraction is equivalent. / X
I can draw the conclusion that when you multiply a fraction by a fraction, the product will be smaller than the given number. / X
5.NF.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. / I can represent word problems involving multiplication of fractions and mixed numbers.
( e.g., by using visual fraction models or equations to represent the problem.) / X / Text: Math connects
Chapter 8 Lesson 2
Chapter 8 Lesson 4
StudyIsland 4C
*Coach Lesson 22
I can solve real world problems involving multiplication of fractions and mixed numbers. / X
5.NF.7abc Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. 1
1Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.
a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) divided by 4, and use a visual fraction model to show the quotient. Use relationships 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. For 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 real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, 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? / I can understand the relationship between multiplication and division. / X / Quotient / Text: Math Connects
Chapter 8 Lesson 1 (Standard 7C)
Coach Lesson 24
BrainPop (multiplying and dividing fractions)
I can interpret division of a unit fraction by a whole number. / X
I can justify my answer using the relationship between multiplication and division.
(eg and by creating story problems, using visual models, and relationship to multiplication, etc.) / X
I can interpret division of a whole number by a unit fraction. / X
I can justify my answer using the relationship between multiplication and division and by representing the quotient with a visual fraction model. / X
I can solve real world problems involving division of unit fractions by whole numbers other than 0 and / X
I can solve real world problems involving division of whole numbers by unit fractions using strategies.
(e.g. such as visual fractions models and equations.) / X
Spiraled Standards:
5.NBT.5
5.NBT.6 / HOT Questions:

* Resource used for more than one Target/Standard.