# home

6th Grade Math
Unit Title: Multiplication and Division of Fractions:
LESSON TITLES:
1. Multiplication of Fractions (Lesson 1 of 5)
2. Division of Fractions (Lesson 2 of 5)
3. Multiplication & Division of Mixed Numbers (Lesson 3 of 5)
4. Weights and Capacity in Customary Units (Lesson 4 of 5)
5. Customary Units: Problem Solving (Lesson 5 of 5)

ANTICIPATED INSTRUCTIONAL TIME: Five 50-minute class periods.

Enduring Understanding: Students will know how to multiply and divide fractions (and mixed numbers, which are also fractions, only they are improper). They will understand a structured order of operations. They will understand the value of a fraction in terms of its relationship with whole numbers, particularly the number 1. They will understand when their answer is going to get larger and when it is going to get smaller. They will apply and demonstrate this understanding using conversion rates.

Rationale (Philosophy): Working as a class will enable the foundation and structuring of a solid learning base. Completion of small homework assignments will ensure that the students are able to work with minimal guidance. Correcting the assignments will allow for explanation and clarification. The next day’s lesson will build on what was learned today. The pre-test and post-test will provide diagnostic information. The post-test will be a summative assessment.
The content involves fractions, the knowledge of how to use these fractions, and the conceptualization of the fractions of numbers. This must be taught to successfully integrate the work and understanding of the previous unit’s lessons. It also must be taught as a foundation for the subsequent unit.

Unit Goals
G.1.1. Work flexibly with fractions to solve multiplication problems.
G.1.2. Conceptualize with the aid of examples that multiplying by a number smaller than one will decrease the original number and that multiplying by a number larger than one will increase the original number.
G.2.1 Appreciate the connection that division with fractions involves using the reciprocal.
G.2.2 Develop meaning for integers and represent and compare quantities with them.
G.2.3 Conceptualize that dividing by a number smaller than one will increase the original number and dividing by a number larger than one will decrease the original number.
G.3.1. Discover the differences between multiplication and division of fractions.
G.3.2. Relate the similarities between multiplication and division of fractions.
G.3.3. Appreciate the relationship between improper fractions and mixed numbers.
G.4.1 Appreciate the mathematics involved in converting one unit of weight and capacity to another unit.
G.4.2. Develop meaning and purpose for conversions from one unit to another.
G 4.3. Conceptualize that by moving to a larger unit that we must divide and that by moving to a smaller unit, we must multiply.
G.5.1. Appreciate the applicability of the knowledge of customary units.
G.5.2. Recall the necessary conversion rates and use multiplication and division appropriately.

Unit Objectives
O.1.1. Students will demonstrate the ability to solve simple multiplication of fraction problems by performing the three necessary steps: 1) writing (copying) the problem, 2) cancellation (simplification), 3) multiplication of the numerator, and multiplication of the denominator.
O.1.2. Students will be able to verbalize that when multiplying fractions less than one, the result will be less than the factors; and that when multiplying fractions that are greater than one, the result will be more than the factors.
O.2.1 Students will be able to divide mixed numbers.
O.2.2. Compare and order fractions efficiently and find their approximate locations on a number line.
O.2.3. Use factors, multiples, prime factorization, and relatively prime numbers to solve problems
O.3.1. Students will demonstrate the ability to differentiate between multiplication and division of fractions with the reciprocal. The reciprocal adds one additional step to the mathematical problem.
O.3.2. Students will be able to verbalize that after finding the reciprocal, a division problem of fractions is the same thing as a multiplication problem of fractions.
O.3.3 Students will be able to convert improper fractions to mixed numbers and mixed numbers to improper fractions.
O.4.1. Use customary units of weight and capacity.
O.4.2. Compare and order weights and capacities efficiently and find their approximate quantities in relation to one another.
O.4.3. Use factors, multiples, prime factorization, and relatively prime numbers to solve problems.
O.5.1. Students will be able to describe the relationship between one customary unit and another.
O.5.2. Students will be able to set up equations for conversions from one customary unit and another.

Unit Standards
6.M.1.1. Select, use, and convert appropriate unit of measurement for a situation.
6.N.1.2. Students are able to find factors and multiples of whole numbers
.
6.N.3.1. Students are able to use various strategies to solve one- and two-step problems involving positive fractions.

Overview of the Instructional Progression of the Unit: Summaries of lessons
- In Lesson 1, students will learn to multiply using fractions. The value of numbers will be considered.
- In Lesson 2, students will be introduced to reciprocals, and will then have the ability to learn to divide fractions. The value of numbers will be considered and what happens to them in terms of enlarging or shrinking will be discussed.
- In Lesson 3, students will be introduced to multiplication and division of mixed numbers and improper fractions. Since these are only more complicated fractions, this day will be a good review and time to spot lingering problems.
- In Lesson 4, students will be introduced to customary units of weight and capacity. After gaining this knowledge, they will be asked to think critically about these values and evaluate them. They will then convert them from one unit to another.
- In Lesson 5, students will extend their learning to problem solving using customary units of weight and capacity. The content of the previous four lessons will be tied together and the experience will be more common to everyday life and include classzone.com. Jeopardy will be used as an assessment of how well the students are prepared as a whole and then the timing of the chapter test will be determined.

Plan for Diagnostic, Formative, and Summative Assessment (matches the assessments with the goals and objectives)
 Assessment Type (D,F,S) Lesson # Quiz/ Pretest D 1-5 McDougall Littell p.316 #12-34 even F & S 1 McDougall Littell p. 336 #10-38 even F & S 2 McDougall Littell p. 341 #10-22 even F & S 3 McDougall Littell p. 346 # 6-24 F & S 4 McDougall Littell p.352 #6-24 even F & S 5 Jeopardy PowePoint F 1-5 Chapter Test S 1-5

Summary of Technology to be Used in the Unit (minimum one lesson requirement)
During this unit, we will visit classzone.com. Here, relationships are made and everyday examples are provided. Several other interactive site suggestions are available depending on the needs of the class. Students will consider things such as how many footballs are equal to the weight of one football player? What unit is used to express the weight of the football and the football player? Students will also participate in an interactive PowerPoint game of Jeopardy. This is a primary form of formative assessment to make sure that I have properly guided the students in their preparation for their upcoming test.

Explanation of How the Unit Fits into a Larger Course of Study
Students must learn to multiply and divide fractions to prepare for Algebra and their following lessons on conversions. Rates are expressed as fractions and conversions are necessary for comparisons. Conversion rates are practical to the real world and truly understanding them will enhance problem solving strategies.

Lesson 1.doc
Lesson 2.doc
Lesson 3.doc
Lesson 4.doc
Lesson 5.doc
Jeopardy.ppt