Essential Questions:
Lesson Plan B.4: Multiplying Fractions
Lesson Seed B.3c: Making Granola
Lesson Seed B.3d: Adding and Subtracting Fractions
Unit Overview
Content Emphasis By Clusters in Grade 4
Progressions from Common Core State Standards in Mathematics
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In this unit, students in grade begin working with addition and subtraction of fractions and mixed numbers with like denominators and multiplication of a fraction by a whole number. Students apply and extend their understanding of these three operations with whole numbers to using these operations with fractions. Students will also apply and extend the work from grade 3 with unit fractions as calculate sums, differences, and products using fractions.
When adding and subtracting fractions, students decompose fractions into a sum of unit fractions in multiple ways. They record those decompositions using an equation. Students justify their decompositions by using visual fraction models. Students solve word problems involving addition and subtraction of fractions of the same whole and having like denominators by using visual fraction models and equations to represent the problem. Students will also apply their understanding of addition and subtraction problem types to solving problems with fractions by identifying the relationship between the whole and the parts represented with fractions.
Multiplying fractions begins in grade 4 as students apply and extend their understanding of multiplication as repeated addition and unit fractions to multiply a fraction times a whole number. Students will see that for example that 3 x ^{2}/_{3} = ^{2}/_{3} + ^{2}/_{3} + ^{2}/_{3} = ^{3 x 2}/_{3} = ^{6}/_{3} . Students will solve word problems involving multiplication using visual models and equations to represent the problem.
At the completion of the unit on Operations with Fractions, the student will understand that:
The student will be able to:
Evidence of Student Learning:
The Partnership for Assessment of Readiness for College and Careers (PARCC) has awarded the Dana Center a grant to develop the information for this component. This information will be provided at a later date. The Dana Center, located at the University of Texas in Austin, encourages high academic standards in mathematics by working in partnership with local, state, and national education entities. Educators at the Center collaborate with their partners to help school systems nurture students' intellectual passions. The Center advocates for every student leaving school prepared for success in postsecondary education and in the contemporary workplace.
Students may think that:
Interdisciplinary Connections:
Interdisciplinary connections fall into a number of related categories:
Sample Assessment Items: The items included in this component will be aligned to the standards in the unit and will include:
Interventions/Enrichments/PD: (Standard-specific modules that focus on student interventions/enrichments and on professional development for teachers will be included later, as available from the vendor(s) producing the modules.)
Vocabulary/Terminology/Concepts: This section of the Unit Plan is divided into two parts. Part I contains vocabulary and terminology from standards that comprise the cluster, which is the focus of this unit plan. Part II contains vocabulary and terminology from standards outside of the focus cluster. These “outside standards” provide important instructional connections to the focus cluster.
visual fraction model: a model that shows operations or properties of fractions using pictures. Example: This model could be used to represent
equivalent fractions: two or more fractions that have the same value. Example #1: Example # 2: What fraction of the set is shaded?
decompose: breaking a ^{1}/_{2} number into ^{2}/_{4} two or more ^{3}/_{6} parts to make it easier with which to work.
Examples: When combining a set of 5 and a set of 8, a student might decompose 8 into a set of 3 and a set of 5, making it easier to see that the two sets of 5 make 10 and then there are 3 more for a total of 13. Decompose the number 4; 4 = 1+3; 4 = 3+1; 4 = 2+2 Decompose the number ^{3}/_{5} ; ^{3}/_{5} = ^{1}/_{5} + ^{1}/_{5} + ^{1}/_{5}
Part II – Instructional Connections outside the Focus Cluster
equation: is a number sentence stating that the expressions on either side of the equal sign are, in fact, equal.
factor pairs: two numbers that when multiplied equal a product. Examples of factor pairs for the number 12 are 2 and 6; 3 and 4; 1 and 12.
multiple: is the product of a whole number and any other whole number. Example: 20 is a multiple of 5 because 4 × 5 = 20.
Math Related Literature:
References: