Grade 5: Multiplication of Fractions

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COMMON CORE STANDARDS

Numbers and Operations-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 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?

5.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

5.NF.B.4(a) Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × 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).

5.NF.B.4(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.

5.NF.B.5 Interpret multiplication as scaling (resizing), by:

5.NF.B.5 (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.

5.NF.B.5 (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.

5.NF.B.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.

Standards for Mathematical Practice

SMP.1  Make sense of problems and persevere in solving them.

SMP.2  Reason abstractly and quantitatively.

SMP.3  Construct viable arguments and critique the reasoning of others

SMP.4  Model with mathematics.

SMP.7  Look for and make use of structure.

English Language Arts/Literacy Standards

Speaking and Listening

SL.5.1 Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly.

SL.5.1(b) Follow agreed-upon rules for discussions and carry out assigned roles.

SL.5.1(c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others.

Sl.5.1(d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions.

SL.5.3 Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence.

Reading Informational Text

RI.5.4 Determine the meaning of general academic and domain-specific words and phrases in a text relevant to a grade 5 topic or subject area.

DESCRIPTION OF UNIT

This Grade 5 unit titled “Multiplication of Fractions” from the Massachusetts Department of Elementary and Secondary Education is intended to be completed in twelve 60-minute lessons of mathematics instruction. The emphasis of this Grade 5 unit is on developing a conceptual understanding of and proficiency with multiplication of fractions with a particular emphasis on understanding fraction multiplication in the context of using the unit fraction. Throughout unit activities, students: create visual models to represent multiplication; explain how and why corresponding equations work; use prior knowledge about multiplication to become proficient with part of whole and part of part multiplication; create and solve word problems. Teacher Think-Alouds, Think-Pair-Share-Writing, rotating station tasks and debriefing sessions provide varied instruction to support students’ conceptual understanding. Formative assessments include a pre-assessment, exit cards and problem tasks. An authentic summative assessment asks students to support or refute an iBaby Advertisement Claim which includes visual models, equations, and a written analysis.

CAUTIONS

Connecticut teachers should be cautioned that the unit materials are extensive and will require familiarity to be used effectively. The prior knowledge required for the successful implementation of this unit is noted in unit materials. It would be helpful for Connecticut teachers to review the Number and Operations Fractions Progression for grades 3–5 prior to teaching this unit. A link to this document is provided below. The unit developer recommends that teachers spend time constructing their own visual models and equations as they work through the problems prior to students doing so. It will be important to consider the variability of learners in the class and make adaptations as necessary.

Number and Operations Fractions Progression for grades 3–5

RATIONALE FOR SELECTION

This unit is an exemplary example of how to target a set of grade level standards CCSS mathematical standards in a focused, coherent instructional plan. Standards for Mathematical Practice that are central to the unit’s lessons are identified, handled in a grade-appropriate way, and are well connected to the content being addressed. The tasks and activities build a deep understanding of and proficiency with multiplication of fractions. The unit presents a balance of mathematical procedures and activities that build students’ conceptual understanding with the use of multiple visual models, including area model, number line and fraction strips. Instructional tips and strategies and anticipated student preconceptions and /or misconceptions are provided for each lesson. An aligned rubric that provides sufficient guidance for interpreting student performance on the summative assessment is included with unit materials.