Madison County Public Schools

MADISON COUNTY PUBLIC SCHOOLS

District Curriculum Map for Mathematics: Grade 4

Unit Description / Unit 5
Fraction Equivalence
Suggested Length: 3 weeks
Big Idea(s)
What enduring understandings are essential for application to new situations within or beyond this content? / Enduring Understanding
Develop an understanding of fraction equivalence and operations with
fractions
Enduring Skills Rubric measures competency of the following skills:
· Consistently compares two fractions with different numerators and denominators.
· Consistently adds and subtracts fractions with like denominators.
· Decompose a fraction into a sum of fractions with the same denominator in more than one way.
Essential Question(s)
What questions will provoke and sustain student engagement while focusing learning? / · What do the numbers in a fraction represent?
· What is the relationship between the size of the denominator and the size of each fractional piece (i.e. the numerator)?
· How can equivalent fractions be identified?
· How can I represent fractions in different ways?
· How can I compare fractions?
Standards / Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them. Students make sense of problems involving equivalent fractions and comparing fractions.
2. Reason abstractly and quantitatively. Students demonstrate abstract reasoning about relative size of fractions.
3. Construct viable arguments and critique the reasoning of others. Students construct and critique arguments regarding the equivalency of fractions.
4. Model with mathematics. Students use fraction strips, fraction squares, fraction circles, cuisenaire rods, and number lines to demonstrate understanding of equivalent fractions.
5. Use appropriate tools strategically. Students select and use tools such as fraction strips, fraction squares, fraction circles, cuisenaire rods, and number lines to identify equivalent fractions.
6. Attend to precision. Students attend to the language of real-world situations to determine if one fraction is greater than another.
7. Look for and make use of structure. Students relate the structure of fractions to the same whole to compare fractions.
8. Look for and express regularity in repeated reasoning. Students relate the structure of fractions to the same whole to identify multiple equivalent fractions.
Standards for Mathematical Content
· 4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
· 4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Supporting Standard(s)
Which related standards will be incorporated to support and enhance the enduring standards? / · 4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
· 4.MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
Instructional Outcomes
What must students learn and be able to do by the end of the unit to demonstrate mastery? / I am learning to….
4.NF.1
· create equivalent fractions with concrete models
· illustrate equivalent fractions with visual models
· explain why two given fractions are equivalent
· recognize equivalent fractions with different denominators
· multiply a given fraction (less than one) by a given fraction (equal to 1) in order to generate equivalent fractions
4.NF.2
· identify benchmark fractions (½, ¼, and ¾)
· explain why comparisons are only valid when fractions refer to the same whole
· compare two fractions when one of those fractions is a benchmark fraction
· compare fractions with different numerators, e.g. by comparing to a benchmark fraction
· compare two fractions with different denominators, e.g. by creating common denominators, or by comparing to a benchmark fraction
· justify the results of comparing two fractions, e.g. by using a visual fraction model
· compare fractions using <, >, and =
Vocabulary
What vocabulary must students know to understand and communicate effectively about this content? / Essential Vocabulary
benchmark fraction
common denominator
common numerator
compare
denominator / equation
equivalent
fraction
line plot
numerator / reasonableness
simplify (do not use “reduce”)
unit fraction
visual fraction model
Supporting Vocabulary
multi-step / number line diagram
<(less than) / >(greater than)
=(equal)
Resources/Activities
What resources could we use to best teach this unit? / Stepping Stones (www.origoeducation.com)
4.NF.1
o Module 3: Lessons 9,10
o Module 5: Lessons 1-5
o Module 6: Lesson 9
o Module 11: Lesson 1
o Module 12: Lesson 3
4.NF.2
o Module 3: Lessons 11, 12
o Module 5: Lessons 3-5
o Module 6: Lesson 9
Engage NY (https://www.engageny.org/resource/grade-4-mathematics)
o Module 5, all Topics
Howard County website
o https://grade4commoncoremath.wikispaces.hcpss.org/Assessing+4.NF.1
o https://grade4commoncoremath.wikispaces.hcpss.org/Assessing+4.NF.2
K-5 Math Teaching Resources
4.NF.1
o http://www.k-5mathteachingresources.com/support-files/creating-equivalent-fractions.pdf
o http://www.k-5mathteachingresources.com/support-files/build-a-fraction-wall.pdf
4.NF.2
o http://www.k-5mathteachingresources.com/support-files/birthday-fractions.pdf
o http://www.k-5mathteachingresources.com/support-files/pattern-block-fractions.pdf
o http://www.k-5mathteachingresources.com/support-files/who-ate-more-4nf2.pdf
o http://www.k-5mathteachingresources.com/support-files/which-is-larger.pdf
o http://www.k-5mathteachingresources.com/support-files/snack-time.pdf
o http://www.k-5mathteachingresources.com/support-files/fractioncompare4nf2.pdf
o http://www.k-5mathteachingresources.com/support-files/fractioncards.pdf
Illustrative Mathematics
4.NF.1
o https://www.illustrativemathematics.org/content-standards/4/NF/A/tasks/1064
o https://www.illustrativemathematics.org/content-standards/4/NF/A/tasks/971
o https://www.illustrativemathematics.org/content-standards/4/NF/A/1/tasks/743
o https://www.illustrativemathematics.org/content-standards/4/NF/A/1/tasks/881
4.NF.2
o https://www.illustrativemathematics.org/content-standards/4/NF/A/2/tasks/183
o https://www.illustrativemathematics.org/content-standards/4/NF/A/2/tasks/811
o https://www.illustrativemathematics.org/content-standards/4/NF/A/2/tasks/812
Illuminations
o http://illuminations.nctm.org/Search.aspx?view=search&cc=1973_1998
o http://illuminations.nctm.org/activitydetail.aspx?id=80
Making Math Magic http://www.makingmathmagic.net/kcm.html
Remember there are other sources in your school that may not be listed on this common resources list due to variation in each individual school. Examples of other great resources your school may have access to include: Everyday Math Games, Investigations, Everyday Partner Games, AVMR file folders, Ongoing Assessment Project, etc. The Kentucky Numeracy Project is also a great resource that can be searched by AVMR strand, CCSS, and grade level. Find this resource at http://knp.kentuckymathematics.org/#!/page_knphome. Kentucky teachers can use it for free. Just put in your school email address and the username “mathfun”, and password is “859”.

Curriculum and Instruction 2015-2016 Page 5 of 5