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CCSS Math Pacing Guide-Interactive
Fourth Six Weeks - 3rd Grade
Number and OperationsFractions (NF) (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)
Develop understanding of fractions as numbers.3.NF.1. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
HYPERLINK "http://math.rice.edu/%7Elanius/Patterns/" \t "_blank" No Matter What Shape your Fractions Are InThese activities are designed to cause students to think; they are not algorithmic. They do not say, To add fractions, do step one, step two, step three. Students will explore geometric models of fractions and discover relations among them. Appropriate grades are: 3rd - 6th, maybe. But precocious kindergarteners could do some of it, and middle schoolers needing another look at fractions could appreciate it as well. "Drawing Fun Fractions" would be good for most middle school students. Lesson Procedures: Students will reinforce their knowledge of fractions by using online pattern block activities. The lessons are designed for students to work independently or with guidance from the teacher. Lessons should be printed so students can draw and color the appropriate shapes.Mathematics Topics: Identifying fractional values, equivalent fractions, adding and subtracting fractions, ordering fractions, and identifying geometric figures and their properties HYPERLINK "http://mathforum.org/paths/fractions/edible.fractions.html" \t "_blank" Edible Fractions on PlatesA lesson plan that provides practice in understanding fractions as part and whole as well as the concept of fractions in real-life situations. Incorporates the use of models to add, subtract and estimate fractions. Refers to the children's book Eating Fractions by Bruce McMillan, Scholastic, Inc.
HYPERLINK "http://illuminations.nctm.org/LessonDetail.aspx?ID=U112" \t "_blank" Eggsactly Fractions - This Fun with Fractions unit consists of five lessons that expose students to the set model and provides an opportunity for them to develop a thorough understanding of this model in multiple applications including eggs and attribute pieces. (Source: Illuminations, NCTM) HYPERLINK "http://illuminations.nctm.org/LessonDetail.aspx?id=U113" \t "_blank" Fun with Pattern Block Fractions- This Fun with Pattern Block Fractions unit consists of five lessons designed to help the students understand fractions when they are represented as a part of a region. Representing fractions in a variety of ways helps students see relationships and develop understanding of later fraction concepts. It is important that students "see" a variety of concrete examples in addition to pictorial representations. These lessons incorporate the use of pattern blocks and virtual manipulatives. Printable activity sheets and links to virtual manipulatives are imbedded in the site. (Source: Illuminations, NCTM) HYPERLINK "http://www.beaconlearningcenter.com/Lessons/6.htm" \t "_blank" But That's Not Fair - In this lesson, students solve problems using fractions through hands-on activities appropriate literature. The book Gator Pie is used. (Source: Beacon Learning Center) HYPERLINK "http://www.beaconlearningcenter.com/Lessons/2511.htm" \t "_blank" All Fractions are Created Equal- This lesson is introducing students to equivalent fractions using concrete materials. (Source: Beacon Learning Center) HYPERLINK "http://mathforum.org/paths/fractions/mars.hunt.html" \t "_blank" Candy Bar Fraction Hunt: Students divide words into fractional parts to solve, analyze clues, and decode a message to find a hidden candy bar: (Source: Math Forum) HYPERLINK "http://themathgames.com/our-games/fraction-games/fractionballs1/league_-1/country_-1/countryNumber_-1" \t "_blank" Fraction Balls: Students use space bar and arrow keys to drop the fraction into the cup with the matching visual. (Source: The Math Games) HYPERLINK "http://books.google.com/books/about/Fraction_fun.html?id=Y1za_GuTAGkC" \t "_blank" Fraction Fun by David Adler: This book is a great resource for teachers. The author shows several different representations of fractions. Can be divided up into sections and used for different lessons. HYPERLINK "http://www.readtennessee.org/math/teachers/k-3_common_core_math_standards/third_grade/sites/www/Uploads/Math6.pdf" \t "_blank" Mathematical Processes- This sample assessment, from the Tennessee Department of Education, aligns to standard 3.NF.1 because it requires the student to recognize that the candy bar is partitioned into 10 equal parts and that 3 of the 10 parts are missing. The student must understand that the 3 is the numerator and is written on the top of the fraction and the 10 is the denominator and is written on the bottom of the fraction.3.NF.2. Understand a fraction as a number on the number line; represent fractions on a number line diagram.
Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.
Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.
HYPERLINK "http://illuminations.nctm.org/LessonDetail.aspx?id=U152" \t "_blank" Fun with Fractions - In this lesson plan, students explore relationships among fractions through work with the length model. This early work with fraction relationships helps students make sense of basic fraction concepts and facilitates work with comparing and ordering fractions and working with equivalency. The unit contains five lessons. (Source: Illuminations)
HYPERLINK "http://illuminations.nctm.org/LessonDetail.aspx?ID=L545" \t "_blank" Inch by Inch - In this lesson, students use a ruler to represent various fractions as lengths. 4 other preceding lessons can be found by clicking on tabs. (Source: Illuminations, NCTM) HYPERLINK "http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/fractions/level4.htm" \t "_blank" Fractions- A Booster Activity - Online student activity in which students are shown a number line from 0 to 1 divided into fractional pieces. They are asked to drag fractions with varying denominators to the correct area of the number line. Students are not allowed to drag incorrectly and receive immediate feedback if an answer is incorrect. (Source: BGFL) HYPERLINK "http://www.visualfractions.com/IdentifyLines/identifylines.html" \t "_blank" Identify Fractions- Online student activity in which students are given a number line from 0-1 that is partially shaded and asked to enter the numerator and denominator for the correct fraction. (Source: Visual Fractions) HYPERLINK "http://www.superteacherworksheets.com/fractions/fractions-number-line.pdf" \t "_blank" Fraction Numberline- Independent Practice or assessment that addresses this standard. (Source: SuperTeacher Worksheet) HYPERLINK "http://books.google.com/books/about/Fraction_fun.html?id=Y1za_GuTAGkC" \t "_blank" Fraction Fun by David Adler: This book is a great resource for teachers. The author shows several different representations of fractions. Can be divided up into sections and used for different lessons. HYPERLINK "http://www.readtennessee.org/math/teachers/k-3_common_core_math_standards/third_grade/sites/www/Uploads/Math3.pdf" \t "_blank" Numbers and Operations - This sample assessment, from the Tennessee Department of Education, aligns to standard 3.NF.2a because it requires the student to recognize that a number line is partitioned into b equal parts from 0 to 1. The student must understand that the number line is partitioned into 4 equal parts and that 4 is the denominator and that each part has sizes ranging from 1 part out of four to 4 parts out of 4.3.NF.3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.
Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.
Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
HYPERLINK "http://mathforum.org/paths/fractions/equiv.fractions.html" \t "_blank" 1/2 = 3/6 - Equivalent FractionsAn activity designed to show students that the notion of several names for a number is similar to the notion of several names for a person. HYPERLINK "http://illuminations.nctm.org/LessonDetail.aspx?id=U112" \t "_blank" Eggsactly with Fractions In this unit, students explore relationships among fractions through work with the set model. This early work with fraction relationships helps students make sense of basic fraction concepts and facilitates work with comparing and ordering fractions and working with equivalency. The unit contains six lessons.Math Content for Eggsactly with Fractions: This unit exposes students to the set model and provides an opportunity for them to develop a thorough understanding of this model in multiple applications. In the set model, the unit is represented by the entire set, and subsets of the unit make up the fractional parts. For example, in a set of 12eggs, 4eggs comprise one-third of the set of 16eggs. The set of12 in this example represents the whole, or1. This notion of referring to a collection of objects makes studying the set model difficult for young children. As students work with a variety of fraction models in contexts that promote reasoning and problem solving, they develop a more thorough understanding of fractions and their relationships. HYPERLINK "http://illuminations.nctm.org/LessonDetail.aspx?id=U152" \t "_blank" Fun with Pattern Block Fractions In this unit, students explore relationships among fractions through work with the region model. This early work with fraction relationships helps students make sense of basic fraction concepts and facilitates work with comparing and ordering fractions and working with equivalency.This unit consists of five lessons designed to help the students understand fractions when they are represented as a part of a region. Subsequent units develop understanding of other fraction models (e.g., set, area, and length). Representing fractions in a variety of ways helps students see relationships and develop understanding of later fraction concepts. It is important that students "see" a variety of concrete examples in addition to pictorial representations. The following lessons incorporate the use of physical and virtual manipulatives.Math Content. Concepts about fractions are basic to mathematics but can pose challenges for students. In elementary schools, the most frequently used fraction models are the region and set models. This unit exposes students to the region model and gives an opportunity for them to develop a thorough understanding of this model in multiple applications. As students work with a variety of fraction models in contexts that promote reasoning and problem solving, they develop a more thorough understanding of fractions and the relationships among them. Measurement and Data (MD)
Represent and interpret data.3.MD.4. Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units whole numbers, halves, or quarters.
HYPERLINK "http://www.nsa.gov/academia/_files/collected_learning/elementary/data_analysis/line-plots_frogs-in-flight.pdf" \t "_blank" Frogs in Flight Lesson Plan - In this lesson plan on data analysis from the NSA, students collect data on how far origami frogs jump by measuring to the nearest inch. Students then create and interpret line plots of the frog jumping data. Although the lesson plan is designated for fifth graders, this lesson would also be suitable for meeting the third grade Common Core Standard of collecting measurement data and representing the data on a line plot. Teacher and student resources needed for the lesson are included. (Source: National Security Agency) HYPERLINK "http://www.nsa.gov/academia/_files/collected_learning/elementary/data_analysis/guinness_book_of_records.pdf" \t "_blank" Are You Ready to Call the Guinness Book of Records? Lesson Plan - In this lesson plan on data analysis from the NSA, students collect data by conducting surveys and display data using a line plot. Students learn how to interpret line plots and how to find measures of central tendency (median, mode, and range) using their data. Students also learn a mnemonic device for remembering all the elements to include in a line plot. Teacher and student resources needed for the lesson are included. (Source: National Security Agency) HYPERLINK "http://www.nsa.gov/academia/_files/collected_learning/elementary/data_analysis/traveling_through_line_plots.pdf" \t "_blank" Traveling Through Line Plots - This mathematics lesson plan from the NSA involves both measurement and data analysis. Students create a line plot using data collected in class and then apply their knowledge of measures of central tendency (mean, median, mode, and range) in order to analyze and interpret the data. Although designed as a lesson for fourth or fifth graders, this lesson addresses the third grade Common Core Standard of collecting measurement data and representing the data on a line plot. Teacher and student resources needed for the lesson are included. (Source: National Security Agency) HYPERLINK "http://www.mathedleadership.org/docs/ccss/GreatTasksSamplerProof2.pdf" \t "_blank" Bugs, Giraffes, Elephants, and More - This document from the National Council of Supervisors of Mathematics includes a sample lesson plan in which students interpret line plots with scales written to the nearest quarter of a unit. The lesson plan begins on page 7 of the document. Although designed for fourth graders, most of the activities in this lesson are well suited for addressing the third grade standard for measuring and recording data on a line plot using quarter units. Examples of student assessment data with educator interpretations of students understanding are also provided. (Source: National Council of Supervisors of Mathematics)
HYPERLINK "http://www.k-5mathteachingresources.com/support-files/measuringpenny2.md1.pdf" \t "_blank" Tradebooks with Lesson Plans- Measuring Penny by Loreen Leedy is a book about a student who discovers the world of measurement. The main character, Lisa, has an important homework assignment--to measure something in several different ways. She has to use standard units like inches and nonstandard units like paper clips to find out height, width, length, weight, volume, temperature, and time. Lisa decides to measure her dog, Penny. The following link is a printable task card to accompany this book that has the students measuring something several different ways and reporting their findings. (Source: K-5 Math Teaching Resources)
HYPERLINK "http://www.amazon.com/Measuring-Penny-Loreen-Leedy/dp/0805053603/ref=sr_1_1?s=books&ie=UTF8&qid=1315533239&sr=1-1" \t "_blank" Amazon Book
HYPERLINK "http://www.k-5mathteachingresources.com/support-files/measuringpaths.pdf" \t "_blank" Measuring Paths This is a printable task card that has the students creating and measuring paths. Discussions questions are included that can be used as an entry in a math journal. (Source: K-5 Math Teaching Resources) Path Activity Cards: There are links provided below for three different printable task cards that have the students analyzing multiple paths in search of the quickest route possible to get to the end. The student is asked to explain their thinking on each task card. This could be used as a journal topic or an open-discussion topic. (Source: K-5 Math Teaching Resources)
HYPERLINK "http://www.k-5mathteachingresources.com/support-files/paths1.pdf" \t "_blank" Path 1
HYPERLINK "http://www.k-5mathteachingresources.com/support-files/paths2.pdf" \t "_blank" Path 2
HYPERLINK "http://www.k-5mathteachingresources.com/support-files/paths3.pdf" \t "_blank" Path 3
HYPERLINK "http://www.k-5mathteachingresources.com/support-files/measuringstripslineplot.pdf" \t "_blank" Measuring Strips Line Plot- This is an activity card that can be used in a center or as an assessment. The students are given a set of strips measuring a variety of lengths. The students are asked to measure the items and record their findings in a line plot. (Source: K-5 Math Teaching Resources)How Tall, How Short, How Faraway by David Adler is a book that discussing various aspects of non-standard and standard measurement. This is a link to a lesson plan to accompany the book that has the students measuring various items. Although the lesson is designed for 2nd grade, the procedures and concepts in the lesson can be used with 3rd graders.
HYPERLINK "http://teachingtoday.glencoe.com/lessonplans/measurement" \t "_blank" Lesson Plan (Source: Teaching Today)
HYPERLINK "http://www.amazon.com/gp/product/0823416321/ref=as_li_tf_tl?ie=UTF8&tag=k5matteares-20&linkCode=as2&camp=1789&creative=9325&creativeASIN=0823416321" \t "_blank" Amazon Book Link (Source: Amazon)
HYPERLINK "http://www.apples4theteacher.com/measure.html" \t "_blank" Measure the Teddy Bears: This is an online activity that can be used as an assessment for measuring to the nearest inch. The students are asked 10 questions with a score given at the end. If the student misses the question, the game provides a quick tutorial. (Source: Apples4Teacher)3.MD.2. Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (Excludes compound units such as cm3 and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. Excludes multiplicative comparison problems
HYPERLINK "http://www.k-5mathteachingresources.com/support-files/estimatingweight.pdf" \t "_blank" Estimating Weight Activity Card- Students are challenged to find items that have an equal weight by adding and removing weights from a scale. (Source: K-5 Math Teaching Resources) HYPERLINK "http://www.k-5mathteachingresources.com/support-files/moreorlessthanaliter.pdf" \t "_blank" More or Less than a Liter? Activity Card: Students are asked to choose other containers that will hold a liter and then investigate to see if their estimates are correct. (Source: K-5 Math Teaching Resources) HYPERLINK "http://www.k-5mathteachingresources.com/support-files/capacitylineup.pdf" \t "_blank" Capacity Lineup- This activity gives students the opportunity to investigate the metric units of capacity. (Source: K-5 Math Teaching Resources)This site is a lesson plan using Stuart Murphys book, Room for Ripley. This lesson contains 6 interactive center ideas that allow the students to explore customary and metric measurement for capacity with a variety of materials. The story uses the amount of water in a fish bowl to teach students the units of measuring capacity. Lesson Plan Link:http://www.uen.org/Lessonplan/preview?LPid=16316 Amazon Book Link: http://www.amazon.com/Room-Ripley-MathStart-Stuart-Murphy/dp/0064467244/ref=sr_1_1?s=books&ie=UTF8&qid=1315533574&sr=1-1Additional Resources and Activities Millions to Measure by David M. Schwartz is an exciting story about the millions of things to measure and as many ways to measure them! Marvelosissimo the Mathematical Magician is back -- and ready to explore the invention of length, weight, and volume measurements. After that, with another wave of his wand, the wizard introduces the world of metrics and makes it easy to understand the basic pattern of meters, liters, and grams. Lesson Plan Link: http://www2.scholastic.com/browse/article.jsp?id=2952 Amazon Book Link: http://www.amazon.com/gp/product/0060848065/ref=as_li_tf_tl?ie=UTF8&tag=k5matteares-20&linkCode=as2&camp=1789&creative=9325&creativeASIN=0060848065 Can You Fill It?: This is a link to a game that students can use to practice estimating how much liquid an object can hold. HYPERLINK "http://pbskids.org/cyberchase/games/liquidvolume/liquidvolume.html" http://pbskids.org/cyberchase/games/liquidvolume/liquidvolume.html
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