Grade 5: NC READY EOG – Math Menu of Activities
Using these EOG review lessons for assessment preparation can serve as a frame for meaningful performance goals as it can help learners to clarify targeted standards; yield evidences of understandings or misunderstandings; and support learning outcomes and benchmarks. The purpose of this resource is to inform teaching and improve learning so students can achieve the highest academic standards possible in mathematics.
Not all of the content in a given grade is emphasized equally in the standards. Some clusters require greater emphasis than others based on the depth of the ideas, the time it takes to master, and/or their importance to future mathematics. Some things having greater emphasis is not to say that anything in the standards can safely be neglected in instruction. The major works for the grade level are listed in the table below
Fifth GradeMajor Clusters / Supporting/Additional Clusters
Number and Operations in Base Ten
· Understand the place value system.
· Perform operations with multi-digit whole numbers and with decimals to hundredths.
Number and Operations—Fractions
· Use equivalent fractions as a strategy to add and subtract fractions.
· Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
Measurement and Data
· Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. / Operations and Algebraic Thinking
· Write and interpret numerical expressions.
· Analyze patterns and relationships.
Measurement and Data
· Convert like measurement units within a given measurement system.
· Represent and interpret data.
Geometry
· Graph points on the coordinate plane to solve real-world and mathematical problems.
· Classify two-dimensional figures into categories based on their properties.
The following outlines the percentages of items in each domain of the NC MATH EOG for the grade level:
Number and Operations-Fractions
47-52%
Numbers and Operations -Base Ten
22-27%
Measurement and Data
10-15%
Operations and Algebraic Thinking
5-10%
Geometry
2-7%
Helping students be ready for the EOG using such strategies as setting criteria for clarity of tasks; providing relevant lessons connected to assessments; and giving feedback so they can successfully learn and meet the expectations will influence students’ motivation to learn.
Released version of the NC Ready EOG can be found at http://www.ncpublicschools.org/docs/accountability/testing/releasedforms/g5mathpp.pdf. All items in review lessons and games come solely from this released version.
Building the Language of Math for Students to be Ready for the EOG
Mathematically proficient students communicate precisely by engaging in discussions about their reasoning using appropriate mathematical language. The terms students should learn to use at this grade level with increasing precision are included in this document. Communication plays an important role in helping children construct links between their formal, intuitive notions and the abstract language and symbolism of mathematics; it also plays a key role in helping children make important connections among physical, pictorial, graphic, symbolic, verbal, and mental representations of mathematical ideas. * Curriculum and Evaluation Standards for School Mathematics, the National Council of Teachers of Mathematics (p. 26)
Mathematical vocabulary however should not be taught in isolation where it is meaningless and just becomes memorization. We know from research that meaningless memorization is not retained nor will it help build the deep understanding of the mathematical content. The students must be provided adequate opportunities to develop vocabulary in meaningful ways such as mathematical explorations and experiences. Students should be immersed into the mathematical language as they experience the following high-level tasks. As student communicate their thoughts, ideas, and justify the reasonableness of their solutions the mathematical language will begin to evolve. * NCDPI
The following resources can be used conjunction with these EOG Ready Lessons to help students understand the math vocabulary as listed on the next page. In each lesson, a math vocabulary game is included; however, if students need more support, please see the direct link below.
Math Vocabulary Development Lesson Activities and Games: *Building Background Knowledge, Marzano http://morethanenglish.edublogs.org/files/2011/08/Vocabulary-Development-Strategies-1vjq96a.pdf
Math Glossary Hyperlinks:
http://www.mathsisfun.com/definitions/index.html
www.amathsdictionaryforkids.com
http://mathlearnnc.sharpschool.com/UserFiles/Servers/Server_4507209/File/Instructional%20Resources/GlossarySP.pdf (words and definitions in English/Spanish for parents, students, and teachers)
These math vocabulary words have been organized by domain and listed in each cluster to better promote connection and precision of the language.
5th Grade Math Vocabulary (NCDPI)Operations and Algebraic Thinking / Number and Operations in Base Ten / Number and Operations- Fractions / Measurement
and Data / Geometry
5–10% of EOG / 22-27% of EOG / 47–52 % of EOG / 10–15% of EOG / 2–7 % of EOG
Write and interpret numerical expressions. parentheses, brackets, braces, numerical expressions, symbols, equation
Analyze patterns and relationships.
numerical patterns, rules, ordered pairs, coordinate plane / Understand the place value system.
place value, decimal, decimal point, patterns, multiply, divide, tenths, thousands, greater than, less than, equal to, ‹, ›, =, compare/comparison, round, digit
Perform operations with multi-digit whole numbers and with decimals to hundredths.
multiplication/multiply, division/division, decimal, decimal point, tenths, hundredths, products, quotients, dividends, divisor, rectangular arrays, area models, addition/add, subtraction/subtract, (properties)-rules about how numbers work, reasoning / Use equivalent fractions as a strategy to add and subtract fractions. fraction, equivalent, addition/ add, sum, subtraction/subtract, difference, unlike denominator, numerator, benchmark fraction, estimate, reasonableness, mixed numbers
Apply and extend previous understanding of multiplication and division to multiply and divide fractions.
fraction, numerator, denominator, operations, multiplication/multiply, division/divide, mixed numbers, product, quotient, partition, equal parts, equivalent, factor, unit fraction, area, side lengths, fractional sides lengths, scaling, comparing, whole / Convert like measurement units within a given measurement system.
conversion/convert, metric and customary measurement
From previous grades: relative size, liquid volume, mass, length, kilometer (km), meter (m), centimeter (cm), kilogram (kg), gram (g), liter (L), milliliter (mL), inch (in), foot (ft), yard (yd), mile (mi), ounce (oz), pound (lb), cup (c), pint (pt), quart (qt), gallon (gal), hour, minute, second, a.m., p.m., clockwise, counter clockwise
Present and interpret data.
line plot, length, mass, liquid volume
Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
measurement, attribute, volume, solid figure, right rectangular prism, unit, unit cube, gap, overlap, cubic units (cubic cm, cubic in. cubic ft. nonstandard cubic units), multiplication, addition, edge lengths, height, area of base / Graph points on the coordinate plane to solve real-world and mathematical problems.
coordinate system, coordinate plane, first quadrant, points, lines, axis/axes, x-axis, y-axis, horizontal, vertical, intersection of lines, origin, ordered pairs, coordinates, x-coordinate, y-coordinate
Classify two-dimensional figures into categories based on their properties.
attribute, prism, plane figure, category, subcategory, hierarchy, properties (attributes, features), defining characteristics and non-defining characteristic, congruent, parallel, perpendicular, two dimensional
From previous grades: polygon, rhombus/rhombi, rectangle, square, triangle, quadrilateral, pentagon, hexagon, cube, trapezoid, half/quarter circle, circle
Wake County Public School System, 2014
Building Fluency Through Games (NCDPI)
Developing fluency requires a balance and connection between conceptual understanding and computational proficiency. Computational methods that are over-practiced without understanding are forgotten or remembered incorrectly. Conceptual understanding without fluency can inhibit the problem solving process. * NCTM, Principles and Standards for School Mathematics, pg. 35
Why Play Games?
People of all ages love to play games. They are fun and motivating. Games provide students with opportunities to explore fundamental number concepts, such as the counting sequence, one-to-one correspondence, and computation strategies. Engaging mathematical games can also encourage students to explore number combinations, place value, patterns, and other important mathematical concepts. Further, they provide opportunities for students to deepen their mathematical understanding and reasoning. Teachers should provide repeated opportunities for students to play games, and let the mathematical ideas emerge as they notice new patterns, relationships, and strategies. Games are an important tool for learning. Here are some advantages for integrating games into elementary mathematics classrooms:
Playing games encourages strategic mathematical thinking as students find different strategies for solving
problems and it deepens their understanding of numbers.
Games, when played repeatedly, support students’ development of computational fluency.
Games provide opportunities for practice, often without the need for teachers to provide the problems.
Teachers can then observe or assess students, or work with individual or small groups of students.
Games have the potential to develop familiarity with the number system and with “benchmark numbers”
– such as 10s, 100s, and 1000s and provide engaging opportunities to practice computation, building a deeper understanding of operations.
Games provide a school to home connection. Parents can learn about their children’s mathematical thinking by playing games with them at home.
Building Fluency
Developing computational fluency is an expectation of the Common Core State Standards. Games provide opportunity for meaningful practice. The research about how students develop fact mastery indicates that drill techniques and timed tests do not have the power that mathematical games and other experiences have. Appropriate mathematical activities are essential building blocks to develop mathematically proficient students who demonstrate computational fluency (Van de Walle & Lovin, Teaching Student-Centered Mathematics Grades K-3, pg. 94). Remember, computational fluency includes efficiency, accuracy, and flexibility with
strategies (Russell, 2000).
The kinds of experiences teachers provide to their students clearly play a major role in determining the extent and quality of students’ learning. Students’ understanding can be built by actively engaging in tasks and experiences designed to deepen and connect their knowledge. Procedural fluency and conceptual understanding can be developed through problem solving, reasoning, and argumentation (NCTM, Principles and Standards for School Mathematics, pg. 21). Meaningful practice is necessary to develop fluency with basic number combinations and strategies with multi-digit numbers. Practice should be purposeful and should focus on developing thinking strategies and a knowledge of number relationships rather than drill isolated facts (NCTM, Principles and Standards for School Mathematics, pg. 87). Do not subject any student to computation drills unless the student has developed an efficient strategy for the facts included in the drill (Van de Walle & Lovin, Teaching Student Centered Mathematics Grades K-3, pp.117) Drill can strengthen strategies with which students feel comfortable—ones they “own”—and will help to make these strategies increasingly automatic. Therefore, drill of strategies will allow students to use them with increased efficiency, even to the point of recalling the fact without being conscious of using a strategy. Drill without an efficient strategy present offers no assistance (Van de Walle & Lovin, Teaching Student-Centered Mathematics Grades K-3, pg. 117)
Cautions
Sometimes teachers use games solely to practice number facts. These games usually do not engage children for long because they are based on students’ recall or memorization of facts. Some students are quick to memorize, while others need a few moments to use a related fact to compute. When students are placed in situations in which recall speed determines success, they may infer that being “smart” in mathematics means getting the correct answer quickly instead of valuing the process of thinking. Consequently, students may feel incompetent when they use number patterns or related facts to arrive at a solution and may begin to dislike mathematics because they
are not fast enough.
Introduce a game
A good way to introduce a game to the class is for the teacher to play the game against the class. After briefly explaining the rules, ask students to make the class’s next move. Teachers may also want to model their strategy by talking aloud for students to hear his/her thinking. “I placed my game marker on 6 because that would give me the largest number.”
Games are fun and can create a context for developing students’ mathematical reasoning. Through playing and analyzing games, students also develop their computational fluency by examining more efficient strategies and discussing relationships among numbers. Teachers can create opportunities for students to explore mathematical ideas by planning questions that prompt students to reflect about their reasoning and make predictions. Remember to always vary or modify the game to meet the needs of your leaners. Encourage the use of the
Standards for Mathematical Practice.
Holding Students Accountable
While playing games, have students record mathematical equations or representations of the mathematical tasks. This provides data for students and teachers to revisit to examine their mathematical understanding. After playing a game have students reflect on the game by asking them to discuss questions orally or write about them in a mathematics notebook or journal:
1. What skill did you review and practice?
2. What strategies did you use while playing the game?
3. If you were to play the games a second time, what different strategies would you use to be more successful?
4. How could you tweak or modify the game to make it more challenging?
For students to become fluent in arithmetic computation, they must have efficient and accurate methods that are supported by an understanding of numbers and operations. “Standard” algorithms for arithmetic computation are one means of achieving this fluency. NCTM, Principles and Standards for School Mathematics, pg. 35.
Overemphasizing fast fact recall at the expense of problem solving and conceptual experiences gives students a distorted idea of the nature of mathematics and of their ability to do mathematics. Seeley, Faster Isn’t Smarter: Messages about Math, Teaching, and Learning in the 21st Century, pg. 95
Fluency refers to having efficient, accurate, and generalizable methods (algorithms) for computing that are based on well-understood properties and number relationships. NCTM, Principles and Standards for School Mathematics, pg. 144
Computational fluency refers to having efficient and accurate methods for computing. Students exhibit computational fluency when they demonstrate flexibility in the computational methods they choose, understand and can explain these methods, and produce accurate answers efficiently.
NCTM, Principles and Standards for School Mathematics, pg. 152
WordSplash!
Purpose: To provide explicit vocabulary concept development for a specific math domain or cluster of standards for the grade level.Lesson Materials Needed:
· EOG Math Vocabulary words from a specific domain or cluster
· Math journal or notebook paper
· Pencils
· Wordsplash! Handout (attached)
Directions:
1. Teacher provides vocabulary concept development for a specific math domain or cluster as listed in the vocabulary section for the grade level.
2. Students work with a partner and use the words that are “splashed” with WordArt displayed on paper or projected to talk about how they are connected.
3. Students then write a journal entry to record in complete statements about how the words are connected using as many words as possible to explain. Journal entries must make sense. Allow time for students to share their journal entries with a small group.
4. The following is an example of a WordSplash! for the grade level. Adapt this activity for any domain or cluster.
WordSplash!