 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.

Operations and Algebraic Thinking
• Represent and solve problems involving multiplication and division.
• Understand properties of multiplication and the relationship between multiplication and division.
• Multiply and divide within 100.
• Solve problems involving the four operations, and identify and explain patterns in arithmetic.
Number and Operations—Fractions
• Develop understanding of fractions as numbers.
Measurement and Data
• Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
• Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
/ Number and Operations in Base Ten
• Use place value understanding and properties of operations to perform multi-digit arithmetic.
Measurement and Data
• Represent and interpret data.
• Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
Geometry
• Reason with shapes and their attributes.

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.

The following outlines the percentages of items in each domain of the NC MATH EOG for the grade level:

Operations and Algebraic Thinking

30-35 %

Number and Operations-Fractions

20-25%

Measurement and Data

22-27%

Geometry

10-15%

Numbers and Operations -Base Ten

5-10%

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 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 know at this grade level with precision is 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 mustbe providedadequate 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

(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.

Operations and Algebraic Thinking / Number and Operations in Base Ten / Number and Operations- Fractions / Measurement
and Data / Geometry
30-35% of EOG / 5-10% of EOG / 20-25% of EOG / 22-27% of EOG / 10-15% of EOG
Represent and solve problems involvingmultiplication and division.
operations, multiplication, division, factor, product, quotient, partitioned equally, equal shares, number of groups, number in the groups, array, equation, unknown, expression, equation
Understand properties of multiplication and the relationship between multiplication and division.
operation, multiply, divide, factor, product, quotient, dividend, divisor, strategies, unknown, (properties)-rules about how numbers work
Multiply and divide within 100.
operation, multiply, divide, factor, product, quotient, unknown, strategies, reasonableness, mental computation, property
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
operation, multiply, divide, factor, product, quotient, subtract, add, addend, sum, difference, equation, expression, unknown, strategies, reasonableness, mental computation, estimation, rounding, patterns, (properties)-rules about how numbers work / Use place value understanding and properties of operations to perform multi-digit arithmetic.
relationship, estimation, base ten model,
more, fewer, total, digits, ones, tens, hundreds, thousands / Develop understanding of fractions as numbers.
partition(ed), equal parts, fraction,
equal distance ( intervals), equivalent, equivalence, reasonable, denominator, numerator, comparison, compare, ‹, ›, = , justify,
inequality, halves,
thirds, fourths, sixths
eighths, area model,
number line, segments,
unit fraction, whole / Solve problems involving measurement andestimation of intervals of time, liquid volumes,and masses of objects.
estimate, time, time intervals, a.m, p.m, digital clock, analog clock, minute, hour, elapsed time, measure, liquid volume, mass, standard units, metric, gram (g), kilogram (kg), liter (L)
Represent and interpret data.
scale, scaled picture graph, scaled bar graph, line plot, data
Geometric measurement: understand concepts
of area and relate area to multiplication and to addition.
attribute, area, square unit, plane figure, gap, overlap, square cm, square m , square in., square ft, nonstandard units, tiling, side length, decomposing
Geometric measurement: recognize perimeter
as an attribute of plane figures and distinguish between linear and area measures.
attribute, perimeter, plane figure, linear, area, polygon, side length / Reason with shapes and their attributes.
attributes, properties, quadrilateral, open figure, closed figure , three-sided, 2-dimensional, 3-dimensional, rhombi, rectangles, and squares are subcategories of quadrilaterals, cubes, cones, cylinders, and rectangular prisms are subcategories of 3-dimensional figures shapes: polygon, rhombus/rhombi, rectangle, square, partition, unit fraction, kite, example and non-example
From previous grades: triangle, quadrilateral, pentagon, hexagon, cube, trapezoid, half/quarter circle, circle, cone, cylinder, sphere

*NC DPI

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 WalleLovin, 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 WalleLovin,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.
1. Students work with a partner and use the words that are “splashed” with WordArt displayed on paper or projected to talk about how they areconnected.
1. 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.
1. The following is an example of a WordSplash! for the grade level. Adapt this activity for any domain or cluster.

WordSplash!

Discuss the following words with a partner that are “splashed” on the page below. Be as precise as possible when talking about how the following words are connected. After discussion, each student will write a journal entry capturing an example to show how the words are connected using as many words as possible. Journal entries must make sense. Be ready to share your entry with a small group. Purpose: To provide an effective and engaging practice activity in reviewing material prior to an assessment and as well as encourage the sharing of information so that all students regardless of levels can master the content and language related to the topic.
Lesson Materials Needed:
-EOG Problem Question Set (attached)
-Whiteboards/Markers
-Blank Paper
-Pencils
-TI-15 Calculators (optional)
-EOG Graph Paper
-Bubble Sheet (optional)

Directions:
1. Groupings are made of heterogeneously mixed students of four. Once grouped, they count off so that each student has a number 1-4.
2. Teacher uses prepared assessment review questions from the EOG Review Question Sets displayed or projected. Problems are revealed one at a time and each group discusses the possible answer choices finding a consensus on the correct answer.
3. The teacher then spins a spinner and calls out a number 1-4. If the number is “2” then all students who are number 2 in each group stand up and give their groups answer. Though everyone in the group is responsible for the answer, only one student in each group will be chosen randomly to report the answer.
4. Use the following sentence frames to support groups’ math talk discussions: It may be helpful to post these on sentence strips or index cards for students to refer to during cooperative group work.
“I disagree with that answer because I think it should be ____ because I know___.”
“I agree that is the correct answer because ______.”
“The correct answer is _____ because ______.”
*Variation: Instead of students having a number 1-4, they can be assigned a letter A-D to represent an multiple choice answer. Teacher then randomly picks a letter card from a bag and then all students with that letter must stand and explain why that answer choice is correct OR why that answer choice is not correct. Teacher facilitates discussion of the correct answer choice while students give rationales as to why the other answer choices would not make sense.

SNAP!