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Glen Ridge Public Schools –Mathematics Curriculum Glen Ridge Public Schools –Mathematics Curriculum

Course Title: Fifth Grade Math

Subject: Mathematics

Grade Level: 5

Duration: One year

Prerequisite: 4th grade

Elective or Required: Required

Mathematics Mission Statement

Since Mathematical and Computational thinking are an integral part of our lives and 21 st Century learning, students must be actively involved in their mathematics education with problem solving being an essential part of the curriculum. The mathematics and computer science curricula will emphasize thinking skills through a balance of computation, intuition, common sense, logic, analysis and technology. Students will be engaged and challenged in a developmentally appropriate, student-centered learning environment. Students will communicate mathematical ideas effectively and apply those ideas by using manipulatives, computational skills, mathematical models and technology in order to solve practical problems. To achieve these goals, students will be taught a standards-based curriculum that is aligned with the National Common Core Standards in Mathematics and the New Jersey Core Curriculum Content Standards in Technology and 21st Century Life and Careers.

Course Description:

In fifth grade math, students will be working to improve and solidify their knowledge in three critical areas: fractions, volume, and division operations. In doing so, students will be exposed to units focusing on algebraic thinking, whole number sense, fraction number sense, measurement, data, and geometry. Students will be practicing the following skills throughout their year: problem solving, reasoning, modeling, using appropriate tools, using structure, recognizing patterns, and checking for precision. In addition, students will use various forms of technology to assist in their mathematical problem solving.

Author: Nicole DilkesDate Submitted: Summer 2012

Fifth Grade Math

Unit One: Number Theory

Approximate # Of Weeks: 3

Essential Questions: How can using arrays help us to understand a number?Why is it important to know the factors of a number?What is the difference between a prime and composite number?What are the characteristics of square numbers?How can numbers be broken down into smaller parts?

Upon completion of this unit students will be able to:1. Diagram numbers into arrays (square, rectangular, or non) using dots. SMP2,

SMP3, SMP4, SMP6, SMP7, SMP8, 5.NBT.22. List factor pairs of numbers by using array diagrams. SMP1, SMP2, SMP4, SMP5,

SMP6, 5.OA.23. Use factoring strategies to compete against teammates. SMP1, SMP3, SMP6, 5.OA.2,

5.NF.5a4. Use problem solving skills to decipher problems and find solutions in various numerical

operations. SMP3, SMP5, 5.OA.2, 5.NBT.25. Use divisibility rules to quickly figure out the divisibility of various numbers. SMP1,

SMP3, SMP5, SMP6, SMP8, 5.NBT.26. Differentiate the qualities of prime numbers and composite numbers. SMP1, SMP2,

SMP3, SMP6, SMP8, 5.NBT.27. Use square arrays to determine which numbers are square numbers. SMP2, SMP3,

SMP5, SMP6, SMP7, SMP8, 5.OA.28. Find the square root (unsquare) of square numbers using array diagrams. SMP1, SMP2,

SMP3, SMP5, SMP6, 5.OA.2, 5.NBT.29. Break down numbers into factor strings and factor trees in order to figure out the prime

factorization for exponential notation. SMP1, SMP2, SMP3, SMP4, 5.OA.1, 5.NBT.210. Write a number in exponential notation and use exponential notation to find a number.

SMP1, SMP2, SMP3, SMP4, 5.OA.1, 5.NBT.2

Interdisciplinary Standards (njcccs.org)

Standard 9.1 21st-Century Life & Career Skills All students will demonstrate the creative, critical thinking, collaboration, and problem-solving skills needed to function successfully as both global citizens and workers in diverse ethnic and organizational cultures.

Standard 8.1 – Computer and Information Literacy

All students will use computer applications to gather and organize information and to solve problems.

Standard 8.2 – Technology EducationAll students will develop an understanding of the nature and impact of technology, engineering, technological design, and the designed world as they relate to the individual, society, and the environment.

Activities – Math Boxes Journal pages Study Links EM games (tactile or online) Use plastic chips, beans, or cereal bits to make arrays Search and collect arrays in everyday life (calendars, peg boards, etc.) Make colorful factor rainbows, connecting factor pairs with different colors Divisibility rules posters Student Reference Book scavenger hunt

Enrichment Activities:

Explore GoldBach's Conjecture Make an array museum with arrays in the world Use the Sieve of Eratosthenes to explore prime numbers Examine palindromes in order to compare to prime number factor strings

Methods of Assessments/Evaluation: SMART clickers Study Island Online or paper tests/quizzes Exit slips WallWisher Thumbs up/down Think/Pair/Share Dry erase boards Find the mistake/error analysis Poster Math Journal Project Class work Homework Self-Assessment Manipulatives Observation Center/workstation activities Open ended questions

Verbal assessment Math Game (score)

Resources/Including Online Resources Everyday Mathematics Online (https://www.everydaymathonline.com/) Everyday Math Program, McGraw-Hill Teacher Webpage SMARTExchange http://www1.center.k12.mo.us/edtech/everydaymath.htm http://www.rmsheilman.com/gamcorr46.htm

Fifth Grade Math

Unit 2: Estimation and Computation


Essential Questions: How does place value affect computation?When is it okay to estimate?How does estimating help you get precise answers?What are the differences and similarities between the algorithms of an operation?

Upon completion of this unit students will be able to:1. Estimate linear distance using a map scale. SMP1, SMP2, SMP3, SMP4, SMP5,

SMP6, SMP8, 5.NBT.2, 5.MD.12. Convert travel times for given distances at a given rate of speed. SMP1, SMP2, SMP3,

SMP4, SMP5, SMP6, SMP8, 5.NBT.2, 5.MD.13. Convert between inches, feet, and miles. SMP1, SMP2, SMP3, SMP4, SMP5, SMP6,

SMP8, 5.NBT.2, 5.MD.14. Write numbers in expanded notation. SMP1, SMP2, SMP3, SMP4, SMP5, SMP6,

SMP8, 5.NBT.2, 5. Make magnitude estimates for addition and subtraction. SMP1, SMP2, SMP3, SMP5,

SMP6, SMP7, SMP8, 5.NBT.1, 5.NBT.3a, 5.NBT.3b, 5.NBT.4, 5.NBT.76. Identify, write, and solve number sentences that model subtraction number stories.

SMP1, SMP2, SMP3, SMP4, SMP6, SMP8, 5.OA.1, 5.OA.2, 5.NBT.3a, 5.NBT.7

7. Use open sentences to solve number stories. SMP1, SMP2, SMP3, SMP4, SMP6, SMP8, 5.OA.1, 5.OA.2, 5.NBT.3a, 5.NBT.7

8. Use line plots to organize reaction-time data. SMP1, SMP2, SMP5, SMP6, SMP8, 5.NBT.4, 5.NBT.7, 5.MD.2

9. Find statistical landmarks. SMP1, SMP2, SMP5, SMP6, SMP8, 5.NBT.4, 5.NBT.7, 5.MD.2

10. Compare and draw conclusions about collected data. SMP1, SMP2, SMP5, SMP6, SMP8, 5.NBT.4, 5.NBT.7, 5.MD.2

11. Express the probability of an event as a fraction, decimal, or percent. SMP1, SMP2, SMP3, SMP4, SMP5, SMP6

12. Use the lattice method for multiplying whole numbers and decimals. SMP1, SMP5, SMP6, SMP8, 5.NBT.2, 5.NBT.7

13. Read and write large numbers. SMP1, SMP3, SMP4, SMP5, SMP6, 5.NBT.1, 5.MD.1

14. Make reasonable estimates for whole number and decimal multiplication problems. SMP1, SMP3, SMP5, SMP6, 5.NPT.2, 5.NBT.4, 5.NBT.7

Interdisciplinary Standards (njcccs.org)Standard 9.1 21st-Century Life & Career Skills All students will demonstrate the creative, critical thinking, collaboration, and problem-solving skills needed to function successfully as both global citizens and workers in diverse ethnic and organizational cultures.

Standard 8.1 – Computer and Information LiteracyAll students will use computer applications to gather and organize information and to solve problems.


Activities – include Math Boxes Journal pages Study Links SB Games Challenge students to solve a real-world estimation problem (how many steps to a

nearby store, for example). Use the column-addition method to add and subtract decimals. Play decimal version of Addition Top-It. Form open sentences to solve a variety of problems. Play Name That Number. Estimate reaction time, then use it as a data set to practice statistical landmarks. Play Multiplication Bull’s Eye.

Play High-Number Toss, to practice reading large numbers. View millions, billions, and trillions and what they might look like online. Use SMARTboard to set up problems according to algorithm Use Excel to calculate statistics


Use the partial-sums algorithm to add and subtract decimals. Play Subtraction Target Practice. Construct spinners that fit a pre-determined situation involving probability. Explore an ancient Egyptian method of multiplying Devise other algorithms Compare algorithms for characteristics

Methods of Assessments/Evaluation: SMART clickers Study Island Online or paper tests/quizzes Exit slips WallWisher Thumbs up/down Think/Pair/Share Dry erase boards Find the mistake/error analysis Poster Math Journal Project Class work Homework Self-Assessment Manipulatives Observation Center/workstation activities Open ended questions Verbal assessment Math Game (score)


Fifth Grade Math

Unit 3: Geometry and The American Tour


Essential Questions: How are all angles related?What are the different ways I can make and measure angles?What are the properties of polygons?Which shapes will tessellate?

Upon completion of this unit students will be able to:1. Use collected data to make predictions. SMP1, SMP2, SMP3, SMP4, SMP5, SMP6,

5.NBT.3b2. Use table data to answer questions. SMP1, SMP2, SMP3, SMP4, SMP5, SMP6,

5.NBT.3b3. Determine the measure of angles by using known measures. SMP1, SMP2, SMP3,

SMP64. Use angle relationships to determine angle measures. SMP1, SMP2, SMP3, SMP65. Define and classify angles according to their measures. SMP1, SMP2, SMP3, SMP66. Use a full-circle and a half-circle protractor to measure and draw angles. SMP2, SMP3,

SMP5, SMP6, 5.G.37. Investigate vertical, opposite, and adjacent angles. SMP1, SMP2, SMP3, SMP68. Explore the relationship between radius and diameter measurements. SMP2, SMP3,

SMP5, SMP6, SMP8, 5.NBT.2, 5.NBT.3a9. Classify triangles as isosceles, equilateral, or scalene. SMP2, SMP3, SMP5, SMP6,

SMP7, SMP8, 5.NBT.410. Use relationships and properties to sort polygons. SMP2, SMP3, SMP5, SMP6,

SMP7, SMP8, 5.G.3, 5.G.4, 5.NBT.2, 5.NBT.3a11. Describe the properties of regular polygons. SMP2, SMP3, SMP5, SMP6, SMP7,

SMP8, 5.G.3, 5.G.4, 5.NBT.2, 5.NBT.3aSMP2, SMP3, SMP5, SMP6, SMP8, 5.NBT.2, 5.NF.5a, 5.G.3, 5.G.4

13. Draw circles of a given radius or diameter. SMP2, SMP3, SMP5, SMP6, SMP8, 5.NBT.2, 5.NBT.3a




Standard 6.1 U.S. History: America in the WorldAll students will acquire the knowledge and skills to think analytically about how past and present interactions of people, cultures, and the environment shape the American heritage. Such knowledge and skills enable students to make informed decisions that reflect fundamental rights and core democratic values as productive citizens in local, national, and global communities.

Standard 6.3 Active Citizenship in the 21st CenturyAll students will acquire the skills needed to be active, informed citizens who value diversity and promote cultural understanding by working collaboratively to address the challenges that are inherent in living in an interconnected world.

Activities – Math Boxes Journal pages Study Links SB games Play High Number Toss (Decimal Version) Compare data from the 1790 Census with the 2000 Census Analyze data from Colonial Census figures. Use pattern blocks to determine angle measurements. Practice measuring and drawing angles. Copy line segments with protractor. Measure angles found by intersecting lines. Copy triangles using a protractor. Play Angle Tangle. Sort polygons by their properties. Play Polygon Capture. Find the sums of angles in polygons. Divide polygons into triangles. Solve problems using the geometry template.


Take a classroom census and post results (website, poster, etc.). Solve place-value puzzles. Inscribe a regular hexagon in a circle.

Play Triangle Sort. Make tessellation with pattern blocks. Solve geometry template challenges.



Fifth Grade Math

Unit 4: Division


Essential Questions: What is the relationship between real distance and map distance?What is the meaning of a remainder?How should I report my quotient?

Upon completion of this unit students will be able to:1. Use “friendly numbers” to divide 2-digit by 1-digit numbers. SMP1, SMP2, SMP5,

SMP6, SMP8, 5.OA.1, 5.OA.2, 5.NBT.2, 5.NBT.6, 5.NF.5a, 5.G.3, 5.G.42. Solve estimation problems. SMP1, SMP2, SMP5, SMP6, SMP8, 5.OA.1, 5.OA.2,

5.NBT.2, 5.NBT.6, 5.NF.5a, 5.G.3, 5.G.43. Measure to nearest half-inch. SMP1, SMP2, SMP3, SMP4, SMP5, SMP6, 5.OA.14. Use a map scale to find distance on a map. SMP1, SMP2, SMP3, SMP4, SMP5,

SMP6, 5.OA.15. Use divisibility rules to identify multiples. SMP1, SMP2, SMP3, SMP4, SMP5, SMP6,

5.NBT.6, 5.NBT.76. Use division vocabulary (dividend, divisor, etc.) SMP1, SMP2, SMP3, SMP4, SMP5,

SMP6, 5.NBT.6, 5.NBT.77. Use algorithms to divide whole numbers and decimals. SMP1, SMP2, SMP3, SMP4,

SMP5, SMP6, 5.NBT.6, 5.NBT.78. Interpret the remainder in number story solutions. SMP1, SMP2, SMP4, SMP5, SMP6,

5.OA.2, 5.NBT.6, 5.NBT.79. Write and solve number sentences that model division number stories. SMP1, SMP2,

SMP4, SMP5, SMP6, 5.OA.2, 5.NBT.6, 5.NBT.710. Solve number sentences for given variables. SMP1, SMP2, SMP4, SMP5, SMP6,

5.OA.2, 5.NBT.6, 5.NBT.7




Standard 6.3 Active Citizenship in the 21st Century

All students will acquire the skills needed to be active, informed citizens who value diversity and promote cultural understanding by working collaboratively to address the challenges that are inherent in living in an interconnected world.

Activities – Math Boxes Journal pages Study Links SB Games

Use mental division strategies to solve for quotients. Rename numbers in a name collection box. Find distances in the U.S. using a map scale. Play Divisibility Dash. Use visual aids to solve number stories by interpreting remainder. Play First-to-100. Write division number stories.


Play Name that Number, with more cards. Mix up algorithms to use. Estimate curved-path distances. Play Algebra Election. Write more advanced (or mental math) division number stories

Methods of Assessments/Evaluation: SMART clickers Study Island Online or paper tests/quizzes Exit slips WallWisher Thumbs up/down Think/Pair/Share Dry erase boards Find the mistake/error analysis Poster Math Journal Project Class work Homework Self-Assessment Manipulatives Observation Center/workstation activities

Open ended questions Verbal assessment Math Game (score)


Fifth Grade Math

Unit 5: Fractions, Decimals, and Percents


Essential Questions: What is the relationship between fractions, decimals, and percents?What is the relationship between improper fractions and mixed numbers?What format is appropriate to report when answering a mathematical question?Why is data reporting important to our lives?

Upon completion of this unit students will be able to:1. Find fractions of a set and find the whole based on a known fraction of a set. SMP1,

SMP2, SMP3, SMP4, SMP5, SMP6, 5.NF.32. Identify and use unit fractions to solve problems. SMP1, SMP2, SMP3, SMP4, SMP5,

SMP6, 5.NF.33. Find equivalent names for fractions and mixed numbers. SMP1, SMP2, SMP3, SMP5,

SMP64. Explore the meaning of fractions using an area model to identify parts or the whole.

SMP1, SMP2, SMP3, SMP4, SMP5, SMP6, 5.NF.35. Compare fractions and mixed numbers. SMP1, SMP2, SMP3, SMP5, SMP66. Add fractions using an area model. SMP2, SMP3, SMP5, SMP6, 5.NF.1, 5.NF.27. Order fractions from least to greatest. SMP2, SMP3, SMP5, SMP6, 5.NF.1, 5.NF.28. Rename fractions and mixed numbers as decimals. SMP1, SMP2, SMP6, SMP89. Round decimals. SMP1, SMP2, SMP5, SMP6, 5.NBT.3a, 5.NBT.4

10. Convert between fractions, mixed numbers, and decimals. SMP1, SMP2, SMP5, SMP6, 5.NBT.3a

11. Differentiate between repeating and terminating decimals. SMP1, SMP2, SMP3, SMP5, SMP6, SMP7, 5.NBT.3a, 5.NBT.4, 5.NF.3

12. Use a calculator to rename fractions as decimals. SMP1, SMP2, SMP3, SMP5, SMP6, SMP7, 5.NBT.3a, 5.NBT.4, 5.NF.3

13. Use correct notation to write terminating and repeating decimals. SMP1, SMP2, SMP3, SMP5, SMP6, SMP7, 5.NBT.3a, 5.NBT.4, 5.NF.3

14. Define the uses and meaning of percents. SMP2, SMP4, SMP6, 5.NBT.3a15. Explore fractions as a property of circle graphs. SMP1, SMP2, SMP3, SMP5, SMP6,

5.NBT.3a, 5.NBT.416. Estimate circle-graph sector sizes. SMP1, SMP2, SMP3, SMP5, SMP6, 5.NBT.3a,

5.NBT.417. Measure sectors of a circle-graph using the Percent Circle. SMP1, SMP2, SMP3,

SMP5, SMP6, 5.NBT.3a, 5.NBT.418. Interpret circle graph sectors. SMP1, SMP2, SMP5, SMP619. Construct circle graphs from table data. SMP2, SMP3, SMP5, SMP6, 5.NBT.720. Solve problems involving ratios. SMP2, SMP4, SMP6, 5.NBT.3a21. Use graphs to ask and answer questions and draw conclusions. SMP1, SMP2, SMP5,

SMP6





Activities Math Boxes Journal pages Study Links

SB Games Review basic fraction ideas. Solve part-and-whole problems with fractions, using pictorial models. Play Fraction Top-It. Use pattern blocks to model mixed numbers. Review fractions on a ruler. Use a fraction-stick to find equivalent fractions and order fractions. Formulate rules for generating equivalent fractions, through students knowledge of

fraction-sticks. Manipulating virtual fraction stick on SMARTBoard Round decimals by looking at bank accounts and race results. Write fractions as decimals through the use of a pictorial model. Play Frac-Tac-Toe, to practice converting between fractions and decimals. Play Frac-Tac-Toe, percent version. Graph snack-survey data onto a bar graph. Demonstrate methods for using a percent circle. Construct circle graphs using percent circle, based on snack survey data. Make fraction sticks (models of fractions by folding construction paper). Play Estimation Squeeze.


Fractions, Decimals, and Percents Museum (classroom display of real life items that involve the figuring and dividing of the above).

Pattern-block puzzles of various difficulty levels. Play Number Top-It (3-place decimals). Act out the construction of a circle graph (human circle graph).

Methods of Assessments/Evaluation: SMART clickers Study Island Online or paper tests/quizzes Exit slips WallWisher Thumbs up/down Think/Pair/Share Dry erase boards Find the mistake/error analysis Poster Math Journal Project Class work Homework Self-Assessment Manipulatives Observation

Center/workstation activities Open ended questions Verbal assessment Math Game (score)


Fifth Grade Math

Unit 6: Using Data; Adding and Subtracting Fractions


Essential Questions: How are statistical landmarks reported?What is a good sample size for a given population?Why is using common denominators important when subtracting or adding fractions?

Upon completion of this unit students will be able to:1. Compare and answer questions about data sets and their organization. SMP2, SMP3,

SMP4, SMP5, SMP6, SMP7, 5.NBT.4, 5.MD.22. Use collected data to make predictions about future outcomes of a simple game. SMP2,

SMP4, SMP5, SMP6, 5.NBT.3a3. Measure to the nearest millimeter, centimeter, and inch. SMP1, SMP2, SMP5, SMP6,

5.NBT.3a, 5.MD.14. Measure finger and hand spans to the nearest millimeter. SMP1, SMP2, SMP5, SMP6,

5.NBT.3a, 5.MD.15. Measure angles with half-circle protractors. SMP1, SMP2, SMP5, SMP6, 5.NBT.3a,

5.MD.16. Interpret line plots and stem-and-leaf plots. SMP2, SMP3, SMP6, 5.NBT.4

7. Make predictions based on sampling. SMP1, SMP2, SMP3, SMP4, SMP5, SMP6, 5.NBT.7

8. Construct bar and circle graphs and a stem-and-leaf plot. SMP1, SMP2, SMP3, SMP4, SMP5, SMP6

9. Investigate the use of contour maps to organize collected data. SMP1, SMP2, SMP3, SMP4, SMP5, SMP6,5.NBT.7

10. Add fractions and mixed numbers with like denominators. SMP1, SMP2, SMP3, SMP5, SMP6, 5.NF.1, 5.NF.2, 5.NF.3

11. Find common denominators. SMP1, SMP2, SMP3, SMP5, SMP6, 5.NF.1, 5.NF.2, 5.NF.3

12. Use clock models and pencil-and-paper algorithms to add and subtract fractions. SMP1, SMP2, SMP3, SMP5, SMP6, SMP7, SMP8, 5.NF.1, 5.NF.2, 5.NF.5b

13. Use common denominators to add and subtract fraction pairs. SMP1, SMP2, SMP5, SMP6, SMP8, 5.NF.1, 5.NF.2





Activities – include Organize class data (states students have visited) as a line plot. Create models for rounding numbers. Find personal measures (finger span, palm width, etc.) Play Finish First, determine if it’s a “fair game.” Organize personal measure data into a stem-and-leaf plot. Measure finger-separation angles. Identify mystery line plots, stem-and-leaf plots.

Use a candy color sample to estimate greater total. Create a stem-and-leaf plot for the class’s favorite sports and entertainment. Introduce contour maps, interpret data. Use slide rule to add and subtract fractions. Use clock to add and subtract fractions. Enrichment Activities:

Create a data landmark poster. Analyze spelling test scores, creating statistical landmarks. Investigate sample size through rolling a six-sided die. Write contour map questions based on pre-existing maps. Play Fraction Capture, advanced. Write Elapsed Time Number Stories.



Fifth Grade Math

Unit 7: Exponents and Negative Numbers


Essential Questions: Why is order of operations so important to follow?What purpose do negative numbers serve in math?When do we use scientific notation?

Upon completion of this unit students will be able to:1. Compare numbers written in exponential notation. SMP1, SMP2, SMP3, SMP5,

SMP6, 5.NBT.22. Describe the number patterns inherent to exponential notation. SMP1, SMP2, SMP3,

SMP5, SMP6, 5.NBT.23. Explore place value using powers of 10. SMP1, SMP2, SMP3, SMP6, SMP7, 5.NBT.1,

5.NBT.24. Translate numbers from scientific notation to standard and number-and-word notation.

SMP2, SMP4, SMP6, SMP7, 5.NBT.25. Use number patterns to solve problems involving exponents. SMP2, SMP3, SMP4,

SMP6, SMp7, 5.OA.1, 5.OA.26. Solve problems involving parentheses and nested parentheses. SMP2, SMP3, SMP4,

SMp6, SMP8, 5.OA.1, 5.OA.2, 5.NBT.27. Insert parentheses in order to make true number sentences. SMP2, SMP3, SMP4,

SMP6, SMP8, 5.OA.1, 5.OA.2, 5.NBT.28. Evaluate numerical expressions using order of operations. SMP2, SMP3, SMP4,

SMP6, SMp7, 5.OA.1, 5.OA.29. Model sums of positive and negative numbers with manipulatives. SMP2, MSP3,

SMP4, SMP5, SMP6, 5.OA.1, 5.NBT.2 10. Write and solve the equivalent addition number model for signed number subtraction

problems. SMP2, SMP6, SMP8, 5.NBT.3b11. Write number sentences that model signed-number addition and subtraction problems.

SMP2, SMP6, SMP8, 5.NBT.3b12. Use rules for numeric patterns to solve patterns. SMP1, SMP2, SMP4, SMP5, SMP6,

5.NBT.5, 5.NBT.6, 5.NBT.7, 5.NF.1, 5.NF.2, 5.MD.213. Use a calculator to add and subtract signed numbers. SMP1, MSP2, SMP3, SMP4,

SMP5, SMP6, 5.NF.314. Use line graphs to organize data. SMP2, SMP3, SMP4, SMP5, SMP6, 5.NF.1






Activities – include Play Exponent Ball. Analyze place value chart for powers of 10. Use scientific notation to describe various events in the history of the earth. Play Scientific-Notation Toss. Match number stories to appropriate expressions (using parentheses). Learn order of operations through mnemonic device (Please Excuse My Dear Aunt

Sally). Use life expectancy data to compare two line graphs. Make line graphs from given data (movie ticket sales, percentage of houses with

televisions). Use MS Excel to analyze and organize data Graph positive and negative numbers on a number line (virtual, paper, and

whiteboard) Use positive and negative counters to calculate account balances. Use positive and negative counters to find the sums of positive and negative numbers. Develop rules for adding positive and negative numbers, and subtracting positive and

negative numbers.

Play 500. Introduce operations with signed numbers on a calculator.


Explore exponent patterns in Fibonacci numbers. Calculate the possible number of computer passwords consisting of 4 characters. Introduce positive and negative exponents. Collect line graphs from newspapers and other real world sources. Skip count with negative numbers. Play Credits/Debits game. Compare elevations of various U.S. locations. Play Broken Calculator.



Fifth Grade Math

UNIT 8: Fractions and Ratios


Essential Questions: What is the relationship between a fraction and a mixed number?Why does the multiplication of fractions algorithm work?How are percents of a number, percent discounts, and fractions of a whole the same?How does the division of fraction algorithm work?

Upon completion of this unit students will be able to:1. Convert between and simplify fractions and mixed numbers. SMP1, SMP2, SMP5,

SMP6, SMP8, 5.NF.1, 5.NF.2, 5.NF.5b2. Add fractions and mixed numbers. SMP1, SMP2, SMP5, SMP6, 5.NF.1, 5.NF.23. Subtract mixed numbers. SMP1, SMP2, SMP3, SMP5, SMP6, 5.NF.1, 5.NF.2, 5.G.3,

5.G.44. Express mixed numbers in simplest form. SMP1, SMP2, SMP3, SMP5, SMP6, 5.NF.1,

5.NF.2, 5.G.3, 5.G.45. Use calculators to solve fraction and mixed-number addition problems. SMP1, SMP2,

SMP4, SMP5, SMP6, 5.NF.1, 5.NF.26. Use unit fractions to find a fraction of a number and to find the whole. SMP1, SMP3,

SMP4, SMP5, SMP6, 5.NF.a, 5.NF.5a, 5.NF.67. Use an area model to find fractions of fractions. SMP2, SMP3, SMP6, SMP8, 5.NF.4a,

5.NF.5a, 5.NF.5b, 5.NF.68. Describe the patterns in the area model for fraction multiplication. SMP2, SMP3,

SMP6, SMP8, 5.NF.4a, 5.NF.5a, 5.NF.5b, 5.NF.69. Use a fraction multiplication algorithm to find fraction-by-whole-number products.

SMP2, SMP4, SMP6, SMP7, SMP8, 5.OA.1, 5.NF.4a, 5.NF.5b, 5.NF.610. Multiply mixed numbers. SMP2, SMP3, SMP4, SMP5, SMP6, SMP8, 5.NF.4a,

5.NF.4b, 5.NF.5a, 5.NF.5b, 5.NF.611. Calculate percents and discounts, and describe strategies used. SMP1, SMP2, SMP3,

SMP4, SMp5, SMP612. Use ratios expressed as percents to solve problems. SMP1, SMP2, SMP3, SMP4,

SMp5, SMP613. Find the unit fraction or percent of a given whole. SMP1, SMP2, SMP3, SMP4,

SMP5, SMP6, SMP7, SMP8

14. Collect and organize data from maps and charts. SMP1, SMP2, SMP3, SMP4, SMP5, SMP6, 5.NF.2

15. Use diagrams and a common denominator method to solve division of fractions problems. SMP1, MSP2, SMP4, SMP6, 5.NF.7a, 5.NF.7b, 5.NF.7c






Activities – Play Build-It Add mixed numbers by finding LCD. Subtract mixed numbers through renaming. Play Mixed-Number Spin. Play Fraction Action, Fraction Friction. Model finding the fraction of a fraction through paper folding. Play Fraction Spin. Create fraction multiplication algorithm through experimentation with area models. Compare how track records would be different on other planets according to gravity

(to practice multiplication of fractions). Calculate a discount on various real world items.

Cookie jar problems (using unit fractions to find the whole). Compare rural and urban populations using online maps.


Order fractions along a rope. Explore a fraction addition pattern. Chart the process of finding common denominators via a flowchart. Calculate discounts based on ads in newspapers. Chart changes in food consumption from 1970-2000. Play Build-It.



Fifth Grade Math

Unit 9: Coordinates, Area, Volume, and Capacity


Essential Questions: What are some real life examples of when we use area and volume and what units are involved?How do we use coordinate grids to find a location?How are area models a useful way to figure out the area of a shape?How are volume and capacity the same and different

Upon completion of this unit students will be able to:1. Use ordered pairs of numbers to name, locate, and plot points in the four quadrants of a

coordinate grid. SMP2, SMP5, SMP6, 5.NBT.2, 5.NF.4a, 5.G.1, 5.G.22. Use rules to generate transformations of plane figures on a coordinate grid. SMP2,

MSP5, SMP6, SMP7, SMP8, 5.NBT.5, 5.G.1, 5.G.23. Construct congruent figures on a coordinate grid. SMP2, SMP3, SMP4, SMP5, SMP6,

5.MD.3a, 5.MD.4, 5.MD.5b, 5.G.1, 5.G.24. Describe reflections and translations of plane figures. SMP2, SMP3, SMP5, SMP6,

SMP8, 5.NF.4b, 5.NF.7a, 5.NF.7b, 5.NF.7c, 5.MD.3a, 5.MD.4, 5.MD.5b5. Describe relationships between U.S. customary and metric square units. SMP2, SMP3,

SMP5, SMP6, 5.NBT.26. Investigate and use formulas to find the area of triangles and parallelograms. SMP2,

SMP5, SMP6, SMP7, SMP8, 5.NF.27. Use latitude and longitude to locate points on Earth. SMP1, SMP2, SMP5, SMP6,

SMP8, 5.NF.68. Use a formula to calculate the volume of prisms and rectangular prisms. SMP1, SMP2,

SMP3, SMP6, SMP7, SMP8, 5.NBT.4, 5.NBT.7, 5.MD.3a, 5.MD.3b, 5.MD.4, 5.MD.5a, 5.MD.5b

9. Write number sentences with variables to model volume problems. SMP1, SMP2, SMP3, SMP4, SMP5, SMP6, SMP8, 5.MD.3a, 5.MD.5b, 5.MD.5c

10. Define and classify prisms according to common properties. SMP1, SMP2, SMP4, SMP6, SMP7, 5.NBT.7, 5.NF.4b, 5.Md.1, 5.MD.3a, 5.MD.3b, 5.MD.4, 5.MD.5a, 5.MD.5b





Activities Plot a turtle on a coordinate grid, using given coordinates. Play the Hidden Treasure game (similar to Battleship). Plot a sailboat in each quadrant of a coordinate grid, using given coordinates. Review of 2-Dimensional figures (vocabulary). Through the “rectangle method,” develop area formulas for triangles and

parallelograms. Determine Earth’s water surface through sampling (practices latitude and longitude). Find the volume of right prisms and rectangular prisms, using 3-dimensional

examples. Demonstrate that one liter equals 1,000 cm (cubed) through a real-world model.

Enrichment Activities: Design pictures on a coordinate graph, plot out the points. Explore the line of reflection by recording coordinates and plot reflections

for their first initials. Read Spaghetti and Meatballs for All, draw all possible table arrangements. Four-4s problems (writing 1-100 using only fours and any operation). Estimate the ground level area of the school.

Methods of Assessments/Evaluation: SMART clickers Study Island Online or paper tests/quizzes Exit slips WallWisher Thumbs up/down Think/Pair/Share

Dry erase boards Find the mistake/error analysis Poster Math Journal Project Class work Homework Self-Assessment Manipulatives Observation Center/workstation activities Open ended questions Verbal assessment Math Game (score)


Fifth Grade Math

Unit 10: Using data, Algebra concepts and skills


Essential Questions: What is pi?What is the relationship between pi, the circumference, and the diameter of a circle?How do you determine the volume of a three dimensional figure?What is the relationship between capacity and weight?

Upon completion of this unit students will be able to:1. Use a pan-balance model to solve linear equations in one unknown. SMP1, SMP2,

SMP3, SMP6, 5.NBT.2, 5.NBT.5, 5. MD.3a, 5.MD.3b, 5.MD.4, 5.MD.5b2. Use a pan-balance model to solve linear equations in two unknowns. SMP1, SMP2,

SMP3, SMP8, 5.NF.5a, 5.MD.2

3. Identify and use patterns in tables to solve problems. SMP2, MSP3, SMP4, SMP6, SMP7, SMP8, 5.OA.1, 5.OA.2, 5.OA.3, 5.NBT.2, 5.NBT.5, 5.MD.5a, 5.MD.5b

4. Write algebraic expressions to model rules. SMP1, SMP2, SMP4, SMP6, SMP8, 5.OA.3, 5.G.1, 5.G.2

5. Represent functions with tables, graphs, and formulas. SMP1, SMP2, SMP3, SMP4, SMP7, SMp8, 5.MD.1

6. Construct line graphs that represent two sets of data. SMp1, SMP2, SMP3, SMP4, SMP5, SMP6, SMP7, SMP8, 5.OA.3, 5.NBT.7, 5.NF.2, 5.G.1, 5.G.2

7. Represent rates with formulas, tables, and graphs. SMP2, SMP3, SMP6, 5.NBT.4, 5.G.1

8. Use ratios to define pi and describe the relationship between circumference and diameter. SMP1, SMp3, SMp4, SMP5, SMP6, SMP7, 5.NBT.4

9. Investigate and apply a formula for finding the area of a circle. SMp1, SMp2, SMP4, SMp5, SMP6, SMP7, SMP8, 5.MD.1



Standard 8.2 – Technology EducationAll students will develop an understanding of the nature and impact of technology, engineering, technological design, and the designed world as they relate to the individual, society, and the environment.Standard 6.3 Active Citizenship in the 21st CenturyAll students will acquire the skills needed to be active, informed citizens who value diversity and promote cultural understanding by working collaboratively to address the challenges that are inherent in living in an interconnected world

Activities – Solve a series of pan-balance problems. Write algebraic expressions based on real-life situations. Chart time and distance data in order to determine rate. Graph time and distance in Excel and generate graph Chart the eruptions of Old Faithful in order to determine when it will next erupt. Graph footrace data, interpret line graph (paper or online). Interpret “mystery” rate graphs. “Discover” pi by comparing the ratio of circumference to diameter in real-world

objects. Find the area of a circle using grid lines, formula, chips, candies, etc..


Solve a penny riddle using pan-balance models. Solve logic puzzles through the use of linear equations. Graph race results, create line graphs. Play First to 100. Explore silhouettes in preparation for interpreting mystery graphs. “Pass” your body through an index card.



Fifth Grade Math

Unit 11: Volume


Essential Questions: What are the differences in finding the area for the types of solids?Can a face be a base, and vice versa?What does the volume of a solid look like when it is not in the sold?

Upon completion of this unit students will be able to:1. Compare and classify geometric solids. SMP2, SMP4, SMP6, 5.MD.3a, 5.MD.3b,

5.MD.4, 5.MD.5a, 5.MD.5b2. Describe and classify polyhedrons according to their faces. SMP2, SMP4, SMP6,

5.MD.3a, 5.MD.3b, 5.MD.4, 5.MD.5a, 5.MD.5b3. Use a Venn diagram to organize data. SMP2, SMP3, SMP5, MSP6, SMP84. Identify congruent faces on geometric solids. SMP2, SMP3, SMP5, MSP6, SMP85. Apply formulas to calculate the area of a circle and the volume of prisms and cylinders.

SMP1, SMP2, SMP4, SMP5, SMP6, SMP8, 5.NBT.4, 5.MD.1, 5.MD.3a, 5.MD.3b, 5.MD.4, 5.MD.5a, 5.MD.5b

6. Compare the volume and the capacity of cylinders. SMP1, SMP2, SMP4, SMP5, SMP6, SMP8, 5.NBT.4, 5.MD.1, 5.MD.3a, 5.MD.3b, 5.MD.4, 5.MD.5a, 5.MD.5b

7. Compare the properties of pyramids, prisms, cones, and cylinders. SMP1, SMP2, SMP3, MSP4, SMP5, SMP6, SMP8, 5.NF.7a, 5.NF.7b

8. Use a displacement method to find the volume of irregular solids. SMP1, SMP2, SMP3, SMP4, SMP5, SMP6, 5.MD.1, 5.MD.5c

9. Convert between standard units of capacity. SMP2, SMP3, SMP4, SMP5, SMP6, SMP8, 5.OA.1, 5.NBT.2, 5.MD.1

10. Measure the dimensions of a cylinder in inches and centimeters. SMP1, SMP2, MSP3, SMP4, SMP5, SMP6, 5.NF.1, 5.NF.2, 5.NF.4b, 5.NF.7c, 5.MD.2, 5.MD.5a, 5.MD.5b

Interdisciplinary Standards (njcccs.org)

Standard 9.1 21st-Century Life & Career Skills All students will demonstrate the creative, critical thinking, collaboration, and problem-solving skills needed to function successfully as both global citizens and workers in diverse ethnic and organizational cultures.




Activities: Use different sided dice to explore regular polyhedrons. In small groups, compare geometric solids. Play 3-D Shape Sort. Verify the cylinder volume formula through real-world examples. Explore the relationship between the volumes of cylinders and cones. Solve volume word problems. Calibrate a bottle, find volume through displacement method. Investigate the capacity of the annual rice consumption of a Thai family. Find the surface area of a can.


Explore a 2-dimensional world using the book Flatland. Construct paper cylinders, compare volumes. Play Rug and Fences. Find the area of concentric circles.




Fifth Grade MathUnit 12: Probability, ratios, and rates


Essential Questions: What are some uses for factor trees?How do ratios show parts of a whole?

Upon completion of this unit students will be able to:1. Use greatest common factors and least common multiples to rename fractions. SMP1,

SMP2, SMp3, SMp5, SMp6, SMP7, 5.NF.7a, 5.NF.7b, 5.NF.7c2. Find greatest common factors and least common multiples using factor strings. SMP1,

SMP2, SMP3, SMP4, SMP5, SMP6, SMP7, 5.NBT.73. Use the Multiplication Counting Principle and tree diagrams to solve probability

problems. SMP1, SMP2, SMP3, SMP4, SMP5, SMP6, SMP7, 5.NBT.74. Express the probability of an event as a fraction. SMP2, SMP5, SMP65. Write ratios in equivalent forms. SMP1, SMP2, SMP3, SMP4, SMP6, 5.NF.7a,

5.NF.7b, 5.NF.7c6. Use equivalent fractions and ratio models to solve ratio number stories. SMP1, SMP2,

SMP4, SMP5, SMP67. Solve rate problems. SMP1, SMP2, SMP3, SMP5, SMP6, SMP8, 5.G.1





Activities – Use factor trees to find common multiples and greatest common factors. Solve combination problems through the use of tree diagrams and the multiplication

counting principle. Use ratios to examine historical trends. Read a pictograph. Solve ratio number stories. Calculate heart rate before and after various amounts of exercise, graph and interpret

results.

Enrichment Activities: Play Factor Captor. Make a Factor Tree poster. Introduce cross multiplication for solving ratio problems. Play Spoon Scramble.


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