Christ the Redeemer

5th Grade Math Curriculum Scope and Sequence

Numbers and Operations

 (Whole Numbers and Integers)

Numbers and Operations

(Fractions)

  • Read and write any numeral from zero through the trillions period.
  • Identify the place value for any number from zero through the trillions period.
  • Round whole numbers to a specific place value.
  • Order a set of rational numbers.
  • Demonstrate fluency in addition and subtraction of whole numbers to solve problems.
  • Demonstrate fluency of multiplication and division facts through 12 x 12.
  • Proficiently multiply multi-digit whole numbers.  
  • Identify the square root of perfect squares.  
  • Rename numbers written in exponential notation and vice versa (i.e. 3 2 = 9).
  • Identify prime and composite numbers using models and factor notation (factor tree).
  • Identify multiples and factors of whole numbers.
  • Use and apply the divisibility rules of 2, 5, and 10.
  • Develop fluency in division of 1-digit, 2-digit and 3-digit divisors.
  • Develop an understanding of the four operations of multi-digit whole numbers to solve problems.
  • Apply the order of operations to simplify numerical expressions using parentheses, brackets, or braces in numerical expressions.
  • Identify prime and composite numbers.
  • Determine prime factorization.
  • Use inverse operations to check answers.
  • Identify and graph integers on a number line.  
  • Compare and order integers.  
  • Read and write negative numbers related to practical applications.
  • Convert a given fraction to equivalent fractions (such as ½ and 3/6 or 4/12 and 1/3).
  • Represent fractions using models.
  • Add and subtract fractions with like and unlike denominators (including mixed numbers).
  • Solve real word problems involving addition and subtraction of fractions, using concrete objects, pictures, words, and numbers.
  • Understand that a fraction is a division problem of the numerator by the denominator (a/b = a ÷b).
  • Solve word problems involving division of whole numbers leading to answers in form of fractions and mixed numbers.
  • Review and apply multiplication of a fraction or a whole number by a fraction.
  • Multiply fractions and mixed numbers to solve real world problems.
  • Divide unit fractions by whole numbers and whole numbers by unit fractions.
  • Divide a unit fraction by a non-zero whole number.
  • Divide a whole number by a unit fraction.
  • Solve real world problems by dividing unit fractions by whole numbers and whole numbers by unit fractions.
  • Use division to reduce (simplify) fractions to lowest terms.
  • Apply the four operations to fractions and mixed numbers to solve real world problems using a variety of methods.
  • Convert between mixed numbers and improper fractions.

Numbers and Operations

(Decimals)

  • Read and identify decimals to the thousandths place.
  • Write, order and compare decimals to the thousandths place.
  • Identify the place value for any decimal through the thousandths.
  • Round decimals to a specific place value.
  • Represent decimals using models.
  • Perform the four operations when using decimals through the thousandths to solve problems.
  • Apply the four operations with multi-digit whole numbers and with decimals to hundredths.
  • Represent the conversion between simple decimals and fractions using models.
  • Convert fractions to decimals to the hundredths place and decimals to fractions with denominators less than or equal to 10.
  • Convert between simple ratios and percents with denominators of 100.
  • Find the percent of a given number for whole number percents less than 100%.

Algebra

Geometry

  • Describe, extend and make generalizations about geometric and numeric patterns.
  • Represent and explain numeric and geometric patterns with concrete materials, tables and graphs and translate among them.
  • Using appropriate algebraic symbols, write open sentences that describe everyday situations.
  • Recognize and apply the commutative, associative and distributive properties to compute with whole numbers.
  • Express mathematical relationships using equations.
  • Solve word problems involving addition and subtraction of fractions.
  • Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.
  • Solve real world problems involving multiplication of fractions and mixed numbers.
  • Understand and explain patterns involving powers of ten in our place value system by relating it to the movement of the decimal point.
  • Analyze tables and graphs to identify algebraic relationships.
  • Interpret tables and graphs for their practical implications.
  • Recognize, describe and compare situations with constant or varying rates of change.
  • Investigate how a change in one variable relates to change in a second variable.

  • Sort and/or classify by properties, a selection of plane figures.
  • Use appropriate vocabulary to describe properties of common 2- dimensional and 3- dimensional figures (i.e. edges, vertices, faces, etc.)
  • Justify why two or more complex figures are congruent or similar.  
  • Recognize the characteristics that make up a Cartesian Plane (rectangular coordinate plane).
  • Plot points on a number line and on a Cartesian Plane, identify the coordinate pair of each.
  • Use technology to explore graphs of linear and non-linear relationships to make predictions or form conclusions.
  • Find vertical and horizontal distances on coordinate systems.
  • Draw a shape that has been rotated about a point or flipped (reflected) above a given line.
  • Describe a series of transformations that will give two congruent shapes the same orientation.
  • Identify and describe line and rotational symmetry.
  • Create a given shape from a set of tangrams or other manipulatives.
  • Separate a two-dimensional complex shape into similar shapes.
  • Construct common three-dimensional shapes using manipulatives and/or two-dimensional nets.
  • Construct a three-dimensional object from a set of two-dimensional plans.
  • Draw a two-dimensional representation of a three-dimensional object.
  • Understand and apply cubic units of measure when determining the volume of a solid.
  • Apply volume problems in real world situations.
  • Determine the volume of a right rectangular prism.
  • Compare and contrast the formulas V = l × w × h and V = B × h for rectangular prisms using whole numbers.
  • Break apart irregularly shaped figures into right rectangular prisms and add their volumes.

Measurement

Data Analysis

  • Select an appropriate metric or customary unit to measure length and the area of a common figure.
  • Describe the attributes and the units of measure for length, area, weight, volume and angles.
  • Create a line graph to display a data set of measurements involving fractional parts.
  • Estimate volume, weight and temperature using metric and customary units.
  • Convert units within the same system, metric and customary.
  • Perform simple conversions between metric and customary systems.
  • Convert among units of time (i.e. seconds, minutes, hours, days, weeks, years).
  • Estimate and measure the approximate area of an irregular polygon or complex figure.
  • Estimate and measure the perimeter of an irregular polygon or complex figure.
  • Explore standard and non-standard units of measure for length, volume, weight and temperature.
  • Understand measurements are approximations and how differences in units affect precision.
  • Recognize and apply the use of reasonable estimates.
  • Make accurate measurements using appropriate tools for length, area, volume, weight, time, temperature and angles.
  • Use formulas for finding the area of rectangles, related triangles and parallelograms.
  • Find the perimeter of polygons and complex shapes.
  • Use formulas to find the volume of rectangular solids.
  • Develop strategies to determine the surface area of rectangular solids.
  • Given a specified amount of money, determine what could be bought and/or the amount of change received from a purchase.
  • Convert within customary and metric measurement systems and use these conversions in solving multi-step, real world problems.

  • Pose questions to peers about themselves, the environment, the school, the community and other content areas.
  • Given a question, identify the data needed to obtain the answer.
  • Develop a plan to collect data using surveys, making observations or measurements, completing a tally sheet or referencing published resources.
  • Represent data in tables, line plots, spreadsheets, pictographs, bar, circle and line graphs.
  • Interpret tables and graphs for their practical implications.
  • Use appropriate title, headings and scale when constructing graphs.
  • Identify, construct and interpret a line or bar graph with an interrupted scale.
  • Construct a stem and leaf or box and whisker plot for a given set of data.
  • Recognize categorical versus numerical data.
  • Explain the meaning of the terms mean (average), median, mode and range.
  • Identify mean, median, mode and range for a given set of data with and without technology.
  • Compare data displayed various ways and evaluate how well it represents the data.
  • Explore the concepts of sampling and biased data.
  • Propose and justify conclusions and predictions based on data represented as bar, line, circle and pictographs.
  • Use the mean, median, mode and range to make conclusions for a given set of data.
  • Explain how mean, median and mode can be used to define the middle of a set of data.
  • Generate additional questions based on their conclusions and predictions.
  • Recognize an event as either certain or impossible.
  • Use “zero” to describe an event that is impossible and “one” if it is certain.
  • Describe an event by its degree (i.e. certain, equally likely, impossible).
  • Recognize that the probability of an event is a number between zero and one.
  • Identify all possible outcomes for a simple sample space (i.e. tossing a die).
  • Conduct experiments to quantify the empirical (experimental) probability of simple events.
  • Make line graphs to display data sets of measurements in decimal units less than 1.
  • Create bar and line graphs.

Objective

Skills

Quarter 1

Numbers and Operations

(Whole Numbers, Integers, Decimals)

Algebra

Review of 4th grade Skills

Understand Place Value

  • Recognize multi digit numbers
  • Whole Numbers and Place Value
  • Place Value and Decimals

Multiply Whole Numbers

  • Perform operations with multi digit whole numbers
  • Multiplication Properties – Distributive Property
  • Multiply by powers of ten

Divide Whole Numbers

  • Find whole number quotients
  • 1-digit and 2-digit divisors
  • Division word problems

Read, Write, Order,

Compare and Round Decimals

  • Read, write, and compare decimals to the thousandths
  • Estimating Sums and Differences of Decimals

Add and Subtract Decimals

  • Add and Subtract decimals to the ten thousandths place
  • Use strategies involving money, place value relationships, and properties

Multiply Decimals

  • Multiply decimals by 10, 100, or 1000
  • Estimate products of a decimal
  • Models for Multiplying Decimals
  • Multiple-Step Problems

Divide Decimals

  • Divide Decimals by 10, 100, or 1000
  • Estimate Decimal Quotients
  • Models for Dividing Decimals
  • Multiple Step Problems

Numerical Expressions, Patterns, and Relationships

  • Variables and Expressions
  • Exponents, Order of Operations
  • Evaluate expressions using decimal numerals
  • Understand and Explain patterns involving powers of ten
  • Add, Subtract, Multiply, Divide Expressions

Compare and Order Integers

  • Use a number line to compare integers
  • Identify absolute value of an integer
  • Identify opposite integers
  • Use a model to add and subtract integers

Quarter 2

Number and Operations

(Fractions)

Algebra

Prime and Composite Numbers

Prime Factorization

  • Draw and use factor trees
  • Represent numbers with exponents
  • Identify GCF and LCM

Squaring Numbers

  • Solve square roots and perfect squares
  • Memorize the perfect squares from 1 to 15
  • Express a perfect square in exponent form

Fractions

  • Identify and find equivalent fractions
  • Locate and place fractions and mixed numbers on a number line
  • Identify and write fractions in simplest form
  • Improper fractions and Mixed Numbers

Adding and Subtract Fractions

  • Estimate sums and differences
  • Add and subtract fractions with common denominators
  • Add and Subtract fractions with unlike denominators

Add and Subtract Mixed Numbers

  • Add mixed numbers in simplest form
  • Subtract mixed numbers in simplest form

Multiply Fractions and Mixed Numbers

  • Estimate products
  • Multiply fractions and mixed numbers

Divide Fractions and Mixed Numbers

  • Estimate quotients
  • Divide fractions and mixed numbers
  • Identify reciprocal numbers

Word Problems with Fractions and Decimals

  • Solve word problems involving fractions and mixed numbers
  • Solve word problems involving money
  • Convert between fractions and decimals

Quarter 3

Geometry

Measurement

 Data Analysis

Customary Units of Measure

  • Convert customary units of length, capacity, and weight
  • Estimate and measure
  • Use the appropriate tool to measure

Metric Units of Measurement

  • Convert metric units of length, capacity, weight
  • Estimate and measure
  • Use the appropriate tool to measure

Solve Word Problems Involving Conversions

  • Convert among different sized standard measurement units and use these conversions in real world problems
  • Solve conversions in solving multi-step, real world problems

Writing and Solving Equations

  • Demonstrate equivalence on both sides of an equation
  • Model and solve multi-step equations

Measurements of Central Tendency

  • Find mean, median, mode, and range to explain data
  • Describe outliers and explain how it can change the measures of central tendency

Data

  • Place and understand data found in line plots
  • Gather data from surveys
  • Measurement data in charts

Graphs

  • Represent data in tables, line plots, spreadsheets, bar graphs, circle graphs, and line graphs.

Ratios and Percents

  • Read, write, and illustrate relationships between decimals, fractions, and percents
  • Generate a table of equal ratios and graph the ordered pairs
  • Read and write rates, and change a rate to a unit rate

Quarter 4

Geometry

Measurement

Data Analysis

Volume

  • Measures volumes by counting unit cubes
  • Use objects and reasoning
  • Find volume using formulas
  • Solve real world and mathematical problems involving volume

Lines and Angles

  • Describe and locate parallel and perpendicular lines
  • Measure and Draw angles
  • Use a protractor to measure angles
  • Label different types of angles: acute, obtuse, straight

Polygons and Triangles

  • Identify, Describe, classify, and draw polygons
  • Regular vs. Irregular Polygons
  • Identify, describe, and classify triangles according to sides and angles

Quadrilaterals

and

2D & 3D Figures

  • Attributes of Quadrilaterals
  • Special Quadrilaterals
  • Classifying quadrilaterals
  • Make and test generalizations about shapes
  • Use appropriate vocabulary to describe properties of common 2-D and 3-D figures
  • Edges, vertices, faces

Perimeter and Area

  • Apply formulas to find the perimeter and area of squares, rectangles, and circles
  • Circumference vs. Area of a Circle

Symmetry and Transformations

  • Introduce transformations
  • Identify and describe line and rotational symmetry
  • Reflections and Rotations

Coordinate Geometry

  • Ordered Pairs
  • Patterns and Graphing
  • Plot points on Coordinate graph to estimate nad determine distance between points

Probability and Statistics

  • Make and test predictions of probability and fairness
  • Design probability experiments and games of chance
  • Identify possible outcomes and events