Mathematics Competency Assurance Documents

5th Grade Mathematics Standards

Number/Computation

INTERMEDIATE MATHEMATICS EXIT PERFORMANCE STANDARD 1: Student will apply number sense, place value, and order relations to compare whole numbers up to 100 million, fractions to the 1/16th, and decimals to the 1,000ths in problem solving situations to perform basic calculations involving addition, subtraction, multiplication and division of whole numbers and money with and without calculators, and will communicate the reasoning used in solving these problems.

Based on Kentucky’s Core Content for Mathematics Assessment, the Kentucky Program of Studies, and Academic Expectations: 1.5-1.9 Mathematical Communication & Reasoning, 1.16 Technology, 2.7 Number, 2.8 Procedures, 2.11 Change, 2.12 Structure; Goal 5 Think & Solve Problems; & Goal 6 Connect & Integrate Knowledge

5th Grade Number Sense Standards:

N/5.1 Demonstrate number sense to 100 million (100,000,000) through modeling, applying and communicating muliple representations (drawings, concrete materials, & symbols) and using order relations

5th Grade Whole Number Operations & Computation Standards:

C/5.1 Select and apply the appropriate computational operations (+,-,x, ¸ by 2-digit with remainders) to solve multi-step problems in real-life situations

C/5.2 Apply appropriate computational method/tool (estimation, mental arithmetic, paper & pencil, calculator, computer) to solve real-life problems

5th Grade Fractions & Decimals Standards:

FD/5.1 Use order relations (<,>,=, number line) to compare fractions and decimals.

FD/5.2 Apply computational operation(s) to solve problems in real-life situations using fractions to the 1/16ths and decimals (add and subtract to the 1000ths & multiply and divide to the 100ths).

FD/5.3 Model, apply and communicate multiple representations of decimals to the 1000ths.

Skills, Concepts, & Relationships

• Use number words, numerals, diagrams, concrete materials, & expanded form to represent numbers to 100 million (100,000,000)
• compare & order (<,>,=, number line) whole numbers to 100 million
• Understand place value to 100 million
• Identify multiples & factors
• Round whole numbers
• Use estimation strategies: compatible numbers, front end, rounding , range, over estimate & under estimate, clustering
• Identify & use square numbers (arrays)
• Identify LCM (Least Common Multiple)
• Identify GCF (Greatest Common Factor)
• Review identifying primes & composites
• Introduce using prime factorization
• Introduce exponents
• Introduce integers using using a number line
• Develop recognizing when an estimate is appropriate

Skills, Concepts, & Relationships

• Add, subtract, multiply, divide money
• Multiply 2-digit & 3-digit numbers by 2-digit numbers
• Divide by 2-digit divisor
• Choose correct operation (+, -, x, ÷ )
• Review adding & subtracting of 3-digit & 4 digit numbers with regrouping (column addition)
• Review fact families for multiplication and division (inverse operations)
• Introduce interpreting remainders (represents part of whole)
• Develop order of operations
• Develop recognizing & using associative (grouping) and commutative (order) properties
• Develop doing multi-step story problems using all operations
• Develop choosing appropriate problem solving strategies
• Develop calculator skills:
• Know 4 basic functions of calculator (+, -, x, ¸ )
• Check answers with a calculator
• Use a calculator in problem solving
• Use a calculator with large cumbersome numbers
• Develop estimating sums, differences, products, & quotients of whole numbers
• Develop using a variety of mathematics vocabulary and symbols (sum, difference, product, quotient, 1/2, x, ¸ , etc.)

Skills, Concepts, & Relationships

• Compare & order fractions to the 1/16th (<,>,=, number line)
• Add & subtract like fractions to the 1/16th
• Rewrite fractions in lowest terms
• Simplify improper fractions and understand mixed numbers
• Compare & order decimals to the 1,000ths (<,>,=, number line)
• Add & subtract decimals to the 1,000ths
• Multiply & divide decimals to the 100ths (money)
• Read, write, identify and round decimals through the 1,000ths
• Recognize simple percents (100%, 75%, 50%, 25%)
• Review using equivalent fractions
• Introduce adding & subtracting simple unlike fractions (1/2 + 3/4)
• Develop using models to solve real world problems using fractions, decimals, & percents
• Develop using zeros as place holders
• Introduce relating fractions, decimals and percents (1/2=.5=50%)
• Develop comparing and ordering decimals to the 10,000ths
• Introduce definition of ratio with multiple representations
• Introduce equal ratios
• Develop estimating sums, differences, products, & quotients of fractions & decimals
• Introduce estimating percents

Geometry/Measurement

INTERMEDIATE MATHEMATICS EXIT PERFORMANCE STANDARD 2: Student will apply properties of measurement (length to 1/16"or mm, weight/mass, temperature, time, money, capacity, perimeter and area of squares, rectangles, triangles) and will use geometric concepts (plane 2D shapes, solid 3D shapes, lines, angles, basic geometric terms) and relationships in problem solving situations and communicate the reasoning used in solving these problems.

Based on Kentucky’s Core Content for Mathematics Assessment, the Kentucky Program of Studies, and Academic Expectations: 1.5-1.9 Mathematical Communication & Reasoning, 1.16 Technology, 2.8 Procedures, 2.9 Space and Dimensionality, 2.10 Measurement, 2.11 Change, 2.12 Structure; Goal 5 Think & Solve Problems; & Goal 6 Connect & Integrate Knowledge

5th Grade Geometry Standards:

G/5.1 Recognize, identify, draw, model, and classify various geometric terms and shapes.

5th Grade Measurement Standards:

M/5.1 Select the appropriate measurement tools and units to make estimates and measurements in solving problems using metric & customary measures.

Skills, Concepts, & Relationships

• Recognize, draw and describe quadrialterals including trapezoids & parallelograms
• Recognize diagonals
• Draw and measure angles (right, obtuse, acute, vertex, side, degree)
• Recognize plane similar figures
• Identify center, diameter, radius, circumference, chord of circles
• Draw & model transformations (flips, slides, turns) of basic 2-D shapes with physical models
• Review recognizing & drawing a line of symmetry
• Review recognizing & matching congruent figures
• Develop using formulas when presented with real-life problems (area, perimeter)
• Develop drawing 2-D views of 3-D figures
• Develop constructing 3-D objects from 2-D pictures
• Introduce recognizing, describing, drawing & comparing triangles (equilateral, isosceles, scalene, and right)

Skills, Concepts, & Relationships

• Use metric & customary measures to determine length (measure to the nearest 1/8th & 1/16th inch or millimeter) weight/mass, temperature, capacity
• Round measurements
• Choose appropriate measurement tools
• Demonstrate knowledge of elapsed time
• Add & subtract time
• Measure area of: squares, rectangles, & triangles
• Review measuring perimeter of: squares, rectangles, triangles, & polygons
• Add, subtract, multiply, & divide money amounts
• Develop measuring circumference with string
• Develop understanding relationships within the same measurement system (customary, metric)
• Develop comparing & ordering by size, length, mass, area, & volume
• Develop estimating length, weight/mass, capacity, volume, perimeter, area and angles in standard units
• Develop creating scale drawing
• Develop estimating time
• Develop reading time zones
• Introduce area of irregular figures with manipulatives (grid paper)

Probability/Statistics

INTERMEDIATE MATHEMATICS EXIT PERFORMANCE STANDARD 3: Student will use data collection, interpretation, organization in basic graphs (bar graph, line graph, pictograph), finding statistics (mean, median, mode, range) and performing simple probability experiments (games of chance) to solve real world problems and communicate the reasoning used in solving these problems.

Based on Kentucky’s Core Content for Mathematics Assessment, the Kentucky Program of Studies, and Academic Expectations: 1.5-1.9 Mathematical Communication & Reasoning, 1.16 Technology, 2.7 Number, 2.8 Procedures, 2.11 Change, 2.12 Structure, 2.13 Probability & Statistics; Goal 5 Think & Solve Problems; & Goal 6 Integrate Knowledge

5th Grade Probability/Statistics Standards:

PS/5.1 Choose, construct, and interpret appropriate displays of data

PS/5.2 Solve problems and make predictions that involve probability and statistics

PS/5.3 Make inferences and convincing arguments based on data analysis

Skills, Concepts, & Relationships

• Draw conclusions and make inferences based on data
• Review constructing, reading, & interpreting line & bar graphs and charts & tables
• Choose the appropriate way(s) to organize data
• Find mean, median, mode & range of data
• Conduct simple probability experiments (games of chance) & make predictions
• Review collecting, organizing, and interpreting data
• Interpret circle graphs
• Develop using graphing software & spreadsheets to create graphs
• Introduce using tables or tree diagrams to list all possible outcomes of an event when order matters
• Introduce using fractions and percents to describe the probability of an event
• Develop using frequency tables with tally marks
• Develop an appreciation for the use of probability in the real world
• Introduce using data to develop & modify probability concepts

Algebraic Ideas

INTERMEDIATE MATHEMATICS EXIT PERFORMANCE STANDARD 4: Student will apply algebraic ideas to predict, analyze, generalize and write rules for patterns involving change in numbers or shapes in problem solving situations and communicate the reasoning used in solving these problems.

Based on Kentucky’s Core Content for Mathematics Assessment, the Kentucky Program of Studies, and Academic Expectations: 1.5-1.9 Mathematical Communication & Reasoning, 1.16 Technology, 2.7 Number, 2.8 Procedures, 2.9 Space and Dimensionality, 2.11 Change, 2.12 Structure; Goal 5 Think & Solve Problems; & Goal 6 Connect & Integrate Knowledge

5th Grade Algebraic Ideas Standards:

AI/5.1 Use written rules to express relationships involving change (patterns, functions).

Skills, Concepts, & Relationships

• Use patterns & functions to represent & solve problems
• Review graphing ordered pairs in the first quadrant of the Cartesian coordinate system (plot points)
• Generalize a rule for ordered pairs (x/y coordinates)
• Review describing, extending, analyzing & creating a wide variety of patterns in the real world
• Solve and use open sentences (simple equations) as a beginning concept of variable using basic addition, subtraction, mulitiplication and division facts (5+__=7 or 5 + n =7)
• Develop using variables to describe patterns
• Develop strategies for logical thinking, inductive and deductive reasoning

Intermediate Problem Solving Strategies

5th Grade Problem Solving Standards:

PSS/5.1 Use an appropriate strategy to solve a problem correctly, completely support the mathematical decisions made with reasoning, and completely show/explain reasonableness of the answer

PSS/5.2 Communicate strategy and solution with accurate mathematical vocabulary and representations

Skills, Concepts, & Relationships

• Use appropriate problem solving strategies:
  • act out
  • use manipulatives
  • draw a picture
  • describe and discuss a problem
  • look for a pattern
  • guess & check
  • make an organized list
  • draw a diagram
  • make and use a table
• Communicate strategies and solutions (including math vocabulary and representations)
• Select most appropriate strategy
• Generate, extend, and solve multi-step story problems
• Show/Explain reasonableness of answers