Mathematics Competency Assurance Documents

4th 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

4th Grade Number Sense Standards :

N/4.1 Demonstrate number sense to 1 million (1,000,000) through modeling, applying and communicating muliple representations (drawings, concrete materials, & symbols) and using order relations

4th Grade Whole Number Operations & Computation Standards:

C/4.1 Select and apply the appropriate computational operations (+,-,x, ¸ by 1-digit with remainders) to solve multi-step problems in real-life situations

4th Grade Fractions & Decimals Standards:

FD/4.1 Demonstrate knowledge and use of decimals to the 100ths.

FD/4.2 Model, apply and communicate multiple representations of fractions to the 1/16ths.

Skills, Concepts, & Relationships

• Use number words, numerals, diagrams, concrete materials, & expanded form to represent numbers to 1million (1,000,000)
• Compare & order (<,>,=, number line) whole numbers to 1 million
• Understand place value to 1 million
• Identify square numbers with arrays
• Identify primes & composites
• Develop identifying multiples & factors
• Introduce LCM (Least Common Multiple)
• Introduce GCF (Greatest Common Factor)
• Develop rounding whole numbers
• Develop recognizing when an estimate is appropriate
• Introduce using estimation strategies: compatible numbers, front end, rounding , range, over estimate & under estimate, clustering

Skills, Concepts, & Relationships

• Add and subtract 3-digit & 4-digit numbers with regrouping (column addition)
• Add, subtract, & multiply money
• Multiply by 1-digit & 2-digit factors
• Use multiples of 10, 100, 1000
• Find missing factors
• Find factor pairs
• Recognize fact families for multiplication and division (inverse operations)
• Divide by 1-digit
• Divide by multiples of 10
• Review multiplication facts to 9
• Introduce division by 2-digit
• Introduce using zeros in quotient
• Introduce order of operations
• Develop choosing the correct operation in multi-step story problems
• 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
• Develop estimating sums, differences, & products of whole numbers
• Develop using a variety of mathematics vocabulary and symbols (sum, difference, product, quotient, 1/2, x, ¸ , etc.)

Skills, Concepts, & Relationships

• Demonstrate knowledge of equivalent fractions (including use of factors & multiples)
• Add and subtract decimals to the 100ths (money)
• Read, write, and identify decimals (to 100ths)
• Model, apply and communicate multiple representations of fractions
• Develop identifying the numerator & the denominator
• Develop comparing & ordering fractions to the 1/16ths
• Introduce adding & subtracting like fractions to the 1/16ths using concrete materials
• Introduce rewriting fractions in lowest terms
• Intro improper fractions and mixed numbers
• Develop using models to solve real world problems with fractions and decimals
• Develop comparing & ordering decimals (10ths, 100ths, 1000ths)
• Develop rounding decimals (10ths, 100ths, 1000ths)
• Introduce using zeros as a place holder
• Develop relating fractions, decimals and whole numbers
• Develop understanding use of negative numbers in real world
• Introduce estimating sums, differences, & products of fractions & decimals
• Develop exploring parts of a set versus parts of a whole

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

4th Grade Geometry Standards:

G/4.1 Demonstrate knowledge of basic geometric terms and shapes (e.g.-lines, rays, segments, point, angles)

4th Grade Measurement Standards:

M/4.1 Measure a wide variety of attributes of a given object using estimation and metric & customary measures.

Skills, Concepts, & Relationships

• Recognize, describe, model, draw, & compare: faces; vertices of solids; edges
• Recognize, describe, model, draw, & compare: vertices of angles; rays; line segments; points; parallel, intersecting, & perpendicular lines
• Recognize, describe, model, draw, & compare: quadrilaterals, pentagons, hexagons, & octagons
• Predict and verify the results of combining, subdividing and changing shapes
• Review recognizing & drawing a line of symmetry
• Review recognizing & matching congruent figures
• Introduce drawing and measuring angles(vertex, side, degree)
• Introduce formulas (perimeter, area)
• Develop finding volume of 3-D objects with physical models and materials
• Develop transformations (flips, slides, turns) with physical models
• Introduce similar figures
• Introduce circles (center, diameter, circumference, radius)
• Develop drawing 2-D views of 3-D figures
• Develop constructing 3-D objects from 2-D pictures

Skills, Concepts, & Relationships

• Use metric & customary measures to determine length (measure to the nearest 1/4th & 1/8th inch or centimeter) weight/mass, temperature, capacity
• Measure area of: squares and rectangles
• Measure perimeter of: squares, rectangles, triangles, and polygons
• Add, subtract, & multiply money amounts
• Develop comparing & ordering by size, length, mass, area, & volume
• Develop estimating length, weight/mass, capacity, volume, perimeter, & area in standard units
• Introduce round measurements
• Introduce finding the area of a triangle
• Develop choosing appropriate measurement tools
• Introduce measuring circumference with string
• Develop exploring scale drawings
• Develop elapsed time
• Develop estimating time
• Introduce adding & subtracting time
• Introduce time zones
• Develop understanding relationships within the same measurement system (customary, metric)

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

4th Grade Probability/Statistics Standards:

PS/4.1 Construct, read, and interpret displays of data (graphs, charts, tables)

PS/4.2 Solve problems that involve probability and statistics

Skills, Concepts, & Relationships

• Construct, read, & interpret line & bar graphs and charts & tables
• Understand the relationship of fractions to probability
• Find the average (mean) of set of numbers
• Conduct simple probability experiments (games of chance) and make predictions
• Review determining likely (near always/near 1) & unlikely (near never/near 0) outcomes
• Review collecting, organizing, and interpreting data
• Develop appropriate ways to organize data
• Develop concepts of mean, median, mode, & range of data
• Introduce drawing conclusions & making inferences based on data
• Develop using graphing software & spreadsheets to create graphs
• Introduce interpreting circle graphs
• Introduce tables or tree diagrams to list all possible outcomes of an event when order matters
• Develop using frequency tables with tally marks
• Develop gathering & sorting information into categories using line & bar graphs and charts & tables

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

4th Grade Algebraic Ideas Standards:

AI/4.1 Analyze & predict using number patterns.

AI/4.2 Generalize patterns (square numbers, etc.) in number sequences.

Skills, Concepts, & Relationships

• Demonstrate knowledge of functions (function machines)
• Represent and describe mathematical relationships through the use of ordered pairs, listings in a table, plotting on a graph, and looking for a pattern
• Graph points on a number line
• Graph ordered pairs in the first quadrant of the Cartesian coordinate system (plot points)
• Review identifying, describing, & creating patterns in real-life situations
• Review recognizing, extending, and finding rules for number patterns (skip counting, odds, evens, etc.)
• Develop using variables & open sentences (simple equations) to express relationships using basic addition, subtraction, multiplication, and division facts (5+__=7 or 5 + n =7)
• Develop using strategies for logical thinking, inductive and deductive reasoning

Intermediate Problem Solving Strategies

4th Grade Problem Solving Standards:

PSS/4.1 Use an appropriate strategy to solve a problem correctly, support the mathematical decisions made with reasoning, and show/explain reasonableness of the answer

PSS/4.2 Communicate strategy and solution with accurate mathematical vocabulary and representations

• Develop/Model 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
• Develop communicating strategies and solutions (including math vocabulary and representations)
• Develop selecting most appropriate strategy
• Develop generating, extending, and solving multi-step story problems
• Develop showing/explaining reasonableness of answers