4th Grade Math
Number and Operations
The student will identify, represent, order, and compare numbers and compute and solve problems.
Understanding Numbers/Representing Numbers/Relationships Among Numbers/Number Systems
⎯read and write numbers from hundred-thousands to hundredths (4-M[HM/Ch 1]A/IT)
⎯represent whole numbers to 9999 (4-M[HM/Ch 1]A/IT)
⎯recognize the place value of a given digit from hundredths to hundred-thousands (4-M[HM/Ch 1]A/IT)
⎯compare and order whole numbers to 9999 using the appropriate symbols (>, <, and =) (4-M[HM/Ch 1]A/IT)
⎯identify fractions as parts of whole units, as parts of sets, as locations on number lines, and as divisions of whole numbers (4-M[HM/Ch Ch 19, 20]A/IT)
⎯generate equivalent forms of whole numbers, commonly used fractions, and decimals (4-M[HM/Ch 19-22]A/IT)
⎯represent numbers as both improper fractions and mixed numbers (4-M[HM/Ch 19-20]A/IT)
⎯represent whole numbers up to 10,000 in expanded form (1,000’s + 100’s +10’s +1’s) (4-M[HM/Ch 1]A/IT)
⎯use estimation to select a reasonable solution to a whole number computation involving addition, subtraction, or multiplication (4-M[HM/Ch 3, 4, 6,7]A/IT)
⎯use concrete or pictorial representations to compare and order commonly used fractions (4-M[HM/Ch 19-20]D/IT)
⎯use concrete and pictorial representations to compare decimals (4-M[HM/Ch 21-22]D/IT)
⎯use various models and equivalent forms to represent, order, and compare whole numbers and commonly used fractions and mixed numbers (e.g., number lines, base ten blocks, expanded notation, Venn diagrams, and hundreds boards) ((4-M[HM/ALL]D/IT)
⎯communicate and use mathematical language and symbols correctly (4-M[HM/ALL]D/IT)
Understand Meanings of Operations and Their Relationships to One Another
⎯explain the relationship between addition and subtraction (4-M[HM/Ch 3]D/IT)
⎯explain the relationship between multiplication and division (4-M[HM/Ch 4]D/IT)
⎯explain how addition, subtraction, multiplication, and division affect the size and order of numbers (4-M[HM/Ch 3,4,6,7]D/IT)
⎯introduce the concept of commonly use percents (50%, 25%) (4-M[HM/Ch 21]D/IT)
⎯demonstrate knowledge and understanding of grade level mathematical terms (4-M[HM/ALL]D/IT)
⎯add and subtract fractions with like denominators (4-M[HM/19-20]A/IT)
⎯multiply efficiently and accurately with single-digit whole numbers (4-M[HM/Ch 4, 6,7]A/IT)
Solve Problems/Compute Fluently/Make Reasonable Estimates
⎯use strategies to estimate the results of whole-number computations and explain the reasonableness of results (4-M[HM/Ch 2, 3, 4]D/IT)
⎯add and subtract fractions with like denominators (4-M[HM/Ch 19-20]D/IT)
⎯multiply and divide efficiently and accurately with single-digit whole numbers (4-M[HM/Ch 4, 6-9]D/IT)
⎯add, subtract, and multiply decimals (includes monetary units) (4-M[HM/Ch 21-22]D/IT)
⎯select appropriate methods and tools for computing with whole numbers (e.g., mental computation, estimation, calculators, paper and pencil, guess and check) (4-M[HM/ALL]D/IT)
⎯solve real-world problems involving one-step addition, subtraction, and multiplication(4-M[HM/Ch 3-4]D/IT)
⎯identify missing information and/or too much information in real-world problems (4-M[HM/ALL]D/IT)
⎯apply logical reasoning to solve real-world problems (4-M[HM/ALL]D/IT)
⎯select the appropriate computational and operational method to solve problems (4-M[HM/ALL]D/IT)
⎯solve real-world problems using whole numbers, fractions, and decimals (4-M[HM/ALL]D/IT)
Algebra
The student will understand and generalize patterns as they represent and analyze quantitative relationships and change in a variety of contexts and problems using graphs, tables, and equations.
Understand patterns, relations, and functions
⎯introduce variables (4-M[HM/Ch 5 & 24]D/IT)
⎯generalize and extend or complete patterns involving geometric figures or numbers (4-M[HM/Ch 16-19]D/IT)
⎯represent and analyze patterns and relationships using words, tables, and graphs (4-M[HM/Ch 24]D/IT)
⎯determine the function rule for data in a function table (4-M[HM/Ch 3-9]A/IT)
⎯extend numerical and geometric patterns (4-M[HM/Ch 16-19]A/IT)
⎯apply basic function rules (4-M[HM/Ch 3-9]A/IT)
Represent and analyze mathematical situations and structures using algebraic symbols
⎯interpret and solve open sentences involving addition and subtraction (4-M[HM/Ch 3]A/IT)
⎯interpret and solve open sentences involving multiplication and division (4-M[HM/Ch 4]A/IT)
⎯represent the idea of a variable as an unknown quantity by using a letter or a symbol (4-M[HM/Ch 5]I/IT)
⎯demonstrate understanding that an equation is a number sentence stating that two quantities are equal (4-M[HM/Ch 3 & 4]D/IT)
Illustrate general properties of operations
⎯use the commutative, associative, zero, and identity properties for addition and multiplication (4-M[HM/Ch 3,4,5,7]D/IT)
Analyze Change in Various Contexts
⎯investigate how a change in one variable relates to a change in a second variable (4-M[HM/Ch 5]D/IT)
⎯connect open sentences to real-world situations (4-M[HM/ALL]A/IT)
⎯use math journals as a means of demonstrating and understanding of math concepts and terms (4-M[HM/ALL]D/IT)
Geometry
The student will develop an understanding of geometric concepts and relationships as the basis for geometric modeling and reasoning to solve problems involving one-, two-, and three-dimensional figures.
Analyze characteristics and properties of two- and three-dimensional shapes
⎯identify, compare, and analyze attributes of two- and three-dimensional shapes (4-M[HM/Ch 16-19]D/IT)
⎯ identify two- or three-dimensional shapes given defining attributes ((4-M[HM/Ch 16019]A/IT)
⎯ develop and use mathematical language to describe characteristics and properties of geometric figures (4-M[HM/Ch 16-19]A/IT)
⎯identify and draw points, lines, line segments, rays, and angles (4-M[HM/Ch 16-19]D/IT)
⎯identify points, lines, and rays (4-M[HM/Ch 16-19]A/IT)
⎯describe the relationships between lines and the characteristics of angles (e.g., parallel, perpendicular, intersecting, right, acute, and obtuse) (4-M[HM/Ch 16-19]I/IT)
⎯ compare properties of two- and three-dimensional geometric figures (4-M[HM/Ch 16-19]D/IT)
⎯ investigate and describe the results of subdividing and combining two-dimensional geometric figures (4-M[HM/Ch 16-19]D/IT)
⎯ recognize congruent geometric figures (4-M[HM/Ch 17]A/IT))
⎯ identify and draw lines of symmetry for two-dimensional geometric figures (4-M[HM/Ch 16-19]D/IT)
⎯ identify lines of symmetry for two-dimensional geometric figures (4-M[HM/Ch 17]A/IT)
Specify locations and describe spatial relationships using coordinate geometry
⎯Use appropriate mathematical language to find and specify points on a grid using whole number coordinates (4-M[HM/Ch 24]D/IT)
Apply transformations and use symmetry to analyze mathematical situations
⎯investigate, predict, and describe the results of transformations of two-dimensional geometric figures (i.e., slides, flips, and turns) (4-M[HM/6]D) (4-M[HM/Ch 16-19]D/IT)
⎯describe a motion that will show that two shapes are congruent (4-M[HM/Ch 16-19]I/IT)
Use visualization, spatial reasoning, and geometric modeling to solve problems
⎯construct and draw two- and three-dimensional geometric figures (4-M[HM/Ch 16-19]I/IT)
⎯create and describe mental images of objects, patterns, and paths (4-M[HM/Ch 16-19]D/IT)
⎯use geometric models to solve real-world problems (4-M[HM/Ch 16-19]D/IT)
⎯locate and specify points in Quadrant 1 of a coordinate system (4-M[HM/Ch 24]A/IT)
⎯identify the result of a transformation (flip or slide) that has been applied to a simple two-dimensional geometric shape (4-M[HM/Ch 16-19]A/IT)
Measurement
The student will become familiar with the units and processes of measurement in order to use a variety of tools, techniques, and formulas to determine and to estimate measurements in mathematical and real-world problems.
Understand measurable attributes of objects and the units, systems, and processes of measurement
⎯demonstrate understanding of the concepts of length, perimeter, area, weight, capacity, volume, time, and angle measure (4-M[HM/Ch 12, 13, 18]D/IT)
⎯apply appropriate estimation strategies using standard units of measure (4-M[HM/Ch 12]D/IT)
⎯demonstrate understanding that measurements are approximations (4-M[HM/Ch 12]D/IT)
⎯demonstrate understanding of the relationships among units of length (4-M[HM/Ch 12]D/IT)
⎯explore perimeter and area using a variety of models (e.g., geoboards, graph paper) (4-M[HM/Ch 18]D/IT)
Apply appropriate techniques, tools, and formulas to determine measurements
⎯select appropriate standard units to measure length, perimeter, area, capacity, volume, weight, time, temperature, and angles (4-M[HM/Ch 12, 13, 18]A/IT)
⎯measure length to the nearest 1/4 inch or nearest centimeter (4-M[HM/Ch 12]A/IT)
⎯tell time to the nearest minute (4-M[HM/Ch 13]A/IT)
⎯read and record temperature using Fahrenheit and Celsius thermometers (4-M[HM/Ch 13]A/IT)
⎯develop strategies for estimating the perimeters and areas (such as counting square units) of geometric figures (4-M[HM/Ch 18]A/IT)
⎯apply the formula for finding the area of a rectangle (4-M[HM/Ch 18]A/IT)
⎯solve real-world problems involving measurement and elapsed time to the quarter hour (4-M[HM/Ch 12 & 13]D/IT)
⎯use estimation to determine if a length or volume measurement is reasonable (4-M[HM/Ch 12 &18]A/IT)
⎯ find the perimeter of rectangles (4-M[HM/Ch 18]A/IT)
⎯ select and use tools to measure weight and volume in customary or metric units (4-M[HM/Ch 12 & 18]D/IT)
⎯solve real-world problems involving elapsed time to the quarter-hour (4-M[HM/Ch 13]A/IT)
Data Analysis and Probability
The student will understand and apply basic statistical and probability concepts in order to organize and analyze data and to make predictions and conjectures
Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer questions
⎯collect data using observations, surveys, and experiment (4-M[HM/Ch 23]I/IT)
⎯understand how data-collection methods could affect the nature of the data set (4-M[HM/Ch 23]I/IT)
⎯represent data using tables, pictographs, line graphs, and bar graphs (4-M[HM/Ch 23]I/IT)
⎯interpret data displayed in simple charts, tables, pictographs, line graphs, and bar graphs (4-M[HM/Ch 23]D/IT)
⎯ interpret data displayed in bar graphs and pictographs (4-M[HM/Ch 23]A/IT)
⎯ connect data in tables to pictographs, line graphs, or bar graphs (4-M[HM/Ch 23]A/IT)
⎯ evaluate how well various representations show the collected data (4-M[HM/Ch 23]I/IT)
Select and use appropriate statistical methods to analyze data
⎯explore and determine measures of central tendency (i.e., mean, median, and mode) (4-M[HM/Ch 24]D/IT)
Make and justify predictions based on data
⎯make predictions from data (4-M[HM/Ch 23-24]I/IT)
⎯design investigations to try to answer a question (4-M[HM/Ch 24]I/IT)
Understand and apply basic concepts of probability
⎯describe the likelihood or chance of events as certain, possible, or impossible ((4-M[HM/Ch 23]I/IT)
⎯explain whether an event is likely or unlikely (4-M[HM/Ch 23]M/IT)
⎯predict the probability of outcomes of simple experiments (4-M[HM/Ch 23]M/IT)
⎯determine the median of a data set (4-M[HM/Ch 24]A/IT)
⎯determine the most likely, least likely, or equally likely outcomes in simple experiments ((4-M[HM/Ch 23]A/IT)
⎯select all possible outcomes of a simple experiment (i.e., spinner, coin toss, number or color cube (4-M[HM/Ch 23]A/IT)
Computation
The student will learn to compute using concrete objects.
⎯add and subtract decimals (includes monetary units) (4-M[HM/Ch 21-22]A/IT)
⎯solve one-step real-world problems involving addition or subtraction of whole numbers and/or decimals (4-M[HM/Ch 3,21,22]A/IT)
⎯estimate the results of whole-number computations (4-M[HM/Ch 3,4,6-9]D/IT)
⎯divide efficiently and accurately with single-digit whole numbers (4-M[HM/Ch 34, 8, 9]D/IT)
⎯multiply decimals (includes monetary units) (4-M[HM/Ch 21-22]I/IT)
⎯select appropriate methods and tools for computing with whole numbers (e.g., mental computation, estimation, calculators, paper and pencil, guess and check) (4-M[HM/ALL]I/IT)
Real World Story Problems
The student will gather information to compute and solve real world problems.
⎯solve one-step real-world problems involving multiplication of whole numbers and/or decimals (4-M[HM/Ch 4,8,9,21,22]A/IT)
⎯solve real-world problems involving addition and subtraction of measurements (4-M[HM/Ch 12] /IT)
⎯identify missing information and/or too much information in word problems (4-M[HM/ALL]I/IT)
⎯apply logical reasoning to solve real-world problems (4-M[HM/ALL]I/IT)
⎯select the appropriate computational and operational method to solve word problems (4-M[HM/ALL]D/IT)
⎯solve story problems using whole numbers, fractions, and decimals (includes money) (4-M[HM/ALL]D/IT)
