Mathematics Standards Grade 4

A. MATHEMATICAL PROCESSES

Content Standard

Students in Wisconsin will draw on a broad body of mathematical knowledge and apply a variety of mathematical skills and strategies, including reasoning, oral and written communication, and the use of appropriate technology, when solving mathematical, real-world* and non-routine* problems.

Performance Standards

By the end of grade four, students will:

A.4.1 Use reasoning abilities to

• perceive patterns
• identify relationships
• formulate questions for further exploration
• justify strategies
• test reasonableness of results

A.4.2 Communicate mathematical ideas in a variety of ways, including words, numbers, symbols, pictures, charts, graphs, tables, diagrams, and models*

A.4.3 Connect mathematical learning with other subjects, personal experiences, current events, and personal interests

• see relationships between various kinds of problems and actual events
• use mathematics as a way to understand other areas of the curriculum (e.g., measurement in science, map skills in social studies)

A.4.4 Use appropriate mathematical vocabulary, symbols, and notation with understanding based on prior conceptual work

A.4.5 Explain solutions to problems clearly and logically in oral and written work and support solutions with evidence

B. NUMBER OPERATIONS AND RELATIONSHIPS

Content Standard

Students in Wisconsin will use numbers effectively for various purposes, such as counting, measuring, estimating, and problem solving.

Performance Standards

By the end of grade four, students will:

B.4.1 Represent and explain whole numbers*, decimals, and fractions with

• physical materials
• number lines and other pictorial models*
• verbal descriptions
• place-value concepts and notation
• symbolic renaming (e.g., 43=40+3=30+13)

B.4.2 Determine the number of things in a set by

• grouping and counting (e.g., by threes, fives, hundreds)
• combining and arranging (e.g., all possible coin combinations amounting to thirty cents)
• estimation, including rounding

B.4.3 Read, write, and order whole numbers*, simple fractions (e.g., halves, fourths, tenths, unit fractions*) and commonly-used decimals (monetary units)

B.4.4 Identify and represent equivalent fractions for halves, fourths, eighths, tenths, sixteenths

B.4.5 In problem-solving situations involving whole numbers, select and efficiently use appropriate computational procedures such as

• recalling the basic facts of addition, subtraction, multiplication, and division
• using mental math (e.g., 37+25, 40x7)
• estimation
• selecting and applying algorithms* for addition, subtraction, multiplication, and division
• using a calculator

B.4.6 Add and subtract fractions with like denominators

B.4.7 In problem-solving situations involving money, add and subtract decimals

C. GEOMETRY

Content Standard

Students in Wisconsin will be able to use geometric concepts, relationships and procedures to interpret, represent, and solve problems.

Performance Standards

By the end of grade four, students will:

C.4.1 Describe two-and three-dimensional figures (e.g., circles, polygons, trapezoids, prisms, spheres) by

• naming them
• comparing, sorting, and classifying them
• drawing and constructing physical models to specifications
• identifying their properties (e.g., number of sides or faces, two- or three-dimensionality, equal sides, number of right angles)
• predicting the results of combining or subdividing two-dimensional figures
• explaining how these figures are related to objects in the environment

C.4.2 Use physical materials and motion geometry (such as slides, flips, and turns) to identify properties and relationships, including but not limited to

• symmetry*
• congruence*
• similarity*

C.4.3 Identify and use relationships among figures, including but not limited to

• location (e.g., between, adjacent to, interior of)
• position (e.g., parallel, perpendicular)
• intersection (of two-dimensional figures)

C.4.4 Use simple two-dimensional coordinate systems to find locations on maps and to represent points and simple figures

D. MEASUREMENT

Content Standard

Students in Wisconsin will select and use appropriate tools (including technology) and techniques to measure things to a specified degree of accuracy. They will use measurements in problem-solving situations.

Performance Standards

By the end of grade four, students will:

D.4.1 Recognize and describe measurable attributes*, such as length, liquid capacity, time, weight (mass), temperature, volume, monetary value, and angle size, and identify the appropriate units to measure them

D.4.2 Demonstrate understanding of basic facts, principles, and techniques of measurement, including

• appropriate use of arbitrary* and standard units (metric and US Customary)
• appropriate use and conversion of units within a system (such as yards, feet, and inches; kilograms and grams; gallons, quarts, pints, and cups)
• judging the reasonableness of an obtained measurement as it relates to prior experience and familiar benchmarks

D.4.3 Read and interpret measuring instruments (e.g., rulers, clocks, thermometers)

D.4.4 Determine measurements directly* by using standard tools to these suggested degrees of accuracy

• length to the nearest half-inch or nearest cm
• weight (mass) to the nearest ounce or nearest 5 grams
• temperature to the nearest 5
• time to the nearest minute
• monetary value to dollars and cents
• liquid capacity to the nearest fluid ounce

D.4.5 Determine measurements by using basic relationships (such as perimeter and area) and approximate measurements by using estimation techniques

E. STATISTICS AND PROBABILITY

Content Standard

Students in Wisconsin will use data collection and analysis, statistics and probability in problem-solving situations, employing technology where appropriate

Performance Standards

By the end of grade four, students will:

E.4.1 Work with data in the context of real-world situations by

• formulating questions that lead to data collection and analysis
• determining what data to collect and when and how to collect them
• collecting, organizing, and displaying data
• drawing reasonable conclusions based on data

E.4.2 Describe a set of data using

• high and low values, and range*
• most frequent value (mode*)
• middle value of a set of ordered data (median*)

E.4.3 In problem-solving situations, read, extract, and use information presented in graphs, tables, or charts

E.4.4 Determine if future events are more, less, or equally likely, impossible, or certain to occur

E.4.5 Predict outcomes of future events and test predictions using data from a variety of sources

F. ALGEBRAIC RELATIONSHIPS

Content Standard

Students in Wisconsin will discover, describe, and generalize simple and complex patterns and relationships. In the context of real-world problem situations, the student will use algebraic techniques to define and describe the problem to determine and justify appropriate solutions.

Performance Standards

By the end of grade four, students will:

F.4.1 Use letters, boxes, or other symbols to stand for any number, measured quantity, or object in simple situations (e.g., N + 0 = N is true for any number)

F.4.2 Use the vocabulary, symbols, and notation of algebra accurately (e.g., correct use of the symbol "="; effective use of the associative property of multiplication)

F.4.3 Work with simple linear patterns and relationships in a variety of ways, including

• recognizing and extending number patterns
• describing them verbally
• representing them with pictures, tables, charts, graphs
• recognizing that different models* can represent the same pattern or relationship
• using them to describe real-world phenomena

F.4.4 Recognize variability in simple functional* relationships by describing how a change in one quantity can produce a change in another (e.g., number of bicycles and the total number of wheels)

F.4.5 Use simple equations and inequalities in a variety of ways, including

• using them to represent problem situations
• solving them by different methods (e.g., use of manipulatives, guess and check strategies, recall of number facts)
• recording and describing solution strategies

F.4.6 Recognize and use generalized properties and relationships of arithmetic (e.g., commutativity* of addition, inverse relationship of multiplication and division)

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