Click to Select Grade Level Performance Standards
K-4 Exit 5-8 Exit K 1 2 3 4 5 6 7 8 Summary
Curriculum Connection Codes:
AR ART MA MATHEMATICS
SR COMMUNITY SERVICE MU MUSIC
EE ENVIRONMENTAL EDUCATION PE PHYSICAL EDUCATION
FL FOREIGN LANGUAGE RE RELIGION
HE HEALTH SC SCIENCE
IT INFORMATIONAL TECHNOLOGIES SS SOCIAL STUDIES
LA LANGUAGE ARTS
Note – Numeric order for the K-8 grade level goals listed in this document aligns with the WI State Academic Standards. Not all grades include each standard sub-category (as indicated by gaps in the numbering system). However, all K-4 goals and 5-8 goals are appropriately addressed by the end of fourth and eighth grades.
Grade 4 EXIT LEVEL
MATHEMATICS PERFORMANCE STANDARDS
Goal A Content Standard: Mathematical Processes
Catholic school students in the Diocese of Madison 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.
FOURTH GRADE EXIT LEVEL PERFORMANCE STANDARDS:
By the end of grade Four, students will:
1. Use reasoning abilities to perceive patterns, identify relationships, formulate questions for further exploration, justify strategies, and test reasonableness of results.
2. Communicate mathematical ideas in a variety of ways, including words, numbers, symbols, pictures, charts, graphs, tables, diagrams, and models.
3. Connect mathematical learning with other subjects, personal experiences, current events, and personal interests; see relationships between various kinds of problems and actual events; and use mathematics as a way to understand other areas of the curriculum (e.g., measurement in science, map skills in social studies).
4. Use appropriate mathematical vocabulary, symbols, and notation with understanding based on prior conceptual work.
5. Explain solutions to problems clearly and logically in oral and written work and support solutions with evidence.
Standard B. Number Operations and Relationships
Catholic school students in the Diocese of Madison will use numbers effectively for various purposes, such as counting, measuring, estimating, and problem-solving.
FOURTH GRADE EXIT LEVEL PERFORMANCE STANDARDS:
By the end of grade Four students will:
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).
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.
3. Read, write, and order whole numbers, simple fractions (e.g., halves, fourths, tenths, unit fractions) and commonly-used decimals (monetary units).
4. Identify and represent equivalent fractions for halves, fourths, eighths, tenths, sixteenths.
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, 40 x 7); estimation; selecting and applying algorithms for addition, subtraction, multiplication, and division: using a calculator.
6. Add and subtract fractions with like denominators.
7. In problem-solving situations involving money, add and subtract decimals.
Standard C. Geometry
Catholic school students in the Diocese of Madison will be able to use geometric concepts, relationships and procedures to interpret, represent, and solve problems.
FOURTH GRADE EXIT LEVEL PERFORMANCE STANDARDS:
By the end of grade Four, students will:
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.
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.
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); (of two-dimensional figures).
4. Use simple two-dimensional coordinate systems to find locations on maps and to represent points and simple figures.
Standard D. Measurement
Catholic school students in the Diocese of Madison 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.
FOURTH GRADE EXIT LEVEL PERFORMANCE STANDARDS:
By the end of grade Four, students will:
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.
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.
3. Read and interpret measuring instruments (e.g., rulers, clocks, thermometers).
4. Determine measurements directly by using standard tools to these suggested degrees of accuracy: length to the nearest half-inch or nearest centimeter; (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.
5. Determine measurements by using basic relationships (such as perimeter and area) and approximate measurements by using estimation techniques.
Standard E. Statistics And Probability
Catholic school students in the Diocese of Madison will use data collection and analysis, statistics and probability in problem-solving situations, employing technology where appropriate.
FOURTH GRADE EXIT LEVEL PERFORMANCE STANDARDS:
By the end of grade Four, students will:
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.
2. Describe a set of data using high and low values, and range; most frequent value (mode); value of a set of ordered data (median).
3. In problem-solving situations, read, extract, and use information presented in graphs, tables, or charts.
4. Determine if the occurrence of future events are more, less, or equally likely, impossible, or certain to occur.
5. Predict outcomes of future events and test predictions using data from a variety of sources.
Standard F. Algebraic Relationships
Catholic school students in the Diocese of Madison 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.
FOURTH GRADE EXIT LEVEL PERFORMANCE STANDARDS:
By the end of grade Four, students will:
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).
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).
3. Work with simple linear patterns and relationships in a variety of ways, including recognizing and extending number patterns; 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.
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).
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.
6. Recognize and use generalized properties and relationships of arithmetic (e.g., commutativity of addition, inverse relationship of multiplication and division).
Grade 8 EXIT LEVEL
MATHEMATICS PERFORMANCE STANDARDS
Goal A Content Standard: Mathematical Processes
Catholic school students in the Diocese of Madison 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.
EIGHTH GRADE EXIT LEVEL PERFORMANCE STANDARDS:
By the end of grade Eight, students will:
1. Use reasoning abilities to evaluate information; perceive patterns; identify relationship; formulate questions for further exploration; evaluate strategies; justify statements; test reasonableness of results; and defend work.
2. Communicate logical arguments clearly to show why a result makes sense.
3. Analyze nonroutine problems by modeling, illustrating, guessing, simplifying, generalizing, shifting to another point of view, etc.
4. Develop effective oral and written presentations that include appropriate use of technology; the conventions of mathematical discourse (e.g., symbols, definitions, labeled drawings); mathematical language; clear organization of ideas and procedures; understanding of purpose and audience.
5. Explain mathematical concepts, procedures, and ideas to others who may not be familiar with them.
6. Read and understand mathematical texts and other instructional materials and recognize mathematical ideas as they appear in other contexts.
Standard B. Number Operations and Relationships
Catholic school students in the Diocese of Madison will use numbers effectively for various purposes, such as counting, measuring, estimating, and problem-solving.
EIGHTH GRADE EXIT LEVEL PERFORMANCE STANDARDS:
By the end of grade Eight students will:
1. Read, represent, and interpret various rational numbers (whole numbers, integers, decimals, fractions, and percents) with verbal descriptions, geometric models and mathematical notation (e.g., expanded, scientific, exponential).
2. Perform and explain operations on rational numbers (add, subtract, multiply, divide, raise to a power, extract a root, take opposites and reciprocals, determine absolute value).
3. Generate and explain equivalencies among fractions, decimals, and percents.
4. Express order relationships among rational numbers using appropriate symbols .
(>, <, ³, £, ¹).
5. Apply proportional thinking in a variety of problem situations that include, but are not limited to ratios and proportions (e.g., rates, scale drawings, similarity); percents, including those greater than 100 and less than one (e.g., discounts, rate of increase or decrease, sales tax).
6. Model and solve problems involving number-theory concepts such as prime and composite numbers; divisibility and remainders; greatest common factors; least common multiples.
7. In problem-solving situations, select and use appropriate computational procedures with rational numbers such as calculating mentally; creating, using, and explaining algorithms using technology (e.g., scientific calculators, spreadsheets).
Standard C. Geometry
Catholic school students in the Diocese of Madison will be able to use geometric concepts, relationships and procedures to interpret, represent, and solve problems.
EIGHTH GRADE EXIT LEVEL PERFORMANCE STANDARDS:
By the end of grade Eight, students will:
1. Describe special and complex two- and three-dimensional figures (e.g., rhombus, polyhedron, cylinder) and their component parts (e.g., base, altitude, and slant height) by naming, defining, and giving examples; comparing, sorting, and classifying them; identifying and contrasting their properties (e.g., symmetrical, isosceles, regular); drawing and constructing physical models to specifications; explaining how these figures are related to objects in the environment.
2. Identify and use relationships among the component parts of special and complex two- and three-dimensional figures (e.g., parallel sides, congruent faces).
3. Identify three-dimensional shapes from two-dimensional perspectives and draw two-dimensional sketches of three-dimensional objects preserving their significant features.
4. Perform transformations on two-dimensional figures and describe and analyze the effects of the transformations on the figures.
5. Locate objects using the rectangular coordinate system.
Standard D. Measurement
Catholic school students in the Diocese of Madison 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.
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EIGHTH GRADE EXIT LEVEL PERFORMANCE STANDARDS:
By the end of grade Eight, students will:
1. Identify and describe attributes* in situations where they are not directly or easily measurable (e.g., distance, area of an irregular figure, likelihood of occurrence).
2. Demonstrate understanding of basic measurement facts, principles, and techniques including the following approximate comparisons between metric and US Customary units (e.g., a liter and a quart are about the same; a kilometer is about six-tenths of a mile); knowledge that direct measurement produces approximate, not exact, measures; the use of smaller units to produce more precise measures.
3. Determine measurement directly using standard units (metric and US Customary) with these suggested degrees of accuracy lengths to the nearest mm or 1/16 of an inch; (mass) to the nearest 0.1 g or 0.5 ounce; liquid capacity to the nearest milliliter; angles to the nearest degree; temperature to the nearest C° or F; elapsed time to the nearest second.
4. Determine measurements indirectly using estimation; conversion of units within a system (e.g., quarts to cups, millimeters to centimeters); ratio and proportion (e.g., similarity, scale drawings); geometric formulas to derive lengths, areas, volumes of common figures (e.g., perimeter, circumference, surface area); the Pythagorean relationship; geometric relationships and properties for angle size (e.g., parallel lines and transversals; sum of angles of a triangle; vertical angles).
Standard E. Statistics And Probability
Catholic school students in the Diocese of Madison will use data collection and analysis, statistics and probability in problem-solving situations, employing technology where appropriate.
EIGHTH GRADE EXIT LEVEL PERFORMANCE STANDARDS:
By the end of grade Eight, students will:
1. Work with data in the context of real-world situations by formulating questions that lead to data collection and analysis; and conducting a statistical investigation; using technology to generate displays, summary statistics, and presentations.
2. Organize and display data from statistical investigations using appropriate tables, graphs, and/or charts (e.g., circle, bar, or line for multiple sets of data); appropriate plots (e.g., line, stem-and-leaf, box, scatter).
3. Extract, interpret, and analyze information from organized and displayed data by using frequency and distribution, including mode and range; central tendencies of data (mean and median); indicators of dispersion (e.g., outliers).
4. Use the results of data analysis to make predictions; develop convincing arguments; draw conclusions.
5. Compare several sets of data to generate, test, and, as the data dictate, confirm or deny hypotheses.
6. Evaluate presentations and statistical analyses from a variety of sources for credibility of the source; techniques of collection, organization, and presentation of data; missing or incorrect data; inferences; possible sources of bias.
7. Determine the likelihood of occurrence of simple events by using a variety of strategies to identify possible outcomes (e.g., lists, tables, tree diagrams); conducting an experiment; designing and conducting simulations; applying theoretical notions of probability (e.g., that four equally likely events have a 25 percent chance of happening).
Standard F. Algebraic Relationships
Catholic school students in the Diocese of Madison 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.
EIGHTH GRADE EXIT LEVEL PERFORMANCE STANDARDS:
By the end of grade Eight, students will:
1. Work with algebraic expressions in a variety of ways, including using appropriate symbolism, including exponents and variables; evaluating expressions through numerical substitution; generating equivalent expressions; and subtracting expressions.
2. Work with linear and nonlinear patterns and relationships in a variety of ways, including representing them with tables, with graphs, and with algebraic expressions, equations, and inequalities describing and interpreting their graphical representations (e.g., slope, rate of change, intercepts); using them as models of real-world phenomena; describing a real-world phenomenon that a given graph might represent.
3. Recognize, describe, and analyze functional relationships by generalizing a rule that characterizes the pattern of change among variables. These functional relationships include exponential growth and decay (e.g., cell division, depreciation).
4. Use linear equations and inequalities in a variety of ways, including writing them to represent problem situations and to express generalizations; solving them by different methods (e.g., informally, graphically, with formal properties, with technology); writing and evaluating formulas (including solving for a specified variable); using them to record and describe solution strategies.
5. Recognize and use generalized properties and relations, including additive and multiplicative property of equations and inequalities; commutativity and associativity of addition and multiplication; property; and identities for addition and multiplication; transitive property.
Grade Level Performance Standards: Kindergarten
Within our kindergarten mathematics curriculum, students will:
GOAL A MATHEMATICAL PROCESSES
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.
A.K.1. Use reasoning abilities to:
a. Perceive patterns.
1) Find patterns in the environment. AR, LA, MU, PE
2) Describe patterns using color, size, or shape.
3) Copy, create, and extend patterns using concrete objects. AR
b. Identify relationships.
1) Use manipulatives to demonstrate the relationships between concrete objects and numerals.
d. Justify strategies.
1) Employ the problem-solving strategies of acting out and using manipulatives.
2) Use a "one-to-one" correspondence to solve a problem.
A.K.2. Communicate mathematical ideas in a variety of ways, including words, numbers, symbols,
pictures, charts, graphs, tables, diagrams, and models. LA
a. Use manipulatives to demonstrate a solution process.
b. Write number sentences based on concrete objects.
A.K.3. Connect mathematical learning with other subjects, personal experiences, current events, and
personal interests. SC, SS, LA, MU, PE, AR, FL
a. See relationships between various kinds of problems and actual events.
1) Use counting, adding, subtracting, to solve real-life problems.
b. Use mathematics as a way to understand other areas of the curriculum (e.g., measurement in science, map skills in social studies, and literature).
A.K.4. Use appropriate mathematical vocabulary, symbols, and notation with understanding.
A.K.5. Explain solutions to problems clearly and logically and support solutions. LA
GOAL B NUMBER OPERATIONS AND RELATIONSHIPS
Use numbers effectively for various purposes, such as counting, measuring, estimating, and problem-solving.
B.K.1. Represent and explain whole numbers with:
a. Physical materials.
1) Count with one-to-one correspondence.
2) Display addition and subtraction number sentences with concrete objects through 10.
b. Number lines and other pictorial models.
c. Verbal descriptions. LA
1) Compare groups to determine more, less, same, most, least.
B.K.2. Determine the number of things in a set by:
a. Grouping and counting (e.g., by twos, fives, tens). FL, AR
1) Recognize and count from 0-30.
2) Count to 100 by tens.
B.K.3. Read, write, and order whole numbers.
a. Read and write the numerals from 0-20.
b. Determine what comes before and after the number.
B.K.5. In problem-solving situations involving whole numbers, select and efficiently use appropriate
computational procedures such as:
a. Recalling the basic facts of addition and subtraction.
1) Add and subtract using concrete objects up to 10.
GOAL C GEOMETRY
Be able to use geometric concepts, relationships and procedures to interpret, represent, and solve problems.
C.K.1. Describe two-dimensional figures by: AR
a. Naming them.
1) Identify circles, rectangles, squares, and triangles. SS, AR
b. Comparing, sorting, and classifying them.
1) Compare groups of objects.
2) Sort objects into groups.
GOAL D MEASUREMENT
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.
D.K.2. Demonstrate understanding of basic facts, principles, and techniques of measurement, including:
a. Appropriate use of non standard and standard units (metric and US Customary). LA, SC
1) Measure and estimate length in nonstandard units.
2) Compare containers using more or less.
3) Compare objects to determine heavier and lighter.
D.K.3. Read and interpret measuring instruments. (e.g., rulers, clocks, calendars, thermometers). SC, SS
a. List days of the week in order.
GOAL E STATISTICS AND PROBABILITY
Use data collection and analysis, statistics and probability in problem-solving situations, employing technology where appropriate.
E.K.1. Work with data in the context of real-world situations by: SC, SS
a. Collecting, organizing, and displaying data.
1) Use concrete and picture graphs.
b. Drawing reasonable conclusions based on data.
GOAL F ALGEBRAIC RELATIONSHIPS (not at this grade level)
Note – Numeric order for the K-8 grade level goals listed in this document aligns with the WI State Academic Standards. Not all grades include each standard sub-category (as indicated by gaps in the numbering system). However, all K-4 goals and 5-8 goals are appropriately addressed by the end of fourth and eighth grades.
These grade level performance standards are listed developmentally. However, each school is uniquely organized. Therefore, a specific grade level standard may not be addressed at the grade indicated, but will be addressed within a 4 year time span (K-4, 5-8).
Grade Level Performance Standards: Grade One
Within our first grade mathematics curriculum, students will:
GOAL A MATHEMATICAL PROCESSES
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.
A.1.1. Use reasoning abilities to:
a. Perceive patterns. AR, LA, MU, PE
1) Recognize and extend patterns having more than one attribute.
2) Copy, create, and extend patterns using concrete objects. AR
b. Identify relationships.
1) Use manipulatives to demonstrate the relationship between addition and subtraction.
d. Justify strategies.
1) Employ the problem-solving strategies of acting out, using manipulatives, and drawing pictures.
A.1.2. Communicate mathematical ideas in a variety of ways, including words, numbers, symbols,
pictures, charts, graphs, tables, diagrams, and models. LA
a. Use manipulatives or pictures to demonstrate a solution process to a grade-appropriate math problem.
b. Use graphs to represent and interpret data. SS, SC
A.1.3. Connect mathematical learning with other subjects, personal experiences, current events, and
personal interests. SC, SS, LA, MU, PE, AR, FL
a. See relationships between various kinds of problems and actual events.
1) Use addition and subtraction to solve real-life problems.
b. Use mathematics as a way to understand other areas of the curriculum (e.g., measurement in
science, map skills in social studies, and literature).
A.1.4. Use appropriate mathematical vocabulary, symbols, and notation with understanding based on prior
conceptual work.
A.1.5. Explain solutions to problems clearly and logically and support solutions with evidence. LA
GOAL B NUMBER OPERATIONS AND RELATIONSHIPS
Use numbers effectively for various purposes, such as counting, measuring, estimating, and problem-solving.
B.1.1. Represent and explain whole numbers, and fractions with:
a. Physical materials.
1) Display addition and subtraction whole number sentences through 20 with concrete objects.
2) Write and solve whole number sentences to 20 with concrete objects.
3) Divide objects into two or four parts.
4) Determine if objects are divided into equal or unequal parts.
b. Number lines and other pictorial models.
1) Write and solve whole number sentences to 10 using pictorial representation.
c. Verbal descriptions.
d. Place-value concepts and notation: identify tens and ones in 2-digit numbers.
B.1.2. Determine the number of things in a set by:
a. Grouping and counting (e.g., by twos, fives, hundreds). FL, SC
1) Count to 100; count by 2’s to 50; count by 5’s and 10’s to 100.
b. Use counting strategies to solve problems (ex: counting forwards, counting backwards).
B.1.3. Read, write, and order whole numbers.
a. Read and write numerals to 100.
b. Order numbers before, after, and between.
c. Compare 1 and 2-digit numbers to determine greater, less, equal to.
B.1.5. In problem-solving situations involving whole numbers, select and efficiently use appropriate
computational procedures such as:
a. Recalling the basic facts of addition and subtraction up to 10.
b. Estimating quantities.
GOAL C GEOMETRY
Use geometric concepts, relationships and procedures to interpret, represent, and solve problems.
C.1.1. Describe two-dimensional figures (e.g., circles, triangles, squares, and rectangles) by:
a. Naming them.
b. Comparing, sorting, and classifying them.
1) Sort objects based on size and shape.
c. Drawing and constructing physical models to specifications. AR, SS
1) Draw circles, squares, rectangles, and triangles.
d. Identifying their properties (e.g., number of sides).
1) Identify number of sides and corners of polygons.
e. Explaining how these figures are related to objects in the environment.
GOAL D MEASUREMENT
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.
D.1.1. 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.1.2. Demonstrate understanding of basic facts, principles, and techniques of measurement, including:
a. Appropriate use of non standard and standard units (metric and US Customary). LA, SC
D.1.3. Read and interpret measuring instruments (e.g., rulers, clocks, thermometers). SC, SS
a. Identify the relationships between days of the week using a calendar.
D.1.4. Determine measurements directly by using standard tools to these suggested degrees of accuracy:
a. Length to the nearest inch and nearest centimeter.
d. Time to the nearest hour and half-hour.
e. Monetary value through identification of coins by name and value (pennies, nickels, dimes, and combinations of these coins).
GOAL E STATISTICS AND PROBABILITY
Use data collection and analysis, statistics and probability in problem-solving situations, employing technology where appropriate.
E.1.1. Work with data in the context of real-world situations by: SC, SS
a. Collecting, organizing, and displaying data.
1) Create concrete and picture graphs.
b. Drawing reasonable conclusions based on data.
E.1.3. In problem-solving situations, read, extract, and use information presented in graphs, tables, or
Charts: (IT)
a. Read and interpret concrete, picture, and bar graphs. SS, SC
GOAL F ALGEBRAIC RELATIONSHIPS (not at this grade level)
Note – Numeric order for the K-8 grade level goals listed in this document aligns with the WI State Academic Standards. Not all grades include each standard sub-category (as indicated by gaps in the numbering system). However, all K-4 goals and 5-8 goals are appropriately addressed by the end of fourth and eighth grades.
These grade level performance standards are listed developmentally. However, each school is uniquely organized. Therefore, a specific grade level standard may not be addressed at the grade indicated, but will be addressed within a 4 year time span (K-4, 5-8).
Grade Level Performance Standards: Grade Two
Within our second grade mathematics curriculum, students will:
GOAL A MATHEMATICAL PROCESSES
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.
A.2.1. Use reasoning abilities to:
a. Perceive patterns. AR, MU, LA, PE
1) Recognize and describe geometric and numerical patterns.
2) Extend and create grade-appropriate geometric and numerical patterns.
b. Identify relationships.
1) Identify fact families through 18.
d. Justify strategies.
1) Employ the problem-solving strategies of acting out, using manipulatives, and drawing pictures.
A.2.2. Communicate mathematical ideas in a variety of ways, including words, numbers, symbols, pictures, charts, graphs, tables, diagrams, and models. LA
a. Use pictures or manipulatives to demonstrate a solution process to a grade-appropriate problem.
b. Use graphs to represent and interpret data. SC, SS
A.2.3. Connect mathematical learning with other subjects, personal experiences, current events, and
personal interests. SC, SS, LA, MU, PE, AR, FL
a. See relationships between various kinds of problems and actual events.
b. Use mathematics as a way to understand other areas of the curriculum (e.g., measurement in science, map skills and graphs in social studies, and literature).
A.2.4. Use appropriate mathematical vocabulary, symbols, and notation with understanding based on prior conceptual work.
A.2.5. Explain solutions to problems clearly and logically in oral and written work and support solutions with evidence. LA
GOAL B NUMBER OPERATIONS AND RELATIONSHIPS
Use numbers effectively for various purposes, such as counting, measuring, estimating, and problem-solving.
B.2.1. Represent and explain whole numbers, and fractions with:
a. Physical materials.
b. Number lines and other pictorial models. SS, SC
c. Verbal descriptions. LA
d. Place-value concepts and notation.
1) Identify place value to 3 digits.
B.2.2. Determine the number of things in a set by:
a. Grouping and counting (e.g., by twos, fives, tens, twenty-fives, hundreds). FL, SC
1) Count through 999. AR
b. Combining and arranging (sets of coins les than $1.00). SS, SC
c. Estimating and rounding.
B.2.3. Read and write, and order whole numbers, simple fractions (e.g., halves, thirds, fourths).
a. Read and write numerals through 999.
b. Compare and order 2-and 3-digit whole numbers.
c. Identify objects divided into halves, thirds, and fourths.
B.2.5. In problem-solving situations involving whole numbers, select and efficiently use appropriate computational procedures such as:
a. Recalling the basic facts of addition, subtraction, multiplication, and division.
1) Memorize addition and subtraction facts to 18.
b. Selecting and applying algorithms for addition, subtraction, multiplication, and division.
1) Add and subtract 2- and 3-digit numbers with and without regrouping.
2) Write and solve number sentences using 2- and 3-digit numbers.
c. Using a calculator to assist and check solutions to problems.
GOAL C GEOMETRY
Use geometric concepts, relationships and procedures to interpret, represent, and solve problems.
C.2.1. Describe two-and three-dimensional figures (e.g., circles, polygons, trapezoids, prisms, spheres) by:
a. Naming two-dimensional figures, such as circles, squares, triangles, rectangles, cones, cubes, cylinders, spheres, pyramids, and prisms.
b. Comparing, sorting, and classifying them.
1) Identify figures with same shape and size.
c. Drawing and constructing physical models to specifications for two-dimensional figures. AR
d. Identifying their properties (e.g., number of side and angles).
C.2.2. Use physical materials to identify properties and relationships, including but not limited to:
a. Symmetry: find a line of symmetry of a figure.
b. Congruency: draw a congruent figure.
GOAL D MEASUREMENT
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.
D.2.1. Recognize and describe measurable attributes, such as length, liquid capacity, time, weight (mass), temperature, monetary value, and identify the appropriate units to measure them.
D.2.2. Demonstrate understanding of basic facts, principles, and techniques of measurement, including: LA
a. Appropriate use of non stadard and standard units (metric and US Customary). SC
D.2.3. Read and interpret measuring instruments (e.g., rulers, clocks, thermometers). SC, SS
a. List days of the week in order.
b. List months of the year in order.
D.2.4. Determine measurements directly by using standard tools to these suggested degrees of accuracy.
a. Length to the nearest foot, inch, or cm. PE
d. Time to 5-minute intervals.
e. Monetary value of dollars and cents to a total of $5.00.
GOAL E STATISTICS AND PROBABILITY
Use data collection and analysis, statistics and probability in problem-solving situations, employing technology where appropriate.
E.2.1. Work with data in the context of real-world situations by: SS, SC
c. Collecting, organizing, and displaying data.
1) Use real, picture and bar graphs to represent data.
2) Record data using tallies. IT
d. Drawing reasonable conclusions based on data.
E.2.3. In problem-solving situations, read, extract, and use information in graphs, tables, or charts. SS, SC
GOAL F ALGEBRAIC RELATIONSHIPS
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.
F.2.1. Use letters, boxes, or other symbols to stand for any number, measured quantity or object in simple situations (e.g. 5 + 2 = 3).
F.2.2. Use the vocabulary, symbols, and notation of algebra accurately (<, >, =, +, -).
F.2.6. Recognize and use generalized properties and relationships of arithmetic (e.g., commutativity of addition).
a. Demonstrate the commutative property of addition using whole numbers.
Grade Level Performance Standards: Grade Three
Within our third grade mathematics curriculum, students will:
GOAL A MATHEMATICAL PROCESSES
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.
A.3.1. Use reasoning abilities to:
a. Perceive patterns. MU, LA, AR, PE
1) Identify the properties or characteristics of patterns.
2) Extend geometric and numerical patterns.
b. Identify relationships between addition and multiplication.
c. Formulate questions for further exploration.
d. Justify strategies.
1) Use a variety of problem-solving strategies.
a) Modeling a mathematical problem by creating a physical example.
b) Using the four-step problem-solving process.
e. Check if results are reasonable.
A.3.2. Communicate mathematical ideas in a variety of ways, including words, numbers, symbols,
pictures, charts, graphs, tables, diagrams, and models. LA
A.3.3. Connect mathematical learning with other subjects, personal experiences, current events, and
personal interests. SC, SS, LA, MU, PE, AR, FL
a. See relationships between various kinds of problems and actual events.
1) Relate actual time to daily activities.
b. Use mathematics as a way to understand other areas of the curriculum (e.g., measurement in
science, map skills in social studies, and literature).
A.3.4. Use appropriate mathematical vocabulary, symbols, and notation with understanding based on prior conceptual work.
A.3.5. Explain solutions to problems clearly and logically in oral and written work and support solutions with evidence. LA
GOAL B NUMBER OPERATIONS AND RELATIONSHIPS
Use numbers effectively for various purposes, such as counting, measuring, estimating, and problem-solving.
B.3.1. Represent and explain whole numbers and fractions with:
a. Physical materials.
b. Number lines and other pictorial models. SS (timelines)
c. Verbal descriptions.
d. Place-value concepts and notation to 100,000.
e. Symbolic renaming (e.g., 43=40+3=30+13 and expanded notation).
B.3.2. Determine the number of things in a set by: AR, SC, SS
a. Grouping and counting (e.g., by twos, fives, hundreds). FL
1) Use number theory principles: identify and continue numerical patterns, skip count odd and even numbers.
b. Combining and arranging (e.g., all possible coin combinations).
1) Compare equivalent and non-equivalent money amounts.
c. Estimation, including rounding.
1) Round whole numbers to nearest tens and hundreds place.
B.3.3. Read, write, and order up to 4-digit whole numbers, simple fractions (e.g., halves, fourths, tenths, and unit
fractions which have 1 as the numerator).
B.3.4. Identify and represent equivalent fractions for halves, fourths, and eighths.
B.3.5. In problem-solving situations involving whole numbers, select and efficiently use appropriate
computational procedures such as:
a. Recalling the basic facts of addition, subtraction, multiplication, and division.
1) Memorize multiplication and division facts from 0-9.
b. Using mental math.
c. Estimation.
d. Selecting and applying algorithms for addition, subtraction, multiplication, and division.
1) Add and subtract 3 and 4-digit numbers with regrouping.
e. Using a calculator to assist and check solutions to problems.
f. Using opposite operations to check computation.
GOAL C GEOMETRY
Use geometric concepts, relationships and procedures to interpret, represent, and solve problems.
C.3.1. Describe two-and three-dimensional figures (e.g., circles, polygons, trapezoids, prisms, spheres) by:
a. Naming them. SS (architecture)
b. Comparing, sorting, and classifying them.
c. Drawing and constructing physical models to specifications for two-dimensional figures. AR, SS
d. Identifying their properties (e.g., number of sides or faces, two- or three-dimensionality, equal
sides, number of right angles).
f. Explaining how these figures are related to objects in the environment.
C.3.2. Use physical materials and motion geometry (such as slides, flips, and turns) to identify properties and relationships, including but not limited to:
a. Symmetry.
b. Congruence.
c. Similarity.
GOAL D MEASUREMENT
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.
D.3.1. 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.3.2. Demonstrate understanding of basic facts, principles, and techniques of measurement, including:
a. Appropriate use of non standard and standard units (metric and US Customary). SC, LA
1) Select appropriate unit of measure (mile/foot/inch).
b. Appropriate use and conversion of units within a system (such as yards, feet, and inches, kilograms and grams; gallons, quarts, pints, and cups).
c. Judging the reasonableness of an obtained measurement as it relates to prior experience and familiar benchmarks.
D.3.3. Read and interpret measuring instruments (e.g., rulers, clocks, thermometers). SS
D.3.4. Determine measurements directly by using standard tools to these suggested degrees of accuracy:
a. Length to the nearest half-inch or nearest cm.
1) Measure lengths to nearest one-quarter inch, inch and foot. PE
c. Temperatures to the nearest 5 degrees.
d. Time to the nearest one-minute interval.
e. Monetary value of dollars and cents to a total of $10.00.
f. Liquid capacity to the nearest fluid ounce.
D.3.5. Determine measurements by using basic relationships (such as perimeter and area) and approximate measurements by using estimation techniques.
a. Estimate lengths to nearest inch and foot, centimeter and meter.
GOAL E STATISTICS AND PROBABILITY
Use data collection and analysis, statistics and probability in problem-solving situations, employing technology where appropriate.
E.3.1. Work with data in the context of real-world situations by: SC, SS
a. Formulating questions that lead to data collection and analysis.
b. Determining what data to collect and how to collect it.
c. Collecting, organizing, and displaying data.
d. Drawing reasonable conclusions based on data. IT
E.3.3. In problem-solving situations, read, extract, interpret, and use information presented in graphs, tables, or charts. SC, SS, LA
E.3.5. Predict outcomes of future events and test predictions using data from a variety of sources. SC
GOAL F ALGEBRAIC RELATIONSHIPS
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.
F.3.1. 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.3.2. 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.3.3. Work with simple linear patterns and relationships in a variety of ways, including:
a. Recognizing and extending number pattern.
b. Describing them verbally. LA
c. Representing them with pictures, tables, charts, graphs.
d. Recognizing that different models can represent the same pattern or relationship.
e. Using them to describe real-world phenomena. LA
F.3.4. 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). SC (balance of nature).
F.3.5. Use simple equations and inequalities in a variety of ways, including:
a. Using them to represent problem situations.
1) Write number sentences that model real-life situations.
b. Solving them by different methods (e.g., use of manipulatives, guess and check strategies, recall of number facts).
c. Recording and describing solution strategies.
F.3.6. Recognize and use generalized properties and relationships of arithmetic (e.g., commutativity of addition, inverse relationship of multiplication and division).
a. Demonstrate the commutative property of multiplication of whole numbers.
Note – Numeric order for the K-8 grade level goals listed in this document aligns with the WI State Academic Standards. Not all grades include each standard sub-category (as indicated by gaps in the numbering system). However, all K-4 goals and 5-8 goals are appropriately addressed by the end of fourth and eighth grades.
These grade level performance standards are listed developmentally. However, each school is uniquely organized. Therefore, a specific grade level standard may not be addressed at the grade indicated, but will be addressed within a 4 year time span (K-4, 5-8).
Grade Level Performance Standards: Grade Four
Within our fourth grade mathematics curriculum, students will:
GOAL A MATHEMATICAL PROCESSES
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.
A.4.1. 1. Use reasoning abilities to:
a. Perceive patterns. AR, MU, LA, SC
1) Describe the properties and characteristics of patterns having two or more attributes.
2) Extend simple geometric and numerical patterns.
b. Identify relationships between multiplication and division.
c. Formulate questions for further exploration.
d. Justify strategies.
2. Use a variety of problem-solving strategies to:
a) Guess and check, modeling, and looking for patterns.
b) Use the 4-step problem solving process.
c) Solve 2-step problems.
3. Check if results are reasonable using estimation.
A.4.2. Communicate mathematical ideas in a variety of ways, including words, numbers, symbols,
pictures, charts, graphs, tables, diagrams, and models. LA
A.4.3. Connect mathematical learning with other subjects, personal experiences, current events, and
personal interests. SC, SS, LA, MU, PE, AR, FL
a. See relationships between various kinds of problems and actual events.
b. Use mathematics as a way to understand other areas of the curriculum (e.g., measurement in science, map skills in social studies, and literature).
A.4.4. Use appropriate mathematical vocabulary, symbols, and notation with understanding based on prior conceptual work (+, -, x, /, >, <, =).
A.4.5. Explain solutions to problems clearly and logically in oral and written work and support solutions with evidence. LA
GOAL B NUMBER OPERATIONS AND RELATIONSHIPS
Use numbers effectively for various purposes, such as counting, measuring, estimating, and problem-solving.
B.4.1. Represent and explain whole numbers, decimals, and fractions with:
a. Physical materials.
b. Number lines and other pictorial models. SS (timelines)
c. Verbal descriptions. LA
d. Place-value concepts and notation with whole numbers up to millions; decimals to hundredths.
e. Symbolic renaming (e.g., 43=40+3=30+13).
B.4.2. Determine the number of things in a set by: SS, SC
a. Grouping and counting (e.g., by threes, fives, hundreds). FL
b. Combining and arranging (e.g., all possible coin combinations).
c. Estimation, including rounding to nearest thousand (know and be able to apply the rules for rounding off numbers).
B.4.3. Read, write, and order whole numbers, simple fractions (e.g., halves, fourths, tenths, unit fractions, or any fraction which has 1 as the numerator) and commonly-used decimals (monetary units).
B.4.4. Identify and represent equivalent fractions for halves, fourths, eighths, tenths, sixteenths. MU
B.4.5. In problem-solving situations involving whole numbers, select and efficiently use appropriate
computational procedures such as:
a. Recalling the basic facts of addition, subtraction, multiplication, and division.
b. Using mental math.
c. Estimation.
d. Selecting and applying algorithms for addition, subtraction, multiplication, and division.
1) Multiply a 2, 3 or 4-digit number by a 1-and 2-digit number with regrouping.
2) Multiply by 10, 100, and 1,000.
3) Divide 3-digit by 1-digit numbers with remainders.
e. Using a calculator to assist and check solutions to problems.
f. Using opposite operations to check computation.
B.4.6. Add and subtract fractions with like denominators.
B.4.7. In problem-solving situations involving money, add and subtract decimals
GOAL C GEOMETRY
Use geometric concepts, relationships and procedures to interpret, represent, and solve problems.
C.4.1. Describe two-and three-dimensional figures (e.g., circles, polygons, trapezoids, prisms, spheres) by:
a. Naming them. SS, AR
b. Comparing, sorting, and classifying them.
c. Drawing and constructing physical models to specifications.
d. Identifying their properties (e.g., number of sides or faces, two- or three-dimensionality, equal sides, number of right angles).
e. Predicting the results of combining or subdividing two-dimensional figures.
f. 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:
a. Symmetry.
b. Congruence.
c. Similarity.
C.4.3. Identify and use relationships among figures, including but not limited to:
a. Location (e.g., between, adjacent to, interior of).
b. Position (e.g., parallel, perpendicular).
c. 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. SS (map coordinates).
GOAL D MEASUREMENT
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.
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: SC
a. Appropriate use of non standard and standard units (metric and US Customary). LA
b. Appropriate use and conversion of units within a system (such as yards, feet, and inches; kilograms and grams; gallons, quarts, pints, and cups; seconds, minutes, and hours).
c. 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). SS
D.4.4. Determine measurements directly by using standard tools (metric and US Customary) to these suggested degrees of accuracy: PE
a. Length to the nearest cm and one-fourth inch.
b. Weight (mass) to the nearest ounce or nearest 5 grams.
d. Time to the nearest minute.
e. Monetary value of dollars and cents to a total of $20.00.
D.4.5. Determine measurements by using basic relationships (such as perimeter and area) and approximate measurements by using estimation techniques.
GOAL E STATISTICS AND PROBABILITY
Use data collection and analysis, statistics and probability in problem-solving situations, employing technology where appropriate.
E.4.1. Work with data in the context of real-world situations by: SS, SC
a. Formulating questions that lead to data collection and analysis.
b. Determining what data to collect and how to collect it.
c. Collecting, organizing, and displaying data.
d. Drawing reasonable conclusions based on data. IT
E.4.2. Describe a set of data using: LA
a. High and low values, and range.
b. Most frequent value (mode).
c. Middle value of a set of ordered data (median).
E.4.3. In problem-solving situations, read, extract, interpret and use information presented in graphs, tables, or charts. SS, SC, LA
E.4.4. Determine if future events are more, less, or equally likely, impossible, or certain to occur. SC
E.4.5. Predict outcomes of future events and test predictions using data from a variety of sources. SC
GOAL F ALGEBRAIC RELATIONSHIPS
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.
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:
a. Recognizing and extending number patterns.
b. Describing them verbally. LA
c. Representing them with pictures, tables, charts, graphs.
d. Recognizing that different models can represent the same pattern or relationship.
e. Using them to describe real-world phenomena. LA
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). SC (balance of nature).
F.4.5. Use simple equations and inequalities in a variety of ways, including:
a. Using them to represent problem situations.
b. Solving them by different methods (e.g., use of manipulatives, guess and check strategies, recall of number facts).
c. 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).
Note – Numeric order for the K-8 grade level goals listed in this document aligns with the WI State Academic Standards. Not all grades include each standard sub-category (as indicated by gaps in the numbering system). However, all K-4 goals and 5-8 goals are appropriately addressed by the end of fourth and eighth grades.
These grade level performance standards are listed developmentally. However, each school is uniquely organized. Therefore, a specific grade level standard may not be addressed at the grade indicated, but will be addressed within a 4 year time span (K-4, 5-8).
Grade Level Performance Standards: Grade Five
Within our fifth grade mathematics curriculum, students will:
GOAL A MATHEMATICAL PROCESSES
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.
A.5.1. Use reasoning abilities to:
a. Evaluate information. SC
b. Perceive patterns. MU, LA, AR
1) Extend growing numerical and geometric patterns.
c. Identify relationships between concepts.
d. Formulate questions for further exploration.
e. Evaluate strategies.
1) Use a variety of problem-solving strategies including using simpler numbers and making a table.
f. Justify statements.
1) Determine if an answer is appropriate for a problem.
2) Use models, known facts and properties to validate thinking.
g. Check if results are reasonable.
h. Defend work.
A.5.2. Communicate logical arguments clearly to show why a result makes sense. SC
A.5.3. Analyze non-routine problems by modeling, illustrating, guessing, simplifying, generalizing, or shifting to another point of view. SS, SC, LA
A.5.4. Develop effective oral and written presentations that include: LA
a. Appropriate use of technology. IT
b. The conventions of mathematics (e.g., symbols, definitions, labeled drawings).
c. Mathematical language.
1. Read and use mathematical terminology consistent with number sense development, such as factor, multiple, composites, prime.
2. Explain orally a solution process to a problem using appropriate terminology
d. Clear organization of ideas and procedures.
e. Understanding of purpose and audience.
A.5.5. Explain mathematical concepts, procedures, and ideas to others who may not be familiar with them.
A.5.6. Read and understand mathematical texts and other instructional materials and recognize mathematical ideas as they appear in other subject areas.
GOAL B NUMBER OPERATIONS AND RELATIONSHIPS
Use numbers effectively for various purposes, such as counting, measuring, estimating, and problem-solving.
B.5.1. Read, represent, and interpret various rational numbers (whole numbers, decimals and mixed decimals through thousandths, and fractions) with verbal descriptions, geometric models, and mathematical notation (e.g., expanded). SS (timelines), MU (notes), AR, LA
a. Identify place value to billions.
b. Round numbers to ten thousand.
c. Write decimals to thousandths.
d. Write improper fractions for numbers.
B.5.2. Perform and explain operations using rational numbers (add, subtract, multiply, divide, raise to a
power, or take opposites and reciprocals).
a. Multiply 3-digit numbers.
b. Divide 3-digit numbers by 2-digit divisors with remainders.
c. Add and subtract fractions having unlike denominators.
d. Add, subtract, multiply, and divide decimals through thousandths.
B.5.3. Generate and explain equivalencies among fractions and decimals.
B.5.4. Express order relationships among rational numbers (decimals) using appropriate symbols (>, <).
B.5.6. Model and solve problems involving number-theory concepts such as:
a. Prime and composite numbers.
1) Use number theory principles: multiples, factors, prime and composite numbers.
B.5.7. In problem-solving situations, select and use appropriate computational procedures with rational numbers such as: (SS)
a. Calculating mentally.
b. Estimating.
c. Creating, using, and explaining algorithms.
d. Using technology. IT
GOAL C GEOMETRY
Use geometric concepts, relationships and procedures to interpret, represent, and solve problems.
C.5.1. Describe two-dimensional figures (e.g., rhombus) by: AR
a. Naming, defining, and giving examples. SS
1) Identify different types of quadrilaterals.
2) Name polygons having 3 to 10 sides.
b. Comparing, sorting, and classifying them.
c. Drawing and constructing physical models to specifications.
1) Measure and draw angles.
d. Explaining how these figures are related to objects in the environment.
C.5.5. Locate objects using the rectangular coordinate system. SS (map skills)
GOAL D MEASUREMENT
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.
D.5.2. Demonstrate understanding of basic measurement facts, principles, and techniques including the following: SC, LA
a. Approximate comparisons between metric and US Customary units (e.g., a liter and a quart are
about the same; a kilometer is about six-tenths of a mile).
D.5.3. Determine measurement directly using standard units (metric and US Customary) with these
suggested degrees of accuracy. SS
a. Lengths to the nearest one-eighth inch, centimeter, and meter.
D.5.4. Determine measurements indirectly using. PE
a. Estimation.
d. Geometric formulas to derive perimeter and area of rectangles and squares.
GOAL E STATISTICS AND PROBABILITY
Use data collection and analysis, statistics and probability in problem-solving situations, employing technology where appropriate.
E.5.2. Organize and display data from statistical investigations using. IT, SC, SS
a. Appropriate tables, graphs, and/or charts (e.g., bar or line for multiple sets of data).
E.5.3. Extract, interpret, and analyze information from organized and displayed data by using. IT, SC, SS
a. Central tendencies of data (mean, median, mode, and range).
E.5.4. Use the results of data analysis to: LA, SC, SS
a. Make predictions.
b. Develop convincing arguments.
c. Draw conclusions.
E.5.7. Determine the likelihood of occurrence of simple events by: SC
d. Applying theoretical notions of probability (e.g., that four equally likely events have a 25% chance of happening).
GOAL F ALGEBRAIC RELATIONSHIPS
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.
F.5.1. Work with algebraic expressions in a variety of ways, including: (SC)
a. Evaluating expressions through numerical substitution of whole numbers
Note – Numeric order for the K-8 grade level goals listed in this document aligns with the WI State Academic Standards. Not all grades include each standard sub-category (as indicated by gaps in the numbering system). However, all K-4 goals and 5-8 goals are appropriately addressed by the end of fourth and eighth grades.
These grade level performance standards are listed developmentally. However, each school is uniquely organized. Therefore, a specific grade level standard may not be addressed at the grade indicated, but will be addressed within a 4 year time span (K-4, 5-8).
Grade Level Performance Standards: Grade Six
Within our sixth grade mathematics curriculum, students will:
GOAL A MATHEMATICAL PROCESSES
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.
A.6.1. Use reasoning abilities to: SC
a. Evaluate information.
b. Perceive patterns. AR, MU, LA
1) Extend numerical patterns.
c. Identify relationships between fractions and decimals.
d. Formulate questions for further exploration.
e. Evaluate strategies.
1) Use a variety of problem-solving strategies including making lists.
f. Justify statements.
1) Analyze a solution to a grade-appropriate problem.
g. Check if results are reasonable.
h. Defend work.
A.6.2. Communicate logical arguments clearly to show why a result makes sense. LA, SC
A.6.3. Analyze non-routine problems by modeling, illustrating, guessing, simplifying, generalizing, or shifting to another point of view. SS, SC, LA
A.6.4. Develop effecti