Whitehall School District #4-47-2

Revised fall of 2003

Table of Contents

K-8 Math Curriculum...... 3-12

K-8 Benchmarks...... 13-29

9-12 Math Curriculum...... 30-38

9-12 Benchmarks...... 39-41

Key for Math Curriculum

I= Introduce

D= Develop

M= Master

Kindergarten MATHEMATICS

1.Content Standard 1 – Students engage in the mathematical processes of problem solving and reasoning, estimation, communication, connections and application, and using appropriate technology.

A.Introduction to guess and check, draw a picture, count back and count on. I

2.Content Standard 2 – Students demonstrate understanding of and an ability to use numbers and operations.

A.Recognize and identify the numbers to 20. I/D

B.Count objects to 20 using one to one correspondence. I/D

C.Demonstrate the ability to count to 100. I\D

D.Add and subtract to 10 using manipulatives. I/D

E.Introduce equal parts and parts of a set. I

3.Content Standard 3 – Students use algebraic concepts, processes, and language to model and solve a variety of real-world and mathematical problems.

A.Introduce aba, aabb and abc patterns.I/D

B.Create aba, aabb and abc patterns. I/D

C.Sort and classify objects.I/D

4.Content Standard 4 – Student demonstrates understanding of shape and an ability to use geometry.

A.Introduce plain figures and space figures. I

5.Content Standard 5 – Students demonstrate understanding of measurable attributes and an ability to use measurement processes.

A.Measure time to the hour. I/D

B.Measure using standard and nonstandard units. I

C.Understand more and less. I

D.Introduce coins and their values. I

E.Introduce weight and measure. I

6.Content Standard 6 – Students demonstrate understanding of an ability to use data analysis, probability, and statistics.

A.Experience collecting data. I

B.Demonstrate the ability to create a bar and pictograph.I

C.Demonstrate the ability to read a bar and pictograph. I

7.Content Standard 7 – Students demonstrate understanding of and an ability to use patterns, relations and functions.

A.Introduce \aba, aabb and abc patterns. I

B.Create aba, aabb and abc patterns I

C.Sort and classify objects.I/D

D.Recognize symbols showing relationships. I

1st Grade MATHEMATICS

  1. Content Standard 1 – Students engage in the mathematical processes of problem solving and reasoning, estimation, communication, connections and application, and using appropriate technology.
  2. Drawing pictures. D
  3. Guess and check. D
  4. Count back. D
  5. Count on. D
  6. Predict and estimate. I
  7. Content Standard 2 – Students demonstrate understanding of and an ability to use numbers and operations.
  8. Understand numbers to 20 without manipulatives. M
  9. Introduce place value to 100. I/D
  10. Master the understanding of addition of numbers to 10 using manipulatives. M
  11. Master addition of numbers to 10. M
  12. Master understanding of subtraction of numbers to 10 using manipulatives. M
  13. Master an understanding of subtraction of numbers to 10. M
  14. Introduce and develop adding and subtracting two digit numbers without regrouping using manipulative. I/D
  15. Demonstrate recognition, modeling, reading, and writing of fractions. I
  16. Content Standard 3 – Students use algebraic concepts, processes, and language to model and solve a variety of real-world and mathematical problems.
  17. Introduce commutative, associative and identity properties using manipulatives and fact families. I
  18. Patterning of coins, numbers, and geometric figures. D
  19. Content Standard 4 – Students demonstrate understanding of shape and an ability to use geometry.
  20. Develop plain and space figures. D
  21. Introduce congruent, open and closed and symmetrical figures. I/D
  22. Content Standard 5 – Students demonstrate understanding of measurable attributes and an ability to use measurement processes.
  23. Understand measurement in the following areas using manipulatives: length, volume, weight and time. D
  24. Develop understanding of value of penny, nickel, dime, quarter and dollar. D
  25. Develop an understanding of counting combinations of pennies, nickels, and dimes. D
  26. Content Standard 6 – Students demonstrate understanding of an ability to use data analysis, probability, and statistics.
  27. Experience collecting data. D
  28. Demonstrate the ability to create a bar and pictograph. D
  29. Demonstrate the ability to read a bar and pictograph. D
  30. Formulate a prediction. I
  31. Content Standard 7 – Students demonstrate understanding of and an ability to use patterns, relations and functions.
  32. Demonstrate patterns using numbers and coins. D
  33. Create aba, aabb and abc patterns. I
  34. Sort and classify objects. I/D
  35. Recognize symbols showing relationships. D

2nd Grade MATHEMATICS

  1. Content Standard 1 – Students engage in the mathematical processes of problem solving and reasoning, estimation, communication, connections and application, and using appropriate technology.
  2. Introduce calculator for addition and subtraction. I
  3. Draw pictures. M
  4. Guess and check. M
  5. Count back. M
  6. Count on. M
  7. Predict and estimate. M
  8. Content Standard 2 – Students demonstrate understanding of and an ability to use numbers and operations.
  9. Review addition and subtraction facts to ten. M
  10. Master addition and subtraction facts to eighteen. M
  11. Master two-digit addition and subtraction with and without trading. I/D/M
  12. Introduce three-digit addition and subtraction with and without trading. I
  13. Explore multiplication and division. I
  14. Demonstrate recognition, modeling, reading, and writing of fractions. I
  15. Content Standard 3 – Student use algebraic concepts, processes, and language to model and solve a variety of real-world and mathematical problems.
  16. Identify patterns of numbers. I/D
  17. Count money. D
  18. Content Standard 4 – Students demonstrate understanding of shape and an ability to use geometry.
  19. Master plane and space figures. M
  20. Explore perimeter, symmetry, and geometric solids. I/D
  21. Content Standard 5 – Students demonstrate understanding of measurable attributes and an ability to use measurement processes.
  22. Master time to the hour and half hour. M
  23. Tell time to the quarter hour and to five minutes. D
  24. Measure length, capacity, weight, and temperature using standard and nonstandard units. D
  25. Develop understanding of value of penny, nickel, dime, quarter, half-dollar, and dollar bills.
  26. Tell dollar and use decimal point to identify cents. I/D
  27. Content Standard 6 – Students demonstrate understanding of an ability to use data analysis, probability, and statistics.
  28. Investigate probability, estimation, graphing and problem solving. D
  29. Content Standard 7 – Students demonstrate understanding of and an ability to use patterns, relations and functions.
  30. Examine place value of ones, tens, and hundreds. D
  31. Examine relationships with money and visual patterns. D

1

3rd Grade MATHEMATICS

  1. Content Standard 1 – Students engage in the mathematical processes of problem solving and reasoning, estimation, communication, connections and application, and using appropriate technology.
  2. Solve simple word problems using estimate and check, applying basic number operations, drawing a picture, and reading a table or graph. D
  3. Introduce knowledge and use of calculators. I
  4. Content Standard 2 – Students demonstrate understanding of and an ability to use numbers and operations.
  5. Develop addition and subtraction to 18 using related facts. D
  6. Develop regrouping to four digits in addition and subtraction . D
  7. Introduce multiplication facts 0-9 using repeated addition. I
  8. Introduce regrouping with two and three-digit multiplication by a single digit. I
  9. Introduce and develop division facts to 9 applying related multiplication facts. I/D
  10. Introduce division with simple remainders. I
  11. Develop place value to 999,999. D
  12. Develop rounding to ten=s and hundred=s place. D
  13. Content Standard 3 – Students use algebraic concepts, processes, and language to model and solve a variety of real-world and mathematical problems.
  14. Introduce missing factors. I
  15. Introduce properties of multiplication (associative, commutative). I
  16. Master zero and ones as factors. M
  17. Continue a pattern of geometric figures and or numbers. D
  18. Create a pattern of geometric figures and or numbers. D
  19. Identify special patterns and sequences in skip counting. D
  20. Develop use and understanding of function tables. I
  21. Introduce and develop the graphing of ordered pairs. I/D
  22. Develop the symbols showing relationships (<, >, =). D
  23. Content Standard 4 – Students demonstrate understanding of shape and an ability to use geometry.
  24. Identify two and three-dimensional shapes. I
  25. Demonstrate understanding of area and volume by counting square and cubic units. I
  26. Recognize congruency and symmetry using manipulatives. D
  27. Content Standard 5 – Students demonstrate understanding of measurable attributes and an ability to use measurement processes.
  28. Tell time to the minute. M
  29. Identify the passage of time. D
  30. Identify the metric and standard units of measurements for length. I
  31. Demonstrate understanding of money and making change. I
  32. Exhibit connections between the concrete and symbolic representation of

fractional models. D

  1. Content Standard 6 – Students demonstrate understanding of an ability to use data analysis, probability, and statistics.
  2. Read a table or graph. (D)
  3. Make a table or graph. (D)
  1. Content Standard 7 – Students demonstrate understanding of and an ability to use patterns, relations and functions.
  2. Continue a pattern of geometric figures and or numbers. D
  3. Create a pattern of geometric figures and or numbers. D
  4. Identify special patterns and sequences in skip counting. D
  5. Develop use and understanding of function tables. I
  6. Introduce and develop the graphing of ordered pairs. I/D
  7. Develop use of symbols (<, >, =) to show relationships between numbers. D

4th Grade MATHEMATICS

  1. Content Standard 1 – Students engage in the mathematical processes of problem solving and reasoning, estimation, communication, connections and application, and using appropriate technology.
  2. Demonstrate understanding of problem solving using a variety of strategies: being able to explain method of acquiring answer. D
  3. Use estimation to determine solution strategies for problem solving. D
  4. Use written and pictorial means to communicate data. D
  5. Demonstrate understanding of real life mathematical applications: buying items, using coupons, percentages off, using fractions in cooking and carpentry. D
  6. Develop knowledge and use of calculators. D
  1. Content Standard 2 – Students demonstrate understanding of and an ability to use numbers and operations.
  2. Demonstrate understanding of basic facts and number concepts: place value to 1,000,000, addition and subtraction facts to 18 multiplication and division facts through 12. D
  3. Introduce multiplication computation ( 3 digit by 2 digit) and division computation ( 1 digit into 3 digit). I
  4. Use models to demonstrate understanding of fractions with like denominators, compare fractions with unlike denominators. D
  5. Content Standard 3 – Students use algebraic concepts, processes, and language to model and solve a variety of real-world and mathematical problems.
  6. Use symbols to represent numbers in simple addition, multiplication and division problems. I
  7. Solve problems using missing variables. D
  8. Use function tables, patterns, associative, commutative and property of zero to solve problems with missing operations. D
  9. Content Standard 4 – Students demonstrate understanding of slope and an ability to use geometry.
  10. Model and be able to explain acute and obtuse angles, congruent figures, line, line segment and rays. I
  11. Introduce area, circumference and perimeter of plane figures. I
  12. Demonstrate understanding of slides, flips, turns, and line symmetry. I
  13. Classify two-and-three dimensional shapes. D
  14. Content Standard 5 – Students demonstrate understanding of measurable attributes and an ability to use measurement processes.
  15. Demonstrate ability to use length, volume, weight, area, time, and temperature. D
  16. Use nonstandard and standard metric units to measure length volume and temperature. D
  17. Select appropriate measurement tools for length and volume. M
  18. Demonstrate understanding of money and making change in problem solving situations. D
  19. Content Standard 6 –Students demonstrate understanding of an ability to use data analysis, probability, and statistics.
  20. Investigate events of probability and chance. I
  21. Construct model to represent data. D
  22. Read and interpret graphic data in a variety of forms. D
  23. Collect and organize data to solve problems. D
  24. Content Standard 7 – Students demonstrate understanding of and an ability to use patterns, relations and functions.
  25. Use function tables and patterns to solve problems D
  26. Apply patterns to show relationships in multiplication and division D
  27. Use associative and commutative properties, and the property of zero to solve problems. D

5th Grade MATHEMATICS

  1. Content Standard 1 – Students engage in the mathematical processes of problem solving and reasoning, estimation, communication, connections and application, and using appropriate technology.
  2. Solve word problems by using appropriate strategies. D
  3. Use estimation strategies to determine solutions. D
  4. Develop knowledge and use of calculators. D
  5. Content Standard 2 – Students demonstrate understanding of and an ability to use numbers and operations.
  6. Write whole and decimal numbers and give place value for any digit. D
  7. Compare and order whole and decimal numbers. D
  8. Round numbers to the nearest tens, hundreds, thousands, and ten thousands.
  9. Add and subtract whole and decimal numbers. D
  10. Divide by one and two digit divisors to get one, two and three digit quotients. D
  11. Introduce finding averages. I
  12. Multiply whole numbers and decimals. I/D
  13. Add, subtract, multiply and divide fractions. I/D
  14. Content Standard 3 – Students use algebraic concepts, processes, and language to model and solve a variety of real-world and mathematical problems.
  15. Solve problems by writing equations. D
  16. Find missing factors. D
  17. Develop an understanding of properties of both addition and subtraction. D
  18. Introduce the distributive property. I
  19. Introduce evaluation of reasonableness of solution. I
  20. Content Standard 4 – Students demonstrate understanding of shape and an ability to use geometry.
  21. Develop understanding of acute and obtuse angles, congruent figures, line, line segment and rays. D
  22. Develop understanding of area, circumference, and perimeter of plane figures. D
  23. Introduce types of triangles ( acute, obtuse, and right ). I
  24. Introduce area, perimeter, and volume using formulas for rectangle, square, triangle, and a parallelogram. I
  25. Develop knowledge of intersecting, parallel, and perpendicular lines. D

  1. Content Standard 5 – Students demonstrate understanding of measurable attributes and an ability to use measurement processes.
  2. Develop the knowledge of the customary English and Metric units of length, area, volume, mass, and temperature. D
  3. Demonstrate ability to use length, area, volume, mass, and temperature. D
  4. Demonstrate use of money and use of it with different operations. D
  5. Content Standard 6 –Students demonstrate understanding of an ability to use data analysis, probability, and statistics.
  6. Introduce median, mode, and range. I
  7. Develop tables and graphs using data collected. D
  8. Develop events of probability and chance. ( ie. Tree diagrams) I/D
  9. Introduce ratios, proportions, percents, and fractions and their relationships. I
  10. Content Standard 7 – Students demonstrate understanding of and an ability to use patterns, relations and functions.
  11. Introduce various graphs and techniques to create them (double bar graph, stem and leaf plots, line graphs, etc.).
  12. Develop knowledge and use of various graphs (D)
  13. Use function tables and patterns to develop and solve problems. D

6th Grade MATHEMATICS

  1. Content Standard 1 – Students engage in the mathematical processes of problem solving and reasoning, estimation, communication, connections and application, and using appropriate technology.
  2. Select and apply appropriate estimation strategies throughout the problem-solving process D
  3. Use problem solving strategies by making a graph, table, finding a pattern and

guessing and checking. D

  1. Develop knowledge and use of calculators. D
  1. Content Standard 2 – Students demonstrate understanding of and an ability to use numbers and operations
  2. Write numbers, give place value for any digit, and write numbers in expanded notation. D
  3. Compare and order whole numbers, fractions, and decimals. D
  4. Round whole numbers, fractions, and decimals to the nearest place values. D
  5. Add, subtract, multiply, and divide whole numbers, fractions, and decimals. D
  6. Find averages(mean), medians, modes, and range. D

i)Develop an understanding of ordered pairs, ratios, and proportions. D

ii)Introduce exponents. I

  1. Content Standard 3 – Students use algebraic concepts, processes, and language to model and solve a variety of real-world and mathematical problems.
  2. Develop a concept of variables, expressions, and equations D
  3. Develop an ability to determine solution strategies. D
  4. Solve equations using concrete, numerical, and algebraic methods. D
  5. Learn to evaluate reasonableness of a solution. D
  6. Content Standard 4 – Students demonstrate understanding of shape and an ability to use geometry.
  7. Identify geometric terms such as: line, parallel, perpendicular, and skew. D
  8. Identify and measure angles (obtuse, acute, and right). D
  9. Identify polygons (triangle, quadrilateral, pentagon, hexagon) space figures, and circles I/D
  10. Identify perimeter, area, and volume. I
  11. Content Standard 5 – Students demonstrate understanding of measurable attributes and an ability to use measurement processes.
  12. Develop the knowledge of the customary English units of length, area, volume, mass, and temperature. D
  13. Develop the knowledge of the Metric units of length, area, volume, mass, and temperature. D
  14. Develop knowledge of elapsed time and time zones. D
  15. Content Standard 6 – Students demonstrate understanding of an ability to use data analysis, probability, and statistics.
  16. Demonstrate knowledge of ratios, proportions, percents, and fractions, and identify the relatedness of these. D
  17. Develop the ability to find the mean, median, mode, and range. D
  18. Develop the knowledge of data gathering and graphing. D
  19. Content Standard 7 – Students demonstrate understanding of and an ability to use patterns, relations and functions.
  20. Describe and represent relationships with tables, graphs, and rules. D
  21. Develop an understanding of mathematical properties (commutative, distributive, associative, etc.) D

7th Grade MATHEMATICS

  1. Content Standard 1 – Students engage in the mathematical processes of problem solving and reasoning, estimation, communication, connections and application, and using appropriate technology.
  2. Engage in mathematical processes by problem solving and reasoning.(inductive/deductive) D
  3. Develop estimation methods. (rounding, front-end method, etc.) M
  4. Using appropriate technology. (calculator, computers, etc.) D
  5. Content Standard 2 – Students demonstrate understanding of and an ability to use numbers and operations
  6. Develop understanding of the Commutative, Associative, and Distributive Properties of the number systems. D
  7. Develop understanding of the Property of Zero for addition and multiplication. D
  8. Master Standard Order of Operations and their use. M
  9. Develop the use of numbers in variety of equivalent forms (changing from fraction to decimal to percent) and extend to the rational number system. D
  10. Content Standard 3 – Students use algebraic concepts, processes, and language to model and solve a variety of real-world and mathematical problems
  11. Develop understanding of variables, expressions, equations, patterns, and one and two-step linear equations solved using manipulative and algebraic methods. D
  12. Introduce Addition Properties for equations and the Property of Zero for addition. I
  13. Introduce the Laws of Exponents in multiplication and division of variables. I
  14. Introduce Multiplication Properties for equations and grouping for manipulatives. I
  15. Introduce patterns in problem solving. I

  1. Content Standard 4 – Students demonstrate understanding of shape and an ability to use geometry.
  2. Develop, identify, and construct plane geometric figures. D
  3. Introduce transformations and rotations. I
  4. Develop one, two, and three-dimensional measurements. D
  5. Introduce the use of geometric formulas including the Pythagorean theorem and appropriate units of measures. I
  6. Content Standard 5 – Students demonstrate understanding of measurable attributes and an ability to use measurement processes.
  7. Develop standard and Metric System of measurement. M
  8. Develop finding Perimeter, Area, and Volume. M
  9. Develop the relationships and formulas for perimeter, area, and volume. D
  10. Develop units of measure. D
  11. Content Standard 6 – Students demonstrate understanding of an ability to use data analysis, probability, and statistics
  12. Develop construction of graphs and tables of central tendency. D
  13. Develop methods of collecting and organizing data. D
  14. Content Standard 7 – Students demonstrate understanding of and an ability to use patterns, relations and functions.
  15. Construct graphs (linear, bar, circle, etc.) D
  16. Introduce independent and dependent variables. I
  17. Develop problem solving and Scientific Methods. D

8th Grade MATHEMATICS