Elementary Mathematics




Web and Software Resources

Grade Three

Number and Number Sense

3.1 The student will read and write six-digit numerals and identify the place value for each digit.

3.2 The student will round a whole number, 999 or less, to the nearest ten and hundred.

3.3 The student will compare two whole numbers between 0 and 9,999, using symbols (>, <, or = ) and words ("greater than," "less than," or "equal to").

3.4 The student will recognize and use the inverse relationships between addition/subtraction and multiplication/division to complete basic fact sentences. Students will use these relationships to solve problems such as 5 + 3 = 8 and 8 - 3 = _____.

3.5 The student will name and write the fractions represented by drawings or concrete materials and represent a given fraction, using concrete materials and symbols.

Activity: Using a drawing program, such as Clarisworks, instruct students to draw shapes divided into different fractions. Example: Draw a rectangle. Divide the rectangle into halves. Paint 1/2 red and 1/2 green.

3.6 The student will compare the numerical value of two fractions having like and unlike denominators, using concrete materials.

3.7 The student will read and write decimals expressed as tenths and hundredths, using concrete materials.

Computation and Estimation

3.8 The student will solve problems involving the sum or difference of two whole numbers, each 9,999 or less, with or without regrouping, using various computational methods, including calculators, paper and pencil, mental computation, and estimation.

3.9 The student will recall the multiplication and division facts through the nines table.

3.10 The student will create and solve problems that involve multiplication of two whole numbers, one factor 99 or less and the second factor 5 or less.

3.11 The student will add and subtract with proper fractions having like denominators of 10 or less, using concrete materials.

3.12 The student will add and subtract with decimals expressed as tenths, using concrete materials and paper and pencil.

3.13 The student will determine by counting the value of a collection of bills and coins up to $5.00, compare the value of the coins or bills, and make change.

Computation and Estimation

3.8 The student will solve problems involving the sum or difference of two whole numbers, each 9,999 or less, with or without regrouping, using various computational methods, including calculators, paper and pencil, mental computation, and estimation.

Activity: Use the built-in calculator on the computer to create and solve problems using the four basic operations. With Windows, see Accessories. With Macintosh, see the Apple menu.

3.9 The student will recall the multiplication and division facts through the nines table.

3.10 The student will create and solve problems that involve multiplication of two whole numbers, one factor 99 or less and the second factor 5 or less.

3.11 The student will add and subtract with proper fractions having like denominators of 10 or less, using concrete materials.

3.12 The student will add and subtract with decimals expressed as tenths, using concrete materials and paper and pencil.

3.13 The student will determine by counting the value of a collection of bills and coins up to $5.00, compare the value of the coins or bills, and make change.

Measurement

3.14 The student will estimate and then use actual measuring devices with metric and U.S. Customary units to measure

  • length-inches, feet, yards, centimeters, and meters;
  • liquid volume-cups, pints, quarts, gallons, and liters;
  • weight/mass-ounces, pounds, grams, and kilograms.
Activity: Using a drawing program with a ruler, such as Clarisworks, instruct students to draw shapes with specific dimensions. Students can then calculate the area or perimeter of the shapes. Example: Draw a square where each side is 2 inches. Paint the square blue. How much blue area is inside the square?

3.15 The student will tell time to the nearest five-minute interval and to the nearest minute, using analog and digital clocks.

3.16 The student will identify equivalent periods of time, including relationships among days, months, and years, as well as minutes and hours.

3.17 The student will read temperature, to the nearest degree, from a Celsius thermometer and a Fahrenheit thermometer. Real thermometers and physical models of thermometers will be used.

Geometry

3.18 The student will analyze plane and solid geometric figures (square, rectangle, triangle, cube, rectangular solid, and cylinder) and identify relevant properties, including the number of corners, square corners, the shape of faces, and edges.

3.19 The student will identify and draw representations of line segments and angles, using a ruler or straightedge.

Activity: Using a drawing program with a ruler, such as Clarisworks, instruct students to draw shapes with specific dimensions. Students can then calculate the area or perimeter of the shapes. Example: Draw a square where each side is 2 inches. Paint the square blue. How much blue area is inside the square?

3.20 The student, given appropriate drawings or models, will identify and describe congruent and symmetrical two-dimensional figures, using tracing procedures.

Probability and Statistics

3.21 The student, given grid paper, will collect data on a given topic of his/her choice and construct a bar graph showing the results. A title and key will be included.

Activity: Students will create a spreadsheet, using a program such as ClarisWorks, on the number of M&Ms for the colors -red, orange, green, brown, yellow, and blue in the small individual bags. Each child will open his/her bag and count the M&Ms for each color in his/her bag. Input the data on a spreadsheet. Instruct students to create several graphs charts on their data. (You could substitute favorite foods, Skittles or Fruit Loops, or other items for the M&Ms.)

3.22 The student will read and interpret data represented in bar and picture graphs.

Activity: Students will create a spreadsheet, using a program such as ClarisWorks, on the number of M&Ms for the colors -red, orange, green, brown, yellow, and blue in the small individual bags. Each child will open his/her bag and count the M&Ms for each color in his/her bag. Input the data on a spreadsheet. Instruct students to create several graphs charts on their data. (You could substitute favorite foods, Skittles or Fruit Loops, or other items for the M&Ms.)

3.23 The student will investigate and describe the concept of probability as chance, and list possible results of a given situation.

Patterns, Functions, and Algebra

3.24 The student will recognize and describe patterns formed using concrete objects, tables, and pictures and extend the pattern.

3.25 The student will analyze a given pattern formed using concrete objects and pictures and then create a pattern with the same attributes.


Grade Four




Number and Number Sense

4.1 The student will

  • identify, orally and in writing, the place value for each digit in a whole number expressed through millions;
  • compare two whole numbers, expressed through millions, using symbols ( >, <, or = ); and
  • round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand.

4.2 The student will identify and represent equivalent fractions and relate fractions to decimals, using concrete objects.

Activity: Using a drawing program, such as Clarisworks, instruct students to draw shapes divided into different fractions. Example: Draw a rectangle. Divide the rectangle into halves. Paint 1/2 red and 1/2 green.

4.3 The student will compare the numerical value of fractions having denominators of 12 or less.

4.4 The student will read, write, represent, and identify decimals expressed through thousandths, and round to the nearest tenth and hundredth, using concrete materials, drawings, calculators, and symbols.

Computation and Estimation

4.5 The student will create and solve problems involving addition and subtraction of money amounts using various computational methods, including calculators, paper and pencil, mental computation, and estimation.

Activity: Use the built-in calculator on the computer to create and solve problems using the four basic operations. With Windows, see Accessories. With Macintosh, see the Apple menu.

4.6 The student will estimate whole-number sums and differences and describe the method of estimation. Students will refine estimates, using terms such as closer to, between, and a little more than.

4.7 The student will add and subtract whole numbers written in vertical and horizontal form, choosing appropriately between paper and pencil methods and calculators.

4.8 The student will find the product of two whole numbers when one factor has two digits or less and the other factor has three digits or less, using estimation and paper and pencil. For larger products (a two-digit numeral times a three-digit numeral), estimation and calculators will be used.

4.9 The student will estimate and find the quotient of two whole numbers given a one-digit divisor.

4.10 The student will

  • add and subtract with fractions having like and unlike denominators of 12 or less and with decimals through thousandths, using concrete materials and paper and pencil; and
  • solve problems involving addition and subtraction with fractions having like and unlike denominators of 12 or less and decimals expressed through thousandths.

Measurement

4.11 The student will

  • estimate and measure weight/mass using actual measuring devices and express the results in both metric and U.S. Customary units, including ounces, pounds, grams, and kilograms; and
  • estimate the conversion of ounces and grams and pounds and kilograms, using approximate comparisons (1 ounce is about 28 grams, or 1 gram is about the weight of a paper clip; 1 kilogram is a little more than 2 pounds)
The intent of this standard is for students to make "ballpark" comparisons and not to memorize conversion factors between U.S. and metric units. 4.12 The student will
  • estimate and measure length using actual measuring devices and describe the results in both metric and U.S. Customary units, including part of an inch (1/2, 1/4, and 1/8), inches, feet, yards, millimeters, centimeters, and meters; and
  • estimate the conversion of inches and centimeters, yards and meters, and miles and kilometers, using approximate comparisons (1 inch is about 2.5 centimeters, 1 meter is a little longer than 1 yard, 1 mile is slightly farther than 1.5 kilometers, or 1 kilometer is slightly farther than half a mile)
The intent of this standard is for students to make "ballpark" comparisons and not to memorize conversion factors between U.S. and metric units.

Activity: Using a drawing program with a ruler, such as Clarisworks, instruct students to draw shapes with specific dimensions. Students can then calculate the area or perimeter of the shapes. Example: Draw a square where each side is 2 inches. Paint the square blue. How much blue area is inside the square?

4.13 The student will

  • estimate and measure liquid volume using actual measuring devices and using metric and U.S. Customary units, including cups, pints, quarts, gallons, milliliters, and liters; and
  • estimate the conversion of quarts and liters, using approximate comparisons (1 quart is a little less than 1 liter, 1 liter is a little more than 1 quart)
The intent of this standard is for students to make "ballpark" comparisons and not to memorize conversion factors between U.S. and metric units.

4.14 The student will identify and describe situations representing the use of perimeter and will use measuring devices to find perimeter in both standard and nonstandard units of measure.

Geometry

4.15 The student will investigate and describe the relationships between and among points, lines, line segments, and rays.

4.16 The student will identify and draw representations of points, lines, line segments, rays, and angles, using a straightedge or ruler.

4.17 The student will identify lines which illustrate intersection, parallelism, and perpendicularity.

Probability and Statistics

Activity: Using a drawing program, such as ClarisWorks, instruct students to draw acute, obtuse and right angles or parallel, perpendicular and intersecting lines.

4.18 The student will determine the probability of a given simple event, using concrete materials.

4.19 The student will collect, organize, and display data in line and bar graphs with scale increments of one or greater than one.

Activity: Students will create a spreadsheet, using a program such as ClarisWorks, on the number of M&Ms for the colors -red, orange, green, brown, yellow, and blue in the small individual bags. Each child will open his/her bag and count the M&Ms for each color in his/her bag. Input the data on a spreadsheet. Instruct students to create several graphs charts on their data. (You could substitute favorite foods, Skittles or Fruit Loops, or other items for the M&Ms.)

Patterns, Functions, and Algebra

4.20 The student will identify and locate missing whole numbers on a given number line.

4.21 The student will extend a given pattern, using concrete materials and tables.

4.22 The student will solve problems involving pattern identification and completion of patterns.


Fifth Grade




Number and Number Sense


5.1 The student will read, write, and identify the place values of decimals through ten-thousandths.

5.2 The student will compare the value of two decimals through ten-thousandths using the symbols >, <, or =.

Computation and Estimation


5.3 The student will create and solve problems involving addition, subtraction, multiplication, and division of whole numbers, using paper and pencil, estimation, mental computation, and calculators.

Activity: Use the built-in calculator on the computer to create and solve problems using the four basic operations. With Windows, see Accessories. With Macintosh, see the Apple menu.

5.4 The student will find the product of two numbers expressed as decimals through thousandths, using an appropriate method of calculation, including paper and pencil, estimation, mental computation, and calculators.

5.5 The student, given a dividend of four digits or less and a divisor of two digits or less, will find the quotient and remainder.

5.6 The student, given a dividend expressed as a decimal through ten-thousandths and a single-digit divisor, will find the quotient.

5.7 The student will add and subtract with fractions and mixed numerals, with and without regrouping, and express answers in simplest form. Problems will include like and unlike denominators, limited to 12 or less.

Activity: Using a drawing program, such as Clarisworks, instruct students to draw shapes divided into different fractions. Example: Draw a rectangle. Divide the rectangle into halves. Paint 1/2 red and 1/2 green.

Measurement

5.8 The student will describe and determine the perimeter of a polygon and the area of a square, rectangle, and triangle, given the appropriate measures.

Activity: Using a drawing program with a ruler, such as Clarisworks, instruct students to draw shapes with specific dimensions. Students can then calculate the area or perimeter of the shapes. Example: Draw a square where each side is 2 inches. Paint the square blue. How much blue area is inside the square?

5.9 The student will identify and describe the diameter, radius, chord, and circumference of a circle.

5.10 The student will differentiate between area and perimeter and identify whether the application of the concept of perimeter or area is appropriate for a given situation.

Activity: Using a drawing program with a ruler, such as Clarisworks, instruct students to draw shapes with specific dimensions. Students can then calculate the area or perimeter of the shapes. Example: Draw a square where each side is 2 inches. Paint the square blue. How much blue area is inside the square?

5.11 The student will choose an appropriate measuring device and unit of measure to solve problems involving measurement of

  • length-part of an inch (1/2, 1/4, and 1/8), inches, feet, yards, miles, millimeters, centimeters, meters, and kilometers;
  • weight/mass-ounces, pounds, tons, grams, and kilograms;
  • liquid volume-cups, pints, quarts, gallons, milliliters, and liters;
  • area-square units; and
  • temperature-Celsius and Fahrenheit units. Problems also will include estimating the conversion of Celsius and Fahrenheit units relative to familiar situations (water freezes at 0°C and 32°F, water boils at 100°C and 212°F, normal body temperature is about 37°C and 98.6°F).

Activity: Using a drawing program with a ruler, such as Clarisworks, instruct students to draw shapes with specific dimensions. Students can then calculate the area or perimeter of the shapes. Example: Draw a square where each side is 2 inches. Paint the square blue. How much blue area is inside the square?


5.12 The student will determine an amount of elapsed time in hours and minutes within a 24-hour period.

Geometry

5.13 The student will classify angles and triangles as right, acute, or obtuse.

Activity: Using a drawing program, such as ClarisWorks, instruct students to draw acute, obtuse and right angles or parallel, perpendicular and intersecting lines.

5.14 The student will measure and draw right, acute, and obtuse angles and triangles, using appropriate tools.

Activity: Using a drawing program, such as ClarisWorks, instruct students to draw acute, obtuse and right angles or parallel, perpendicular and intersecting lines.

5.15 The student will identify the ordered pair for a point and locate the point for an ordered pair in the first quadrant of a coordinate plane.

Probability and Statistics

5.16 The student will

  • solve problems involving the probability of a single event by using tree diagrams or by constructing a sample space representing all possible results; and
  • create a problem statement involving probability based on information from a given problem situation. Students will not be required to solve the problem created.

5.17 The student will collect, organize, and display a set of numerical data in a variety of forms, given a problem situation, using bar graphs, stem-and-leaf plots, and line graphs.

Activity: Students will create a spreasheet, using a program such as ClarisWorks, on the number of M&Ms for the colors -red, orange, green, brown, yellow, and blue in the small individual bags. Each child will open his/her bag and count the M&Ms for each color in his/her bag. Input the data on a spreadsheet. Instruct students to create several graphs charts on their data. (You could substitute favorite foods, Skittles or Fruit Loops, or other items for the M&Ms.)

5.18 The student will find the mean and mode of a set of data.

Patterns, Functions, and Algebra

5.19 The student will investigate, describe, and extend numerical and geometric patterns, including triangular numbers, perfect squares, patterns formed by powers of 10, and arithmetic sequences. Concrete materials and calculators will be used.

5.20 The student will

  • investigate and describe the concept of variable;
  • use a variable to represent a given verbal quantitative expression, involving one operation; and
  • write an open sentence, using a variable to represent a
  • given mathematical relationship.

5.21 The student will create a problem situation based on a given open sentence using a single variable.


Web and Software Resources

Web Sites

Ask Dr. Math

Math Forum

Math Forum Links

Math Plans, Games and Links

MathMagic on the Web

Kathy Schronk's Guide for Educators

Software Resources

Math Blaster - In Search of Spot (Grade 1-6) Davidson, $59.95 (school version) Teaches basic mental math and problem-solving skills.

The Graph Club (Grade K-4) Tom Synder Prod., $99.95 (one copy) Emphasizes graphing (units, fractions and percentages).

Math Workshop (Grade 3 - adult) The Learning Co., $79.95 (school version) Shows students how to use spreadsheets in everyday life.

Cruncher (Grade 3 - adult)The Learning Co., $45.95 (school version) Uses fast-paced game format to review whole-number operations and solve word problems.

SuperSolvers OutNumbered! The Learning Co., $45.95 (school version) Uses fast-paced game format to review whole-number operations and solve word problems.

Main Page

Send all additional ideas, resources, or notices of dead links to C. Shields