Fourth Grade Mathematics Curriculum Oultine (updated fall 2006)

National Council Teachers of Mathematics Standard

Nebraksa Standards Competency or Indicator

Teacher created concept, objective, outcome, competency

Curriculum investigations, units, chapters, modules...

Activities

Evaluation Levels

Numeration/Number Sense

4.1 Numeration/Number Sense

       
  4.1.1 demonstrate place value of whole numbers through the millions and decimals to the hundredth place.

       
  Read and write numerals (in digits and words) through the millions place and decimals to the hundredth place.

4.1Recognize the tenths and hundredths place of decimals

  With a partner, verbally identify the place & value of an underlined digit in a number.

Generate random numbers, write them on the board and read them.

 
  Order and compare whole numbers through the millions place and decimals to the hundredth place using the symbols <, >, and =.

Round whole numbers to the nearest named place, such as rounding 1,234 to the nearest hundred would be 1,200.

     
.

4.1.2 write and illustrate equivalencies of whole numbers in expanded form, decimals, and fractions

       
  Whole numbers in expanded form

Write numbers in expanded form, such as 432 = 400 + 30 + 2.

Combine and decompose numbers to create equivalent forms.

Say, read, and write numbers in expanded notation

  Match number cards with expanded notation cards (Concentration or Old Maid).

 
  Fractional numbers in expanded form

Represent equivalent fractions with denominators of 2, 4, 5, 8 and 10 (1/2 = 2/4) using concrete objects.

Create fractional parts of a whole

Create fractional parts of a group

Find equivalent fractions

Different Shapes, Equal Pieces Assessment Master 27


1. Understands that equal fractions of a whole have the same area but are not necessarily congruent (Different Shapes, Equal Pieces)


2. Reorganizes parts to make equivalent wholes (mentally or by cutting and pasting) (Different Shapes, Equal Pieces)


3. Understands the relationships among halves, fourths, and eighths (Different Shapes, Equal Pieces)


4. Understands the relationships among thirds, sixths, and twelfths (Different Shapes, Equal Pieces)


5 . Identifies equivalent fractions (1/2 = 2/4) (Different Shapes, Equal Pieces)


6. Understands that equal fractions of different-sized wholes are different in area (eg. ½ of a small pizza is not the same size as ½ of a large pizza) (Different Shapes, Equal Pieces)


7. Combines different fractions to make a whole (Different Shapes, Equal Pieces)


8. Understand and uses fractions that have numerators larger than 1 (Different Shapes, Equal Pieces)

   
.

Compare fractions using <, >, and = for like and unlike denominators

  9. Compares any fraction to the landmarks 0, ½, 1, 2 (Different Shapes, Equal Pieces)


10. Orders fractions using both numerical reasoning and the area model (Different Shapes, Equal Pieces)


11. Understands how to use the sizes of the numerators to compare fractions having the same denominator and can also use the denominators to compare fractions having the same numerator (Different Shapes, Equal Pieces)


12. Understands that fractions that are missing one piece are ordered inversely to the sizes of the missing pieces (Different Shapes, Equal Pieces)

  .

  Decimal numbers in expanded form

       
  Write equivalent decimals (.4 = .40).

       
  Write decimals as fractions using denominators of 10 and 100 (.68 = 68/100).

Compare decimals to fractions

     
  4.1.3 will describe and apply relationships between whole numbers, decimals, and fractions by order, comparison, and operation.

      .

  Illustrate mathematical concepts by using objects and drawing pictures or diagrams (subtraction as the opposite of addition and multiplication as repeated addition).

       
  Order and compare whole numbers, common fractions, and decimals using the symbols <, >, and =.

Recognize counting patterns

Identify inequalities <,> and =

Round numbers to 10,000

  On a hundred chart color multiples of 3 red, and multiples of 4 blue.

Repeat with a new grid for 2 multiples, 5 and 6.

Repeat with a 99 chart for multiples

Fill in the missing numbers on a number grid starting with a number above 10,000.

 
  Use input/output or function box to identify and extend patterns.

 

Name that Portion
Assessment Master 5
1. Identifies everyday situations that involve fractions, decimals, and percents. 1, 2, 16 (Name that Portion)
2. Use fractions to describe portions of groups. 3, 4 (Name that Portion)
3. Use percents to describe portions of groups. 3 (Name that Portion)
4. Understand percent as "out of 100" 5, 6, 28 (Name that Portion)
5. Understands decimals as part of the base ten system. 19 (Name that Portion)
6. Uses decimals to describe portions of groups. 19 (Name that Portion)
7. Breaks fractions, decimals, and percents into familiar parts 11, 17 (Name that Portion)
8. Approximates data as familiar fractions, as percents, and in circle graphs 7, 11, 12, 27, 30 (Name that Portion)
9. Identifies and uses equivalent fractions, decimals, and percents. 3, 5, 14, 15, 16, 1`, 11, 17, 30 (Name that Portion)
10. Compares and orders fractions. 1, 8, 14, 20, 24, 25 (Name that Portion)
11. Chooses appropriate models and notations to compute with fractions, decimals, and percents. 18, 21, 22, 23 (Name that Portion)
12. Identifies, orders, and labels fractions between 0 and 1 on a number line. 8, 10, 13, 15 (Name that Portion)
13. Solves word problems involving fractions, decimals, and percents express answers appropriately. 9, 17, 23 (Name that Portion)
14. Finds decimals that are smaller than, larger than, or in between other decimals. 20 (Name that Portion)
15. Plans and conducts surveys and presents the resulting data using fractions, decimals, and percents. 26, 29, 30 (Name that Portion)
16. Communications mathematical thinking through written language and spoken language. 10, 18, 24, 25, 28, 29, 30 (Name that Portion)

   
     

Thinking Assessment Master 5 at Grade 4
1. Groups things for more efficient counting (Thinking)
2. Reorders numbers for more efficient adding (Thinking)
3. Finds how many more are needed in a comparison problem (Thinking)
4. Estimates how many hundreds are in a group of 3-digit numbers (for example, 235, 365,550, and 1100) (Thinking)
5. Rec. ognizes the values of US coins and groups of coins for more efficient counting (Thinking)
6. Counts money accurately using US coins (Thinking)
7. Recognizes the decimal point on the calculator; uses dollars and cents on the calculator (Thinking)
8. Uses known answers to find others (Thinking)
9. Subtracts using a variety of strategies, including mentally, by taking away 100s, by using a 300 chart, and by using a calculator (Thinking)
10. Adds and subtracts multiples of 10 (Thinking)
11. Distinguishes between geometric patterns and random designs (Thinking)
12. Distinguishes between mirror and rotational symmetry (Thinking)
13. Collects, represents, and interprets data (Thinking)
14. Estimates totals and differences of 2- and 3- digit numbers (Thinking)

   
  Use input/output or function box to identify and extend patterns.

       
  Solve and check a mathematical problem by using the related facts.

       
  4.1.4 identify examples of positive and negative numbers and zero.

       
  Demonstrate simple concepts of positive and negative numbers (a thermometer for temperature or distances to the right or left of zero on a number line).

Identify examples in life where positive and negative numbers are used.

Record steps toward solutions and solutions to problems with pictures, chart, graphs, models, in writing, orally, and with symbols.

  Make a human number line by drawing a positive or negative number card and lineup in order according to the number on the card. Trade cards and repeat.

 
  4.1.5 make change and count out in amounts up to $20.00.

Identify all coins and paper money up to $100

     
  Count back change from purchase price to amount given using fewest coins possible

       
  Calculate change through subtraction and choose correct bills and coins to make this amount.

Describe how to make change from any combination of money up to $100

     
  4.2 Computation/Estimation

       
  4.2.1 estimate, add, subtract, multiply, and divide whole numbers without and with calculators and solve word problems.

       
  Demonstrate with accuracy and reasonable speed the basic facts of addition (1-20), subtraction (1-20), multiplication (1-144), and division (1-44).

  1. Finds and counts by factors of 100 (Landmarks in the Thousands)


2. Recognizes factor pairs in 100 and uses this information to find factors of multiples of 100 (Landmarks in the Thousands)


3. Uses landmarks to find the differences between numbers up to 100 (for example: the difference between 48 and 100 is 52 because 48 is 2 away from 50, and then 50 more is 100) (Landmarks in the Thousands)


4. Uses knowledge of the factors of 100 to explore multiples of 100 (ex. There are four 25s in 100, so there are eight 25s in 200) (Landmarks in the Thousands)


5. Relates knowledge of factors to division situations and to standard division notation (ex. 100/25=4 because 4x25=100) (Landmarks in the Thousands)


6. Adds and subtracts multiples of 10 to or from a number in the hundreds, and later, adds and subtracts multiples of 100 to or from numbers in the thousands (ex. 346+40) (Landmarks in the Thousands)


7. Solves addition and subtraction problems by reasoning from known relationships (Landmarks in the Thousands)


8. Reads, writes, and locates in sequence numbers up to 10,000 (Landmarks in the Thousands)


9. Identifies and uses important landmarks up to 1000 (25, 50, 75, 100, 125, 150) (Landmarks in the Thousands)


10. Uses strategies for adding and subtracting numbers in the hundreds (Landmarks in the Thousands)


11. Makes some sense of the magnitude of numbers up to 10,000 and understands how numbers this large are structured from thousands, hundreds, and so on (Landmarks in the Thousands)

   
  Add and subtract accurately five-digit numbers including columns of numbers.

Add and subtract 5 digit numerals with/without regrouping

     
  Multiply up to a three-digit number by a two-digit number.

       
  Divide up to a three-digit number by a one-digit divisor.

       
  Choose correct operation and solve word problems.

       
      1. Uses skip counting as a model for multiplication (Arrays and Shares)


2. Sees multiplication as an accumulation of groups of a number (Arrays and Shares)


3. Recognizes the multiplication patterns of numbers, including number patterns on the 100 chart (Arrays and Shares)


4. Uses known multiplication relationships to solve harder number relationships (ex. 4x5=20, 40x5=200) (Arrays and Shares)


5. Uses and explains an array to model multiplication (Arrays and Shares)


6. Recognizes a prime number as a number with only one pair of factors and one array (Arrays and Shares)


7. Understands division notation and a variety of division situations (ex. Sharing and partitioning) (Arrays and Shares)


8. Determines what to do with leftovers, depending on the problem (Arrays and Shares)


9. Partitions numbers to solve them more easily (ex. 7x23=(7x10) + (7x10) + (7x3); 46x5= (40x5) + (6x5)) (Arrays and Shares)


10. Recognizes patterns that are useful for multiplying by multiples of 10 (ex. 2x7=14, 2x70=140, 20x7=140) (Arrays and Shares)


11. Demonstrates fluency of multiplication pairs through 12x12 (ex. Either automatically knows the pairs or has one quick strategy for finding the answer). (Arrays and Shares)


12. Recognizes and accurately uses the terms multiple, factor, and prime number (Arrays and Shares)

   
  4.2.2 estimate, add, and subtract decimals without and with calculators and solve word problems.

      .

  Add and subtract decimals to the hundredth place.

Add and subtract decimals

    .

  4.2.3 estimate, add, and subtract fractions with like denominators without calculators and solve word problems.

       
  Solve problems involving fractions of halves, fourths, and eighths using the operations of addition and subtraction.

Add and subtract fractions with like and unlike denominators

     
Measurement

Measurement 4.3

       
  4.3.1 estimate, measure, and solve word problems using metric units for linear measure, area, mass/weight, capacity, and temperature.

       
  Use the appropriate units of measurement.

       
  Estimate and accurately measure length to the nearest meter or centimeter and calculate area.

Cm and m.

     
  Estimate and accurately measure mass/weight to the nearest gram.

       
  Estimate and accurately measure capacity to the nearest milliliter.

Measure liquid amounts up to a gallon and liter

  You are asked to create a container that makes people think there is more in the container than there actually is. First collect a variety of containers that you think would cause this to happen and ones that would not (at least ten), put them in order according to their volume by sight, record the data, measure their volume, put them in order according to their actual volume, what shape of containers make people think there is more than there actually is?

 
  Measure and read temperature accurately to the nearest degree using Celsius thermometer

       
      Money, Miles, and Large Numbers Assessment Master 35


1. Estimates sums, including total amounts of money (Money, Miles, and Large Numbers)


2. Has developed a strategy for comparing and combining numbers up to 10,000 (Money, Miles, and Large Numbers)


3. Uses landmark numbers (multiples of 10,100, .10, and 1.00) to compare and find the difference between two quantities (Money, Miles, and Large Numbers)


4. Uses standard addition and subtraction notation to record combining and comparing situations (Money, Miles, and Large Numbers)


5. Uses the calculator to solve problems and can interpret decimals on the calculator as amounts of money (Money, Miles, and Large Numbers)


6. Estimates familiar distances in miles and tenths of miles; develops a sense of about how long a mile and .1 mile are (Money, Miles, and Large Numbers)


7. Compares and combines decimal numbers and, later, quantities having decimal portions (Money, Miles, and Large Numbers)


8. Sees the relationships of decimal parts to the whole (Money, Miles, and Large Numbers)


9. Measures distances on maps using scales (Money, Miles, and Large Numbers)


10. Is familiar with common decimal and fraction equivalents (Money, Miles, and Large Numbers)

   
  4.3.2 estimate, measure, and solve word problems using standard units for linear measure, area, mass/weight, capacity, and temperature.

    Measure the classroom and draw a scale map.Measure and map the school playground.

 
  Use the appropriate units of measurement.

       
  Estimate and accurately measure length to the nearest yard, foot, inch, and quarter inch and calculate area.

       
  Estimate and accurately measure mass/weight to the nearest ounce and pound.

Convert ounces to pounds

  Using food package labels put them in order from lightest to heaviest. Measure sand or water in 4, 8, 12, and 16 ounces. Blind fold a partner and have them feel the containers (no shaking just lifting) and put them in order. How good are people at telling the difference in weight by feel?

 
  Estimate and accurately measure capacity to the nearest fluid ounce.

Measure liquid amounts up to a gallon

Convert liquid amounts to gallons.

     
  Measure and read temperature accurately to the nearest degree using Fahrenheit thermometer.

       
  4.3.3 tell and write correct time to the minute using an analog clock.

       
  Set an analog clock to a given time.

       
  State time in different ways (8:35, 35 minutes after 8:00 or 25 minutes until 9:00).

       
  Identify time of day (AM, PM, noon, and midnight).

Tell the correct time to the minute

Solve problems with time

Identify time zones in the world and the international date line.

Identify the time zones in the United States

Calculate time in two different zones

  Create and solve time problems using a television guide.

Use a globe and find the number of time zones in the world.

Calculate the difference from the studentÕs time zone to other zones in the USA
.

  Money

Identify all coins and paper money up to $100.00.

Describe how to make change from any combination of money up to $100.00

    .

Geometry

4.4 Geometry/Spatial

       
  4.4.1 identify, describe, and create two and three dimensional geometric shapes.

Shapes

Identify 3-D geometric shapes (sphere, cone, cube)Describe and create 2 and 3 dimension shapes

  Use 3-D shapes to make nets for each shape. Compare the properties of each net to 2-D shapes. Record the different shapes on a chart for all 3-D shapes and compare the shapes to the shapes names and type of 3-D shapes and see what patterns can be found.

 
     

Seeing Solids and Silhouettes Assessment Master 16
1. Is developing concepts and language needed to be able to think about and communicate about spatial relationships in 3-D environments Seeing Solids and Silhouettes
2. Understands standard drawings of 3-D cube configurations Seeing Solids and Silhouettes
3. Is developing the skill of translating 2-dimensional pictures into 3-dimensional structures Seeing Solids and Silhouettes
4. Is beginning to relate cube configurations and the spatial relationships in 3-D objects to volume Seeing Solids and Silhouettes
5. Has some understanding of how 3-D solids project shadows with 2-D shapes (eg. How a cone projects a triangular shadow Seeing Solids and Silhouettes
6. Has an understanding of geometric perspective Seeing Solids and Silhouettes
7. Can visualize objects from different perspectives and then iterate these views to form a mental picture of the whole object (eg. Can look at the top, side, and front views of a 2-D drawing and visualize what the whole object would look like in its 3-D form and then build the object) Seeing Solids and Silhouettes
8. Can interpret different types of instructions for building with cubes and evaluate the effectiveness of different forms of how to instructions Seeing Solids and Silhouettes
9. Can communicate effectively about 3-dimensional objects and is developing a vocabulary that allows effective communication about 3-D geometry Seeing Solids and Silhouettes

   
  4.4.2 identify and draw points, lines, line segments, rays, and angles.

Identify and draw points, lines, segments, rays, and angles.

Identify angles (obtuse, right, acute).

Identify parallel and perpendicular lines

  Define a point, line, ray, line segment, and angle and give examples.

List examples for each geometric term.

Construct 10 angles and classify them into at least three groups.

 
     

Sunken Ships and Grid Patterns Assessment Master 51
1. Uses positive and negative coordinates to name and locate points on grids (Sunken Ships and Grid Patterns)
2. Calculates distances on a grid based on paths along grid lines (Sunken Ships and Grid Patterns)
3. Explores numerical patterns that represent geometric situations (Sunken Ships and Grid Patterns)
4. Connects visual and numerical descriptions of distances on a grid (Sunken Ships and Grid Patterns)
5. Applies knowledge of coordinates to locate points on a computer screen (Sunken Ships and Grid Patterns)
6. Describes geometric figures such as rectangles and squares in several ways (Sunken Ships and Grid Patterns)
7. Understands how Geo-Logo commands and patterns of commands reflect the properties of geometric figures (Sunken Ships and Grid Patterns)
8. Creates and applies patterns and mental arithmetic strategies to solve Geo-Logo turtle geometry problems (Sunken Ships and Grid Patterns)
9. Uses mirror and rotational symmetry to place rectangles on a grid and to design complex patterns of rectangles (Sunken Ships and Grid Patterns)

   
  4.4.3 By the end of fourth grade, students will identify, analyze, and compare two-dimensional geometric figures using congruence, symmetry, similarity, and simple transformations.

Analyze, compare, and solve problems with congruence, symmetry, similarity and simple transformations.

    .

.

  Calculate perimeter of a shape in inches and centimeters

Calculate area of a shape in square feet and square yards

  You want to help a friend that is going to wall paper a room. The room is 12 foot x 10 foot and the walls are about seven and one-half feet tall. There is a door and one window. However, they can be discounted because when the pattern is matched the drop-off probably won't be of much use since they will be too small for the height of the room after the pattern is matched. Your friend also wants to put a border around the ceiling. How much will s/he need. The border comes in inches or centimeters.

 
Data Analysis

4.5 Data Analysis, Probability, and Statistical Concepts

       
  4.5.1 collect, organize, record, and interpret data and describe the findings.

       
  Collect, organize, and interpret data in line plots, tables, charts, and graphs (pie graphs, bar graphs, and pictographs).

       
  Draw valid conclusions from displayed data.

       
     

The Shape of the Data Assessment Master 31
1. Makes quick sketches, including a line plot, of use as working tools during analysis (The Shape of the Data)
2. Describes the overall shape of the data, including clumps and gaps, range, and outliers (The Shape of the Data)
3. Summarizes what is typical of the data (The Shape of the Data)
4. Compares two sets of data using the shape of each set and what's typical in that set (The Shape of the Data)
5. Finds the median in a set of data arranged in numerical order (The Shape of the Data)
6. Finds the median in a set of data grouped by frequency (The Shape of the Data)
7. Uses the medians to compare two sets of data (The Shape of the Data)
8. Understands that he median is only one landmark in the data (The Shape of the Data)
9. Carries out all phases of a data-analysis investigation (Emphases 10-16 below) (The Shape of the Data)
10. Chooses and refines a research question (The Shape of the Data)
11. Defines the way data will be collected (The Shape of the Data)
12. Records collected data accurately (The Shape of the Data)
13. Organizes collected data (The Shape of the Data)
14. Writes a description of data collected (The Shape of the Data)
15. Writes an interpretation of the findings from data collected (The Shape of the Data)
16. Revises sketches to make a presentation graph or chart (The Shape of the Data)

   
     

Changes Over Time Assessment Master 42
1. Decides how to group data (Changes Over Time)
2. Invents representations of data (Changes Over Time)
3. Interprets different kinds of graphs (Changes Over Time)
4. Develops a scale that includes all the data (Changes Over Time)
5. Establishes conventions for consistency (Changes Over Time)
6. Understands how changes and the total are related (Changes Over Time)
7. Develops strategies for solving missing-information problems (Changes Over Time)
8. Writes missing-information problems (Changes Over Time)
9. Makes and interprets representations that show change (Changes Over Time)
10. Distinguishes between representations of something that can change and representations that show change (Changes Over Time)
11. Uses curves to communicate information (Changes Over Time)
12. Understands the difference between continuous and discrete changes (Changes Over Time)
13. Makes, interprets, and compares line graphs (Changes Over Time)
14. Integrates quantitative, qualitative, and graphical descriptions of the same data (Changes Over Time)
15. Makes and interprets different graphical shapes (Changes Over Time)

   
  Investigate and record patterns in a simple probability situation in an organized way.

       
     

Three out of Four Like Spaghetti Assessment Master 55
1. Partitions a group according to a rule (Three out of Four Like Spaghetti)
2. Finds familiar fractions of a group (Three out of Four Like Spaghetti)
3. Collects, records, and analyzes categorical data (Three out of Four Like Spaghetti)
4. Describes data in terms of fractions (Three out of Four Like Spaghetti)
5. Uses fractions to compare data from two groups, including groups of different sizes (Three out of Four Like Spaghetti)
6. Recognizes that fractions are always fractions of a particular whole (Three out of Four Like Spaghetti)
7. Estimates complex fractions using familiar fractions (ex. 12/25 is about ½) (Three out of Four Like Spaghetti)
8. Organizes data into categories and refines categories to accommodate additional data (Three out of Four Like Spaghetti)
9. Makes judgments about sets of categories (Three out of Four Like Spaghetti)
10. Represents categorical data, including use of bar graphs, and describes the data (Three out of Four Like Spaghetti)

   
Algebra

4.6 Algebraic Concepts

       
  4.6.1 use and interpret variables and mathematical symbols to write and solve one-step equations.

       
  Use letters, boxes, or other symbols to stand for any number, measured quantity, or object in simple situations to demonstrate the beginning concept of a variable and writing formulas.

       
  Identify and use various indicators of multiplication (parentheses, x, *) and division (/, ).

       
  4.6.2 identify, describe, and extend arithmetic patterns, using concrete materials and tables.

       
  Use input/output or function box to identify and extend patterns.

       
    Identify and create patterns (arithmetic progressions {created by adding a constant to each proceeding term: 1, 3, 5, 7, 9; or 0, 5, 10, 15,} or geometric progressions {created by multiplying each proceeding term by a constant:1, 2, 4, 8, 16,; or 1, 3, 9, 27,}) and describe them mathematically.

Packages and Groups Assessment Master 47
1. Identifies and uses patterns of multiples (Packages and Groups)
2. Skip counts by multiples of larger numbers (Packages and Groups)
3. Identifies factors of larger numbers, including 3-digit numbers (Packages and Groups)
4. Uses familiar landmark numbers to solve problems (Packages and Groups)
5. Partitions large numbers to multiply them more easily (Packages and Groups)
6. Solves double-digit multiplication problems (Packages and Groups)
7. Understands how division notation can represent a variety of division situations, including sharing and partitioning (Packages and Groups)
8. Creates a story problem that is representative of a division problem (Packages and Groups)
9. Uses multiplication and division relationships to solve problems (Packages and Groups)
10. Demonstrates fluency of multiplication pairs through 12 x 12 (Packages and Groups)
11. Divides a 3-digit number by a 2 digit number (Packages and Groups)

   

Dr. Robert Sweetland's Notes ©