BY: BART J. CARLSON
Introduction:
Objectives: The student will read and write whole numbers to hundred millions, know place value to hundred millions and will round off each group of numbers to a variety of units including: units , thousands, and millions. The student will also demonstrate the ability to use the Internet to locate data as needed.
Prior Knowledge: The student should have some prior understanding of place value, the charts for place value, rounding off, knowledge of standard and expanded notations, use of the Internet, numbers and what a census is.
Grade Level : 4-6
Resources :
1. Start with data collection of the classroom and the classrooms of the school. Teacher aided gathering of data.
2. Record the information on Worksheet #2 (HTML) (PDF)
3. Cut out digits - worksheet #1 (HTML) (PDF) - and begin with place value lessons for the population of the classroom, grade levels and total school population. Include a lesson on expanded and standard notation with collected data.
4. Students give data to a general discussion within the classroom and check with each other. The teacher then gives the correct place value for each section and expanded and standard notations.
5. Using the same data, students round off each of the classroom data to the nearest tens' place value. The school total can be rounded to nearest ten and hundreds. Use worksheet #2 (HTML) (PDF)
6. Quick check of place value, rounding off, and expanded and standard notation worksheet .(Teacher made assessment sheet.)
LESSON FOLLOW UP:
1. Start by collecting data of the population of cities, states, and countries on worksheet #3 (HTML) (PDF) following the table format. Go to US.gov.census.(Interlinked under resources)
2. Record information on worksheet #3 (HTML) (PDF)
3. Use the cut out digits - worksheet #1 (HTML) (PDF) - and have students read out loud their individual number by cities, states and countries. Playing cards can also be used for this activity.(Face cards are 0)
4. Using the individual digit squares from worksheet #1 (HTML) (PDF), or playing cards, have the students round off each category to the nearest ten, hundreds, thousands, ten thousands, hundred thousands, and millions.
5. Place value: students read out their individual data numerals by cities, states, and countries. Use the individual digit squares to figure out place value of the numerals read by the students. Students should check with each other and then the teacher should model the correct answer on the board or overhead. The teacher can also include a short lesson on standard and expanded notation using the collected data.
6. Rounding off: students use each of the figures from the cities, states and countries and place on worksheet # 3 (HTML) (PDF).
7. Teacher uses some of the population data given by students and passes out worksheet #4 (HTML) (PDF) and passes this out to students. Teacher will read out the data for each category and students will fill in the table. This can be used as a quick check and later reused for assessment of place value.
Evaluation
Learning Advice:
Extensions
B. Travel Distances between cities
D. Pages in a variety of literature or text books
Conclusion:
This lesson was designed so that the children will have pre-practice with place value and rounding off. It is also designed so that the children will learn how to use the Internet as a data retrieval source. The later practice and assessment will enable the teacher to assess the learning. The extension lessons are suggested to meet the individual needs of the student population in different areas. It is highly suggested that the teacher go through the lesson on the computer first so that the teacher can guide the students through the process of extrapolating data from the Internet.
California Academic Content Standards
Grade 4:
Number Sense
1.0 Students understand place value of whole numbers and decimals to two decimal places, how these relate to simple fractions, and use concepts of negative numbers.1.1 read and write whole numbers in the millions
1.3 round whole numbers through the millions to the nearest ten, hundred, thousand, ten thousand, or hundred thousand
1.4 decide when a rounded solution is called for and explain why such a solution may be appropriateMathematical Reasoning
1.0 Students make decisions about how to approach problems.1.1 analyze problems by identifying relationships, discriminating relevant from irrelevant information, sequencing and prioritizing information, and observing patterns2.0 Students use strategies, skills, and concepts in finding solutions.
2.2 apply strategies and results from simpler problems to more complex problems3.0 Students move beyond a particular problem by generalizing to other situations.
3.2 note method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problemsGrade 5:
Number Sense
1.0 Students compute with very large and very small numbers, positive integers, decimals, and fractions and understand the relationship between decimals, fractions, and percents. They understand the relative magnitudes of numbers.1.1 estimate, round, and manipulate very large (e.g., millions) and very small (e.g., thousandths) numbersAlgebra and Functions
1.0 Students use variables in simple expressions, compute the value of the expression for specific values of the variable, and plot and interpret the results.1.1 use information taken from a graph or equation to answer questions about a problem situationStatistics,Data Analysis and Probability
1.0 Students display, analyze, compare, and interpret different data sets, including data sets of different sizes.1.2 organize and display single-variable data in appropriate graphs and representations (e.g., histogram, circle graphs) and explain which types of graphs are appropriate for various data sets
1.3 use fractions and percentages to compare data sets of different sizeMathematical Reasoning
1.0 Students make decisions about how to approach problems.1.1 analyze problems by identifying relationships, discriminating relevant from irrelevant information, sequencing and prioritizing information, and observing patterns2.0 Students use strategies, skills and concepts in finding solutions.
2.3 use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoningGrade 6:
Statistics, Data Analysis and Probability
2.0 Students use data samples of a population and describe the characteristics and limitations of the samples.2.1 compare different samples of a population with the data from the entire population and identify a situation in which it makes sense to use a sample
NCTM K-4:
STANDARD 1: MATHEMATICS AS PROBLEM SOLVING
STANDARD 3: MATHEMATICS AS REASONING
STANDARD 4: MATHEMATICAL CONNECTIONS
STANDARD 12: FRACTIONS AND DECIMALS
NCTM 5-8:
STANDARD 1: MATHEMATICS AS PROBLEM SOLVING
STANDARD 3: MATHEMATICS AS REASONING
STANDARD 4: MATHEMATICAL CONNECTIONS
STANDARD 7: COMPUTATION AND ESTIMATION
STANDARD 8: PATTERNS AND FUNCTIONS
STANDARD 9: ALGEBRA
STANDARD 10: STATISTICS
Copyright © Kings County Office of Education
June 1998
Revised June 15, 2000
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