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Math Unit Plan
David Riddick
Stage Three
Appendix 13.31
Unit
Planning Outline
1. Title of the Unit
“The People of California”
2. Unit
Overview
A. Topic of the unit
Population
B. Broad Learning Goals Of The Unit That Promote The
Identified State Content Standards
Students will have an understanding of the diverse population of California through the study of place value in mathematics, and the integration of language, arts, science, social studies, physical education, art and technology. Students will gain a broader understanding of their own diverse population and compare it with other groups.
Students will acquire an awareness of the diverse groups of people who live in the four geographic regions of California. These regions include coastal, mountains, central valley and desert.
Students will develop skills to interpret data by comparing past and present populations of California, diverse groups that make up California, immigration and migration of the population.
Students will have an awareness of how to compare
and order population numbers by understanding place value through the millions.
C. Concepts To Be Understood Through The Unit
Students will learn through the use of population to classify diverse groups of Californians through the study of place value.
Students will answer the question, “Who are Californians?” They will investigate and write about the population and people who make up the four geographic regions of California.
Throughout the unit, students will respond to the following:
- What makes one a Californian?
- How are Californians alike?
- How are Californians different?
- Why are the most popular regions so popular?
- Why has California’s population changed over time?
D. Standards
Number Sense
1.0.
Students understand the place value of whole numbers
and decimals to two decimal places and how whole numbers and decimals relate to
simple fractions. Students use the concepts of negative numbers:
1.1 Read and write whole numbers in the millions.
1.2 Order and compare whole numbers and decimals to two decimal places.
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 appropriate.
Mathematical Reasoning
1.0 Students make decisions about how to approach problems:
1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.
2.0 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 reasoning.
2.4 Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.
3.2 Note the method of deriving the solution and
demonstrate a conceptual understanding of the derivation by solving similar
problems.
E. Timeline For The Unit
Duration of unit is approximately two weeks with a
minimum of six lessons.
At least 1 hour a day, students read, listen, talk, and interpret place value using the population of California as their theme.
F. List Of References Used To Plan The Unit
About
Teaching Mathematics by Marilyn
Burns
Elementary
and Middle School Mathematics by
John Van De Walle
California
Mathematics Textbook by Scott
Foresman
My
Backyard History by David Weitzman
Websites
The Place Value Game: http://education.jlab.org/placevalue/gamepage.html Online Place Game offering an interactive way for students to learn about place value.
US Census Bureau: http://www.census.gov/ American Population Numbers
California Census: Diverse Population of
California
California Census: http://www.dof.ca.gov/HTML/DEMOGRAP/SCDC_Products.HTM California Population Numbers
California Census: Immigration Population: http://www.dof.ca.gov/HTML/DEMOGRAP/repndat.htm#immigration
Southern California Association of Governments: http://www.scag.ca.gov/census/ Southern California population numbers.
RAND California: http://ca.rand.org/stats/popdemo/popdemo.html Population and Demographic Statistics.
3. Instruction
A. Students
4th Grade
27 Students. 14 boys and 13 girls. 4 EO's; 6 IFEP's; 3 RFEP's; 14 ELD3-4: GATE class - advanced learners
B. Learning
Style Considerations
· Social atmosphere; encourage students to listen to each other.
· Connect this unit to the life of the learner.
· Use concrete activities
· Integrate reading, language, technology, cooperative learning
C.
Modifications
· Instruction must connect and become integrated with students’ prior experiences.
· Factor in gender considerations, integrate and use groups flexibly
· Focus and support inquires while interacting with students
· Challenge students to accept and share responsibility for their own learning
D. Learning Objectives
Cognitive: Students will make inferences about population to classify and interpret data on the diverse groups of California through the study of place value through the millions. Students will learn skills to interpret and connect patterns of California’s population. Students will learn the place value of California’s counties through the millions.
Objective: Students will make connections and analyze population data. Students will play a place value game to create the most populated county in California. Students will color code California counties on a map to compare and organize the population of California. Counties will be estimated and rounded to the nearest hundred thousand. Using information from the Internet and other sources, students will complete a written assignment interpreting why the most populated counties are so popular.
Criteria: Students will learn through the use of population to examine and interpret the various groups of California from the past and present. Students will examine and identify population patterns through journal assignments, standardized tests with at least 75% accuracy, and the completion of a writing assignment explaining why certain counties are heavily populated.
A criterion rubric will be utilized to assess proficiency of writing assignment.
Lesson 1
– California Counties
Introduce California population by comparing California’s population to the other states of America.
Students will compare Los Angeles County’s population with the populations of other counties in California. Students will be given a black and white map of California and a color code chart. Students will color counties blue, red, orange, and yellow based on their populations.
Students will work in cooperative groups and pick the names of 10 counties. Students will present their states to the class by coloring them on an overhead transparency. Students will listen to one another and color code all of the counties on the California map.
High achieving students will use excel to graph
population trends and depict populations in percentages.
Lesson 2
– Place Value Through the Millions
Students will learn to read and write numbers through the millions using the population of California counties. Students will learn the most heavily populated counties are in Southern California.
Students will understand how the millions period and thousands period of a place value are alike and how they are different. Students will learn how to read and write the populations in expanded form, standard form, and word form.
Given a list of county populations, students will identify which numbers are in the millions period, thousands period, and ones period.
Lesson 3
– The Place Value Game
Students will learn place value through the millions by playing a dice game trying to create the largest fictional county in California. Teacher models how to role the dice on the overhead and place the number rolled in the most appropriate column. Columns include hundred millions on the left to ones on the far right. Students will use the website Jefferson Lab http://education.jlab.org/placevalue/index.html to play a similar place value game online.
Extension: Where would the most populated county you created be located? Why?
Students may also create the smallest county in California. Where would the least populated county be located? Why?
High achieving students will expand the lesson and write a summary of the climate, resources, diversity, and industry of their fictional county.
Lesson 4
– Compare and Order Numbers
Students will compare and order the California counties through the millions. Students will utilize a list of 10 California counties and list them in order from most populated to least populated. Students will use the Internet and handouts to locate populations of counties.
Students may use their color-coded maps of the California counties as a reference.
High Achieving students will plot a specific ethnic group’s population over a period of time and develop hypothesis/correlations to region selection. Students may do a mock interview as a class presentation or video.
Lesson 5
– Round Diverse Population Numbers of California
Student will learn to round numbers of a variety of diverse groups in California to the nearest ten, hundred, thousand, ten thousand, hundred thousand, or million. Students will determine the place value of a population number.
Students will use the rounded numbers to list the ethnic groups of California from the least to greatest. Students will address the following questions:
When is it important to round numbers to the millions?
When is it important to round
numbers to the thousands?
Lesson 6
– Find a Pattern of Immigration to California.
Students will use the Internet to find a pattern interpreting immigration of population to California from 1970 to 2000. Students will write a summary to interpret immigrant populations to address the following questions:
What patterns have you noticed about immigration population?
How have immigration patterns changed?
What regions have shown the greatest shift in population?
What do you think will happen to the immigration patterns over the next twenty years?
High achieving students will use excel to graph immigration trends and depict populations in percentages.
4. Assessment
Plan
Students will determine the relevance of customs and traditions among their own heritage and relate to others while studying a variety of literature genre. Students will be assessed by means of:
- Student observations
- Student interviews
- Portfolios
- Projects and laboratory experiences
- Creative assessments
- Short-answer tests
- Journals
5. Personal
reflection of the unit.
This
math unit, “California Population,” exemplified the complex nature of
mathematics instruction by linking the goals, concepts, and objectives with the
California Mathematics Content Standards.
The unit allowed me to integrate the concept of population across the
curriculum from math though the use of literature, technology, and Gardner’s
Multiple Intelligence Theory. Stuqdents
were able to visually make a connection to the value of a number and compare
them with other numbers.
Having
a theme has greatly enhanced student understanding of place value. Students were able to make a connection to
the place value of numbers to the millions with a tangible understanding of
population. Students were very
successful in distinguishing the large counties from the smaller ones. As an extension activity, students made
posters to explain if they would like to live in a heavily populated county or
a lightly populated county. Likewise, students made posters to explore whether
a heavily populated county is more beneficial than a lightly populated county.
Several
students made an extension to the lesson by memorizing a few of the California
county populations. Students did this
on their own to understand how to read and write population numbers. High achieving students worked with low
achieving students to better understand the concept of place value. I’ve tried to create a culture where
students feel comfortable asking one another for help. Students also made posters to explain how to
read and write their answers.
I
correctly anticipated the students would be engaged by the use of manipulatives
to study place value. I modeled how to
roll the dice with “overhead dice” on the overhead during the Place Value
Game. I rolled the times a few times to
explain the strategy of the game. I
talked out my strategies for the class to understand what I was thinking as I
placed my rolled numbers in the appropriate columns. Students were highly engaged in the lesson and on task. It was exciting to hear them say, “I win”
and to see they correctly understood the concept of place value. If I were to teach this lesson again, I would’ve
liked to incorporate students reading of the numbers correctly to one another. I could have made a box to check yes or no
to allow students the opportunity to quiz one another if they were reading the
words correctly.
Students
appeared to easily grasp how to read and write numbers to the millions. However, rounding proved to be a more
cumbersome challenge for my students. I
extended the “Rounding” lesson longer to accommodate my students’ needs. I did an initial assessment prior to the
lesson to check their understanding.
After assessing student understanding, I grouped high achieving students
with students who were struggling. This
was a successful grouping strategy.
Students were able to explain why numbers are rounded and offer
techniques to explain how.
Enabling the students to color code immigrant populations made excellent use of materials, resources and technology to make the study of place value accessible to all students. Students were independently making connections and identifying patterns as they worked in cooperative groups. I correctly anticipated students would connect to the anticipatory set of the lessons. I continue to be amazed at how powerful the anticipatory set can be. I’m convinced powerful lessons derive from an engaging anticipatory set.