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4th Grade Unit 1: / Mathematical Thinking—Place Value and Problem Solving / Suggested Time Frame: / 24 days
TAKS Objectives: / 1, 2, 3, 4, 6 / TEKS: / 4.1A, 4.1B, 4.3A, 4.3B, 4.5A, 4.7, 4.10, 4.12B
Unit Overview
Number Operations
Problem solving come one and all. Adding and Subtracting we'll have a ball. Use Place Value and Decimals, too. Learning is what we're going to do!
Enduring Understandings
  • Every number has a value.
  • Models can be used to solve problems.
  • Estimation is an indicator of reasonableness.
  • Mathematics can be applied to everyday situations.
  • Problem solvers question, investigate, and explore solutions to problems.
/ Essential Questions
  • What is a number?
  • How can models help in adding and subtracting decimals?
  • Why is estimation an important part of problem solving?
  • How do mathematicians become good problem solvers?
  • How does justifying solutions to problems help a person to become a decision maker?
/ Mathematics Skills/Process – ALWAYS DO!
4.14 Underlying processes and mathematical tools. The student applies mathematics to solve problems connected to everyday experiences and activities in and outside of school. The student is expected to:
Include for 4.14A, 4.14B, 4.14C:
  • Explore problems using concrete manipulatives
  • Draw a picture (pictorial)
  • Share thoughts with peers
  • Journal thoughts
  • Justify answer
4.14Aidentify the mathematics in everyday situations
4.14Bsolve problems that incorporate understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness
Include:
  • Create questions
  • Record or communicate with words/pictures/numbers
4.14Cselect or develop an appropriate problem solving plan or strategy, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem
Include:
  • Record or communicate with words/pictures/numbers
4.14Duse tools such as real objects, manipulatives, and technology to solve problems
Include:
  • Numerical representation
  • Work with and make connections among the different representations: concrete/pictorial/abstract
  • Use calculators
4.15Underlying processes and mathematical tools. The student communicates about mathematics using informal language. The student is expected to:
4.15A explain and record observations using objects, words, pictures, numbers, and technology
Include:
  • Describe the process in words (written and/or orally)
  • Journal writing/drawing is imperative
  • Oral explanation is a must
  • Calculators
  • 4.15Brelate informal language to mathematical language and symbols
Include:
  • Students write and understand words, numbers, and symbols
  • Journal writing is imperative
  • Oral explanation is a must (students should talk to other students, the teacher, and to the class)
4.16Underlying processes and mathematical tools. The student uses logical reasoning to make sense of his or her world. The student is expected to:
4.16Amake generalizations from patterns or sets of examples and non examples
Include:
  • Identify attributes of examples
  • Identify examples false to statement given
  • Examples may have nonsense words
4.16Bjustify why an answer is reasonable and explain the solution process
Include:
  • Students justify and prove their solutions in written/spoken words, pictures, concrete objects, and/or numbers
  • Journal writing (may include process or explanation, etc.)
  • Peer explanations
  • Classroom discussions

Facts
  • Our number system is based on patterns of tens.
  • Each place has ten times the value of the place to its right.
  • Numbers to the left of the decimal represent whole numbers; those to the right of the decimal represent parts of a whole.
  • Problems can be solved using a variety of problem solving strategies.
  • Story problems may include extraneous information.
  • A line is made up of points.
  • All points on a number line have value.
/ Relationships and/or Connections that should emerge
  • Order numbers by value in everyday situations.
  • Interpret graphical data in math and science.
  • Compare populations in social studies.

Products students will develop
  • Book of 10, Investigations; Coins, Coupons and Combinations, p.8
  • Book of Magic Pot Riddles; Coins, Coupons, and Combinations, p. 24
  • Class chart of addition facts to 20, MLC, p.198

Language of Instruction
Place Value
base 10 system
decimal number
digit
expanded form
greater/less than
number line
numeral
period
point
whole number
zero
Problem Solving
equation
expression
logical
number sentence
range
solution
strategy / Estimation
approximate
compatible
estimate
front-end
reasonable
round
Computation
addend
difference
regroup
sign
sum
symbol
/ Mathematical Connections to Literature
  • Big Number(Packard)
  • Fun With Numbers(Chats)
  • How Much Is A Million(Schwartz)
  • Matilda (Dahl)
  • The Elephant’s Child (Kipling)
  • Alexander Who Used to be Rich Last Week (Viorst)
  • How the Second Grade Got $8205.50 to Visit the Statue of Liberty (Zimelman)
  • Annabelle Swift, Kindergartner (Amy Schwartz)
  • Counting on Frank (Clement)
  • A Million Fish – More or Less (McKissack)
  • Two Ways to Count to Ten (Dee)
  • How Much is a Million? (Schwartz)
  • Esio Trot (Dahl)

4th Grade Unit 1: / Mathematical Thinking—Place Value and Problem Solving / Suggested Time Frame: / 24 days
TAKS Objectives: / 1, 2, 3, 4, 6 / TEKS: / 4.1A, 4.1B, 4.3A, 4.3B, 4.5A, 4.7, 4.10, 4.12B
Unit Overview
Problem solving come one and all. Adding and Subtracting we'll have a ball. Use Place Value and Decimals, too. Learning is what we're going to do!
Text Resources
Investigations
  • Mathematical Thinking at 4th Grade
  • Landmarks in the Thousands
  • Money, Miles, and Large Numbers
MathLearningCenter
  • Volume 1
  • Volume 2
  • Volume 3
Vocabulary Adventures
Count On It
Measuring Up
The Super Source
Problem Solver
Math Essentials / Enrichment Centers
Technology & Electronic Resources
Other(i.e., Speakers, Field Trips) / Method(s) of Assessment
Observation
AObservation evaluated by peers
BStudents engaged in learning activities
CDirect questioning
DObservation of performance or process
Teacher Checkpoint:
  • Draw pictorial representation of concrete examples.
  • Apply operations of addition and subtraction using
  • manipulative and pictorial representations
Constructed Response
  1. TEKSCheck
Assessment Sourcebook: End-Of Unit Assessment Tasks 1-4
  1. Open-ended
  2. Essay
  3. Research Paper
  4. Log / Journal
  5. Story / Play / Poem
  6. Model / Map / Video
  7. Oral / Visual / Multimedia Presentation
Selected Response
1Fill-in-the-blank test
2Matching test
3Multiple choice test
4True/False test
Collaborative Student Explorations
A44.1A3E1
40,987; 40,897; 48,790; 48,709
Using the digits above only once, what is the smallest number you could create between 40,000 and 49,000? What is the largest number you can create between 40,000 and 49,000? List all of these numbers as they would appear on the number line. Explain your process.
Answer:Smallest: 40,789
Largest:48,970
40,789; 40,897; 40,987; 48,709; 48,790; 48,970 / A44.5A3E2
Use the digits 1, 2, 3, 6, & 8 to create all the numbers possible that when rounded to the thousands place are less than 87,000 but greater than 62,000. Explain your process.
63,000 / 81,000 / 82,000 / 83,000 / 86,000
62,813 / 81,236 / 81,623 / 82,613 / 86,123
62,831 / 81,263 / 81,632 / 82,631 / 86,132
81,362 / 82,136 / 83,126 / 86,231
81,326 / 82,163 / 83,162 / 86,213
82,361 / 83,261 / 86,321
82,316 / 83,216 / 86,312
Answer:
Rounded to:
There are 32 possible combinations. / A44.5A3E1 (See Instructional Resources)
NOTES:

Fourth Grade Mathematics Unit 1 Overview

In this brief summary, the dates will fluctuate according to your students, calendar, and special events.

Unit One: Mathematical Thinking –

Place Value and Problem Solving

Suggested 24 days

  • Use place value to read, write, compare and order whole numbers.
  • Introduce decimal place value using money.
  • Use addition and subtraction to solve problems involving whole numbers.
  • Add and subtract decimals to the hundredths place using concrete objects and pictorial models.
  • Round whole numbers to the nearest ten, hundred, or thousand to verify reasonable results in problem situations.
  • Identify and extend addition and subtraction patterns/relationships in tables and lists.
  • Locate and name whole numbers and decimals on a number line.
  • Introduce the following problem solving strategies:

Write a Number Sentence

Act I

8/27/2007DRAFT 3