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4th Grade Unit 4 / Decimals and Fractions: Naming Quantities less than One Whole / Suggested Time Frame: / 22 days
TAKS Objectives: / 1, 3, 6 / TEKS: / 4.2A, 4.2B, 4.2C, 4.2D. 4.3B, 4.10
Unit Overview
Decimals are interesting and full of surprise. With whole numbers they have strong family ties. Learning their place on the big number line will help you understand how they’re clearly defined. Fractions, decimals, and wholes all have their place. Knowing this should put a smile on your face.
Enduring Understandings
  • Fractions and decimals are used interchangeably in our world.
  • The fractional and decimal values between the whole numbers are infinite.
  • All matter is made up of parts.
/ Essential Questions
  • Why is it necessary to have decimals in real world situations?
  • Why would it be necessary to change fractions to decimals?
  • How are part to whole relationships represented?
/ 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
  • The numerator of a fraction names a certain number of equal parts.
  • The denominator of a fraction names the total number of equal parts.
  • Decimals are a way to write fractions with denominators of multiples of 10.
  • A fraction can be shown on a number line.
  • The space between two whole numbers can be represented in fraction and decimal form.
  • Equivalent fractions are two fractions that appear to be different but actually name equal parts.
  • A fraction names a part of a whole or part of a group.
  • Fractions and decimals name the infinite values between the whole numbers
  • . Numbers greater than one can be expressed as a decimal, mixed number, or improper fraction
/ Relationships and/or Connections that should emerge
  • Decimals and fractions represent parts of wholes.
  • Decimals are a way to write fractions with denominators of tenths and hundredths.
  • Number lines model fraction and decimal numbers as well as whole numbers.
  • Fractions can be used to divide pizza, candy, cake, etc. equally.

Suggested products students will develop
Language of Instruction
decimal form / forma decimal
denominator / denominador
fractional form / forma fraccional
hundredth / centésimo
mixed number / numero mixto
numerator / numerador
tenth / décimo
decimal
fraction
equivalent fraction
improper fraction
fractional part
/ Mathematical Connections to Literature
Apple Fractions
By Pallotta
Funny & Fabulous Fraction Stories
By Greenburg
4th Grade Unit 4 / Decimals and Fractions: Naming Quantities less than One Whole / Suggested Time Frame: / 22 days
TAKS Objectives: / 1, 3, 6 / TEKS: / 4.2A, 4.2B, 4.2C, 4.2D. 4.3B, 4.10
Unit Overview
Decimals are interesting and full of surprise. With whole numbers they have strong family ties. Learning their place on the big number line will help you understand how they’re clearly defined. Fractions, decimals, and wholes all have their place. Knowing this should put a smile on your face.
Text Resources
Investigations
Mathematical Thinking at 4th Grade
Different Shapes, Equal Pieces
MathLearningCenter
Teaching Reference Manual
Volume 1 – Contact
Volume 2 - Contact
Volume 3
TEXTEAMS
Count On It
Vocabulary Adventures
Measuring Up
SuperSource
Problem Solver
Math Essentials
Enrichment Centers(i.e., AIMS) / Technology & Electronic Resources
  • (Excellent problem solving)
Other(i.e., Speakers, Field Trips)
  • TEXTEAMS (Book of Tenths)
/ Method(s) of Assessment
Observation
AObservation evaluated by peers
BStudents engaged in learning activities
CDirect questioning
DObservation of performance or process
Teacher Checkpoints
Draw pictorial representation of concrete examples.
Apply operations of addition and subtraction using manipulative and pictorial representations
Constructed Response
  1. TEKS Check
Assessment Sourcebook: End-Of Unit
  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
A44.3B3E1
Look at the grid below.
Mrs. Hudson has been saving stamps from the gas station for an entire year. She has completely filled in every square on the above page. She plans on using the stamps to buy three items. Each item costs 0.31 of a page of stamps. How much of her page will she have left? Explain your process.
Answer:0.07
A44.3B3S1
Mira la cuadrícula de abajo.
La Sra. Hudson ha estado guardando por un año estampillas de la estación de gasolina. Ha llenado completamente cada cuadrado de la página de arriba. Ella planea usar las estampillas para comprar tres artículos. Cada artículo cuesta 0.31 de la página de estampillas. ¿Cuánto le quedará de su página de estampillas?
Respuesta: 0.07 / +
=
A44.3B3E2
Find the sum of the decimal models above. Create an equation which would have a solution that would equal the sum of the two models above? Explain your process.
Answer:1.00 – 0.34 =?
A44.3B3S2
Halla la suma de los modelos decimales de arriba. Crea una ecuación que tendría una solución igual a la suma de los dos modelos de arriba. Explica cómo encontraste tu respuesta.
Answer:1.00 – 0.34 =? / A44.1B3E1
Te high school track team listed the five fastest runners in the mile race. Scott’s score was accidentally erased. We know that he was faster than Emily but slower than Jason. After finding Scott’s score, list all five runner’s scores from fastest to slowest. Explain your process.
Emily: 5.13
Scott:
Jeff:5.03
Jason:5.11
Shelby5.33
Answer: 5.03, 5.11, 5.12, 5.13, 5.33
A44.1B3S1
El equipo de carreras atléticas de pista y campo de la escuela secundaria, hizo una lista de los cinco corredores más rápidos de la carrera de la milla. El resultado de la carrera de Scott fue borrado por sin querer. Sabemos que él fue más rápido que Emily, pero más lento que Jason. Después de encontrar el resultado de la carrera de Sergio, haz una lista de los resultados de las carreras de todos los cinco corredores desde el más rápido hasta el más lento. Explica cómo encontraste tu respuesta.
Emily: 5.13
Scott:
Jeff:5.03
Jason:5.11
Shelby:5.33
Respuesta: 5.03, 5.11, 5.12, 5.13, 5.33
See Instructional Resources Unit 11
A44.2D4E1
A44.2D4S1

Fourth Grade Mathematics Unit 4 Overview

2007-2008

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

Unit Four: Fraction and Decimals:

Naming Quantities less than One Whole

Suggested 22 days

  • Extend decimal place value concepts introduced in Unit 1 with money including adding and subtracting decimals to the hundredths place.
  • Use concrete objects and pictorial models to generate equivalent fractions.
  • Model fractions, improper fractions, and mixed numbers.
  • Compare and order fractions using models.
  • Relate decimals to fractions that name tenths and hundredths.
  • Locate and name points on a number line using fractions and decimals.
  • Introduce the following problem solving strategies
  • Find a Pattern
  • Draw a Picture

8/27/2007DRAFT 3