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5th Grade Unit 1:

Whole Number Concepts and Problem Solving

Suggested Time Frame:

29 days

TAKS Objectives:

1, 2, 3, 5, 6

TEKS:

5.1A, 5.3D, 5.5A, 5.5B, 5.13A, 5.13C,

Unit Overview

In unit 1, Students will explore factors and multiples by solving problems and puzzles using a variety of strategies. This unit will help students become acclimated to a mathematics class in which the emphasis is on developing strategies, solving problems for which there is no single procedure, and constructing conjectures about mathematical ideas based on evidence that they gather themselves.



Enduring Understandings

  • Factors and multiples can be used to solve problems.

  • Factors are components of numbers.

  • There are a variety of strategies for solving problems.

Essential Questions

  • What is the relationship between factors and multiples?

  • How can a number be broken down into its smallest factors?

  • How do good problem solvers determine the best strategy to use?

Mathematics Skills/Processes – ALWAYS DO!

5.14 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:

5.14A identify the mathematics in everyday situations

5.14B solve problems that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness

Include:

  • Explore problems using concrete manipulatives

  • Draw a picture (pictorial)

  • Share thoughts with peers

  • Create questions

  • Journal thoughts

  • Record or communicate with words/pictures/numbers

  • Justify answer

5.14C select 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:

  • Explore with concrete manipulatives

  • Draw a picture (pictorial)

  • Share thoughts with peers

  • Journal thoughts

  • Record or communicate with words/pictures/numbers

  • Justify answer

5.14D use tools such as real objects, manipulatives, and technology to solve problems

Include:

  • Explore with concrete manipulatives

  • Draw a picture (pictorial)

  • Share thoughts with peers

  • Journal thoughts

  • Numerical representation

  • Justify answer

  • Work with and make connections among the different representations: concrete/pictorial/abstract

  • Use calculators

5.15 Underlying processes and mathematical tools. The student communicates about mathematics using informal language. The student is expected to:

5.15A 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

5.15B relate 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)

5.16 Underlying processes and mathematd ical tools. The student uses logical reasoning to make sense of his or her world. The student is expected to:

5.16A make generalizations from patterns or sets of examples and non examples

Include:

5.16B justify 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

  • Factor pairs can be represented as dimensions of a rectangular array.

  • Problems can be solved using a variety of strategies and may have one, more than one, or no solution.

  • Whole numbers other than 0 and 1 are identified as either prime or composite.

  • Powers of 10 can be used to explore landmarks in our number system using factors, factor pairs, and multiples of those factors.

  • A variety of strategies can be developed for exploring number composition, such as repeated addition, skip counting, finding factors, finding factor pairs, and using a calculator to check divisibility.



Relationships and/or Connections that should emerge

  • Relate to reading and interpreting graphical sources

  • When buying packaged food for a party, knowledge of factors and multiples help determine how many packages of each item are to be purchased. For example, how many packages of buns and wieners will result in no leftover?




Products students will develop

  • student -produced arrays for display

  • number puzzles

  • visual representation of prime, composite and square numbers

  • Student -made problem clusters

Language of Instruction

array

matriz

bar graph




composite

compuesto

data

datos

digit




even

par

expanded form




factor

factor

factor pairs

parejas de factores

factor tree




greater/less than




infinite




line graph




multiple

multiplo

odd

impar

pattern

patron

pictograph




place value




prime

primo

round




skip counting

contar saltando

Venn diagram




whole number













Mathematical Connections to Literature


5th Grade Unit 1:

Whole Number Concepts and Problem Solving

Suggested Time Frame:

29 days

TAKS Objectives:

1, 2, 3, 5, 6

TEKS:

5.1A, 5.3D, 5.5A, 5.5B, 5.13A, 5.13C,

Unit Overview

In unit 1, Students will explore factors and multiples by solving problems and puzzles using a variety of strategies. This unit will help students become acclimated to a mathematics class in which the emphasis is on developing strategies, solving problems for which there is no single procedure, and constructing conjectures about mathematical ideas based on evidence that they gather themselves.



Text Resources
Investigations
Mathematical Thinking at Grade 5





Math Learning Center
TEXTeams
Vocabulary Adventure
The Problem Solver
Math Essentials
Count On It
Measuring Up
Fifth Sense

Technology & Electronic Resources


  • http://nlvm.usu.edu/en/nav/category_g_2_t_1.html


Virtual Manipulatives-

  • http://www.multiplication.com/


Skill interactive practice

  • http://oswego.org/ocsd-web/games/mathmagician/cathymath.html


Skill interactive practice

  • http://www.eduplace.com/math/brain/arch/index.html

  • http://atschool.eduweb.co.uk/toftwood/100hunt2.html


Other (i.e., Speakers, Field Trips)


Method(s) of Assessment
Observation

    1. Observation evaluated by peers

    2. Students engaged in learning activities

    3. Direct questioning

    4. Observation of performance or process


Constructed Response

  1. TEKSCheck

End of Unit Assessment Talks (Assessment Sourcebook-Curriculum Units Package)

  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

  1. Fill-in-the-blank test

  2. Matching test

  3. Multiple choice test

  4. True/False test

COLLABORATIVE STUDENT EXPLORATIONS

See Resources - A55.1A3E1

Mrs. Matthews math class was assigned the task of making the largest even number possible using the digits:


3, 7, 6, 1, 2, 8, 9, 4
Mrs. Matthews also told the class that they could not repeat any of the digits. What is the largest number the class could have made? Explain your process.
Answer: 98,764,312

----------------------------------------------------------



See Resources - A55.1A3S1
A la clase de la Sra. Matthews le asignaron la tarea de formar el número más grande posible usando los dígitos:
3, 7, 6, 1, 2, 8, 9, 4
La Sra. Matthews también le dijo a la clase que no podían repetir ninguno de los dígitos. ¿Cuál es el número más grande que la clase pudo haber formado? Explica tu proceso.
Respuesta: 98,764,312



See Resources - A55.3D4E1

Julio and Alfredo were working as partners on their math practice. They had to find the prime factors of 72. So far Julio has

2 x 2 x 2 x ___ x 3. Julio thinks that the missing number is 2. Alfredo thinks the missing number is 3 or 5. Which of the boys is correct and what number do they need to complete the prime factors of 72? Explain your process.
Answer: Alfredo is correct; the missing number is 3
----------------------------------------------------------

See Resources - A55.3D4S1
Julio y Alfredo estaban trabajando juntos en su práctica de matemáticas. Ellos encontraron los factores primos de 72. Hasta ahora Julio tiene 2 x 2 x 2 x ___ x 3. Julio piensa que el número que falta es 2. Alfredo piensa que el número que falta es 3 ó 5. ¿Cuál de ellos está correcto y qué número necesitan para completar los factores primos de 72? Explica cómo resolviste el problema.

Respuesta: Alfredo está correcto; el número que falta es 3



See Resources - A55.5B3E1

Christopher and Richard are keeping a log on the amount of rainfall collected in a rain gage during a thunderstorm. The following are the results they have recorded:


Time


Amount of Rainfall

4:00

1.5 inches

5:00

3.0 inches

6:00

4.5 inches

If the rain continues to fall at the same rate, what time would it be when the time and amount of rainfall are the same number? Explain your process.
Answer: It would be 9:00. The amount of rainfall would be 9 inches and the time would be 9:00.

------------------------------------------------------



See Resources - A55.5B3S

Christopher y Richard mantienen un diario de la cantidad de lluvia que ha caído dentro de un pluviómetro durante una tormenta. Los siguientes son los resultados de lo que ellos registraron:


Hora


Cantidad de lluvia

4:00

1.5 pulgadas

5:00

3.0 pulgadas

6:00

4.5 pulgadas

Si la lluvia continúa cayendo al mismo ritmo, ¿qué hora sería cuando la hora y la cantidad de lluvia fueran el mismo número? Explica tu proceso.
Respuesta: Serían las 9:00. La cantidad de lluvia sería 9 pulgadas y la hora sería las 9:00.

Fifth Grade Mathematics Unit 1 Overview

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



Unit One: Whole Number Concepts and

Problem Solving

Suggested 29 days

14 Days


  • Whole number place value concepts including comparing and ordering and rounding

  • Introduce “Find a Pattern” problem solving strategy


15 Days


  • Factors, multiples, primes, and composites

  • Introduce “Make a Table” problem solving strategy.

  • Introduce “Make a Graph” strategy.


8/27/2007 DRAFT 3


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