Longview ISD Page 3
4th Grade Unit 3: / Patterns and Problem Solving with Multiplication and Division / Suggested Time Frame: / 20 daysTAKS Objectives: / 1, 2, and 6 / TEKS: / 4.4A, 4.4B, 4.4C, 4.4D, 4.4E, 4.5B, 4.6A, 4.6B, 4.7
Unit Overview
Simple multiplication makes repeated addition a snap! Finding patterns that exist will help to close the gap.
Without this important knowledge, division would be lost. So learn those facts—it’s worth the cost!
Enduring Understandings
· Patterns are present in everyday life.
· Patterns are used to predict and analyze solutions to problems.
· Patterns and relationships can be represented graphically, numerically, symbolically, and verbally. / Essential Questions
· How does studying patterns help mathematicians solve problems?
· How can the knowledge of fact families help in problem solving?
· How does data presented graphically help identify patterns?
· What are the symbols used to represent patterns? / 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
4.14A identify the mathematics in everyday situations
4.14B solve 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
4.14C 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:
· Record or communicate with words/pictures/numbers
4.14D use 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
4.15 Underlying 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
4.15B 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)
4.16 Underlying processes and mathematical tools. The student uses logical reasoning to make sense of his or her world. The student is expected to:
4.16A make 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
4.16B 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
· Patterns can be found using multiplication and division.
· Multiplication is an operation used to add a number to itself a specific number of times.
· Division is an operation that partitions an object or group of objects into smaller equal groups.
· Fact families are patterns of multiplication and division.
· Functional relationships can be represented graphically and symbolically. / Relationships and/or Connections that should emerge
· Using skip counting as a model for multiplication
· Seeing multiplication as an accumulation of group of number
· Interpreting standard multiplication and division notation
· Understand how division notation can represent a variety of division situations
Suggested products students will develop
Language of Instruction
area / área
array/matrix / matriz
dividend / dividendo
divides / dividir
divisor / divisor
dozen
estimate / estimar
fact families / familia de operaciones
factor
inverse operation
operation / operación
pattern
product
quotient
remainder
skip count
Tools
· Base Ten Pieces
· Items such as straws, toothpicks, Q-tips bundled in tens and hundreds / Mathematical Connections to Literature
Amanda Bean's Amazing Dream
By Cindy Neuschwander
Each Orange Has 8 Slices A Counting Book
By Paul Giganti, Jr.
A Grain of Rice
By Helena Pittman
A Remainder of One
By Elinor Pinczes
4th Grade Unit 3: / Patterns and Problem Solving with Multiplication and Division / Suggested Time Frame: / 20 days
TAKS Objectives: / 1, 2, and 6 / TEKS: / 4.4A, 4.4B, 4.4C, 4.4D, 4.4E, 4.5B, 4.6A, 4.6B, 4.7
Unit Overview
Simple multiplication makes repeated addition a snap! Finding patterns that exist will help to close the gap.
Without this important knowledge, division would be lost. So learn those facts—it’s worth the cost!
Text Resources
Investigations
· Arrays and Shares
· Landmarks in the Thousands
· Packages and Groups
Math Learning Centers -
Teacher Reference Manual
· Volume 1
· Volume 2
· Volume 3
TEXTEAMS
Vocabulary Adventure
Count On It
Measuring Up
Super Source
Math Essentials
Problem Solver / Enrichment Workstations
· Investigation- Arrays and
Shares Extension Activity pg. 7
· Investigation – Arrays and Shares
Make arrays for higher numbers pg. 22
Technology & Electronic Resources
· www.internet4classrooms.com/skills_4th _original.htm
· http://nlvm.usu.edu/en/nav/frames_asid_199_g_2_t_1.html
· http://www.gamequarium.com/multiplication.html
· http://www.gamequarium.com/division.html
· www.cdli.ca/CITE/math_problems.htm (Excellent problem solving)
Other (i.e., Speakers, Field Trips)
· TEXTEAMS / Method(s) of Assessment
Observation
Assessment Sourcebook: End-Of Unit
A Observation evaluated by peers
B Students engaged in learning activities
C Direct questioning
D Observation of performance or process
Constructed Response
I. TEKSCheck
II. Open-ended
III. Essay
IV. Research Paper
V. Log / Journal
VI. Story / Play / Poem
VII. Model / Map / Video
VIII. 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
P44.4A0E1.doc
Troy wants to arrange his eighteen toy cars in equal rows. How many different ways can he do this? Explain your process.
P44.4A0S1.doc
Troy quiere organizar sus dieciocho carros de juguete en hileras iguales. ¿De cuántas formas diferentes puede él hacer esto? Explica cómo encontraste tu respuesta. / P44.6A0E1.doc
To make 1 dozen cupcakes you need: 2 cups flour, 3 eggs, and 1 cup milk. How much of each ingredient would you need to make 3 dozen cupcakes? For 5 dozen? For 8 dozen? Explain your process.
P44.6A0S1.doc
Para hacer 1 docena de pastelitos necesitas: 2 tazas de harina, 3 huevos y 1 taza de leche. ¿Cuánto necesitarías de cada ingrediente para hacer 3 docenas de pastelitos? ¿Para 5 docenas? ¿Para 8 docenas? Explica tu respuesta. / P44.70E2.doc
One kite takes 13 square tiles to build.
Two kites take square 26 tiles to build.
How many square tiles would it take to build 3 kites? 10 kites? 100 kites? 1000 kites? Explain your process.
P44.70S2.doc
Se necesitan 13 losetas para construir una cometa.
Se necesitan 26 losetas para construir dos cometas.
¿Cuántas losetas de color se necesitarán para construir 3 cometas? ¿10 cometas? ¿100 cometas? ¿1,000 cometas? Asegúrate de explicar qué patrón usaste para resolver el problema.
Fourth Grade Mathematics Unit 3 Overview
In this brief summary, the dates will fluctuate according to your students, calendar, and special events.
Unit Three: Patterns and Problem Solving with
Multiplication and Division
Suggested 20 days
· Model factors and products using arrays and area models.
· Represent multiplication and division situations in picture, word, and number forms.
· Recall and apply multiplication facts through 12 x 12.
· Use multiplication and division to solve problems.
· Estimate solutions to multiplication and division problems using rounding and compatible numbers.
· Identify and use patterns in multiplication and division including fact families and multiplying by 10 and 100.
· Introduce the following problem solving strategies:
Ø Make a Table (apply to money, also)
Ø Guess and Check
Ø Solve a Simpler Problem
8/27/2007 DRAFT 3