Mathematics

Grade / Unit / Title and Unit Overview / Time Frame: / TAKS and TEKS / Enduring Understandings / Essential Questions
4 / 1 / Mathematical Thinking—Place Value from whole numbers through decimals(in relationship to money)
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! / 12 days--
3 Weeks / TAKS:
1, 3, 6
TEKS:
4.1A, 4.1B, 4.3A, 4.3B, 4.5A /
  • Every number has a value.
  • Units within a system are built upon each other.
  • The decimal system allows mathematicians to write numbers of all types and sizes.
  • Estimation is an indicator of reasonableness.
/
  • What is a number?
  • Can everything be quantified?
  • How are numbers ordered?
  • Do all numbers have decimals?
  • How can models help in adding and subtracting decimals?
  • How are numbers classified to the right and to the left of the decimal?
  • What does it mean to reason mathematically?
  • When is estimation better to use than counting and when is it not better?
  • What are the practical applications of estimation?
  • What information is necessary to determine what type of strategy will be most helpful when solving a problem?

5 / 1 / Landmarks in the Number System 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. / 20 Days--
6 Weeks / TAKS:
1, 2, 3, 4, 5, 6
TEKS:
5.1, 5.1A, 5.3D, 5.5B, 5.11A, 5.14C, 5.15A, 5.16B /
  • Factors and multiples can be used to solve problems.
  • Factors are components of numbers.
  • Multiples are extensions of numbers.
  • There are a variety of strategies for solving problems.
/
  • How can a number be broken down into its smallest factors?
  • What is the relationship between factors and multiples?
  • How would the most effective problem solving strategy be determined?

Facts / Relationships and/or Connections that should emerge / Vocabulary / Text Resources
  • Our number system is based on patterns of tens.
  • Each place has ten times the value of the place to its right.
  • The place value tells how much each digit stands for.
  • Use “and” when reading numbers with decimals.
  • Numbers to the left of the decimal represent whole numbers; those to the right of the decimal represent parts of a whole.
/
  • Order numbers by value in everyday situations.
  • Interpret graphical data in math and science.
  • Compare populations in social studies.
/ comparison / comparar
decimal / decimal
digit / digito
hundred thousands / centenas de millar
hundreds / centenas
hundredths / centésimos
millions / millón
ones / unidades
periods / punto
place value / valor relativo
regrouping / reagrupar
ten thousands / decenas de millar
tens / decenas
tenths / decimos
thousands / millar , millares
/ Investigations—
Mathematical Thinking at 4th Grade:
Investigation 1, Session 4 pg. 23
Investigation 2, Session 1&2 pg. 34-37
Investigation 3, Session 1 &2 pg.48
Landmarks in the Thousands:
Investigation 3,
Session 1 pg. 38;
Session 5 pg.45
Investigation 4,
Sessions 1-3 pg.54
Money, Miles, and Large Numbers:
Investigation 1, Session 4 &5 pg.18-21
MathLearningCenter –
Volume 1 – Insight
Lessons 16 – 20
Lessons 22 -27
Lesson 29
Lessons 32 – 34
Volume 2 - Insight
Lessons 68-70
Lessons 72-74
Volume 3
Lessons 13 and 24
  • 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.
/
  • 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?
/ array / matriz
clusters / grupos
column / columna
composite / compuesto
data / datos
different / diferente
dimensions / dimensiones
double / doble
even / par
factor / factor
factor pairs / parejas de factores
grid / cuadricula
landmark / piedra milaria
multiple / multiplo
odd / impar
pattern / patron
prime / primo
prime factorization / factorizacion prima
rectangle / rectangulo
repeated addition / adicion repetitiva
row / fila
skip counting / contar saltando
square / cuadrado
wide / ancho
/ Investigations-
Mathematical Thinking at Grade 5
“Introduction Landmarks in the Number System”

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