TEKS STUDY 2006

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TEKS STUDY2006

• Grade 5
• Whats New?

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New to Introduction

• (3)Throughout mathematics in Grades 3-5,
  students develop numerical fluency with
  conceptual understanding and computational
  accuracy. Students in Grades 3-5 use knowledge of
  the base-ten place value system to compose and
  decompose numbers in order to solve problems
  requiring precision, estimation, and
  reasonableness. By the end of Grade 5, students
  know basic addition, subtraction, multiplication,
  and division facts and are using them to work
  flexibly, efficiently, and accurately with
  numbers during addition, subtraction,
  multiplication, and division computation.

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numerical fluency withconceptual understanding
and computational accuracy

• Understanding is built from the concrete to the
  abstract.
• Everything done with numbers must be done with
  meaning.
• Attend to concepts that build number sense and
  operation sense.

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numerical fluency withconceptual understanding
and computational accuracy
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1

Example 11 x 13 (10 1) x (10 3) (10 x
10) (10 x 3) (1 x 10) (1 x 3)
10
100
10

3
5
numerical fluency withconceptual understanding
and computational accuracy
450 25 18 25 450 - 250 product of (10 x
25) 200 - 100 product of (4 x 25)
100 - 100 product of (4 x 25) 0

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New to Introduction

• (3)Throughout mathematics in Grades 3-5,
  students develop numerical fluency with
  conceptual understanding and computational
  accuracy. Students in Grades 3-5 use knowledge of
  the base-ten place value system to compose and
  decompose numbers in order to solve problems
  requiring precision, estimation, and
  reasonableness. By the end of Grade 5, students
  know basic addition, subtraction, multiplication,
  and division facts and are using them to work
  flexibly, efficiently, and accurately with
  numbers during addition, subtraction,
  multiplication, and division computation.

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compose and decompose numbers

• Here is one way to solve this problem
• 38 46
• 38 (2 44)
• (38 2) 44
• 40 44
• 84
• Try It Decompose and compose 38 46 to solve
• it another way.

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compose and decompose numbers

• Often in computations it is useful to recognize
  that a number can be made up of a nice number
  and some more.
• John Van de Walle

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compose and decompose numbers

• Children must be able to name numbers flexibly in
  order to have what is called number sense. For
  example
• 1035 can be
• 1000 30 5
• 1000 35
• 1000 20 15

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compose and decompose numbers
Children must be able to name numbers flexibly in
order to have what is called number sense.

• Example 1
• 4000 1 3999
• - 2793 1 2792 1207

• Example 2
• 643 5 648
• 295 5 300
• 348

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compose and decompose numbers

• The way you compose or decompose numbers depends
  on the question you are trying to solve.
• Try It Which expression would you choose to
  use to help find the product of 8 times 19?
• (8 x 15) (8 x 4)
• (8 x 10) (8 x 9)
• (4 x 19) (4 x 19)
• (8 x 20) (8 x 1)

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compose and decompose numbers

• The way you compose or decompose numbers depends
  on the question you are trying to solve.
• Try It Which expression would you choose to
  use to help find the quotient of 132 4?
• (100 4) (32 4 )
• (120 4) (12 4)
• (132 2) 2

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compose and decompose numbers

• When a primary goal is the development of sound
  understanding of the number system, students will
  spend much of their math time putting together
  and pulling apart different numbers as they
  explore the relationships among them.
• Beyond Arithmetic
• What will you do daily to develop this
  understanding in your classroom?

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New to Introduction

• (3) Throughout mathematics in Grades 3-5,
  students develop numerical fluency with
  conceptual understanding and computational
  accuracy. Students in Grades 3-5 use knowledge of
  the base-ten place value system to compose and
  decompose numbers in order to solve problems
  requiring precision, estimation, and
  reasonableness. By the end of Grade 5, students
  know basic addition, subtraction, multiplication,
  and division facts and are using them to work
  flexibly, efficiently, and accurately with
  numbers during addition, subtraction,
  multiplication, and division computation.

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know basic facts TEKS Expectations
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know basic facts

• Work on fact fluency begins as soon as a child
  has an effective strategy for finding the answer.
• Assess students fluency with basic facts.
• Identify which facts are known and unknown.
• Provide intervention and acceleration that
  includes strategies for mastering facts.
• Provide multiple opportunities to practice. These
  opportunities should include the use of
  technology, games, relational flashcards and
  drill.

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• GRADE 5
• Student Expectations
• A Closer Look

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TEKS 5.1A

• (5.1) Number, operation, and quantitative
  reasoning. The student uses fractions in
  problem-solving situations.
• The student is expected to
• (A) Use place value to read, write, compare, and
  order whole numbers through 999,999,999,999.

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TEKS 5.2A

• (5.2) Number, operation, and quantitative
  reasoning. The student uses fractions in
  problem-solving situations.
• The student is expected to
• (A) generate a fraction equivalent to a given
  fraction such as ½ and 3/6 or 4/12 and 1/3.

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TEKS 5.2B

• (5.2) Number, operation, and quantitative
  reasoning. The student uses fractions in
  problem-solving situations.
• The student is expected to
• (B) generate a mixed number equivalent to a
  given improper fraction or generate an improper
  fraction equivalent to a given mixed number.

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5.2(B) Generate a mixed number equivalent to a
given improper fraction or generate an improper
fraction equivalent to a given mixed number.

• Whats New?
• This expectation is completely new to grade 5.
  
• Note In fourth grade, students work with
  fractions greater than one with concrete objects
  and pictures. Fifth graders must advance to
  making the conversions without pictures.

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5.2(B) Generate a mixed number equivalent to a
given improper fraction or generate an improper
fraction equivalent to a given mixed number.

• Try It
• Draw a picture of 2 1/2. Explain how this
  picture can also be representative of 5/2.
• How do you find a mixed number when given an
  improper fraction without a picture? Does your
  method always work?

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TEKS 5.3C

• (5.3) Number, operation, and quantitative
  reasoning. The student adds, subtracts,
  multiplies, and divides to solve meaningful
  problems.
• The student is expected to
• (C) Use division to solve problems involving
  whole numbers (no more than two-digit divisors
  and three-digit dividends without technology),
  including interpreting the remainder within a
  given context.

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5.3(C) Use division to solve problems involving
whole numbers (no more than two-digit divisors
and three-digit dividends without technology),
including interpreting the remainder within a
given context.

• Whats New?
• The TEKS now include interpreting remainders
  based on the context.

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5.3(C) Use division to solve problems involving
whole numbers (no more than two-digit divisors
and three-digit dividends without technology),
including interpreting the remainder within a
given context.

• Try It
• Interpreting Remainders 25 8
• Jan has 25 and wants to buy some plants that
  cost 8 each. How many plants can she buy?
• On a field trip, one adult is needed for every
  8 children. There are 25 children. How many
  adults are needed?
• Marie has 25 yards of ribbon for making crafts
  to share with her 7 friends. How much ribbon will
  each person receive?

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TEKS 5.3D

• (5.3) Number, operation, and quantitative
  reasoning. The student adds, subtracts,
  multiplies, and divides to solve meaningful
  problems.
• The student is expected to
• (D) identify common factors of a set of whole
  numbers.
• Note Prime has moved to 5.5B. It is still a
  fifth grade concept.

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TEKS 5.4

• (5.4) Number, operation, and quantitative
  reasoning. The student estimates to determine
  reasonable results.
• The student is expected to
• use strategies, including rounding and
  compatible numbers to estimate solutions to
  addition, subtraction, multiplication, and
  division problems.

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5.4 use strategies, including rounding and
compatible numbers to estimate solutions to
addition, subtraction, multiplication, and
division problems.

• Whats New?
• The use of compatible numbers to estimate
  solutions.
• For example
• 256 46 760 . . . Think 250 50 750, which
  is about 1,050.
• 78 X 96 can be estimated as 78 X 100 or 7800.
• 5096 26 . . . Think 5000 25, which would be
  about 200.

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5.4 use strategies, including rounding and
compatible numbers to estimate solutions to
addition, subtraction, multiplication, and
division problems.

• Try It
• What compatible numbers would you use to estimate
  the following?
• Maria has 61 cookies to share equally with 7
  friends.
• Maria has 190 cookies for classes of 32.
• Maria has 356 cookies to put into 13 boxes.

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5.4 use strategies, including rounding and
compatible numbers to estimate solutions to
addition, subtraction, multiplication, and
division problems.
Remember The focus for this TEKS is now on
reasonableness.
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TEKS 5.5A

• (5.5) Patterns, relationships, and algebraic
  thinking. The student makes generalizations based
  on observed patterns and relationships.
• The student is expected to
• (A) describe the relationship between sets of
  data in graphic organizers such as lists, tables,
  charts, and diagrams.

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5.5(A) describe the relationship between sets of
data in graphic organizers such as lists, tables,
charts, and diagrams.
Whats New? The example of such as a procedure
for determining equivalent fractions has been
removed from this TEKS, thus making the
expectation broader.

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5.5(A) describe the relationship between sets of
data in graphic organizers such as lists, tables,
charts, and diagrams.

• In what ways might we show relationships by
  using
• Lists?
• Tables?
• Charts?
• Diagrams?

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TEKS 5.6

• (5.6) Patterns, relationships, and algebraic
  thinking. The student describes relationships
  mathematically.
• The student is expected to select from and use
  diagrams and equations such as y 5 3 to
  represent meaningful problem situations.

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5.6 The student is expected to select from and
use diagrams and equations such as y 5 3 to
represent meaningful problem situations.

• Whats New?
• New wording emphasizes the use of algebra to
  express relationships.

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TEKS 5.8A

• (5.8) Geometry and spatial reasoning. The
  student models transformations. The student is
  expected to
• (A) sketch the results of translations,
  rotations, and reflections on a Quadrant I
  coordinate grid.
• (B) identify the transformation that generates
  one figure from the other when given two
  congruent figures on a Quadrant I coordinate
  grid.
• Whats New?
• Transformations are limited to Quadrant I. This
  is not a change, but a clarification.

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Quadrant 1

• 
  Quadrant 1
• _
• _ X (1, 2) over 1, up 2
• 
  I I

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TEKS 5.10A

• (5.10) Measurement. The student applies
  measurement concepts involving length (including
  perimeter), area, capacity/volume, and
  weight/mass to solve problems.
• The student is expected to
• (A) Perform simple conversions within the same
  measurement system (SI (metric) or customary).

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5.10(A) Perform simple conversions within the
same measurement system (SI (metric) or
customary).

• Whats New?
• The term SI is new to the TEKS. It stands for
  system internationale, or the metric system.
• Students are now explicitly expected to make
  simple conversions to solve problems. TEKS 5.11B
  previously read, describe numerical
  relationships between units of measure.

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5.10(A) Perform simple conversions within the
same measurement system (SI (metric) or
customary).

• The TAKS Measurement Chart gives measurement
  equivalencies. It is not necessary for students
  to memorize equivalencies. Students should be
  very familiar with this chart.

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5.10(A) Perform simple conversions within the
same measurement system (SI (metric) or
customary).
Try It This is now a typical 4th grade problem.
Revise it for 5th grade. Susie needs 12 feet of
ribbon to make frames for her friends. The store
is having a sale on ribbon, 1 yard for 1.00. Use
the table below to find how many yards of ribbon
Susie needs.

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TEKS 5.10B

• (5.10) Measurement. The student applies
  measurement concepts involving length (including
  perimeter), area, capacity/volume, and
  weight/mass to solve problems.
• The student is expected to
• (B) Connect models for perimeter, area, and
  volume with their respective formulas.

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5.10(B) Connect models for perimeter, area, and
volume with their respective formulas.

• Whats New?
• This expectation is completely new to grade 5.
  Students are to connect models with formulas in
  order to understand that formulas are
  generalizations that have meaning.
• Formulas on TAKS Mathematics Chart
• Perimeter----Squares and rectangles
• Area-----Squares, rectangles and triangles
• Volume-----Rectangular prism

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5.10(B) connect models for perimeter, area, and
volume with their respective formulas.
Try It Area AS2 Alw Abh
A1/2 bh 1. The dimensions of the rug are 10 feet
by 8 feet. Which formula could be used to find
the area of the rug? 2. Use the cut rectangle
below to explain the formula used to find the
area of a triangle.

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TEKS 5.10C

• (5.10) Measurement. The student applies
  measurement concepts involving length (including
  perimeter), area, capacity/volume, and
  weight/mass to solve problems.
• The student is expected to
• (C) select and use appropriate units and
  formulas to measure length, perimeter, area, and
  volume.

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5.10(C) select and use appropriate units and
formulas to measure length, perimeter, area, and
volume.

• Whats New?
• There is a new emphasis on using a formula to
  solve measurement problems.
• Emphasize the most appropriate unit for a given
  situation.
• Can students select between square units and
  cubic units when asked to find the area?
• Can they find area, perimeter, or volume when the
  numbers are too large to count efficiently?
• Can they select the formula to solve a given
  problem?

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5.10(C) select and use appropriate units and
formulas to measure length, perimeter, area, and
volume.
Try It For which of these figures can you use
the formula l x w x h to find the volume?

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5.10(C) select and use appropriate units and
formulas to measure length, perimeter, area, and
volume.

• Try It
• Which formula would you use to find the area of
  this shape?
• 4s
• bh/2
• lw
• lwh

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TEKS 5.11A

• (5.11) Measurement. The student applies
  measurement concepts. The student measures time
  and temperature (in degrees Fahrenheit and
  Celsius).
• The student is expected to
• (A) solve problems involving changes in
  temperature.

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(5.11) Measurement. The student applies
measurement concepts. The student measures time
and temperature (in degrees Fahrenheit and
Celsius).

Whats New? Fahrenheit and Celsius are now
specified in the knowledge and skills statement.
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TEKS 5.11B

• (5.11) Measurement. The student applies
  measurement concepts. The student measures time
  and temperature (in degrees Fahrenheit and
  Celsius).
• (B) solve problems involving elapsed time.

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5.11(B) solve problems involving elapsed time.
Whats New? Elapsed time is no longer in the
third grade. Fourth grade students use tools,
such as clocks with gears, to solve problems
involving elapsed time. Elapsed time is not new
to fifth grade however, fifth grade is now the
first grade for elapsed time without tools.

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TEKS 5.12C

• (5.12) Probability and statistics. The student
  describes and predicts the results of a
  probability experiment.
• The student is expected to
• (C) list all possible outcomes of a probability
  experiment such as tossing a coin.

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.
(5.12C) list all possible outcomes of a
probability experiment such as tossing a coin.
Whats New? This TEKS has moved from fourth grade
to fifth grade. The fifth grade focus is being
able to list all the possibilities in a
probability experiment. Students must do more
than tell how many possibilities there are.

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TEKS 5.13B

• (5.13) Probability and statistics. The student
  solves problems by collecting, organizing,
  displaying and interpreting sets of data.
• The student is expected to
• (B) describe characteristics of data presented
  in tables and graphs including median, mode, and
  range.

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5.13(B) describe characteristics of data
presented in tables and graphs including median,
mode, and range.

Whats New The vocabulary is more formal. The
words median, mode, and range are used. Mode is
new to the Grade 5 TEKS.
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5.13(B) describe characteristics of data
presented in tables and graphs including median,
mode, and range.
Try It Can you find the mode from this chart?

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5.13(B) describe characteristics of data
presented in tables and graphs including median,
mode, and range.

Try It Can you find the mode from this
graph? How is finding the mode from a graph
similar to finding the mode from a chart? How is
it different?
Letter Count
60

• Elementary Mathematics TEKS Implementation
• 2006-2007
• New TEKS implemented in classrooms.
• The new TEKS may be tested on district benchmarks.

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Resources

• Lessons for Extending Division, Grades 4-5 by
  Marilyn Burns
• Math By All Means, Division Grades 3-4 by Marilyn
  Burns
• Math to Know by Great Source
• Elementary and Middle School Mathematics by John
  Van de Walle

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• What have you learned?
• T Tools (What new materials will you need to
  teach the TEKS?)
• E Eliminate (What past curriculum can you give
  up?)
• K Know (What expectations are new to fifth
  grade?)
• S Support (How will your team work together to
  help each other implement the new TEKS?)

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Area The dimensions of the rectangle are 10 units
by 8 units. What is the area of the
rectangle? Cut out each of the following
rectangles that are congruent to the original
rectangle. Next cut out the triangle inside each
rectangle by cutting on the dotted lines. Use the
remaining pieces (A1 and A2, B1 and B2) to make a
triangle congruent to triangle A and triangle B.
What is the area of these triangles compared to
the area of the rectangle? A.
B. Cut
--------------------------------------------------
------------------------------------
B2
B
B1
A2
A
A1