Math in Motion

New Math TEKS for Leaders

TEPSA – October 2013 1

New TEKS Time Line* School Year Gr. K – 8 High School

2011-12 Revision Process Revision Process

2012-13 lead4ward lead4ward

2013-14 Selection of Instructional

Materials lead4ward

2014-15 Implementation of

New TEKS*

Selection of Instructional

Materials

2015-16 Implementation of

New TEKS* Implementation of

New TEKS*

*Pending Legislative approval for funding instructional materials 2

CONTACT INFORMATION FOR

SCHOOL ADMINISTRATORSFor questions about:• STAAR• Accountability• Special Education• Technical Support

info@lead4ward.com

For questions about:• English Language Arts

Gayla Wigginsgayla@lead4ward.com

• MathematicsNancy Crouchnancy@lead4ward.com

Ward Robertsward@lead4ward.com

• ScienceDiane Seufertdiane@lead4ward.com

• Social StudiesJodi Dentonjodi@lead4ward.com

CONTACT INFORMATION FOR

TEACHERS

For questions about:• Workshop invoices• Registration information• Follow-up presentations• Future staff development opportunities

pd@lead4ward.com

For questions about:• Products• Product Store

store@lead4ward.com

CONTACT INFORMATION FOR

WORKSHOP MATERIALS

Visit http://lead4ward.com/workshops/logins/• Click on the workshop you attended• Use the password provided by your

presenter ______________________

To access the materials used in a session:

lead4ward.com | store.lead4ward.com | info@lead4ward.com

HAVE QUESTIONS?Just ask. We're here to help.

ADDITIONAL

RESOURCES

Texas Association of Supervisor's of Mathematics (TASM) www.livebinders.com/play/play?id=707766

Local Education Service Center:Introduction to New Math TEKS: Grades K-2; 3-5; 6-8

Texas Education Agency www.tea.state.tx.us/index2.aspx?id=6148&menu_id=720&menu_id2=785

3

Key: Change of grade level Change of strand NEW Standard © 2012 lead4ward

Number and Operations grade

3 3.4 The student applies mathematical process standards to develop and use strategies and methods for whole number computations in order to solve

problems with efficiency and accuracy. The student is expected to:

Change New Standard (Implementation Year 2014-2015)

Current Standard Cognitive Change Content Change

3.4F recall facts to multiply up to ten by ten with automaticity and recall the corresponding division facts

3.4A learn and apply multiplication facts through 12 by 12 using concrete models and objects

3.6 C identify patterns in related multiplication and division sentences (fact families) such as 2 x 3 = 6; 3 x 2 = 6; 6 ÷ 2 = 3; 6 ÷ 3 = 2 (Patterns, Relationships, and Algebraic Thinking Strand)

changed “learn and apply” multiplication facts to “recall”

added with “automaticity”

changed strand from “Patterns,Relationships, and Algebraic Thinking” to “Number and Operations”

limited the facts to 10 x 10

deleted the use of concrete models and objects; however, it can be applied toprocess standards (see 3.1C)

combined the recalling of multiplication and division facts

3.4G use strategies and algorithms, including the standard algorithm, to multiply a two-digit number by a one-digit number; strategies many include mental math, partial products, and the commutative, associative, and distributive properties

3.4B solve and record multiplication problems (up to two digits times one digit)

changed the “solving and recording” of two digit by one digit multiplication to “using” strategies

identified strategies to include mental math, partial products, and number properties

3.4H determine the number of objects in each group when a set of objects is partitioned into equal shares or a set of objects is shared equally

3.4C use models to solve division problems and use number sentences to record the solutions

added the understanding of division as thetotal number of objects when a set ofobjects is partitioned equally

3.4I determine if a number is even or odd using divisibility rules

3.4J determine a quotient using the relationship between multiplication and division

3.6 C identify patterns in related multiplication and division sentences (fact families) such as 2 x 3 = 6; 3 x 2 = 6; 6 ÷ 2 = 3; 6 ÷ 3 = 2 (Patterns, Relationships, and Algebraic Thinking Strand)

changed the “identifying” of patterns in multiplication/division to “determining” the quotient using the relationship

changed strand from “Patterns,Relationships, and Algebraic Thinking” to “Number and Operations”

deleted the term fact families

3.4K solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts

3.4B solve and record multiplication problems (up to two digits times one digit)

3.4C use models to solve division problems and use number sentences to record the solutions

4.4 multiply and divide to solve meaningful problems involving whole numbers

added the use of two-step problems moved the solving of multiplication a division problems from grade 4 to grade 3

defined problems through products of 100

identified the types of strategies to be used (i.e. arrays, area models, equal groups, properties of operations, or recall of facts)

4

5 grade Algebraic Reasoning

5.4 The student applies mathematical process standards to develop concepts of expressions and equations. The student is expected to:

Change New Standard (Implementation Year

2014-2015)

I already do this

I need to be doing

this

This is new to

me

Implement Now?

Instructional Considerations

5.4C generate a numerical pattern when given a rule in the form y=ax or y = x + a and graph

No

As this standard would take a significant amount of time to develop and will not be tested this academic school year on STAAR, we would not be able to implement this concept during our study of algebraic reasoning. However, as 5th grade does not have any ineligible standards in the current assessed curriculum, it would be possible to introduce this standard after the administration of STAAR.

5.4D recognize the difference between additive and multiplicative numerical patterns given in a table or graph

Yes

Students already identify the difference between additive and multiplicative patterns when they define the rule for a given set of data (see current standards 5.5A). As students identify the rule for a given set of data in a table, perhaps students could journal about the differences they observed in the two different types of patterns to better emphasize this new standard. When student begin to graph coordinates in the first quadrant, ensure that students have exposure to graphing additive and multiplicative patterns examples. Be more intentional to ask how the two graphs are similar/different.

5.4E describe the meaning of parentheses and brackets in a numeric expression

Yes

Students already use parentheses when writing number sentences with multiple steps. However, I may need to include the use of brackets and really emphasize the intentions of such grouping symbols.

5

Key: Change of grade level Change of strand NEW Standard

grade

4 Geometry & Measurement

Scaffolding the Content to Support Transitioning Students

2013-2014: Current Standards (4th Grade/5th Grade)

2014-2015: New Standards (5th Grade/6th Grade)

2015-2016: New Standards (6th Grade)

4.8A identify and describe right, acute, and obtuse angles

extend the definition of angle as a part of circle whose center is the vertex of the angle

define rays

5.5 classify two-dimensional figures in a hierarchy of sets and subsets using graphic organizers based on their attributes and properties

introduce the use of the protractor and have students measure angles to identify and describe the different types of angles which defines their essential attributes

define degrees

define a circle in terms of degrees

draw two-dimensional figures given various attributes such as a given angle measurement

6.8A extend previous knowledge of triangles and their properties to include the sum of angles of a triangle, the relationship between the lengths of sides and measures of angles in a triangle, and determining when three lengths form a triangle, and determining when three lengths form a triangle

5.7 generate geometric definitions using critical attributes and identify essential attributes… of two- and three-dimensional geometric figures

extend the definition of angle as a part of circle whose center is the vertex of the angle

define rays

introduce the use of the protractor and have students measure angles to identify and describe the different types of angles which defines their essential attributes

define degrees

define a circle in terms of degrees

draw two-dimensional figures given various attributes such as a given angle measurement

6.8A extend previous knowledge of triangles and their properties to include the sum of angles of a triangle, the relationship between the lengths of sides and measures of angles in a triangle, and determining when three lengths form a triangle, and determining when three lengths form a triangle

4.7 The student applies mathematical process standards to solve problems involving angles less than or equal to 180 degrees. The student is expected to:

Change New Standard (Implementation Year 2014-2015)

Current Standard Cognitive Change Content Change Grade Level Change Implications

4.7A illustrate the measure of an angle as the part of a circle whose center is at the vertex of the angle that is “cut out” by the rays of the angle; angle measures are limited to whole numbers 4.7B illustrate degrees as the units used to measure an angle, where 1/360 of any circle is 1 degree and an angle that “cuts” n/360 out of any circle whose center is at the angle’s vertex has a measure of n degrees; angle measures are limited to whole numbers 4.7C determine the approximate measures of angles in degrees to the nearest whole number using a protractor 4.7D draw an angle with a given measure

6.8C measure angles

added “illustration/drawing” of measurement angles

added detailed understanding of the measurement of angles

limited angles measurements to whole numbers

identified the required use of a measurement tool (protractor)

holes and gaps may surface in student’s learning as they move through the grade spans

grade 4 and 5 teachers may need professional development to strengthen their knowledge of the content

protractors may need to be purchased for grades 4 and 5

6

© 2012 lead4ward Implementation Year 2014-2015

3-5 Content Alignment Tool

Data Analysis 3-5 Data Analysis

3rd Grade 4th Grade 5th Grade

NEW

TEK

S

3.8 The student applies mathematical process standards to solve problems by collecting, organizing, displaying, and interpreting data.

4.9 The student applies mathematical process standards to solve problems by collecting, organizing, displaying, and interpreting data.

5.9 The student applies mathematical process standards to solve problems by collecting, organizing, displaying, and interpreting data.

Co

llect

ion

an

d

Org

aniz

atio

n o

f D

ata 3.8A summarize a data set with

multiple categories using a frequency table, dot plot, pictograph, or bar graph with scaled intervals

4.9A represent data on a frequency table, dot plot, or stem-and-leaf plot marked with whole numbers and fractions

5.9A represent categorical data with bar graphs or frequency tables and numerical data, including data sets of measurements in fractions or decimals, with dot plots or stem-and-leaf plots

5.9B represent discrete paired data on a scatter plot

Ap

plic

atio

n o

f D

ata

3.8B solve one- and two-step problems using categorical data represented with a frequency table, dot plot, pictograph, or bar graph with scaled intervals

4.9B solve one- and two-step problems using data in whole number, decimal, and fraction form in a frequency table, dot plot, or stem-and-leaf plot

5.9C solve one- and two-step problems using data from a frequency table, dot plot, bar graph, stem-and-leaf plot, or scatter plot

3.3 The student applies mathematical process standards to represent and explain fractional units. The student is expected to:

Change New Standard (Implementation Year 2014-2015)

Current Standard Cognitive Change Content Change

3.3C explain that the unit fraction 1/b represents the quantity formed by one part of a whole that has been partitioned into b equal parts where b is a non-zero whole number

3.2C use fraction names and symbols to describe fractional parts of whole objects or sets of objects

changed “using” fraction symbols to “explaining” the representation of a fraction symbol

added the understanding of the denominator being a non-zero whole number

3.3D compose and decompose a fraction a/b with a numerator greater than zero and less than or equal to b as a sum of parts 1/b

3.2C use fraction names and symbols to describe fractional parts of whole objects or sets of objects

added the “composing/decomposing” of fractions

added the representations of fractions as a sum of the parts of 1/b

! 3.6E decompose two congruent two-dimensional figures into parts with equal areas and express the area of each part as a unit fraction of the whole and recognize that equal shares of identifcal wholes need not have the same shape.

14. Teacher asks: Is it possible to have zero as a

denominator?

15. Student responds: No, you cannot divide

something into zero parts.

16. Teacher asks: Can we write a number sentence to

represent how the four parts equal one whole.

17. Student responds: ¼ + ¼ + ¼ + ¼ = 1

18. Teacher asks: Shade in 2/4 of the whole.

19. Students color in two equal parts of the four.

20. Teacher asks: Can we write a number sentence to

represent the amount of parts that are shaded?

21. Student responds: ¼ + ¼ = 2/4

1. Students are given a square.

2. Teacher asks: If this square represents one whole, can you

partition this polygon into fourths?

3. Students decompose the square into four equal parts

(students may divide the square differently).

4. Teacher asks: How many parts did you divide the polygon into?

5. Student responds: four

6. Teacher ask: What fraction represents one

(triangle/square/rectangle) of the square?

7. Student responds: ¼

8. Teacher asks: What does the numerator represent?

9. Student responds: One part of the whole.

10. Teacher asks: What does the denominator represent?

11. Student responds: The total number of equal parts.

12. Teacher asks: Does this triangle labeled ¼ represent the same unit

fractions as this rectangle labeled ¼?

13. Student responds: Yes, the shapes may be different but the

amount of area if covers of the one whole is the same.

Then Now

1. Teacher asks: What fractional part of the

rectangle is shaded?

2. Student responds: 1 out of 4 are shaded

3. Teacher asks: How can you represent

that as a fraction?

4. Student responds: ¼

5. Teacher asks: What does the

numerator represent?

6. Student responds: The number of

parts shaded.

7. Teacher asks: What does the

denominator represent?

8. Student responds: The total number

of parts.

8

Grade 3