ARE YOU READY FOR THE REVISED 3-5 MATHEMATICS TEKS?

Pam Harris, Mary Alice Hatchett, Ann Roman, Krislyn Stephens

CONFERENCE FOR THE ADVANCEMENT OF MATHEMATICS

In this session:

¨  Highlight major changes in TEKS grades 3-5: ¤ Shifts in focus, coherence, rigor ¤ Examples:

n Place-value n Multiplication n Fractions

Strong Standards

¨  FOCUS ¨  COHERENCE ¨  RIGOR

Shift in Focus

DECREASE in Knowledge and Skills

¨  The number of Knowledge and Skills has decreased.

K 1 2 3 4 5

Old 16 13 14 16 16 16

New 9 9 11 9 10 10

Shifts in Focus

¨  The primary focal areas in Grade 3 are place value, operations of whole numbers, and understanding fractional units. These focal areas are supported throughout the mathematical strands of number and operations, algebraic reasoning, geometry and measurement, and data analysis. In Grades 3-5, the number set is limited to positive rational numbers. In number and operations, students will focus on applying place value, comparing and ordering whole numbers, connecting multiplication and division, and understanding and representing fractions as numbers and equivalent fractions. In algebraic reasoning, students will use multiple representations of problem situations, determine missing values in number sentences, and represent real-world relationships using number pairs in a table and verbal descriptions. In geometry and measurement, students will identify and classify two-dimensional figures according to common attributes, decompose composite figures formed by rectangles to determine area, determine the perimeter of polygons, solve problems involving time, and measure liquid volume (capacity) or weight. In data analysis, students will represent and interpret data.

Shifts in Focus for Grade 3

The primary focal areas in Grade 3 are place value, operations of whole numbers, and understanding fractional units. These focal areas are supported throughout the mathematical strands of number and operations, algebraic reasoning, geometry and measurement, and data analysis. In Grades 3-5, the number set is limited to positive rational numbers. In number and operations, students will focus on applying place value, comparing and ordering whole numbers, connecting multiplication and division, and understanding and representing fractions as numbers and equivalent fractions. In algebraic reasoning, students will use multiple representations of problem situations, determine missing values in number sentences, and represent real-world relationships using number pairs in a table and verbal descriptions. In geometry and measurement, students will identify and classify two-dimensional figures according to common attributes, decompose composite figures formed by rectangles to determine area, determine the perimeter of polygons, solve problems involving time, and measure liquid volume (capacity) or weight. In data analysis, students will represent and interpret data.

Shifts in Focus for Grade 4

The primary focal areas in Grade 4 are use of operations, fractions, and decimals and describing and analyzing geometry and measurement. These focal areas are supported throughout the mathematical strands of number and operations, algebraic reasoning, geometry and measurement, and data analysis. In Grades 3-5, the number set is limited to positive rational numbers. In number and operations, students will apply place value and represent points on a number line that correspond to a given fraction or terminating decimal. In algebraic reasoning, students will represent and solve multi-step problems involving the four operations with whole numbers with expressions and equations and generate and analyze patterns. In geometry and measurement, students will classify two-dimensional figures, measure angles, and convert units of measure. In data analysis, students will represent and interpret data.

Shifts in Focus

The primary focal areas in Grade 5 are solving problems involving all four operations with positive rational numbers, determining and generating formulas and solutions to expressions, and extending measurement to area and volume. These focal areas are supported throughout the mathematical strands of number and operations, algebraic reasoning, geometry and measurement, and data analysis. In Grades 3-5, the number set is limited to positive rational numbers. In number and operations, students will apply place value and identify part-to-whole relationships and equivalence. In algebraic reasoning, students will represent and solve problems with expressions and equations, build foundations of functions through patterning, identify prime and composite numbers, and use the order of operations. In geometry and measurement, students will classify two-dimensional figures, connect geometric attributes to the measures of three-dimensional figures, use units of measure, and represent location using a coordinate plane. In data analysis, students will represent and interpret data.

Time to shift your thinking

The purpose of the new standards is to move away from surface understanding and ensure deeper understanding of mathematical concepts.

Activity 1- Place Value

¨  What do the students need to know to complete

each sheet?

Place Naming vs. Place Value

¨  Being flexible with numbers ¨  A deep conceptual understanding of numbers and

not just a process and/or algorithm ¨  Students need to think of numbers in more than one

way ¨  Promotes mathematical thinking

Shift in Coherence

Number & Operations

¨  THIRD GRADE 4G: ¤  Use strategies and algorithms, including the standard algorithm,

to multiply a two-digit number by a one digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties

¨  FOURTH GRADE 4D: ¤  Use strategies and algorithms, including the standard algorithm,

to multiply up to a four-digit number by a one-digit number and to multiply a two-digit number by a two-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties

¨  FIFTH GRADE 3E: ¤  Solve for products of decimals to the hundredths, including

situations involving money, using strategies based on place-value understandings, properties of operations, and the relationship to the multiplication of whole numbers

Coherence

Activity 2 - Multiplication

¨ How would you multiply 25 x 28?

How many of you thought:

20 + 8

20 + 5

400 160

100 40

OR

28 x 25

40 100 160 400 700

OR

28 x 25 400 160 100 40

700

OR even 28 x 25 = (20 + 8) x (20 + 5) = (20 x 20) + (20 x 5) + (8 x 20) + (8 x 5)

How many of you thought (con’t):

20 + 8

25

500 200 25 x 28 = 25 x (20 + 8) = (25 x 20) + (25 x 8) = 500 + 200 = 700

How many of you thought (con’t):

25

50

100

28 14 7

28 x 25

14 x 50

7 x 100

How many of you thought (con’t):

25

30

750

25

30 - 2

700

50

Now it is YOUR turn

Solve this problem using any method other than our standard algorithm. A school ordered 52 packages of paper. There were 88 sheets of paper in each package. How many sheets of paper did the school order?

Coherence – Progression across grades

¨  “The coherence and sequential nature of mathematics dictate the foundational skills that are necessary for the learning of algebra. The most important foundational skill not presently developed appears to be proficiency with fractions (including decimals, percents, and negative fractions). The teaching of fractions must be acknowledged as critically important and improved before an increase in student achievement in algebra can be expected.”

Final Report of the National Mathematics Advisory Panel (2008, p. 18)

Shift in Rigor

Mathematical Process Standards Application of Skills in Problem Solving Situations.

(1)  Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: ¨  (A)  apply mathematics to problems arising in everyday life, society, and the workplace; ¨  (B)  use a problem-solving model that incorporates analyzing given information, formulating a

plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;

¨  (C)  select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems;

¨  (D)  communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;

¨  (E)  create and use representations to organize, record, and communicate mathematical ideas; ¨  (F)  analyze mathematical relationships to connect and communicate mathematical ideas; and ¨  (G)  display, explain, and justify mathematical ideas and arguments using precise

mathematical language in written or oral communication.

(4)  Number and operations. 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:

Number & Operations

¨  THIRD GRADE 3D: ¤ Compose and decompose a fraction with a numerator

greater than zero and less than or equal to b as a sum of parts .

¨  FOURTH GRADE 3A: ¤ Represent a fraction as a sum of fractions , where a

and b are whole numbers and b>0, including when a>b.

¨  FIFTH GRADE 3L: ¤ Divide whole numbers by unit fractions and unit

fractions by whole numbers

What is a Unit Fraction?

¨  1/𝑏  ¤  3/4   is three 1/4 ’s or 3 one-fourths ¤  4/5  is four 1/5 ’s or 4 one-fifths

Number & Operations

¨  THIRD GRADE 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

¨  FOURTH GRADE 3A: ¨  Represent a fraction a/b as a sum of fractions 1/b,

where a and b are whole numbers and b >0, including when a>b.

¨  FIFTH GRADE 3L: ¨  Divide whole numbers by unit fractions and unit

fractions by whole numbers

Depth & Rigor

Questions to ask yourself when studying a standard Ø  What do the standards in the grades before and

after your require? Ø  How do the standards in this grade in the other

categories relate/interact? Ø  What depth and complexity does this standard

require (skill, analysis)? Ø  What tools are available to help me study the

standard? Ø  How do the process standards work with the

content?

What now?

¨  Grades 3-5 TEKS Support Handout ¤ Other CAMT TEKS Sessions from TEA ¤ Professional Development Available at you local ESC ¤ Where can you find the revised TEKS posted?

n http://www.tea.state.tx.us/index2.aspx?id=2147499971

¤ Other resources will be posted online: n www.projectsharetexas.org