Excerpts from the Algebra Standard

Excerpts from the Algebra Standard

Understand patterns, relations, and functions

Grades PK-2

• Sort, classify, and order objects by size, number, and other

properties

• Recognize, describe, and extend patterns such as sequences

of sounds and shapes or simple numeric patterns and translate

from one representation to another

• Analyze how both repeating and growing patterns are

generated

Grades 3-5

• Describe, extend, and make generalizations about geometric

and numeric patterns

• Represent and analyze patterns and functions, using words,

tables, and graphs

Analyze change in various contexts

Grades PK-2

• Describe qualitative change, such as a student’s growing

taller

• Describe quantitative change, such as a student’s growing

two inches in one year

Grades 3-5

• Investigate how a change in one variable relates to a change

in a second variable

• Identify and describe situations with constant or varying rates

of change and compare them

Principles and Standards for School Mathematics

National Council of Teachers of Mathematics

2000

Master 14-1: Algebra Excerpts (Patterns and Change)

Excerpts from the Algebra Standard

Represent and analyze mathematical situations and

structures using algebraic symbols.

PK-2

• Illustrate general principles and properties of operations, such

as commutativity, using specific numbers

• Use concrete, pictorial, and verbal representations to develop

an understanding of invented and conventional symbolic

notations

3-5

• Identify such properties as commutativity, associativity, and

distributivity and use them to compute with whole numbers

• Represent the idea of a variable as an unknown quantity using

a letter or symbol

• Express mathematical relationships using equations

Use mathematical models to represent and understand

quantitative relationships.

Grades PK-2

• Model situations that involve the addition and subtraction of

whole numbers, using objects, pictures, and symbols

Grades 3-5

• Model problem situations with objects and use

representations such as graphs, tables, and equations to draw

conclusions

Principles and Standards for School Mathematics

National Council of Teachers of Mathematics

2000

Master 14-2: Algebra Excerpts (Representation and Models)

Using Patterns

These drawings suggest some patterns.

Look the drawings over carefully and describe a pattern.

If you were building the “next square”, describe the next backward “L” you would need.

Use a pattern to predict the sum when n = 10. Check to see if your prediction is correct.

Now use a pattern to predict the sum when n = 20.

Tell how you would express this relationship as a formula.

Master 14-3: Using Patterns

Consider the fractions:

, , , , , , ,

Think of each fraction as a division

problem and compute each quotient.

Do you observe anything of interest?

Suppose a different denominator had

been selected, for example 11.

Look at the fractions through

repeating the process outlined above.

Do you observe any patterns?

Can you predict 7 ÷ 11 from the

information gathered?

Master 14-4: Fraction Patterns

These are word palindromes:
WOW TOOT NOON
Are the following number palindromes?
6556 1231 44 232 9887
How would you define palindrome?
Circle all palindromes on the hundred
chart.
Consider 57. Can we transform 57 to form
a palindrome?
Start with 57 + 75 = 132 (not a palindrome)
Try 132 + 231 = 363 (Palindrome!)
We call 57 a two-step palindrome.
Choose another number and see how many
steps it takes to form a palindrome.
Investigate other numbers on the hundred
board. Mark one-step, two-step, three
step palindromes using different colors for
each category. Is there a pattern?

Master 14-5: Palindromes