CONTENT LITERACY INSTRUCTIONAL

SHIFTS FOR MATH

FacilitatorAuddie Mastroleo ҉ OCM BOCES Network Team

Balancing Informational & Literary Texts (Grades PK-5)

Knowledge in the Disciplines (Grades 6-12)

Staircase of Complexity

Text-based Answers

Writing from Sources

Academic Vocabulary

COMMON CORE SHIFTS ELA & CONTENT LITERACY

SHIFT 1

GradesPK-5

BALANCING INFORMATIONAL &

LITERARY TEXTSRange of Text Types

Literature = Stories, Dramas, Poetry

Informational = Literary Nonfiction, Historical,

Scientific, & Technical Texts

50% fiction 50% nonfiction40% fiction 60% nonfiction

20% fiction 80% nonfiction

4th grade

8th grade

12th grade

Increase in teaching

and learning with non-

fiction text

SHIFT 2

Grades6-12

KNOWLEDGE IN THE DISCIPLINES

Reading & Writing Literacy

Standards

• Complement, not replace content standards

Depending on text rather than

referring to it

•Read a president’s speech & write a response•Read scientific papers & write an analysis

Think sophisticated

non-fiction

•Analyze and evaluate texts within disciplines•Gain knowledge from texts that convey complex information through diagrams, charts, evidence, & illustrations

Expectation of rigorous

domain specific literacy

instruction outside of

ELA

SHIFT 1

Balancing Information

al and Literary

Texts

SHIFT 2

Building Knowledge

in the Disciplines

Core Text

Pre-CCLS

SHIFT 1

Balancing Information

al and Literary

Texts

SHIFT 2

Building Knowledge

in the Disciplines

Paired Texts: The Golden Ratio

Core Texts

Post-CCLS

MATH PRE AND POST SHIFT NOTES

With a partner…

Share your initial thinking and

reactions

TURN AND TALK

SHIFT 3

STAIRCASE OF COMPLEXITY

Increase in text complexity at each grade level

QualitativeLevels of meaningStructureClarity of languageKnowledge demands

QuantitativeWord length

Sentence length

Text cohesion

Reader & Task MotivationKnowledgeExperience

Appendix B:

Text Exemplars

and Sample Performance

Tasks

Expectation of proficiency

and independence

in reading grade level

text

SHIFT 3

Staircase of Complexity

PRE-CCLSA ratio compares two numbers by division. The ratio of two numbers a and b can be written as a to b, a:b, or a/b, where b=0. For example, the rations 1 to 2, 1:2, and ½ all represent the same comparison.

A proportion is an equation stating that two ratios are equal. In the proportion a/b=c/d, the values a and d are the extremes. The values b and c are the means. When proportion is written as a:b=c:d, the examples are the first and last positions. The means are in the two middle positions.

SHIFT 3

Staircase of

Complexity

POST-CCLSIn everyday life, we use the word

”proportion” either for the comparative relation between parts of things with respect to size or quantity or when we want to describe harmonious relationship between different parts. In mathematics, the term “proportion” is used to describe equality of the type: nine is to three as six is to two.

The Golden Ratio has been used in [art, architecture, design, and music] to achieve what we might term as “visual (or audio) effectiveness.” One of the properties contributing to such effectiveness is proportion – the size and relationships of part to one another and to the whole. The history of art shows that in the long search for an elusive canon of “perfect” proportion, one would somehow automatically confer aesthetically pleasing qualities on all works of art, the Golden Ratio has proven to be the most enduring.

SHIFT 4

TEXT-BASED ANSWERS

Questions tied directly to the text, but extend beyond the

literal

Students must cite

text to support answers

Personal opinions,

experiences, and

connections to the text

are minimized in favor of what

the text actually says

or doesn’t say

Questions are purposefully planned &

direct students to

closely examine the

text

SHIFT 4

Text-based Answers

Question:The ratio of the side lengths of a quadrilateral is 2:3:5:7, and its perimeter is 85ft. What is the length of the longest side?

PRE-CCLS

A ratio compares two numbers by division. The ratio of two numbers a and b can be written as a to b, a:b, or a/b, where b=0. For example, the rations 1 to 2, 1:2, and ½ all represent the same comparison.

A proportion is an equation stating that two ratios are equal. In the proportion a/b=c/d, the values a and d are the extremes. The values b and c are the means. When proportion is written as a:b=c:d, the examples are the first and last positions. The means are in the two middle positions.

SHIFT 4

Text-based Answers

Question:Describe how the idea of proportion can be applied to mathematical concepts as well as life and culture.

Use specifi c examples from the text to support your answer.

POST-CCLSIn everyday life, we use the word

”proportion” either for the comparative relation between parts of things with respect to size or quantity or when we want to describe harmonious relationship between different parts. In mathematics, the term “proportion” is used to describe equality of the type: nine is to three as six is to two.

The Golden Ratio has been used in [nature, art, architecture, design, and music] to achieve what we might term as “visual (or audio) effectiveness.” One of the properties contributing to such effectiveness is proportion – the size and relationships of part to one another and to the whole. The history of art shows that in the long search for an elusive canon of “perfect” proportion, one would somehow automatically confer aesthetically pleasing qualities on all works of art, the Golden Ratio has proven to be the most enduring.

MATH PRE AND POST SHIFTS NOTES

With a partner…

Share your initial thinking and

reactions

TURN AND TALK

SHIFT 5

WRITING FROM SOURCES

Three Text Types

Argument

Supporting a claim with sound reasoning and relevant evidenceInformational

/Explanatory Writing

Increase subject knowledge

Explain a process

Enhance comprehension

Narrative Writing

Conveys experience i.e. fictional stories, memoirs, anecdotes, autobiographies

Appendix C: Samples of

Student Writing

Argumentative writing is especially

prominent in the CCLS

SHIFT 5

Writing from

Sources

1. Is the ratio 6:7 the same as 7:6? Why or why not?2. Susan wants to know if the fractions 3/7 and 12/18 are equivalent. Explain how she can use the properties of proportions to find out.3. Copy and complete the graphic organizer. In the boxes, write the definition of a proportion, the properties of proportions, and examples and non-examples of a proportion.

Pre-CCLS

SHIFT 5

Writing from

Sources

Architect, mathematician, and engineer, Richard Buckminster Fuller once said,

“When I am working on a problem, I never think about beauty. I think only of how to solve the problem. But when I have finished, if the solution is not beautiful, I know it is wrong.”

Use your knowledge of proportions and the text, The Golden Ratio to agree or disagree with this quote.

Define and explain the

mystery of the golden ratio.

Provide examples of

mathematical and real life

applications of the golden

ratio.

Show the mathematics of the golden

ratio as it applies to your

examples.

Post-CCLS

SHIFT 6

ACADEMIC VOCABULARY

Tier One

Words

• Words of everyday speech

Tier Two

Words

• Not specific to any one academic area

• Generally not well-defined by context or explicitly defined within a text

• Wide applicability to many types of reading

Tier Three Words

• Domain specific• Low-frequency• Often explicitly defined • Heavily scaffolded

Ramp up instruction of Tier Two

words

SHIFT 6

Academic Vocabular

y

Pre-CCLS

ratio

proportion

extremes

means

SHIFT 6

Academic Vocabular

y

Post-CCLS

MATH PRE AND POST SHIFTS NOTES

With a partner…

Share your initial thinking and

reactions

TURN AND TALK

QUESTIONS? CONCERNS? NOTICES?