Depth and Complexity Planning Guide

Grade: 4th Content Area: Math Subject: Math Workshop

Topic: Multiplication/Geometry Discipline(s): Mathematics

Language of the Discipline –

What specialized vocabulary, skills, tasks, and tools are specific to the discipline and this area of study? / *factor *parallel
*multiple *array
*perpendicular *acute angle
*right angle *obtuse angle
*polygons

Details –

What attributes, characteristics, and elements distinguish this idea or topic from other things? / What is the difference between a factor and a multiple?
What strategy is used to solve multiplication combinations?
What are the names of the angles?
What is the difference between parallel lines and perpendicular lines?
Can scholars describe polygons and their attributes?

Z

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Patterns –

What recurring elements, events, or ideas are repeated? Is there a pattern? Can it be predicted?

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What are the patterns when describing polygons?

What are the patterns seen when playing Factor Pairs?
What patterns are seen when comparing factors and multiples?
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Trends –

What on-going factors have influenced this study? What patterns have occurred over time? / After scholars complete math workshop, do they notice a trend in their understanding of multiplication and polygons?
Do scholars know the difference between a factor and a multiple?
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Unanswered Questions –

What is still unclear and unknown? What areas require further exploration or evidence of support? / Can scholars use their knowledge of factors and multiples when multiplying greater numbers?
Can scholars identify polygons by their angles and sides?
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Rules –

What are the stated and unstated factors that govern this area of study? How is it structured? / Polygons have the same number of sides and vertices.
An array is a rectangular arrangement made up of equal amounts in columns and rows.
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Ethics –

What are the moral or ethical implications? Is there any bias, prejudice, or discrimination?
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Generalizations/Big Ideas –

What general statement, overarching idea, or conclusion best describes this area of study? / Factors and multiples are the basis for future learning in math. Scholars need to be able to identify and describe the difference between a factor and a multiple.
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Over Time –

How and why do things change or remain the same over time? How are ideas related within or during a specific time period? / Over time, scholars will have an increased knowledge of factors, multiples, and polygons due to the skills practiced in Math Workshop.
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Multiple Points of View –

What are the varying theories and viewpoints regarding this area of study? What evidence supports these viewpoints? Is there conflict?
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Interdisciplinary Connections –

How does this area of study relate to or integrate with another area of study, topic, or discipline? / Where are polygons used/seen in our classroom and in the world?
Scholars make connections with polygons and multiplication in math and science.
Do scholars see arrays in their homes?

Theme: Structures

Generalizations:

1. Patterns provide structure.

2. Structures change, and those changes have consequences

3. Structures are natural or person made

4. Structural design is a consequence of need.

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Adapted from Facilitating the Understanding of Depth and Complexity developed with funds from USDE Javits Grant t the University of Southern California by Dr. Sandra Kaplan, 1997.