BrainMath Supplement:Curriculum Organization

Table of Contents

• Introduction• Classification of the Curriculum– Skills and Above (Units, Grade, Subject, Strand)– Skills and Below (Lesson, Problem Type, Problems, …)

• SmartGuide– Skills and Above– Skills and Below

Introduction• This document gives a theoretical overview on how the Curriculum

and SmartGuide are structured.• Fractions.docx contains the entire fraction subject. Read it to see

real examples on – Units– Skills– Lessons (Text, Examples, Exercises)– Problem Types– Problems

• BrainMath - All.png: illustrates how the curriculum translates onto the web page. Includes wireframes for:– “Curriculum Navigator”: how students browse/search for a skill– “Learn and Practice”: how students learn/practice a skill

Classification of the Curriculum• Skill & Above

– The most important item is the skill.– Skills are organized into units. (many-to-many relationship). – Skills also belong to grades. (many-to-many relationship).– Units belong to subjects. (many-to-many relationship). – Subjects belong to strands. (many-to-one relationship).

• Skill & Below– Skills are made of lesson, and problem types.

• Each skill has at most one lesson (one-to-one relationship).• Each skill can have many problem types, and a problem type can be long to several skills (many-to-many relationship).

– Each lesson is made of text, examples, and exercises—all on one page.– Each problem type can have at most one example. (one-to-one relationship). – Each problem type can have many problems, and a problem can belong to several problem types. (many-to-

many relationship).• Tests and Quizzes

– Sometimes, quizzes are required to pass a skill. A quiz is simply a modified problem-type.– Sometimes, tests are required to pass a unit. A test is simply a modified problem-type.

Units

Skills

GradesSkills and AboveGrades, Subjects, Units, and Skills

Subjects

Addition and Subtraction with Mixed Numbers

Adding and Subtracting Fractions

Mixed Numbers and Improper Fractions

Many-to-Many

Addition and Subtraction with

Like Denominators

Addition and Subtraction with Related

Denominators

Addition and Subtraction using LCM

Multiplication of Fractions

Prime Numbers and Prime Factorization

Identify Mixed Numbers and

Improper Fractions

Convert between Mixed Numbers and

Improper Fractions

Fundamentals 3 Fundamentals 4 Fundamentals 5 Fundamentals 6

Strands

Many-to-Many

FractionsNumber Theory

Many-to-Many

Factors, Multiples, GCF, and LCM

Fractions, Decimals, Ratios, and Percents

Whole Numbers

Addition and Subtraction

Many-to-One

Tests (basically a modified Problem-

Type)

Tests (basical

ly a modifie

d Proble

m-Type)

Many-to-One

Units

Tests

LEGEND

Skills and Tests

Grades

Subjects

Strands

Skill and BelowLessons, Problem Types, Quizzes, and Problems/Text/Example/Exercises

Addition and Subtraction with Mixed Numbers

Lesson

Problems

Problem Type

Problem TypeProblem Type

Many-to-Many

Addition and Subtraction with Mixed Numbers

Problem Type

Problem

One-to-One

Lesson

One-to-One

Problems

Many-to-ManyText

Example

Exercise

Text

Exercise

Quiz (basically

a modified Problem-

Type)

Many-to-One

Skills

Problem Type

Lesson

Quiz

Quiz (basically

a modified Problem-

Type)

Many-to-Many

Lessons, Problem Types, and Quizzes

Skills

Problems, and

Text/Example/Exercises

ProblemsExample

One-To-One

Problems, Text, Example, Exercises

Que

stio

n

Answ

er

Solu

tion

Que

stio

n

Solu

tion

SmartGuidePassing Criteria

• A student passes a skill if:– He passes all the problem types within that skill.• Even if he passed that problem type while officially

practicing a different skill.

– He passes all the quizzes within that skill (if any).• A student passes a unit if – He passes all the skills within that unit.– He passes all the tests within that unit (if any).

Units

SmartGuidePrerequisite Map (within Skills and Tests)Arrows indicate prerequisite relationship.

Addition and Subtraction with Mixed Numbers

Addition and Subtraction with Like Denominators

Addition and Subtraction with Related Denominators

Addition and Subtraction using

LCM

Identify Mixed Numbers and

Improper Fractions

Convert between Mixed Numbers and Improper

Fractions

Tests (basically a modified Problem-

Type)

Tests (basically a modified Problem-

Type)

Problem Type

Problem Type

Problem Type

Quiz

Problem Type

Tests (basically a modified Problem-

Type)

[Unit] Addition and Subtraction of Fractions

[Unit] Mixed Numbers and improper fractions

Skills

Problem Type

Quiz/Test

Units