Category Archives: Mathematics

Math Tutorial: Opening Sessions

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Reference: Critical Thinking in Education

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The following outline may help you get started as a tutor with a new student. Simply use the introductory materials form Remedial Math Level 1.

There are many ways to start with a new student; but the following is the best way to start with students from middle and high schools. This outline is good for couple of beginning sessions.

NOTE: For youngers students, start from step 4, and go over each lesson very closely. Explain each paragraph to them in simple language so they can understand the materials. 

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(1) Ask the student the meaning of the word MATHEMATICS.

Use SECTION 1 from Math Overview to explain it. It is also okay if you just show him the two points of SECTION 1, while explaining it to him. Have him give an example per the exercise in that section.

(2) Ask the student, “Why should somebody study mathematics?”

Use SECTION 2 from Math Overview to explain it. Ask him the three puzzles. Give him some hints if he is having trouble solving them. If he can’t solve a puzzle show him the answer.

(3) Ask the student, “What are the three main parts of mathematics?”

Use SECTION 3 from Math Overview to explain it. Explain each part and its meaning as given. Demonstrate the use of each part per the sample problem provided.

(4) Ask the student about the difference between a NUMBER and a DIGIT.

Use SECTION 2 from Lesson 1: Arithmetic & Numbers to explain it.

(5) Ask the student about the place values on an abacus.

Use the understanding from the reference MS A1 Numbers to explain what an abacus is, and to demonstrate the place values on it.

(6) Go over Lesson 1: Arithmetic & Numbers with the student.

Have the student read each numbered section silently one at a time. You read silently along with him. Have him do the exercises after each section. Explain anything that he does not understand.

(7) Lightly supervise the student as he studies subsequent lessons.

Keep an eye on the student as he is starts to study the subsequent lessons on his own. Make sure he does the exercise of each section till he can apply the materials. Check his answers for correctness. Explain anything that he does not understand.

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Remedial Math Level Pre-0

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Reference: Remedial Math

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For application by parents

Lesson 1: ORIENTATION & SPATIAL SENSE

Lesson 2: QUANTITY & NUMBER SENSE

Lesson 3: PATTERNS & RELATIONAL SENSE

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Remedial Math Level 0

Abacus

Reference: Remedial Math

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For application by parents

Lesson 1: Orientation & Spatial Sense

Lesson 2: Numbers & Place Values

Lesson 3: Units & Fractions

Lesson 4: Counting & Measurements

Lesson 5: Numbers & Operations

Lesson 6: Patterns & Relational Sense

Lesson 7: Data Analysis & Probability

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Some Old Books

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ARITHMETIC TEXTBOOKS

1885 Ray’s Practical Arithmetic

1893 Dubb’s Arithmetical Problems

ALGEBRA TEXTBOOK

1896 Elementary Algebra

GEOMETRY TEXTBOOK

1913 Wentworth Smith

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Math Online Materials

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ALGEBRA

Algebra Cheat Sheet

Preliminaries

Solving Equations and Inequalities

Graphing and Functions

Common Graphs

Polynomial Functions

Exponential and Logarithm Functions

Systems of Equations

TRIGNOMETRY

Trig Cheat Sheet

Trigonometry Index

Algebra/Trig Review

CALCULUS

Calculus Cheat Sheet

Volumes by Cylindrical Shells

Calculus I

[Practice Problems] [Assignment Problems]

Calculus II

[Practice Problems] [Assignment Problems]

Calculus III

[Practice Problems] [Assignment Problems]

Differential Equations

HMC Online Tutorials