Math is my favorite subject. Why? To be honest, it doesn’t involve too much memorization. You only need to know the basics and everything is like chain reaction. For example, you cannot solve a word problem if you don’t understand the basic mathematical operations. I also like how the lessons are related to real-world objects.
(Math evolves over time) Everything I’ve learned, I can till use moving forward, even those I’ve learned during 1st grade.
The most important thing to realize when solving difficult mathematical problems is that one never solves such a problem on the first attempt.
I have summarized what I have learned on the outline below. It started with the easy ones then progressed to challenging lessons.
Lesson 1. Reviewing Place Value
- Each place value in the Hindu-Arabic numeration is 10 times the value of the place to its right.
- The place value position of a digit in a number determines the value of the digit.
Lesson 2. Comparing Whole Numbers
- Align the digits with the same place value.
- Start comparing the digits in the highest place value position.
- Keep comparing the aligned digits in the next place value postions until you find a difference.
Lesson 3.Understanding Exponential Notations
- Exponent tells how many times a base number is taken as a factor.
- Any number raised in the zero power is equal to 1.
Lesson 4.Under standing Hindu-Arabic and Roman Numerals
- The Roman numeration system uses the letters I,V,X,L,C,D and M to write numerals.
- Unlike the Hindu-Arabic numeration system, there is no symbol for zero in the Roman numeration system.
Lesson 5. Finding Terms in a Pattern or Sequence
- To find the pattern in a sequence, compare consecutive pairs of terms in the sequence and analyze them. The pattern may be based on addition, subtraction, multiplication, division or a combination of these operations.
Lesson 6. Reviewing Whole Number Operations
- Addition is putting together quantities while subtraction is taking away quantity from another.
- Multiplication is repeated addition while division is repeated subtraction.
Lesson 7.Reviewing Properties of Whole Numbers
- Commutative property refers to changing the order while associative property.
- Multiplication is distributive over addition and subtraction.
- Never divide by 0.
Lesson 8. Reviewing Order of Operations
The rules for the order of operations state that:
- After doing the operations in parentheses, calculate first the exponents then multiply or divide before adding or subtracting.
- Always start from left to right when performing the operations.
Lesson 9.Understanding mental addition and subtraction
- Mastery of the basic facts is important for mental computation.
Lesson 10. Reviewing Ways to Solve Word Problems
- Understanding the problem is very important in solving word problems.
- Check if the answer to the problem makes sense.
- Always label the answer by naming the object or unit that problem asked.
Lesson 11.Finding Hidden Questions in Word Problems
- Look for hidden question/s in the problem.
- Answer the hidden question/s first before answering what is asked in the problem.
Lesson 12. Rounding Whole Numbers
- Rounding a number is giving an estimate or the number that is near or close to the actual number.
Lesson 13. Estimating Sums and Difference
- To estimate the sum or difference of numbers, round the numbers first to the desired place value before adding or subtracting
Lesson 14. Adding and Subtracting Large Numbers
- To add or subtract large numbers, arrange to minuend and subtrahend in column in such a way that the digits belonging to the same place value position are aligned.
- To check the answer in subtraction, add the difference to the subtrahend. The answer is correct if the result is equal to the minuend.
Lesson 15. Subtracting with Zeros in the Minuend
- Regroup and rename the number in the minuend if the digit in the subtrahend is greater than the digit in the minuend.
Lesson 16.Multiplying and Dividing Multiples of 10
- To multiply multiples of 10, multiply the nonzero digits and annex to the product as many zeros as there are in the factors.
- To divide multiples of 10, cancel the zeros in the divisor and the corresponding number of zeros in the dividend. Divide the nonzero digits and annex the zeros left in the dividend to the quotient.
Lesson 17. Estimating Products and Quotients
- To estimate products or quotients, round the numbers before multiplying or dividing.
- Use shortcuts in multiplying or dividing multiples of 10.
Lesson 18.Multiplying by Two- to Three-digit Multipliers
- The partial-products method uses the distributive property of multiplication.
Lesson 19. Dividing by Two- to Three-digit Divisors
- Use estimation to get that partial quotients when dividing large numbers. Add the partial quotients.
- The sequence of operations used in dividing large numbers is dive, multiply and subtract.
- To check the answer to division with remainder, multiply the quotient by the divisor and add the remainder to the product. The result must be equal to the dividend.
Lesson 20.Solving More Word Problems
- Read or listen to the problem carefully to understand what it says.
- Find hidden question/s and answer it/them first.