Four Operations

Unit Review Sheet

Facts and Definitions

Lesson 1: Basic Operations with Multi-Digit Numbers

• Algorithm: sequence of steps to follow when completing a math operation
• The standard algorithm for multiplication involves stacking partial products and then adding them together.

Lesson 2: Prime Factorization

• To factor means to break a number down into factors.
• A factor rainbow is a visual aid to help find all of the factors in a number.
• The prime factorization of a composite number is when the number is broken down into all of the prime factors that make up the number, usually written in order from least to greatest.
• A factor tree is a visual aid to help find all of the prime factors in a number.

Lesson 3: Dividing Multi-Digit Numbers

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Lesson 4: Adding Decimals

• To add decimal numbers, stack them vertically with the decimals lined up, adding zeros as needed. Then add just as you would whole numbers, starting at the smallest place and moving to the left, carrying as needed. When you are done adding, bring the decimal point down into the answer.

Lesson 5: Subtracting Decimals

• To subtract decimal numbers, stack them vertically with the decimals lined up, adding zeros as needed. Then subtract just as you would whole numbers, starting at the smallest place and moving to the left, borrowing as needed. When you are done subtracting, bring the decimal point down into the answer.

Lesson 6: Decimal Problem Solving

• If a sum or difference has a zero at the end of a decimal number, you can simplify the answer by dropping the zero or zeros. For example, 1.20 would simplify to 1.2. Money is an exception — $1.20 should not be simplified.

Lesson 7: Multiplying Decimals

• To multiply decimal numbers, first remove the decimal points, multiply as usual, count how many numbers are to the right of the decimal points in BOTH original numbers and add them together, and then place the decimal point in the product to show that number.
• When multiplying decimal numbers, if you round both numbers to the nearest whole number and multiply, you can compare that answer to the answer you get from the standard algorithm to see if your answer looks correct and to confirm that your decimal is in the right place.

Lesson 8: Dividing Decimals

• To divide decimal numbers, write the problem in long division form, and then divide as you would divide whole numbers, ignoring the decimal as you divide. After dividing, put the decimal point in the quotient directly above where it is in the dividend.
• If you are dividing whole numbers and want to find a quotient with an exact amount rather than a remainder, you can add a decimal and one or more zeros to the dividend. For some division problems, this process allows you to divide until there are no remainders.
• If the divisor has a decimal point, move the decimal to the end of the divisor, move the decimal in the dividend to the right the same number of times, and then divide as normal.
• You can use multiplication to check the answers for division problems. Multiply the quotient by the divisor — the answer should be the dividend. For example, to check the accuracy of 256 ÷ 8 = 32, multiply 32 × 8.

Lesson 9: Solving Problems Using the Four Operations

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Lesson 10: Mathematical Expressions

• Parentheses / brackets: math symbols that show grouping: ( ) or [ ]
• Mathematical/numerical expression: a math sentence that includes at least two numbers and one or more operators (+,−,×,÷)

Lesson 11: Introducing Order of Operations

• Order of operations: rules that define the order in which to complete operations (such as addition, subtraction, multiplication, division) when solving a mathematical/numerical expression
• An exponent tells how many times to multiply the base number by itself. For example, in 5³, 5 is the base number and 3 is the exponent, so 5 should be multiplied by itself 3 times: 5×5×5
• PEMDAS: abbreviation for the order of operations (Parentheses and Brackets, Exponents, Multiplication or Division, Addition or Subtraction)

Lesson 12: Working With PEMDAS

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Lesson 13: Unit Test

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Final Project: Teaching Presentations

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