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Student example record possible areas for making a square pen.

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Order of Operations

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Organization of the real numbers.

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- A whole number exponent is repeated multiplication of a number times itself.
- Exponents are first introduced to students in 5th grade relating to powers of 10 and place value.
- A common confusion for students is whether to add or multiply the exponents.
- Teachers can connect what students already know with area to exponents through a pen picture chart.

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- Positive/negative whole numbers and zero
- Context for positive and negative numbers:
- Temperature, altitude, golf, money, timelines, football yardage
- Absolute value is the distance from zero
- The negative sign (minus sign) can be confusing to students
- Effective models for teaching Positive/Negative numbers, should be chosen based on context:
- Counters
- Number Lines
- Addition and subtraction: ask questions such as Where did you start? How far did you go? Where are you now?
- Multiplication and division:  3 x -4 is the same thing as positive 3 sets of -4, -2 x -3 is the same thing as negative 2 sets of -3 less than zero (make zero pairs then take away two pairs of -3 and you are left with positive 6)

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- Scientific notation means a number is changed to be the product of a number greater than or equal to 1 and less than 10 multiplied by a power of 10.

Example: In 2014, the population of the world was 7, 171,919,206. This number can be expressed in a number of ways using scientific notation:
- 7,172 million
- 7.2 x 10^9
- Nearly 7 billion

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- It is not just a convention, it is based on the meaning of operations
- Why are exponents solved before addition?
- Students can see why adding before solving the exponents changes the meaning of the problem and the answer
- Ex. 8 + 3 x 5  = 23
- PEMDAS or BODMAS/BEDMAS/BIDMAS
- parentheses/bracket,
- exponents/order/indices
- Can lead students to think addition is done before subtraction and multiplication is done before division
- Visuals can be more beneficial