Metrics and Estimates

prerequisite knowledge

• Understand and use arbitrarily sized decimals, measurements, and integer digit values
• It uses four operations with formal notations that apply to integers and decimals.
• Sort positive and negative integers, decimals, and fractions. Use the number line as a model for the ordering of real numbers. =, ≠,<、>Use the symbols , ≤, ≥

key concepts

• 2³, where 2 is the base and 3 is the power. Raise the base to power.
• Students should understand that dividing by a decimal and multiplying by a reciprocal are equivalent. Because this leads to dividing by a fraction.
• All powers of zero are equal to one. Students need to understand this that a number divided by itself is equal to 1.
• The multiplication rule can be defined as n^a ×n^b = n^(a+b). The splitting rule is defined as n.^a÷n^b = n^(ab).
• power rule (2³)² = 2⁶ An extension of the multiplication rule. The power-of-zero rule is an extension of the division rule.
• A number raised to the negative power of one is the reciprocal of that number.
• When rounding 3.5 to one significant digit, 3 is the most significant and 1/5 rounds up to 4.
• If you write the number with the standard index of the number before the decimal point, it must be in the range 1 to 9.

work mathematically

develop fluency

• Choose and use appropriate calculation methods to solve increasingly complex problems.

justify mathematically

• Extends and formalizes knowledge of ratios and ratios in dealing with measures and geometry and formulating proportional relationships algebraically.
• Make and test guesses about patterns and relationships. Look for proofs and counterexamples.

problem solving

• Develop the use of formal mathematical knowledge to interpret and solve problems.

Subject content

number

• Use conventional notation for arithmetic precedence, such as parentheses, powers, roots, and reciprocals.
• Uses integer powers and related real roots (square, cubic, and higher) and recognizes powers of 2, 3, 4, and 5
• Interpret and compare numbers in normal form A × 10ⁿwhere 1≤A<10 and n is a positive or negative integer or zero
• Round numbers and measurements to the appropriate precision [for
  example, to a number of decimal places or significant figures]
• Estimate the answer using rounding approximation and write the inequality notation a
• Accurately calculate and properly interpret results using calculators and other techniques