Fractions, Decimals, and Percentages

• Topics covered include fractions, decimals, percentages, geometry, sequences, and functions

Fraction of an Amount

• Calculate a fraction of an amount by multiplying the amount by the fraction

Multiplying and Dividing Fractions

• Multiply fractions by multiplying the numerators and denominators separately
• Divide fractions by inverting the second fraction and then multiplying

Multiplying and Dividing Mixed Numbers

• Convert mixed numbers to improper fractions before multiplying or dividing
• Multiply or divide as with regular fractions

Converting Decimals to Fractions and Vice Versa

• Convert decimals to fractions by placing the decimal over the appropriate power of 10
• Simplify the fraction
• Divide the numerator by the denominator to convert fractions to decimals

Ordering Decimals

• Compare decimals by lining up the decimal points and comparing digits from left to right

Adding and Subtracting Decimals

• Add or subtract decimals by lining up the decimal points and adding or subtracting digits in the same place value

Multiplying Decimals by Whole Numbers

• Multiply decimals by whole numbers as if the decimal weren't there
• Place the decimal point in the product so that it has the same number of decimal places as the original decimal

Dividing Decimals by Whole Numbers

• Divide decimals by whole numbers as if the decimal weren't there
• Place the decimal point in the quotient directly above the decimal point in the dividend

Making Decimal Calculations Easier

• Round numbers to make calculations easier
• Adjust the answer to compensate for the rounding

Types of Angles

• Acute angles: less than 90 degrees
• Right angles: exactly 90 degrees
• Obtuse angles: greater than 90 degrees but less than 180 degrees
• Straight angles: exactly 180 degrees
• Reflex angles: greater than 180 degrees but less than 360 degrees

Angles of Triangles and Quadrilaterals

• The angles in a triangle add up to 180 degrees
• The angles in a quadrilateral add up to 360 degrees

Angles in Intersecting and Parallel Lines

• Vertically opposite angles are equal
• Alternate angles are equal
• Corresponding angles are equal
• Co-interior angles add up to 180 degrees

Lines of Symmetry

• A line of symmetry divides a shape into two identical halves

Rotational Symmetry

• Rotational symmetry is when a shape looks the same after a rotation of less than 360 degrees

Circle and Polygon

• A circle is a round shape with all points equidistant from the center
• A polygon is a closed shape with straight sides

Congruent Shapes

• Congruent shapes are identical in size and shape

3D Shapes

• Common 3D shapes include cubes, cuboids, spheres, cylinders, and cones

Generating Sequence. Term-to-Term Rule

• A term-to-term rule defines how to get from one term in a sequence to the next

Sequence in Patterns

• Patterns can generate sequences of numbers or shapes

Position-to-Term Rule. Finding Nth Term

• A position-to-term rule defines how to find any term in a sequence based on its position
• This is often expressed as a formula for the nth term

Function Machine

• A function machine takes an input, applies a rule, and produces an output

Fractions, Decimals, Percentages

• Fractions, decimals, and percentages are different ways of representing the same value

Percentage of an Amount

• Calculate a percentage of an amount by multiplying the amount by the percentage as a decimal

Percentage Increase and Decrease

• Calculate percentage increase or decrease by finding the difference between the new and original amounts, dividing by the original amount, and multiplying by 100

Percentage Change

• Percentage change = ((New Value - Old Value) / Old Value) * 100