Months of the year

Learning Objectives Calculate and simplify ratios using various properties of the months of the year (e.g., number of days, letters in name). Set up and solve proportions to find unknown values in problems related to calendar data. Calculate and interpret unit rates in the context of months, such as events per month. Distinguish between part-to-part and part-to-whole ratios when analyzing the calendar year. Apply proportional reasoning to verify claims about relationships between different groups of months. Use algebraic expressions to represent quantities in a ratio and solve for them. Is the ratio of summer months to winter months proportional to the ratio of months starting with 'J' to months starting with 'A'? 🤔 Let's use math to find out! In t...

TermDefinitionExample RatioA comparison of two or more quantities, showing their relative sizes. Ratios can be written as a:b, a/b, or 'a to b'.The ratio of months with exactly 30 days (4 months: Apr, Jun, Sep, Nov) to the total months in a year (12) is 4:12, which simplifies to 1:3. RateA special type of ratio that compares two quantities with different units.If there are 6 school holidays spread across the 3 months of summer, the rate is 6 holidays / 3 months. Unit RateA rate that has been simplified to have a denominator of 1.Using the rate of 6 holidays / 3 months, the unit rate is 2 holidays per month. ProportionAn equation stating that two ratios are equal. It is used to determine if two sets of quantities have the same relative relationship.The proportion 3/6 = 4/8 shows...

Proportion Equation \frac{a}{b} = \frac{c}{d} This is the fundamental structure of a proportion, where a/b and c/d are two equivalent ratios. It reads 'a is to b as c is to d'. Cross-Multiplication Property If \frac{a}{b} = \frac{c}{d}, then ad = bc To solve for an unknown variable in a proportion, you can multiply the numerator of one ratio by the denominator of the other. This is the most common method for solving proportions.