Mathematics Grade 6 15 min

Seasons

Seasons

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1

Introduction & Learning Objectives

Learning Objectives Calculate the percentage of a year represented by each season. Determine and simplify ratios comparing daylight hours to nighttime hours in different seasons. Use integers to represent and calculate temperature changes between seasons. Analyze seasonal data to find averages and ranges of temperature or daylight. Apply algebraic expressions to model simple linear changes in seasonal data, such as daylight hours. Convert between different units of time (days, weeks, months) when analyzing seasonal durations. Have you ever noticed how the weather changes throughout the year, or how the days get longer and shorter? ☀️❄️ What mathematical patterns do you think are hidden in these seasonal shifts? In this lesson, we'll explore the mathematics behind the s...
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Key Concepts & Vocabulary

TermDefinitionExample Seasonal DurationThe length of time each of the four main seasons (Spring, Summer, Autumn/Fall, Winter) lasts, typically measured in days or months.Summer in the Northern Hemisphere typically lasts about 93 days, from late June to late September. Daylight HoursThe number of hours of sunlight a location receives in a 24-hour day, which varies significantly with the seasons.On the Summer Solstice, a city might have 15 hours of daylight, while on the Winter Solstice, it might have only 9 hours. Temperature RangeThe difference between the highest and lowest temperatures recorded over a specific period, often used to describe seasonal temperature variations.If the highest summer temperature is 30°C and the lowest winter temperature is -5°C, the annual temperature range is...
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Core Formulas

Percentage Calculation $$ \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100\% $$ Use this to find what portion of a whole (like a year) a specific part (like a season's duration) represents, expressed as a percentage. Ratio Representation $$ a:b \quad \text{or} \quad \frac{a}{b} $$ Use this to compare two quantities, such as daylight hours to nighttime hours. Ratios should often be simplified to their simplest form. Temperature Change (Integers) $$ \text{Change} = \text{Final Temperature} - \text{Initial Temperature} $$ Use this to calculate the difference in temperature between two points in time or two seasons. Remember to use integer rules for positive and negative numbers. Average Calculation $$ \text{Average} = \frac{\text...

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Sample Practice Questions

Challenging
The amount of daylight in minutes, `M`, increases after the winter solstice according to the formula `M = 500 + 4d`, where `d` is the number of days past the solstice. How many weeks will it take for the daylight to increase from 500 minutes to 640 minutes?
A.4 weeks
B.7 weeks
C.5 weeks
D.35 weeks
Challenging
The duration of the four seasons in a region are in a simplified ratio of 5:5:4:4. If the entire year is 360 days for easier calculation, how many more days are in a long season compared to a short season?
A.10 days
B.20 days
C.30 days
D.40 days
Challenging
In a city, the number of daylight hours on the summer solstice is 16. The number of daylight hours `h` can be modeled by `h = 10 + 0.05t` where `t` is the number of days after the spring equinox. How many days are there between the spring equinox and the summer solstice in this model?
A.50 days
B.60 days
C.100 days
D.120 days

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