Teacher worksheet: compare, scale and describe
This printable practice set connects ratio reasoning with descriptive statistics. Students should show the operation used, preserve the order of ratio terms, and label a variance as sample or population. Allow about 15 minutes for independent work, then use the answer key for discussion. To print, use your browser’s Print command and choose the paper size and scale that fit your class.
Part A: ratios and proportions
- Simplify 6:9. State the greatest common factor and show the division applied to both terms.
- Solve 6:9 = 12:x. Show either a scale factor or a cross-product equation, then check that both ratios are equivalent.
- Interpret 2:3 as shares of one whole. If the first and second parts are the only parts, what fraction and percentage of the whole belongs to each?
- Scale a recipe. A soup recipe uses 6 cups of stock for 4 servings. How many cups of stock are needed for 10 servings if the recipe stays proportional?
- Find a class share. In a class, 12 students travel by bus and the other 18 use another method. Simplify the bus-to-other ratio, then find the fraction and percentage of the whole class who travel by bus.
Part B: one dataset, two variance choices
Use 2, 4, 4, 4, 5, 5, 7, 9. Find the count, mean, median, mode, range and sum of squared deviations from the mean. Then calculate both population variance and standard deviation, dividing by n, and sample variance and standard deviation, dividing by n − 1. Finish this sentence: “I would use the sample result when …”
Check after working by hand
Students can compare their method with the Ratio and Proportion Calculator and their dataset summary with the Descriptive Statistics Calculator. A calculator check should follow the written reasoning rather than replace it.
Worked answer key
Ratios
The greatest common factor of 6 and 9 is 3, so 6:9 = (6 ÷ 3):(9 ÷ 3) = 2:3. For 6:9 = 12:x, the scale factor is 12 ÷ 6 = 2, giving x = 9 × 2 = 18. Equivalently, 6x = 9 × 12 = 108, so x = 18. In 2:3, the whole has 2 + 3 = 5 parts: the first share is 2/5 = 40% and the second is 3/5 = 60%.
For the recipe, 4 servings:6 cups = 10 servings:x cups. The scale factor is 10 ÷ 4 = 2.5, so x = 6 × 2.5 = 15 cups. For the class, bus-to-other is 12:18 = 2:3. There are 12 + 18 = 30 students, so the bus share is 12/30 = 2/5 = 40%.
Statistics
There are 8 values with sum 40 and mean 5. The median is 4.5, mode is 4, and range is 9 − 2 = 7. The squared deviations sum to 32. Population variance is 32 ÷ 8 = 4, so population standard deviation is 2. Sample variance is 32 ÷ 7 = 4.5714 and sample standard deviation is 2.1381, rounded to four decimals. Use the sample result when these observations represent part of a larger population.
References: OpenStax: Ratios and Proportions and OpenStax: Measures of the Spread of the Data.