Using benchmarks to estimate percentages

Have you ever made an analogy or compared things in relation to something else? You might have used a bag of rice as a guide to estimate the weight of a backpack or a pumpkin. Benchmarks are ways that we can use a point of reference to make it easier for us to estimate or compare values. Today’s lesson is focused on using benchmarks to figure out percentages. If we had 350 balloons, and wanted to give out 10% of the balloons, how would we be able to figure out the number of balloons? How can you estimate sales tax on an item that costs $29.99 and has a sales tax of 13%? When might benchmarks be helpful when we are using data that includes percentages?

Benchmarks

There are different benchmarks you can use to help you figure out percentages.

Percentages as fractions

Percentages represent fractions. 1% represents $\frac{1}{100}$ and 25% represents $\frac{25}{100}.$  When you represent percentages as fractions, it helps to break down the number into parts that are easy to interpret and build upon. For example, if you had 500 apples and wanted to know how many you would share if you wanted to donate 75%, you could imagine that 50% of 500 is 250 apples. Half of that would be 25%, or 125 apples. In order to get to 75%, you could add 50% and 25% or in our example, 250 + 125 = 375 apples. Therefore, 75% of 500 apples is 375.

Adding 10% and 1%

Another strategy is to think about 10% and 1% as helpful benchmarks. You can calculate any percentage this way. For example, if you had 500 apples and you wanted to know how many you would share if you wanted to donate 32%, you could imagine that 10% of 500 is 50 apples and 1% of 500 is 5 apples. In order to get 32% you could add 10% and 1% until you got your number, or in our example, 50 + 50 + 50 + 5 + 5 = 160 apples. Therefore 32% of 500 apples is 160 apples. Therefore 32% of 500 apples is 160 apples.

Mental math

The goal of mental math is to be able to make everyday calculations without using a calculator or paper and pencil. Often when we think of mental math, we immediately think about minute math and quickly coming to the solution. This is not always the case. Mental math also supports a deeper understanding of math concepts when we are able to explore the relationships between numbers.

What do you think is the benefit of mental math? How can mental math help you?

Task: Calculating donation percentages

Each year, various charity organizations receive donations to support efforts to combat climate change. Throughout the year, these organizations need to predict how much of their annual donations they will receive throughout the year. They need to consider the different times of the year when people are more likely to give.

You have been asked to predict the data from an organization called Give Back, which usually receives about $500,000.00 from different organizations. Make a prediction about the percentage of donations they will receive each month (these percentages must add up to 100%).

Then, using mental math, calculate how that percentage changes into dollars each month. Provide a rationale for your thinking.

You can record your responses in an audio recording, using the following chart, or an organizational chart of your own.

If you would like, you can complete this activity using TVO Mathify. You can also use your notebook or the following fillable worksheet.

Going the distance

If possible, it would be a great opportunity to share your thinking with a peer. How did you estimate? What strategies did you use? How was your thought process similar or different from your peers’?

Task 1: Rest stop distances in a marathon

A half marathon is about 21 km. There are rest stops at 5%, 15% and 50% marks through the race. What distance would you be able to find each rest stop? Did you figure out the distances in a specific order? Why? How did it help you?

Task 2: Markers for personal goals

We often have various personal goals and markers of personal achievement: running distances, weight training, distances travelled, etc. Choose a goal that someone might create for themselves. Highlight what the 1%, 5%, 10%, 15%, 25% and 50% would be for that goal.

If you would like, you can complete this activity using TVO Mathify. You can also use your notebook or the following fillable and printable document.

Reflection

As you read through these descriptions, which sentence best describes how you are feeling about your understanding of this learning activity? Press the button that is beside this sentence.

Now, record your ideas using a voice recorder, speech-to-text, or writing tool.

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