Expressing one Quantity as a Percentage of Another

Working Mathematically Indicators

Understand how percentages can be represented as one quantity over another, and solve problems based around this (Communicating, Fluency, Understanding)

Syllabus Dot Points

express one quantity as a percentage of another, using mental, written and calculator methods, eg 45 minutes is 75% of an hour

Learning Goals

Students will be able to find a percentage of one quantity over another. In doing this students will be able to form a fraction using these two numbers and multiply it by a hundred. They will then demonstrate an ability to obtain a percentage from this calculation, and if necessary, work with decimals.

Students will develop the skills to find the answer to a problem such as this:

Resources

(1) Worksheet (LIT)

This resource can be used as a follow-up to an exploration of the concept. Students could also work on this worksheet in pairs and compare answers to ensure that collaboration occurs through a discussion of how they arrived at an answer.

Expressing One Quantity as a Percentage as Another (WORKSHEET)

(2) Using Microsoft Excel (ICT)

Microsoft Excel is a valuable tool which can be used to find the percentage of two quantities. The students could be given these percentage problems to solve in Excel to underpin the process of how they would go about calculating this percentage. Using Excel would also be beneficial for students as it would enhance an understanding through a visual representation of the data that is easy to analyse.

Handing out an instruction sheet in addition to an explanation would be helpful for students. I have attached it here: Excel Percentages Instructions

This link contains instructions for more advanced concepts as well. In relation to the activity below, only the initial explanations on Percentage basics and Basic Excel percentage formula are relevant.

Excel Activity

There are multiple methods in which students could undertake an excel activity to express one quantity as a percentage of another. Providing students with planned quantities for them to find the percentages of is an option. An example could be like this:

Here students can fill out the percentage columns themselves or even with another student by following the instructions.

Moreover, students could also derive their own quantities, and find the percentages of the numbers they have chosen. They could potentially make some interesting discoverers by themselves here. For example, they could find a percentage that is larger than a hundred. To avoid confusion, a condition could be that the first quantity needs to be smaller than the second.

Lesson Plan

Lesson Description

9:00am Introduction:

The teacher will reflect on what was learnt last lesson. The teacher will once again ask students questions such as, "when might we want to find the percentage of one quantity over another?" The teacher will then emphasise the importance of calculating percentages when we have one quantity over another. The students will then be arranged into small groups and they will be asked to think of a few examples where we might need to calculate percentages in this fashion. In doing this the students will be forced to think for themselves and imagine situations where they have encountered calculations like this in the past. A group discussion will follow, and students will benefit from hearing examples from other peers. This group discussion would be a good stepping stone for the teacher to demonstrate an example on the board; using one of the examples posed by the students.

9:10am Worksheet:

The students will then work on a worksheet where these questions are modeled (potentially individually this time to have students learn in a different way). The teacher will walk around the classroom and ensure that all students are on task.

9:20am Excel Demonstration and Activity:

The teacher will begin the excel activity by asking students questions like, "Are there other ways we can calculate these answers?" The teacher will then demonstrate how Microsoft Excel can be an effective tool to calculate these questions. Excel would be beneficial for students as it would enhance an understanding through a different representation of the data that is easy to analyse. The students can work in pairs during this activity. Using Excel would provide them with insights into how percentages can be calculated with other programs, and not just the common calculator.

9:50am Homework Check

The teacher will check homework to observe student progress. This will also provide the teacher with insights as to whether any students are struggling.

9:55am Conclusion:

The teacher will reflect on what has been learnt during the lesson. "Remind me, what were some real-life examples that we came up with before?" The teacher will conclude the lesson by stressing how Microsoft Excel can be a very effective tool for mathematical data.

Evaluation Questions:

Did all students contribute during the group discussion?
Did all students display an understanding of how to calculate the percentage of one quantity over another?
How could I make the Excel activity more investing?

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