About Percentage

Arthur Lee, Mar 17, 2024

About percentage

Table of Contents

  1. using bar model
    1. Part, Whole and Percentage
    2. Percentage Change 百分改變
    3. Percentages: Selling Problems, Profit & Loss
    4. Cost, Marked Price & Selling Price 成本、標價與售價
    5. Finding Percentage Increase
    6. Finding the Missing Values in Percentage Relationships Using Tape Diagrams
    7. Percentage Change Estimation (whole class activity)
  2. Using elastic percentage ruler
    1. percentage ruler (mixture)
    2. percentage ruler (2 groups)
    3. percentage for comparison
    4. successive percentage changes
  3. simple and compound interest
    1. From simple to compound interest
    2. Compound Interest
    3. Simple Interest 單利息
    4. Compound Interest 複利息
  4. using double number line
    1. Double Number Line - Percent Change
    2. Double Number Line – Percent Change (2)
  5. ratio and proportion
    1. estimate fraction in a set
    2. Comparing Mixtures (24 cups)
  6. more online resources
    1. introduce percentage change in Desmos

1.

using bar model

These are common bar model activities for learning about percentage or percentage change in various contexts.

  • 1. Part, Whole and Percentage
  • 2. Percentage Change 百分改變
  • 3. Percentages: Selling Problems, Profit & Loss
  • 4. Cost, Marked Price & Selling Price 成本、標價與售價
  • 5. Finding Percentage Increase
  • 6. Finding the Missing Values in Percentage Relationships Using Tape Diagrams
  • 7. Percentage Change Estimation (whole class activity)

1.1.

Part, Whole and Percentage

– Anthony OR 柯志明

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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2.

Using elastic percentage ruler

In these activities, we use an elastic 'percentage ruler' to show percentages based on a selected whole. We can shrink or stretch the ruler by dragging the 100% mark in order to match any quantity as a whole. This process of adjusting the ruler may simulate the continuous scaling action associated with multiplicative thinking.

  • 1. percentage ruler (mixture)
  • 2. percentage ruler (2 groups)
  • 3. percentage for comparison
  • 4. successive percentage changes

2.1.

percentage ruler (mixture)

Use a slider to mix the apples and mangos or undo the mixing. Learners may guess the percentages before or after the mixing.[br][br]When the items are arranged in a line, the percentage ruler can be used to visualise the percentages by adjusting the 100% mark. [br][br]Click the apples or mangos sliders and use the style bar to hide the labels (which include the numbers) if needed.
You may use the following calculator to show and record your calculation.
– Arthur Lee

2.2.

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2.3.

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2.4.

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3.

simple and compound interest

  • 1. From simple to compound interest
  • 2. Compound Interest
  • 3. Simple Interest 單利息
  • 4. Compound Interest 複利息

3.1.

From simple to compound interest

Chinese version:[br]https://www.geogebra.org/m/vaqwpvzk
– Arthur Lee

3.2.

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3.3.

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3.4.

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4.

using double number line

These are extracted from the Percentage Change Collection by the EDC in Maine: https://www.geogebra.org/m/fjtmqm8b

  • 1. Double Number Line - Percent Change
  • 2. Double Number Line – Percent Change (2)

4.1.

Double Number Line - Percent Change

[br]Related apps available from [url=https://www.geogebra.org/u/edc+in+maine]EDC in Maine[/url] include [url=https://www.geogebra.org/m/Gdj6JVJK]Double Number Line - Percent Change (2)[/url] and [url=https://www.geogebra.org/m/XUMdVduR]Double Number Line[/url].[br][br]Contact us at ptierneyfife@edc.org if this resource should be updated, or with questions or suggestions. We appreciate your help maintaining the quality of this resource.
– EDC in Maine

4.2.

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5.

ratio and proportion

In this section, we include some activities that reinforce or refresh learners' understanding about ratio and proportion, which is closely related to understanding about percentage. Comparing Mixtures task is part of collection by EDC: https://www.geogebra.org/m/wv49ht3k A reference is provided there: https://www.geogebra.org/m/wv49ht3k#material/q3uzrrbf

  • 1. estimate fraction in a set
  • 2. Comparing Mixtures (24 cups)

5.1.

estimate fraction in a set

In this activity, visualise or estimate the fraction of dots that are blue. The examples can be manipulated by the teacher in front of the learners. This may allow discussion about the meaning of fraction and developing a sense of the fraction size. [br][br]The fraction is shown as f1 or f2 (on the left or right), before or after simplification. The dots can be ordered in columns (use the 'move' slider) or sorted for better visualisation. The number of column can be adjusted to show more clearly the fraction. Learners may suggest how many columns would be better.[br][br]When the fractions are hidden, the dots are scattered and mixed, learners may guess the fraction. Their estimation can be updated when the dots are rearranged. When one of the fractions is shown, they can also estimate or work out another one. [br][br]If you want to show the value of part or whole without showing the entire fraction (f1), click one of the slider, use the style bar to change the option of label from 'caption' to 'value'.
– Arthur Lee

5.2.

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6.

more online resources

  • 1. introduce percentage change in Desmos

6.1.

introduce percentage change in Desmos

This Desmos activity asks students to distinguish relative and absolute changes, as a starting point for learning about percentage change: https://teacher.desmos.com/activitybuilder/custom/6567e312275831f4f075843c [br][br]In slides 6, 11 and 13, students can estimate the changes by dragging on the screen.
– Arthur Lee

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