Visualizing Addition and Subtraction Facts

This activity helps students learn addition and subtraction facts up to 20, reinforcing quick recall and number fluency. It visually connects the abstract number sentence to a concrete representation with animated penguins.

How to Use the Activity

Visualizing Addition

The activity starts with ten penguins on the left iceberg, representing the addition fact 10 + 0 = 10.

Clicking the right arrow moves a penguin from the left iceberg to the right one, instantly updating the equation to 9 + 1 = 10. With each click, students can see the relationship between the number of penguins on each iceberg and the corresponding numbers in the equation. The left-arrow moves penguins back in the other direction.

Creating Problems

To test understanding, you can hide different parts of the activity.

• Hide Numbers: Click on any number in the equation, and it will flip over to reveal a ?.
• Hide Penguins: Click the first cloud or second cloud to cover the penguins on either iceberg.
• Random Problem: Click the dice to generate a random problem where the penguins are hidden and all numbers are replaced with ?. You can then reveal parts of the problem one by one to challenge students.

Changing Totals and Using the Number Line

While the arrows change the distribution of penguins, the total remains the same. To change the total, click the edit button. Two sliders will appear:

• The top slider adjusts the total number of penguins.
• The bottom slider adjusts the number of penguins on the first iceberg.

Click the number line button to display a number line below the icebergs. This provides another powerful visual, showing how the addition fact is represented as jumps along the line.

Switching to Subtraction Facts

To switch from addition to subtraction, click the iceberg button. The second iceberg moves away, and any penguins on it jump into the water.

This action transforms the equation: the + sign flips to a −, and the total swaps places with the first number to form a subtraction problem. The number line also updates, showing the subtraction as a red arc moving backward from the starting total. The arrow buttons now move penguins between the iceberg and the water.

To hide the number of penguins in the water, click the water button. This makes the water opaque, hiding the penguins. In subtraction mode, clicking the dice will automatically hide them, allowing students to solve for the missing number.

Learning Objectives

This activity is designed to help students develop key mathematical concepts and strategies, including:

• Understanding that addition is commutative (e.g., 8 + 2 is the same as 2 + 8).
• Recognizing that subtraction is the inverse of addition.
• Using number facts to find the difference between two numbers.
• Developing mental math strategies, such as counting on from the first number to find a total.